# Three methods to detect the predicted $D\bar{D}$ scalar meson $X(3700)$

C. W. Xiao 1 and E. Oset 1 1Departamento de Física Teórica and IFIC, Centro
Mixto Universidad
de Valencia-CSIC, Institutos de Investigación de Paterna, Apartado 22085,
46071 Valencia, Spain

###### Abstract

In analogy to the $f_{0}(500)$, which appears as a $\pi\pi$ resonance in
chiral unitary theory, and the $f_{0}(980)$, which appears as a quasibound
$K\bar{K}$ state, the extension of this approach to the charm sector also
predicts a quasibound $D\bar{D}$ state with mass around 3720 MeV, named as
$X(3700)$, for which some experimental support is seen in the $e^{+}e^{-}\to
J/\psi D\bar{D}$ reaction close to the $D\bar{D}$ threshold. In the present
work we propose three different experiments to observe it as a clear peak. The
first one is the radiative decay of the $\psi(3770)$, $\psi(3770)\to\gamma
X(3700)\to\gamma\eta\eta^{\prime}$. The second one proposes the analogous
reaction $\psi(4040)\to\gamma X(3700)\to\gamma\eta\eta^{\prime}$ and the third
reaction is the $e^{+}e^{-}\to J/\psi X(3700)\to J/\psi\eta\eta^{\prime}$.
Neat peaks are predicted for all the reactions and the calculated rates are
found within measurable range in present facilities.

##  I Introduction

The use of the chiral unitary approach in the meson-meson interaction gives
rise to the $f_{0}(500)(or\ \sigma),\ f_{0}(980),\ a_{0}(980)$ scalar mesons
npa ; norbert ; markushin ; rios1 ; rios2 ; juanclassic ; juanenrique  from
the unitarization in coupled channels of the meson-meson interaction provided
by the chiral Lagrangians weinberg ; gasser . The $f_{0}(500)$ appears
basically as a $\pi\pi$ resonance and the $f_{0}(980),\ a_{0}(980)$ as
basically $K\bar{K}$ quasibound states that decay into $\pi\pi$ and $\pi\eta$
respectively. The similarity between $\bar{K}$ and $D$ ($K$ and $\bar{D}$)
suggest that there could be also a $D\bar{D}$ quasibound state around
$3700\textrm{ MeV}$, that we shall call $X(3700)$, decaying into pairs of
light pseudoscalars, $\pi\pi,\ \eta\eta,\ \eta\eta^{\prime},\ K\bar{K}$. In an
extrapolation of the chiral unitary approach to the SU(4) sector danione  it
was found that, indeed, a quasibound scalar $D\bar{D}$ state with $I=0$
emerged with a small width, since transition matrix elements from $D\bar{D}$
to the light sector were strongly suppressed. This finding has been
corroborated recently in manolito ; carlos  using models that incorporate
heavy quark symmetry.

Later on it was found in daniee  that the bump in the $D\bar{D}$ spectrum
close to the $D\bar{D}$ threshold observed at Belle in the $e^{+}e^{-}\to
J/\psi D\bar{D}$ reaction eebelle  was better interpreted in terms of the
bound state below threshold, with $M_{X}\simeq 3723\textrm{ MeV}$ than with a
new resonance as suggested in eebelle . So far, this is the strongest
experimental support for this state, in spite of the fact that some other
reaction has been suggested to observe it. Indeed, in danirad  a suggestion
was made to detect the state in the radiative decay of the $\psi(3770)$. The
idea is based in the fact that the $\psi(3770)$ couples strongly to $D\bar{D}$
and with the emission of a photon one can bring the $D\bar{D}$ state below the
threshold into the region of the resonance. A width of $\Gamma_{\psi\to\gamma
X}=(1.05\pm 0.41)\textrm{ KeV}$ was found which would be in the measurable
range. However, a problem of this suggestion is that this peak would have to
be seen over a background of $\psi\to\gamma\ +$ anything, which is estimated
to have a branding ratio of the order of $10^{-2}$, judging by the rate of
some measured channels reported in the Particle Date Group (PDG) pdg , while
$\Gamma_{\psi\to\gamma X}/\Gamma_{\psi}\simeq 4\times 10^{-5}$. The signal
would be of the order of 1% of smaller on top of a background and the
prospects to see it there would be dim. There is another problem since the
peak for the decay appears at small photon momentum where there would be
radiative decays displaying Bremsstrahlung of the photons, with accumulated
strength at low photon energies, precisely where the peak of the $X$ would
appear. The selection of a particular decay channel where the background would
be much reduced would be then much welcome and this is what we do here,
suggesting the $\eta\eta^{\prime}$ channel for reasons that would be clear
later on.

On the other hand, with the advent of BESIII the production of the
$\psi(4040)$ state is being undertaken and in this case the photon has more
energy in the radiative decay, removing the peak from the Bremsstrahlung
region, with obvious advantages.

We have also investigated another method, taking the same reaction as
performed in eebelle  but looking for $e^{+}e^{-}\to J/\psi\eta\eta^{\prime}$.
We predict a peak for $\eta\eta^{\prime}$ production and compare the strength
of the peak with the cross sections measured in eebelle  for the $J/\psi
D\bar{D}$ production.

With all these studies we find out three methods which would allow to see the
neat peak for that state and the widths or cross sections are found within
present measuring range, such that devoted experiments would be most
opportune.

##  II Formalism

In danirad  the radiative decay of $\psi(3770)$ into $\gamma X(3700)$ was
studied. The work of danione  was redone including the channels $D^{+}D^{-},\
D^{0}\bar{D}^{0},\ D^{+}_{s}D^{-}_{s},\ \pi^{+}\pi^{-},\ K^{+}K^{-},\
\pi^{0}\pi^{0},\ K^{0}\bar{K}^{0},\ \eta\eta,\ \eta\eta^{\prime},\
\eta^{\prime}\eta^{\prime},\ \eta_{c}\eta,\\\ \ \eta_{c}\eta^{\prime}$. Using
a potential derived from an SU(4) extension of the SU(3) chiral Lagrangians
weinberg ; gasser  with an explicit SU(4) breaking for terms exchanging charm,
the Bethe-Salpeter equations were solved to obtain the scattering matrix

$T=[1-VG]^{-1}V,$ (1)

with $V$ the potential and $G$ the loop function for the integral of
intermediate two meson propagators. With this formalism a pole was obtained
for the $T$ matrix around $3722\textrm{ MeV}$ below the $D\bar{D}$ threshold.
What is of relevance for the present work is the coupling of this state to the
different channels. In Table 1 we show the results obtained in danirad :

Table 1: Coupling of the pole at $(3722-i18)\textrm{ MeV}$ to the channels. channel | Re($g_{X}$) [MeV] | Im($g_{X}$) [MeV] |  $|g_{X}|$ [MeV]
---|---|---|---
$\pi^{+}\pi^{-}$ | 9 | 83 | 84
$K^{+}K^{-}$ | 5 | 22 | 22
$D^{+}D^{-}$ | 5962 | 1695 | 6198
$\pi^{0}\pi^{0}$ | 6 | 83 | 84
$K^{0}\bar{K}^{0}$ | 5 | 22 | 22
$\eta\eta$ | 1023 | 242 | 1051
$\eta\eta^{\prime}$ | 1680 | 368 | 1720
$\eta^{\prime}\eta^{\prime}$ | 922 | -417 | 1012
$D^{0}\bar{D}^{0}$ | 5962 | 1695 | 6198
$D^{+}_{s}D^{-}_{s}$ | 5901 | -869 | 5965
$\eta_{c}\eta$ | 518 | 659 | 838
$\eta_{c}\eta^{\prime}$ | 405 | 9 | 405

As we can see, the largest couplings are for $D\bar{D}$ and
$D_{s}\bar{D}_{s}$. However, the separation in energy of the
$D_{s}\bar{D}_{s}$ component makes the $D\bar{D}$ component to stand as the
more relevant meson-meson component of this state, which qualifies
approximately as a $D\bar{D}$ quasibound state. The width obtained from the
decay of this state in all the allowed channels is $36\textrm{ MeV}$. Note
that the transition to light, open, channels is suppressed and this determines
the large lifetime of the state. We observe from the Table that the largest
coupling to the light channels is to $\eta\eta^{\prime}$ which also contains
two different particles, hence, this will be the channel that we will adopt to
have the $X(3700)$ state detected.

In danirad  the decay of $\psi(3770)$ to $\gamma X$ was evaluated recalling
that the $\psi(3770)$ decays basically with $D\bar{D}$. This allows one to
obtain the coupling of $\psi(3770)$ to $D^{+}D^{-}$ and then, from the
triangular diagram of Fig. 1, the $\psi(3770)\to\gamma X$ transition

Figure 1: Diagram for $\psi(3770)\to\gamma X$ that contains the $d$ term.

amplitude was evaluated. We do not repeat here the steps of the calculations
in danirad  and quote the final results. The transition amplitude for the
diagram of Fig. 1 is given by

$i{\cal M}=i\epsilon_{\psi}^{\mu}(P)\epsilon_{\gamma}^{\nu}(K){\cal
T}_{\mu\nu},$ (2)

and since the problem has two independent four momenta, by Lorentz invariance
one may write

${\cal
T}_{\mu\nu}=ag_{\mu\nu}+bP_{\mu}P_{\nu}+cP_{\mu}K_{\nu}+dP_{\nu}K_{\mu}+eK_{\mu}K_{\nu}.$
(3)

Due to gauge invariance only the structures $ag_{\mu\nu}$ and
$dP_{\nu}K_{\mu}$ (with $P,\ K$ the $\psi$ and $\gamma$ momentum), which leads
to a convergent integral, survive, and, in addition, one has $a=-d\,K\cdot P$.
The $d$ coefficient is evaluated using the Feynman parameterization of the
loop function corresponding to the diagram of Fig. 1 and one finds

$d=-\sum_{j}\frac{g_{\psi}g_{X,j}e}{2\pi^{2}}\int_{0}^{1}dx\int_{0}^{x}dy\frac{y(1-x)}{s+i\epsilon},$
(4)

with $s$ given by

$s=(1-x)(xM_{\psi}^{2}-m_{2}^{2}-2yP\cdot K)-xm_{1}^{2},$ (5)

with $e$ the electron charge ($e^{2}/4\pi=\alpha=1/137$), $g_{\psi}$ the
coupling of $\psi(3770)$ to $D^{+}D^{-},\ g_{\psi}=11.7$, and $j$ summing over
the two relevant channels $D^{+}D^{-}$ and $D^{+}_{s}D^{-}_{s}$. The partial
decay width for $\psi(3770)\to\gamma X$ is given by

$\Gamma_{\psi\rightarrow\gamma X}=\frac{|\vec{K}|}{12\pi
M_{\psi}^{2}}\;(P\cdot K)^{2}\;|d|^{2}.$ (6)

The result obtained in danirad  is 111Within uncertainties it turned out to be
$\Gamma_{\psi\rightarrow\gamma X}=(1.05\pm 0.41)\textrm{ KeV}$. We refer to
the value $0.65\textrm{ KeV}$ here obtained with the standard parameters for
comparison reasons.

$\Gamma_{\psi\rightarrow\gamma X}=0.65\textrm{ KeV}.$ (7)

As mentioned in the Introduction, determining the peak corresponding to this
process over a background of $\gamma X$ events is problematic and thus we
choose the $\eta\eta^{\prime}$ to detect the $X$ peak. For this the diagram of
Fig. 1 has to be changed to the one of Fig. 2.

Figure 2: Diagram for $\psi(3770)\to\gamma X\to\gamma\eta\eta^{\prime}$.

Technically all we have to do is substitute $d$ by $d\,^{\prime}$ where

$d\,^{\prime}=d\frac{1}{M_{inv}^{2}-M_{X}^{2}+iM_{X}\Gamma_{X}}g_{X,\eta\eta^{\prime}},$
(8)

with $d$ defined in Eq. (4),

$M_{inv}^{2}=(p_{\eta}+p_{\eta^{\prime}})^{2},$ (9)

and $g_{X,\eta\eta^{\prime}}$ the coupling of the $X$ to the
$\eta\eta^{\prime}$ channel given in Table 1.

The relevant magnitude now is

$\frac{d\Gamma}{dM_{inv}}=\frac{1}{4(2\pi)^{3}}\frac{1}{M_{\psi}^{2}}\,p_{\gamma}\,\tilde{p}_{\eta}\,\overline{\sum}\sum|T|^{2},$
(10)

which provides the invariant mass distribution, where

$\displaystyle p_{\gamma}$ $\displaystyle=$
$\displaystyle\frac{\lambda^{1/2}(M_{\psi}^{2},0,M_{inv}^{2})}{2M_{\psi}},$
(11) $\displaystyle\tilde{p}_{\eta}$ $\displaystyle=$
$\displaystyle\frac{\lambda^{1/2}(M_{inv}^{2},m_{\eta}^{2},m_{\eta^{\prime}}^{2})}{2M_{inv}},$
(12) $\displaystyle\overline{\sum}\sum|T|^{2}$ $\displaystyle=$
$\displaystyle\frac{2}{3}\,|d\,^{\prime}|^{2}(K\cdot P)^{2},$ (13)

with $p_{\gamma}$, $\tilde{p}_{\eta}$ the $\gamma$ momentum in the
$\psi(3770)$ rest frame and the $\eta$ momentum in the $\eta\eta^{\prime}$
rest frame respectively.

In Fig. 3 we show this distribution,

Figure 3: The mass distribution of the $\eta\eta^{\prime}$ in the decay of
$\psi(3770)$ to $\gamma X(3700)\to\gamma\eta\eta^{\prime}$.

and we see a clear peak at $M_{inv}\simeq 3722\textrm{ MeV}$ with a narrow
width. The peak is still around the upper threshold for the invariant mass.
However, the fact that we have chosen a neutral channel to identify the $X$
state prevents Bremsstrahlung to occur and the identification of a peak there
would be a clear signal of a state. The integrated width around the peak
($3600<M_{inv}<3770\textrm{ MeV}$) gives

$\Gamma=\int_{3600}^{3770}\frac{d\Gamma}{dM_{inv}}dM_{inv}=0.293\textrm{
KeV},$ (14)

which is smaller than the total width of Eq. (7) which integrates over the
whole range of $M_{inv}$.

The largest contribution comes from the $D^{+}D^{-}$ channel which by itself
provides 73% of the rate. The coherent sum with the $D_{s}^{+}D_{s}^{-}$
contribution makes up for the rest of the rate.

The width of Eq. (14) represents a branching ratio of $10^{-5}$. In this sense
one should note that CLEO has set thresholds of the order of magnitude of
$10^{-4}$ and at BESIII one can get a production $\psi(3770)$ of about a
factor one hundred times bigger, which would make this measurement feasible in
that Lab.

##  III Radiative decay of the $\psi(4040)$

The $\psi(4040)$ shares the same quantum numbers as the $\psi(3770)$, however
the largest branching ratio is not to $D\bar{D}$ but to $D^{*}\bar{D}+cc$.
From the data in the PDG we find that

$\displaystyle\frac{\Gamma(D\bar{D})}{\Gamma(D^{*}\bar{D}+cc)}$
$\displaystyle=$ $\displaystyle 0.24\pm 0.05\pm 0.12,$ (15)
$\displaystyle\frac{\Gamma(D^{*}\bar{D}^{*})}{\Gamma(D^{*}\bar{D}+cc)}$
$\displaystyle=$ $\displaystyle 0.18\pm 0.14\pm 0.03,$ (16)

Assuming that the $D^{*}\bar{D}+cc$, $D\bar{D}$ and $D^{*}\bar{D}^{*}$ provide
most of the contribution, this allows us to get the coupling

$g_{\psi(4040),D^{+}D^{-}}=2.15,$ (17)

and then we can recalculate the invariant mass distribution and width for
$\psi(4040)\to\gamma X(3700)$. In Fig. 4 we show the results for the invariant
mass distribution.

Figure 4: The mass distribution of $\eta\eta^{\prime}$ in the $\psi(4040)$
decay to $\gamma X(3700)\to\gamma\eta\eta^{\prime}$.

We find now a neat peak around the mass of the $X$. The novelty here is that
the peak is far away from all thresholds which could eventually be seen in the
spectrum of inclusive $d\Gamma/dE_{\gamma}$ without the risk to confuse the
peak with Bremsstrahlung like in the case of the $\psi(3770)\to\gamma X$. In
any case, as advocated here, the direct measurement of the $\eta\eta^{\prime}$
channel should drastically reduce the background and allow a clear peak to be
identified. The integrated width around this peak ($3600<M_{inv}<3800\textrm{
MeV}$) gives

$\Gamma=\int_{3600}^{3800}\frac{d\Gamma}{dM_{inv}}dM_{inv}=0.496\textrm{
KeV},$ (18)

which is about double than in the case of the $\psi(3770)$. In this case, the
larger phase space for decay has overcome the reduction due to the reduced
coupling of Eq. (17).

We should note that the largest contribution comes from the $D^{+}D^{-}$
channel, this channel alone providing about half the rate of Eq. (18) while
$D_{s}^{+}D_{s}^{-}$ alone only given 19% of this rate.

The width of Eq. (18) is a bit bigger than the one obtained for the
$\psi(3770)$, yet, the rate of production at BESIII is smaller. Present plans
are to produce 2.8 million $\psi(4040)$ events and no plans are made for the
future yet 222We would like to thank Cheng-Ping Shen for providing us the
information.. With this statistics and the width of Eq. (18), which
corresponds to a branching ratio of $6.2\times 10^{-6}$, one could get about
17 events of this radiative decay. It is clear that more statistics would be
needed to see a clear peak.

##  IV The $e^{+}e^{-}\to J/\psi X\to J/\psi\eta\eta^{\prime}$ reaction

In daniee  the $e^{+}e^{-}\to J/\psi X\to J/\psi D\bar{D}$ reaction was
studied and it was concluded that the data on the $D\bar{D}$ invariant mass
distribution was better described in terms of the $X(3700)$ resonance that in
terms of a new state suggested in eebelle . The mechanism for this reaction is
given in Fig. 5.

Figure 5: Feynman diagram of the reaction $e^{+}e^{-}\to J/\psi X\to J/\psi
D\bar{D}$.

The differental cross section is given by daniee

$\frac{d\sigma}{dM_{inv}(D\bar{D})}=\frac{1}{(2\pi)^{3}}\frac{m_{e}^{2}}{s\sqrt{s}}|\vec{k}|\;|\vec{p}|\;|T|^{2},$
(19)

with

$\displaystyle|\vec{k}|$ $\displaystyle=$
$\displaystyle\frac{\lambda^{1/2}(M_{inv}^{2}(D\bar{D}),m_{D}^{2},m_{D}^{2})}{2M_{inv}(D\bar{D})},$
(20) $\displaystyle|\vec{p}|$ $\displaystyle=$
$\displaystyle\frac{\lambda^{1/2}(s,M_{J/\psi}^{2},M_{inv}^{2}(D\bar{D}))}{2\sqrt{s}},$
(21)

where $T$ is given by

$T=C\frac{1}{M_{inv}^{2}(D\bar{D})-M_{X}^{2}+i\Gamma_{X}M_{X}}.$ (22)

As in daniee  we restrain from giving absolute values but we can give relative
values with respect to $D\bar{D}$ production simply multiply $T$ of Eq. (22)
by $g_{X,\eta\eta^{\prime}}/\sqrt{2}g_{X,D^{+}D^{-}}$, where the factor
$\sqrt{2}$ will take into account in $|T|^{2}$ that we compare
$\eta\eta^{\prime}$ production versus $D^{+}D^{-}+D^{0}\bar{D}^{0}$
production.

Figure 6: The mass distribution of the final states $J/\psi\eta\eta^{\prime}$
compared to $J/\psi D\bar{D}$.

In Fig. 6 we show the results for $\eta\eta^{\prime}$ production with the same
scale as for $D\bar{D}$ production. We can see that the strength of the peak
is bigger for $\eta\eta^{\prime}$ production than for $D\bar{D}$, in spite of
having a smaller coupling to $X(3700)$. The reason is that the
$\eta\eta^{\prime}$ production is not suppressed by the threshold factors that
inhibit $D\bar{D}$ production. The peak seen in the $\eta\eta^{\prime}$ mass
spectrum is neat and the strength larger than for $D\bar{D}$ production. Since
$D\bar{D}$ has been observed in eebelle , this guarantees that the
$\eta\eta^{\prime}$ peak is within present measurable range.

##  V Conclusions

In the present work, we have investigated some reactions by means of which one
could observe the predicted scalar meson formed as a quasibound state of
$D\bar{D}$. This state appears in analogy to the $f_{0}(500)$ and $f_{0}(980)$
states which are described within the chiral unitary approach as a $\pi\pi$
resonance and a quasibound $K\bar{K}$ state respectively. Some suggestion had
been made before to observe this state in the $\psi(3770)\to\gamma X(3700)$
decay by looking at the $\gamma$ energy distribution. Yet, this has the
inconvenience of having to observe a small peak in a large background. In
order to suppress the background we have chosen one of the main decay channels
of the $X(3700)$ state, the $\eta\eta^{\prime}$ channel, and suggest to look
at the $\eta\eta^{\prime}$ invariant mass distribution in the reaction
$\psi(3770)\to\gamma X(3700)\to\gamma\eta\eta^{\prime}$. Since BESIII already
can produce the $\psi(4040)$, we also suggest to look at the
$\psi(4040)\to\gamma X(3700)\to\gamma\eta\eta^{\prime}$ decay channel. A third
reaction was motivated by the only indirect experimental “evidence” of this
state. Indeed, in the BELLE reaction $e^{+}e^{-}\to J/\psi D\bar{D}$ eebelle ,
a peak was observed in the $D\bar{D}$ invariant mass distribution close to the
$D\bar{D}$ threshold, which was interpreted in daniee  as a signal of a
$D\bar{D}$ resonance below the $D\bar{D}$ threshold. In the present work we
have suggested to look at the reaction $e^{+}e^{-}\to
J/\psi\eta\eta^{\prime}$, allowing the $X(3700)$ to be produced and decay into
$\eta\eta^{\prime}$.

We find clear peaks in all the invariant mass distributions of
$\eta\eta^{\prime}$. In the two radiative decays, the rates are within present
measurable range at BESIII, although in the case of $\psi(4040)$ radiative
decay the statistics with presently planned $\psi(4040)$ production would be
very low. In the case of the $e^{+}e^{-}$ reaction we do not evaluate absolute
cross sections and we find more instructive to compare the cross section of
the $e^{+}e^{-}\to J/\psi\eta\eta^{\prime}$ reaction with the one of
$e^{+}e^{-}\to J/\psi D\bar{D}$ already measured. We observe that the cross
section for the former reaction is bigger than for the latter one and produces
a clear peak that does not have the ambiguity of a threshold enhancement as in
the $e^{+}e^{-}\to J/\psi D\bar{D}$ reaction. This is the best guarantee that
the reaction is within measurable range.

The experimental search for this state is timely and its observation would
clarify issues concerning the interaction of hadrons in the charm sector,
which is not so well known as the non charmed one, and which would be much
welcome.

## Acknowledgements

This work is partly supported by DGICYT contract number FIS2011-28853-C02-01,
and the Generalitat Valenciana in the program Prometeo, 2009/090. We
acknowledge the support of the European Community-Research Infrastructure
Integrating Activity Study of Strongly Interacting Matter (acronym
HadronPhysics3, Grant Agreement n. 283286) under the Seventh Framework
Programme of the EU.

## References

  * (1) J. A. Oller and E. Oset, Nucl. Phys. A 620, 438 (1997) [Erratum-ibid. A 652, 407 (1999)] [hep-ph/9702314].
  * (2) N. Kaiser, Eur. Phys. J. A 3, 307 (1998).
  * (3) M. P. Locher, V. E. Markushin and H. Q. Zheng, Eur. Phys. J. C 4, 317 (1998) [hep-ph/9705230].
  * (4) J. R. Pelaez and G. Rios, Phys. Rev. Lett. 97, 242002 (2006) [hep-ph/0610397].
  * (5) C. Hanhart, J. R. Pelaez and G. Rios, Phys. Rev. Lett. 100, 152001 (2008) [arXiv:0801.2871 [hep-ph]].
  * (6) J. Nieves and E. Ruiz Arriola, Phys. Lett. B 455, 30 (1999) [nucl-th/9807035].
  * (7) J. Nieves and E. Ruiz Arriola, Phys. Rev. D 80, 045023 (2009) [arXiv:0904.4344 [hep-ph]].
  * (8) S. Weinberg, Physica A 96, 327 (1979).
  * (9) J. Gasser and H. Leutwyler, Annals Phys. 158, 142 (1984).
  * (10) D. Gamermann, E. Oset, D. Strottman and M. J. Vicente Vacas, Phys. Rev. D 76, 074016 (2007) [hep-ph/0612179].
  * (11) J. Nieves and M. P. Valderrama, Phys. Rev. D 86, 056004 (2012) [arXiv:1204.2790 [hep-ph]].
  * (12) C. Hidalgo-Duque, J. Nieves and M. P. Valderrama, arXiv:1210.5431 [hep-ph].
  * (13) D. Gamermann and E. Oset, Eur. Phys. J. A 36, 189 (2008) [arXiv:0712.1758 [hep-ph]].
  * (14) P. Pakhlov et al. [Belle Collaboration], Phys. Rev. Lett. 100 (2008) 202001 [arXiv:0708.3812 [hep-ex]].
  * (15) D. Gamermann, E. Oset and B. S. Zou, Eur. Phys. J. A 41, 85 (2009) [arXiv:0805.0499 [hep-ph]].
  * (16) J. Beringer et al. [Particle Data Group Collaboration], Phys. Rev. D 86, 010001 (2012).


# Is there progress in activity progress prediction?

Frans de Boer1
Jan C. van Gemert1
Jouke Dijkstra2
Silvia L. Pintea1,2
1 Computer Vision Lab, Delft University of Technology
2 Division of Image Processing (LKEB), Leiden University Medical Center

###### Abstract

Activity progress prediction aims to estimate what percentage of an activity
has been completed. Currently this is done with machine learning approaches,
trained and evaluated on complicated and realistic video datasets. The videos
in these datasets vary drastically in length and appearance. And some of the
activities have unanticipated developments, making activity progression
difficult to estimate. In this work, we examine the results obtained by
existing progress prediction methods on these datasets. We find that current
progress prediction methods seem not to extract useful visual information for
the progress prediction task. Therefore, these methods fail to exceed simple
frame-counting baselines. We design a precisely controlled dataset for
activity progress prediction and on this synthetic dataset we show that the
considered methods can make use of the visual information, when this directly
relates to the progress prediction. We conclude that the progress prediction
task is ill-posed on the currently used real-world datasets. Moreover, to
fairly measure activity progression we advise to consider a, simple but
effective, frame-counting baseline.

##  1 Introduction

Visual activity progress prediction is vital to our day-to-day lives: _e.g_.
in cooking, we predict how fast the food is ready; in healthcare, estimating
how long a surgery will take allows for better resource allocation and shorter
waiting times; and for video-editing knowing where an activity begins and ends
helps with automatic cropping of the desired video ranges. Here, we define
activity progress prediction as the task of predicting the percentage of
completion of an activity in a video in an online setting, _i.e_.: without
access to the length of the video. For our purpose, each video contains a
single activity, which covers the complete duration of the video and may
consist of multiple phases. However, we assume there are no phase annotations
available, as is generally the case in real-world scenarios. The main
challenge for progress prediction is extracting meaning from the visual
inputs, which, ideally relates to the specific phases of the activity and,
thus, enables predicting progress.

To address this challenge, current methods rely on deep networks, such as
VGG-16 [23], ResNet [9], YOLOv2 [22], or I3D [4] to extract visual
information. Furthermore, to remember information over time, current progress
prediction methods [3, 26] rely on memory blocks and recurrent connections
[12]. While these embeddings and recurrent connections are useful for
extracting visual information and keeping track of the activity progression
over time, they may also overfit to uninformative artifacts. Here, we aim to
analyze if such undesirable learning strategies are occurring when performing
progress prediction.

To this end, we consider the state-of-the-art progress prediction methods [3,
17, 26], as well as two more simple learning-based methods: a 2$D$-only
ResNet, and a ResNet model augmented with recurrent connections. We evaluate
all these learning methods across three video datasets used for progress
prediction: UCF101-24 [24], Breakfast [15, 16], and Cholec80 [25].
Additionally, we compare the learning-based methods with simple non-learning
baseline methods such as simply frame counting.

We evaluate models on various dataset types and regimes. We examine the
learning methods when they are presented with the full videos during training.
In addition, to avoid overfitting to absolute time/frame progression, we also
evaluate methods when trained on randomly sampled video segments. For randomly
sampling video segments, it is not possible to do frame-counting, and only the
visual information is available for activity progress prediction. If the
methods should fail to extract useful information from the visual data, they
would perform on par with non-learning methods based on frame-counting.
Finally, we design a precisely controlled synthetic progress prediction
dataset, Progress-bar, on which the visual information is directly related to
the progress.

Figure 1:  Length distributions for UCF101-24, Cholec80, and Breakfast.
UCF101-24 are grouped into bins of size 10, for Cholec80 and Breakfast the
bins are of size 100. Most notable is the long-tail distribution of the video
lengths in the Breakfast dataset, which makes progress prediction difficult.
The vertical red line depicts the mean of each dataset.

Difficulties in current progress prediction. Progress prediction methods [3,
17, 26] evaluate on complicated and realistic datasets such as UCF101-24 [24],
Breakfast [15, 16], and Cholec80 [25]. The appearance of the activities in
these videos is diverse. And the activity length drastically varies between
videos in these datasets, as shown Fig. 1. UCF101-24 and Breakfast follow a
long-tail distribution, with few videos containing long activities. Moreover,
there can be unexpected activity progressions: _e.g_. the pancake gets burned,
or there is a surgery lag. Also, some of the activities in these datasets do
not have a clearly defined endpoint: _e.g_. ‘skiing’, ‘walking the dog’, etc.
Predicting progress on these activities would be difficult even for a human
observer. Therefore, we arrive at two main questions we aim to address here:
(i) How well can methods predict activity progression on the current datasets?
and (ii) Is it at all possible to predict progress from visual data only?

##  2 Related work

Activity progress Prediction. The task of progress prediction was formally
introduced in [3]. Because the progress of an activity is an easy-to-obtain
self-supervision signal, it is often used as an auxiliary signal in a multi-
task prediction problem, as in [13] to improve the performance of spatio-
temporal action localisation networks. Progress prediction is also used as a
pretext task for phase detection [18], or to create embeddings to perform
unsupervised learning of action classes [17, 28]. The progress prediction
problem can also be modelled as a classification problem, choosing from $n$
bins each of size $1/n$ as is done in [7]. Based on the literature surveyed,
of works done on progress prediction, only [3, 21] have progress prediction as
their primary task. This work is also on the topic of progress prediction, but
we do not propose our own progress prediction method. Instead, we consider the
methods from [3, 17] in our analysis and analyze their performance on the
currently used datasets.

Remaining Duration. A topic closely related to progress prediction is
Remaining Duration (RD) prediction. While the goal of progress prediction is
to predict the course of the activity as a percentage value in $[0,100\%]$, RD
aims at predicting the remaining time $t$ in minutes or seconds. Previous work
that researches the RD problem often does this in a surgical setting [1, 20,
26, 30] and thus refers to it as the Remaining Surgery Duration (RSD) problem.
Early methods work by pretraining a ResNet-152 model to predict either the
surgical phase [1] or the surgery progress [26], and then using the frame
embeddings created from the ResNet-152 model in an LSTM block to perform RSD
prediction. Building on top of this is the observation in [20] that predicting
extra information such as surgeon skill, may be beneficial to do RSD
prediction. Finally, RSD can also be modelled in a way closer to progress. By
dividing all RSD values by the highest possible RSD, the RSD can be predicted
as a value between $0$ and $1$ [29]. Unlike these methods that model the
passage of time as a decreasing remaining duration, we model it as an
increasing progress value. We use RSDNet [26] in our analysis, as it performs
both RSD and progress prediction.

Phase prediction. If an action consistently consists of separate sub-tasks or
phases of similar duration, then recognizing the current phase gives a good
approximation of the progress. Previous work jointly performs phase-based
progress prediction and surgical gesture recognition [27], jointly predicting
the phase and the surgery tools [25], or by using the embeddings in an LSTM to
predict the surgical phase online [31]. More recent work applies transformers
to perform surgical phase recognition [14, 19]. In this work, we do not
consider phase-prediction methods as they are an inaccurate proxy for
progress. Furthermore, when activities are non-linear, phase prediction is no
longer a good indicator of activity progress. Knowing which phase is happening
may be useful as an extra signal, however we do not consider this, as it
requires additional annotations.

Activity Completion. The progress for each frame can be calculated using
linear interpolation if the current activity time, $t$, the starting activity
time, $t_{\text{start}}$, and the ending activity time, $t_{\text{end}}$, are
available. Early work on this topic only predicts if an activity has been
completed or not using an SVM [5]. Follow-up work of Heidarivincheh _et al_.
[10] uses a CNN-LSTM architecture to predict the exact frame at which the
activity is completed, _i.e_. the activity completion moment. The detection of
the activity completion moment is done in a supervised setting [10], where the
exact frame at which the activity ends is annotated. Alternatively, activity
completion can be done in a weakly supervised setting where the only available
annotation is if the activity has been completed or not [11]. Although related
to progress prediction, activity completion only aims at predicting the
completion moment. In contrast, we focus on the more fine-grained targets of
activity progression at every frame.

##  3 Activity progress prediction

We formulate activity progress prediction as the task of predicting a progress
value $p_{n}^{i}\in[0,100]\%$ at frame $i$ in a video indexed by $n$, where

$p_{n}^{i}=\frac{i}{l_{n}},$ (1)

$l_{n}$ is the total number of frames for video $n$. Each video consists of a
single activity which starts at frame $1$ and ends at frame $l_{n}$. The
activity may consist of multiple phases, but we do not use any phase
annotation.

We predict progress percentages at every frame in the test videos. During
training, the videos can be presented to the methods in two different ways:
full-videos and video-sequences. We start by using complete videos during
training – full-videos, where each video frame represents a data sample.
Subsequently, we make the problem more realistic by applying two sampling
augmentations, as done in [3]: (a) for every video, we sample a segment by
randomly selecting a start and end point; (b) we randomly subsample every such
segment to vary its speed. We denote the video sampling strategy implementing
both points (a) and (b), as video-segments. On video-segments the methods can
only rely on the visual information for predicting progress.

###  3.1 Progress prediction methods

We consider 3 progress prediction methods from previous work: ProgressNet [3],
RSDNet [26], and UTE [17]. We select these methods as they are the only
methods in the surveyed literature that report results on the progress
prediction task. Furthermore, these methods are the only methods in surveyed
literature that do not require additional annotations, such as body joints
[21].

ProgressNet [3]: A spatio-temporal network which uses a VGG-16 [23] backbone
to embed video frames and extracts further features using spatial pyramid
pooling (SPP) [8] and region of interest (ROI) pooling [6]. Additionally, the
model uses 2 LSTM layers to incorporate temporal information. Becattini _et
al_. also introduce a Boundary Observant (BO) loss. This loss enables the
network to be more accurate around the areas of phase transitions. In our
work, we do not use the BO loss because it requires annotating the phase
boundaries. ProgressNet uses ROI pooling and requires per-frame bounding box
annotations. We use the complete frame as the bounding box on datasets where
we do not have bounding box annotations.

RSDNet [26]: It uses a ResNet-152 [9] backbone, followed by an LSTM layer with
512 nodes, and two additional single-node linear layers to jointly predict RSD
and video progress. The trained ResNet model creates embeddings from all the
frames, which are concatenated with the elapsed time in minutes. RSDNet
jointly trains on RSD and progress prediction but evaluates only on RSD
prediction. Here, we evaluate only the progress prediction head and train with
both the RSD and progress loss.

UTE [17]: This is a simple 3-layer MLP (Multilayer Perceptron) which takes as
input features extracted from RGB video frames such as dense trajectories [30]
or I3D network embeddings [4]. Both dense trajectories and I3D embed frames
over a sliding window which encodes temporal information into the features.
This gives the UTE network access to temporal information. Here, we use 3$D$
convolutional embeddings from the I3D backbone of dimension $1024$ and an
embedding window of size $16$ on all datasets. We use precisely the same
network design as in [17].

###  3.2 Learning based baselines

Next to the published methods above, specifically designed for progress
prediction, we also consider two more baselines. The first is a spatial only
ResNet-2D model, and the second is a spatio-temporal ResNet-LSTM model. We use
ResNet-LSTM as it is a progress-only variation of RSDNet. Furthermore, the
2$D$ variant ResNet-2D can give us insights into the spatial-only information
contained in the datasets, for progress prediction. We do not consider other
architectures, such as a Video Transformer [2], because they do not share the
same architecture structure as the progress prediction methods we consider in
Section 3.1, so they would not display similar behaviors during training.

ResNet-2D. A spatial 2$D$ ResNet [9] architecture that can only make use of
2$D$ visual data present in individual video frames, without access to any
temporal information. The last layer of the ResNet predicts the progress at
each frame via a linear layer, followed by a sigmoid activation.

ResNet-LSTM. Additionally, we extend the above ResNet-2D with an LSTM block
with 512 nodes, and a final progress-prediction linear layer using a sigmoid
activation. The LSTM block adds temporal information, which allows us to test
the added value of the memory blocks for activity progress prediction.

###  3.3 Naive baselines

Next to the learning-based baselines, we consider a set of naive non-learning
baselines. These non-learning baselines represent upper-bounds on the errors
we expect the learning-based methods to make.

Static-0.5. This is the most obvious non-learning baseline, which always
predicts $50\%$ completion at every frame. This is the best guess without any
prior information.

Random. Additionally, we consider a random baseline that predicts a random
value in $[0,100]\%$ at every frame. This represents the worst progress
prediction a model can make, indicating that it failed to learn anything.

Frame-counting. Finally, we consider a non-learning baseline which computes
training-set statistics. It is a frame-counting strategy that makes per-frame
average progress predictions. For frame $i$ in video $n$ this baseline
predicts a progress value equal to the average training-progress at frame $i$
of all training videos indexed by $m\in\\{1,...,N_{i}\\}$:

$\hat{p}^{i}_{n}=\frac{1}{N_{i}}\sum_{m=1}^{N_{i}}p^{i}_{m},$ (2)

where $N_{i}$ is the count of all the training videos with a length of at
least $i$ frames.

##  4 Empirical analysis

###  4.1 Datasets description

Each of the considered progress prediction methods evaluates on different
datasets: RSDNet on Cholec80 [25], ProgressNet on UCF101-24 [24], and UTE on
Breakfast [15, 16]. To analyze these methods, we use all 3 datasets for all
methods.

Cholec80 [25]: Consists of 80 videos of endoscopic cholecystectomy surgery.
Note that [26] uses an extended version of this dataset, Cholec120, containing
40 additional surgery videos. However, Cholec120 is not publicly available, so
we used Cholec80 to report our results. We randomly create four folds of the
data, and follow the same train/test dataset split sizes as in [26]. This
dataset has limited visual variability both across training and test splits.
Moreover, the presence of different medical tools in the frames informs of the
different surgery phases, which could aid the progress prediction task.

UCF101-24 [24]: Consists of a subset of UCF101 containing 24 activities, each
provided with a spatio-temporal action tube annotation.111Following [3] we use
the revised annotations available at https://github.com/gurkirt/corrected-
UCF101-Annots Becattini _et al_. [3] split the dataset into 2 categories:
telic and atelic activities. Telic activities are those with a clear endpoint,
such as ‘cliff diving’, while atelic activities, such as ‘walking the dog’, do
not have a clearly defined endpoint. Predicting progress for atelic activities
is more difficult than for telic ones. The original implementation of
ProgressNet first trains on telic activities, and then fine-tunes on all
activities. We did not observe a difference when using this training
procedure, and instead train all methods on the full dataset.

Breakfast [15, 16]: Contains 10 cooking activities: _e.g_. ‘making coffee’,
‘baking pancakes’, or ‘making tea’, etc., performed by 52 individuals in 18
different kitchens. We use the default splits and train each model across all
cooking activities. Because the tasks are performed by different individuals
in different kitchens, the video appearance varies even within the same task,
making this dataset extra challenging for progress prediction.

UCF101-24 contains training videos of up to 599 frames, while Cholec80 and
Breakfast contain videos with thousands of frames. When training on full-
videos, we could not train the ProgressNet model on the original Cholec80 and
Breakfast datasets, because of the long videos leading to memory problems.
Thus, for the experiments on full-videos, we use a subsampled version of
Cholec80 from 1 fps to 0.1 fps (the original fps is 25; [26] subsamples this
down to 1 fps); and we subsample the Breakfast dataset from 15 fps down to 1
fps. For our experiments on video-segments we use the original datasets.

---
|  |
(a) UCF101-24 on full-videos. | (b) Breakfast on full-videos. | (c) Cholec80 on full-videos.
Figure 2: MAE scores on full-videos. We plot the MAE in percentages for all
learning methods when inputting both full-video data and random-noise. (a) MAE
for the UCF101-24 dataset: For all methods except ProgressNet inputting
random-noise performs on par or better than inputting full-videos. (b) MAE for
the Breakfast dataset: When using random-noise as input to the methods, they
perform on par or better than when inputting full-videos, indicating that the
methods overfit to training artifacts. (c) MAE for the Cholec80 dataset: On
this dataset, using visual full-videos is better than inputting random-noise,
however the frame-counting baseline remains hard to exceed.

###  4.2 Experimental setup

For the considered progress prediction methods only the code for UTE is
published.222https://github.com/Annusha/unsup_temp_embed For the other
methods, we follow the papers for implementation details and training
procedures. We train RSDNet in a 2-step procedure following [26], however for
training the LSTM blocks we found that using the Adam optimizer with a
learning rate of $10^{-4}$ and no weight decay, for $30$k iterations works
best. For ProgressNet not all training details are mentioned in the paper, so
we use Adam with a learning rate of $10^{-4}$ for $50$k iterations, and we
keep the VGG-16 backbone frozen during training. For all experiments we report
the MAE (Mean Absolute Error) in percentages. Our code is available online at
https://github.com/Frans-db/progress-prediction.

###  4.3 _(i) How well can methods predict activity progression on the current
datasets?_

(i.1) Progress predictions on full-videos. Here we want to test how well the
learning-based models perform when trained on full-videos. We compare this
with using random-noise as input – we replace each frame with randomly sampled
noise. Intuitively, learning from random-noise over complete videos will give
recurrent models access to frame indices, and this should reach the frame-
counting baseline, which computes dataset statistics per frame. If the models
learn to extract useful appearance information, their MAE scores should be
considerably higher than when inputting random-noise. Additionally, we compare
the learning-based methods with the naive baselines: static-0.5, random, and
frame-counting.

Fig. 2(a) shows that the full-video visual information (blue bars) is less
useful than inputting random-noise (orange bars). When training on the full-
videos of UCF101-24 both the ResNet-2D and UTE models perform on par with the
static-0.5 baseline. This is because these spatial-only networks do not have
any way of integrating temporal information and they fail to extract progress
information from the visual data alone. When provided with random-noise as
inputs, they always predict $0.5$ and score on par with the static-0.5
baseline. The results are similar for the recurrent models on full-videos,
ResNet-LSTM and RSDNet who are both close to the static-0.5 baseline. We
observe that the recurrent models overfit on the embedded features and fail to
generalise. When these recurrent networks are provided with random-noise they
can only rely on the number of frames seen so far, and thus reach the frame-
counting baseline. ProgressNet is the only outlier here: when given full-
videos it performs better than when given random-noise as input. However,
ProgressNet still cannot outperform the non-learning frame-counting baseline.

For Breakfast in Fig. 2(b) the results look very similar to those on
UCF101-24. Both the ResNet-2D and UTE models cannot learn from visual
information alone. ResNet-LSTM and RSDNet both perform worse than the
static-0.5 baseline on full-videos, indicating that they are overfitting on
the training data. When provided with random-noise as input, they again can
only rely on the number of frames seen, and thus approach the frame-counting
naive baseline.

Cholec80 in Fig. 2(c) is the only dataset where the spatial-only networks
ResNet-2D and UTE perform better than the static-0.5 baseline. Here, we see
that using the full-videos (blue bars) is better than inputting random-noise
(orange bars). This hints to the visual information present in this dataset
being indicative of the activity progress. When inputting random-noise the
spatial-only methods again perform on par with the static-0.5 baseline, as
expected. However, this dataset still remains challenging as the methods are
not far from the frame-counting baseline. ResNet-LSTM and RSDNet are the only
who perform slightly better than this naive baseline, indicating that they can
extract some useful visual information from the video frames.

Observation: _The current datasets make it difficult for the progress
prediction methods to extract useful visual information. Therefore, the
methods overfit to training set artifacts, and are outperformed by simple
baselines based on dataset statistics._

---
|  |
(a) UCF101-24 on video-segments. | (b) Breakfast on video-segments. | (c) Cholec80 on video-segments.
Figure 3: MAE scores on video-segments. We plot the MAE in percentages for all
considered methods when inputting both video-segments and frame-indices. (a)
MAE for the UCF101-24 dataset: For all methods inputting frame-indices is
better than inputting video-segments. ResNet-2D and UTE get the biggest boost
in performance because they can learn the one-to-one mapping from index to
progress during training. (b) MAE for the Breakfast dataset: Also here frame-
indices are more informative than the visual data. (c) MAE for the Cholec80
dataset: All learning methods perform on par with the frame-counting baseline,
except for RSDNet which is slightly worse. This could be due to suboptimal
hyperparameter settings.

(i.2): Progress predictions on video-segments. We test the performance of
learning methods when trained to predict progress from video-segments. Using
video-segments should encourage the methods to focus more on the visual
information and not on the temporal position of the frames, as this is no
longer informative. We compare inputting video-segments with inputting frame-
indices – the absolute index of each frame, replicated as images. Intuitively,
learning from frame-indices should be on par with the frame-counting baseline,
since the only information available is the dataset statistics per frame.
Ideally, we would expect all methods to solve the progress prediction task by
relying on visual information, and therefore having lower errors than when
inputting frame-indices. Again, we also compare with the naive baselines:
static-0.5, random and frame-counting.

Fig. 3(a) shows that the visual information encoded in video-segments (green
bars) is less useful than knowing the current frame index (red bars). When
trained on video-segments of UCF101-24 all methods perform on par with the
static-0.5 baseline. Thus, the models cannot learn to predict progress from
the visual video data. Interestingly, ProgressNet using full-videos in Fig.
2(a) is better than the frame-counting baseline, however, here it fails to
learn when trained on video-segments. When provided with frame-indices as
input, all methods improve. The improvement is most visible for ResNet-2D and
UTE, which do not use recurrent blocks. This is because the non-recurrent
methods can learn the one-to-one mapping from index to progress during
training.

The results on the Breakfast dataset in Fig. 3(b) are similar to those of
UCF101-24 in Fig. 3(a). None of the networks can extract useful information
from the video-segments. All methods improve when trained on frame-indices.
The improvement is again more obvious for ResNet-2D and UTE. Moreover, all
results are on par with, or worse than the frame-counting baseline.

On Cholec80 in Fig. 3(c) all results are close to the frame-counting baseline.
This is dissimilar to Fig. 2(c) where inputting visual data was better than
inputting random noise of the same length as the full video. Again, ResNet-2D
and UTE improve when provided with frame-indices as input. For ResNet-LSTM and
ProgressNet and RSDNet the performance is on par with the frame-counting
baseline when trained on video-sequences indicating that these methods overfit
to the training data. When trained on frame-indices most methods approach the
frame-counting baseline, as this is the information encoded in the frame
indices across the full training set. RSDNet performs worst when given frame-
indices as inputs; we hypothesise that this is due suboptimal hyperparameter
settings.

Observation: _When restricting the models to rely only on visual information,
the models are outperformed by simply considering the current frame index, and
performing dataset statistics. This is due to the current progress prediction
datasets not containing sufficient visual information to guide progress
prediction._

###  4.4 _(ii) Is it at all possible to predict activity progress from visual
data only?_

We observe that current progress prediction datasets are not well-suited for
the task, as the learning models fail to extract useful information from
visual data alone. To test that the problem is indeed with the datasets used
for evaluation and not the learning models, we test here if progress
prediction is possible from visual data alone. For this we aim to construct a
synthetic dataset in such a way that the learning-based methods perform
optimal using visual information, and outperform all the naive baselines.

Our synthetic Progress-bar dataset, shown in Fig. 4, contains a progress bar
(similar, for example, to a download bar) that slowly fills up from left to
right. Each frame has a resolution of $32{\times}32$px. We generate $900$
videos for the training split, and $100$ for the test split. Each bar has its
own rate of progression, but there is a variance per notch causing some
uncertainty. Therefore, even on this simple dataset it is impossible to make
no errors. This is why in the first image the progression appears to be
slightly beyond 25%, but because the video may slow down after this section it
is actually at 22.2%. Due to the large variance in video length, ranging from
$19$ to $145$ frames, the frame-counting baseline, and thus frame-counting
strategies, will give worse results than relying on visual information. Also,
because of the different progress rates per video, the learning methods cannot
just rely on visual information alone, but also have to use temporal
information to perform well on this progress prediction task.

Figure 4: Visualisation of a progress bar from our synthetic Progress-bar
dataset at timesteps $t{=}0$, $t{=}15$, $t{=}35$, $t{=}58$, and $t{=}71$. Each
coloured section indicates visually a 25% section, but due to variance in the
speed, the actual video progress may differ at these points.

Due to the reduced frame resolution and data complexity of our synthetic
dataset, we scale down the ResNet backbone, for these experiments.
Specifically, to avoid overfitting, we use ResNet-18 as a backbone for
ResNet-2D, ResNet-LSTM, and RSDNet. ProgressNet and UTE remain unchanged.

Fig. 5 shows the results of all the learning-based methods when predicting
progress from both full-videos and video-segments. For this dataset the frame-
counting baseline has an MAE of $12.9$%, which is outperformed by all
learning-based methods. UTE performs the best out of all the networks, even
though it does not have memory. This is because UTE relies on 3D convolutional
embeddings over a temporal-window of size $16$ frames. This temporal-window
gives the method information about $7$ future frames, which is sufficient on
this simple dataset. For the LSTM-based methods inputting full-videos still
performs slightly better than inputting video-segments. At a closer look, this
is because the video-segments sampling method has a bias towards frames in the
middle of a video. The earlier frames are less likely to get sampled, thus the
progress prediction methods will have a higher error there.

Observation: _It is feasible for the progress prediction methods to make
effective use of the visual data present in the videos and outperform the
frame-counting baseline, when the visual data is a clear indicator for the
video progression. _

Figure 5: MAE scores on our synthetic Progress-bar dataset, when training on
full-videos and video-segments. The frame-counting baseline has an MAE of
$12.9\%$, while the static baseline is at $25\%$ and the random baseline at
$33.3\%$. We see that all methods outperform the frame-counting baseline. UTE
obtains the best result due to its $15$-frame temporal window, which allows it
to see $7$ frames into the future. We conclude that the progress prediction
methods are able to learn progress from visual information, if it is clearly
present in the videos.

##  5 Discussion and limitations of our analysis

|
---|---
(a) Video-04 of Cholec80 | (b) Video-05 of Cholec80
Figure 6: Activity progress prediction examples of Cholec80. (a) Video-04 at
timestamps $t{=}210$ and $t{=}1250$. (b) Video-05 at timestamps $t{=}200$ and
$t{=}1650$. At $t{=}210$ and $t{=}200$ the methods recognize the medical tool,
and correct their progress downwards to signal the start of the medical
procedure. At $t{=}1250$ and $t{=}1650$ the methods recognize the collection
bag and correct their progress to signal the end of the procedure. Figure 7:
Progress prediction example on Video-00015 of our synthetic Progress-bar
dataset at timestamps $t{=}10$ and $t{=}55$. The learning methods can almost
perfectly follow the ground truth.

Discussion. This paper empirically shows that the current progress prediction
datasets do now allow for learning useful visual information, and methods are
outperformed by naive baselines relying on dataset statistics. We observe that
the progress prediction models perform well on the training data, yet cannot
generalize well to the unseen test data. As future research, it would be
interesting to pinpoint the photometric artifacts that the models overfit to.
However, we also saw that some useful visual information was learned on the
Cholec80. This may be due to the presence of clear visual phase delineators.
Fig. 6(a) and Fig. 6(b) show examples of predictions on the Cholec80 dataset.
The first frames highlighted in these videos ($t{=}210$ and $t{=}200$) are the
moment when the first medical tool is present in the video, and the progress
prediction methods adjust their predictions to this new visual information.
Similarly, the second highlighted timesteps ($t{=}1250$ and $t{=}1650$)
represent the moment the collection bag is present which signals the end of
the procedure. On our synthetic Progress-bar dataset in Fig. 7 we also show
the predictions and highlight two moments in the videos. Here, the networks
almost perfectly follow the ground truth progression. These results illustrate
that for progress prediction is essential to have clearly recognizable visual
transition points, that consistently correspond to a certain progress
prediction percentage. This is related to the idea of Becattini _et al_. [3]
who use phase annotations to increase the loss around the phase boundaries.

Limitations. The first limitation of our research is that we could only find 3
progress prediction methods to analyze, on 3 datasets. Additionally, we do not
consider here other video-architectures such as a Video Transformer [2], as
these are not directly related to the progress prediction methods we analyze.
However, we do consider 2D (ResNet) and 3D (I3D) convolutional embeddings, as
well as recurrent networks (with LSTM blocks). Thirdly, we were unable to
match the results of ProgressNet exactly as reported in [3]: when trained on
video-segments, the authors report an MSE of $0.052$ (MAE of approximately
$22.8$%), while we obtain an MAE of $25.9$%. Nonetheless, the frame-counting
outperforms the result reported in [3], which still validates our conclusions.
Finally, we observed that on both UCF101-24 and Breakfast the methods have a
tendency to overfit. Maybe better strategies to overcome this overfitting
phenomenon could improve the results.

##  6 Conclusion

In this paper, we investigate the behaviour of current progress prediction
methods on the currently used benchmark datasets. We show that on the
currently used datasets, the progress prediction methods can fail to extract
useful information from visual data, and are exceeded by simple non-learning
baselines based on frame counting. Additionally, we evaluate all the methods
on a synthetic dataset we specifically design for the progress prediction
task. On our synthetic dataset the results show that all the methods can make
use of the visual information and outperform the naive, non-learning
baselines. We conclude that in its current form the task of progress
prediction is ill-posed, as the currently used datasets for progress
prediction are not suitable for this task.

Acknowledgements. This work was done with the support of the Eureka cluster
Program, IWISH project, grant number AI2021-066. Jan van Gemert is financed by
the Dutch Research Council (NWO) (project VI.Vidi.192.100).

## References

  * [1] Ivan Aksamentov, Andru Putra Twinanda, Didier Mutter, Jacques Marescaux, and Nicolas Padoy.  Deep neural networks predict remaining surgery duration from cholecystectomy videos.  In International Conference on Medical Image Computing and Computer-Assisted Intervention, 2017.
  * [2] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid.  Vivit: A video vision transformer, 2021.
  * [3] Federico Becattini, Tiberio Uricchio, Lorenzo Seidenari, Lamberto Ballan, and Alberto Del Bimbo.  Am i done? predicting action progress in videos, 2017.
  * [4] Joao Carreira and Andrew Zisserman.  Quo vadis, action recognition? a new model and the kinetics dataset, 2018\.
  * [5] Majid Mirmehdi Farnoosh Heidarivincheh and Dima Damen.  Beyond action recognition: Action completion in rgb-d data.  In Edwin R. Hancock Richard C. Wilson and William A. P. Smith, editors, Proceedings of the British Machine Vision Conference (BMVC), pages 142.1–142.11. BMVA Press, September 2016.
  * [6] Ross Girshick.  Fast r-cnn, 2015.
  * [7] Tengda Han, Jue Wang, Anoop Cherian, and Stephen Gould.  Human action forecasting by learning task grammars, 2017.
  * [8] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.  Spatial pyramid pooling in deep convolutional networks for visual recognition.  In Computer Vision – ECCV 2014, pages 346–361. Springer International Publishing, 2014.
  * [9] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.  Deep residual learning for image recognition, 2015.
  * [10] Farnoosh Heidarivincheh, Majid Mirmehdi, and Dima Damen.  Action completion: A temporal model for moment detection, 2018.
  * [11] Farnoosh Heidarivincheh, Majid Mirmehdi, and Dima Damen.  Weakly-supervised completion moment detection using temporal attention.  In 2019 IEEE/CVF International Conference on Computer Vision Workshop (ICCVW), pages 1188–1196, 2019.
  * [12] Sepp Hochreiter and Jürgen Schmidhuber.  Long short-term memory.  Neural computation, 9(8):1735–1780, 1997.
  * [13] Bo Hu, Jianfei Cai, Tat-Jen Cham, and Junsong Yuan.  Progress regression rnn for online spatial-temporal action localization in unconstrained videos, 2019.
  * [14] Muhammad Abdullah Jamal and Omid Mohareri.  Surgmae: Masked autoencoders for long surgical video analysis, 2023.
  * [15] Hilde Kuehne, A. B. Arslan, and T. Serre.  The language of actions: Recovering the syntax and semantics of goal-directed human activities.  In Proceedings of Computer Vision and Pattern Recognition Conference (CVPR), 2014.
  * [16] Hilde Kuehne, Juergen Gall, and Thomas Serre.  An end-to-end generative framework for video segmentation and recognition.  In Proc. IEEE Winter Applications of Computer Vision Conference (WACV 16), Lake Placid, Mar 2016.
  * [17] Anna Kukleva, Hilde Kuehne, Fadime Sener, and Juergen Gall.  Unsupervised learning of action classes with continuous temporal embedding, 2019.
  * [18] Xinyu Li, Yanyi Zhang, Jianyu Zhang, Yueyang Chen, Shuhong Chen, Yue Gu, Moliang Zhou, Richard A. Farneth, Ivan Marsic, and Randall S. Burd.  Progress estimation and phase detection for sequential processes, 2017\.
  * [19] Yang Liu, Maxence Boels, Luis C. Garcia-Peraza-Herrera, Tom Vercauteren, Prokar Dasgupta, Alejandro Granados, and Sebastien Ourselin.  Lovit: Long video transformer for surgical phase recognition, 2023.
  * [20] Andrés Marafioti, Michel Hayoz, Mathias Gallardo, Pablo Márquez Neila, Sebastian Wolf, Martin Zinkernagel, and Raphael Sznitman.  Catanet: Predicting remaining cataract surgery duration, 2021.
  * [21] Davide Pucci, Federico Becattini, and Alberto Del Bimbo.  Joint-based action progress prediction.  Sensors, 23(1), 2023.
  * [22] Joseph Redmon and Ali Farhadi.  Yolo9000: Better, faster, stronger, 2016.
  * [23] Karen Simonyan and Andrew Zisserman.  Very deep convolutional networks for large-scale image recognition, 2015\.
  * [24] Khurram Soomro, Amir Roshan Zamir, and Mubarak Shah.  Ucf101: A dataset of 101 human actions classes from videos in the wild, 2012.
  * [25] Andru Putra Twinanda, Sherif Shehata, Didier Mutter, Jacques Marescaux, Michel de Mathelin, and Nicolas Padoy.  Endonet: A deep architecture for recognition tasks on laparoscopic videos, 2016.
  * [26] Andru Putra Twinanda, Gaurav Yengera, Didier Mutter, Jacques Marescaux, and Nicolas Padoy.  RSDNet: Learning to predict remaining surgery duration from laparoscopic videos without manual annotations.  IEEE Transactions on Medical Imaging, 38(4):1069–1078, apr 2019\.
  * [27] Beatrice van Amsterdam, Matthew J. Clarkson, and Danail Stoyanov.  Multi-task recurrent neural network for surgical gesture recognition and progress prediction, 2020.
  * [28] Rosaura G. VidalMata, Walter J. Scheirer, Anna Kukleva, David Cox, and Hilde Kuehne.  Joint visual-temporal embedding for unsupervised learning of actions in untrimmed sequences, 2020.
  * [29] Bowen Wang, Liangzhi Li, Yuta Nakashima, Ryo Kawasaki, and Hajime Nagahara.  Real-time estimation of the remaining surgery duration for cataract surgery using deep convolutional neural networks and long short-term memory, 2023\.
  * [30] Heng Wang and Cordelia Schmid.  Action recognition with improved trajectories.  In 2013 IEEE International Conference on Computer Vision, pages 3551–3558, 2013.
  * [31] Gaurav Yengera, Didier Mutter, Jacques Marescaux, and Nicolas Padoy.  Less is more: Surgical phase recognition with less annotations through self-supervised pre-training of cnn-lstm networks, 2018.


# In-source and in-trap formation of molecular ions in the actinide mass range
at CERN-ISOLDE

M. Au<EMAIL_ADDRESS>M. Athanasakis-Kaklamanakis  L. Nies  J. Ballof  R.
Berger  K. Chrysalidis  P. Fischer  R. Heinke  J. Johnson  U. Köster  D.
Leimbach111Present address: University of Gothenburg, Sweden B. Marsh  M.
Mougeot222Present address: University of Jyväskylä, Finland J. Reilly  E. Reis
M. Schlaich  Ch. Schweiger  L. Schweikhard  S. Stegemann  J. Wessolek  F.
Wienholtz  S. G. Wilkins  W. Wojtaczka  Ch. E. Düllmann  S. Rothe  CERN,
Geneva, Switzerland  Johannes Gutenberg-Universität Mainz, Mainz, Germany  KU
Leuven, Leuven, Belgium  Universität Greifswald, Greifswald, Germany  FRIB,
Michigan State University, East Lansing, Michigan  Philipps-Universität
Marburg, Marburg, Germany  Institut Laue-Langevin, Grenoble, France  Max
Planck Institut für Kernphysik, Heidelberg, Germany  The University of
Manchester, Manchester, United Kingdom  Technische Universität Darmstadt,
Darmstadt, Germany  Massachusetts Institute of Technology, Cambridge, United
States of America  GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt,
Germany  Helmholtz Institute Mainz, Mainz, Germany

###### Abstract

The use of radioactive molecules for fundamental physics research is a
developing interdisciplinary field limited dominantly by their scarce
availability. In this work, radioactive molecular ion beams containing
actinide nuclei extracted from uranium carbide targets are produced via the
Isotope Separation On-Line technique at the CERN-ISOLDE facility. Two methods
of molecular beam production are studied: extraction of molecular ion beams
from the ion source, and formation of molecular ions from the mass-separated
ion beam in a gas-filled radio-frequency quadrupole ion trap. Ion currents of
U+, UO_1-3^+, UC_1-3, UF_1-4^+, UF_1,2O_1,2^+ are reported. Metastable
tantalum and uranium fluoride molecular ions are identified. Formation of
UO_1-3^+, U(OH)_1-3^+, UC_1-3, UF_1,2O_1,2^+ from mass-separated beams of U+,
UF_1,2^+ with residual gas is observed in the ion trap. The effect of trapping
time on molecular formation is presented.

††journal: Nucl. Inst. and Methods in Physics Research B

##  1 Introduction

There is interdisciplinary interest in radioactive molecules bridging fields
of molecular physics, atomic physics and nuclear physics, as well as physics
beyond the standard model [1]. Experimental research possibilities with many
radioactive molecules are currently constrained by their limited production.
This is particularly the case for radioactive molecules containing an actinide
element. Only actinides in the decay chains of primordial 232Th and 235,238U
are available in macroscopic quantities in nature. All others must be produced
artificially.

The Isotope Separation On-Line (ISOL) method allows production of a wide range
of radioactive nuclides across the nuclear chart through reactions induced by
the impact of an accelerated particle beam hitting a thick target. The ISOLDE
facility at CERN [2] uses 1.4-GeV protons accelerated by CERN’s Proton
Synchrotron Booster (PSB) and can employ a variety of target and ion source
systems. Once created, the reaction products must diffuse out of the target
material and effuse to the ion source, where they are ionized and extracted as
a beam of charged particles. For refractory species, forming volatile
compounds has been employed as a technique to improve extraction from the
target by delivering the isotopes of interest as molecular ion beams [3, 4, 5,
6]. In specific cases, the formation of molecules can reduce the isobaric
contamination remaining after mass separation. The production of actinide
molecules could address the scarcity and purity problems limiting many
experiments on actinide isotopes. In addition, they present promising cases
themselves [1, 7, 8, 9].

##  2 Method

The ISOLDE facility was used to study actinide species produced from four
porous micro-structured uranium carbide (UC${}_{\textrm{x}}$) target units: a
previously-irradiated target coupled to a rhenium surface ion source; a
previously-irradiated target coupled to a tungsten surface ion source; and two
new targets coupled to Forced Electron Beam Induced Arc Discharge (FEBIAD) ion
sources [10]. The ISOLDE Resonance Ionization Laser Ion Source (RILIS [11])
was used to resonantly ionize atomic U with the ionization scheme shown in
Fig. 1. Ion beams were extracted from the ion source using a 30-kV potential
difference and separated by their mass-to-charge ratio in the separator
magnet. Mass-separated ion beams were either sent to a MagneToF detector or
cooled and bunched in the ISOLTRAP Radio-Frequency Quadrupole cooler-buncher
(RFQ-cb) [12]. The bunched beam was sent to the Multi-Reflection Time-of-
Flight Mass Spectrometer (MR-ToF MS) [13], where ions were separated based on
their mass-to-charge ratios, including isobars, which were identified through
ToF mass measurements. The experimental setup is shown schematically in Figure
1.

Figure 1: Schematic of the experimental setup. Molecules are generated in the
UC${}_{\textrm{x}}$ target or from the mass-separated ion beam in the ISOLTRAP
RFQ-cb. The mass-separated beam is sent to a MagneToF detector or bunched and
sent to the MR-ToF MS for identification. The uranium resonant ionization
scheme shown uses a single titanium:sapphire laser [14].

##  3 In-source molecular formation

The target units with the tungsten surface ion source and the two FEBIAD type
ion sources were equipped with calibrated leaks (1.3E-4, 3E-4 and 5.7E-5 mbar
L s-1) through which carbon tetrafluoride (carbon tetrafluoromethane, CF4) gas
was injected as a reagent for fluoride molecule formation. Using the two
different types of ion sources, surface-, electron-impact-, and non-resonantly
laser-ionized-molecules were observed. Experimental parameters are indicated
in the captions of Figures 2 and 3.

Uranium molecules from the target material were identified using mass scans
performed with the ISOLDE mass separator magnets (Fig. 2) and verified using
the ISOLTRAP MR-ToF MS. 235,238U are present in the target as well as trace
amounts of 234U as a product of 238U decay. These formed UO+ and
UO${}_{2}^{+}$ with 16,18O present from residual gas or oxide residues in the
target. Depending on the degree of oxidation, the molecular oxide ion
intensity decreased with time and target heating in the presence of excess
carbon from the UC${}_{\textrm{x}}$ target. At higher temperatures, uranium
carbides (UC+ and UC${}_{2}^{+}$) were observed, formed from both 12,13C (Fig.
2). With the addition of CF4, UF${}_{1,2,3}^{+}$ and UFO+ dominated the total
surface- or plasma-ionized beam. Details of experimental parameters are given
in Fig. 3.

Figure 2: Ion beam current recorded on the MagneToF detector during a scan of
the GPS mass separator magnet showing the surface-ionized molecules from a
rhenium ion source coupled to a previously irradiated UCx target at a target
temperature of a) 1600 ∘C and b) 2100 ∘C. Note the logarithmic scale.

###  3.1 Non-resonant laser and plasma ionization

Figure 3: Mass spectra of ion beams from UC${}_{\textrm{x}}$ targets using the
GPS mass separator magnet. a) a tungsten surface ion source without (black)
and with 38 W of 532-nm laser light at a repetition rate of 10 kHz (red).
Target at 1650 ∘C and ion source at 1370 ∘C. b) a FEBIAD ion source before
(black) and after injection of CF4 through a calibrated leak for an ion source
internal pressure of approximately 7.5E-5 mbar (red). Target at 1200 ∘C and
ion source at 1830 ∘C.

UO+ and UO${}_{2}^{+}$ dominate the ion beam for oxidized targets. With first
ionization potentials of 6.0313(6) eV and 6.128(3) eV for UO and UO2,
respectively [15], these species are observed with both surface and FEBIAD ion
sources. With CF4 injection, tungsten surface ionization, and 30 W of 532-nm
laser light, UF+ and UF${}_{2}^{+}$ are the most intense uranium molecular ion
beams. Surface-ionized UF${}_{3}^{+}$ is detectable with a Faraday Cup;
UF${}_{4}^{+}$ is not observed (Fig. 3 a). Using a FEBIAD ion source, the
UF${}_{3}^{+}$ sideband is dominant and UF${}_{4}^{+}$ is observed. Higher
rates of U+ likely result from the breakup of uranium molecules in the FEBIAD
ion source before extraction as an ion beam. Sideband ratios depend strongly
on the concentration of CF4, favouring UF${}_{2,3}^{+}$ with higher leak rates
of CF4. Bond dissociation energies of UO (7.856(135) eV), UO2 (7.773(145) eV)
[15] suggest that some dissociation of neutral and singly-charged oxides
should occur within the FEBIAD ion source.

###  3.2 Metastable molecular ions

In mass spectrometry, the term ‘metastable’ is used to describe molecular ions
possessing sufficient excess energy to fragment in the field-free region after
leaving the ion source [16]. Upon fragmentation, the fragment ions retain a
fraction of the kinetic energy of the extracted precursor ion. This causes
fragment ions to pass through the mass separator magnetic field with an
apparent mass $m^{*}$ corresponding to [16]

$m^{*}=\frac{m_{f}^{2}}{m_{p}}$ (1)

where $m_{f}$ represents the mass of the fragment ion and $m_{p}$ represents
the mass of the precursor metastable molecular ion. Fragment ions and their
precursors were identified from the apparent mass and studied as a function of
the target and surface ion source temperatures (Fig. 4). Increasing the ion
source temperature significantly increased the fragment ion intensity,
suggesting that at high temperatures, the molecules are more likely to have
sufficient excess energy to reach the metastable states that fragment after
extraction. Fragment molecules are indicated where observed in Fig. 3.

Figure 4: Rates of ion beams from a tungsten surface ion source recorded on a
Faraday Cup after mass separation from the ISOLDE separator magnets shown in
logarithmic scale. a), b), c): as a function of ion-source temperature for a
target temperature of 1578 ∘C. d) e) f): rates as a function of target
temperature for an ion source temperature of 2230 ∘C. c) and f): rates of
fragment ions measured on the apparent mass corresponding to the indicated
dissociation of metastable molecular ions.

##  4 In-trap molecular formation

To study in-trap molecular formation, the ISOLTRAP RFQ-cb was employed with a
buffer gas (here He at up to 10-5 mbar measured within 1 m of the injection)
to cool and bunch the ions. Mass-separated beams ionized using each of the
studied ion sources were sent to the RFQ-cb for cooling and bunching. For
studies of beam composition and in-trap molecular formation, a sample of the
continuous ion beam was taken into the RFQ-cb. Ions were confined in the RFQ-
cb for a trapping time during which interaction occurred between the ions, the
buffer gas and residual gas contamination. The ion bunch was then ejected from
the RFQ-cb and the arrival times of ions in each shot were measured with
respect to the ejection time. Identification was performed with the MR-ToF MS
using expected ToF values extracted from a calibration using 85,87Rb+, 133Cs+
from the ISOLTRAP offline ion source [17], and online 238U+ from ISOLDE. ToF
spectra were accumulated over a number of shots as seen in Figures 5, 6, and
7.

The atomic uranium resonant laser ionization scheme in the ion source affected
the count rates of uranium molecules (e.g. UO+ and UOH+ in Fig. 5) observed
from the RFQ-cb ion trap. Combined with the mass-separation step of the
separator magnets, this indicates that the molecules are formed from ions in
the mass-separated U+ beam rather than in the target or ion source. For U and
Ta, ratios depend on the trapping time as shown in Figures 6 and 7. In
addition to atomic ions forming molecules, molecular ions mass-separated by
ISOLDE (including UF+, UF${}_{2}^{+}$, TaF+, TaF${}_{2}^{+}$) reacted with the
residual gas or buffer-gas contaminants to form molecules by pickup of C, O, H
and OH (Figs. 7,8) and in some cases (UF+, UF${}_{2}^{+}$) were observed with
higher charge states (UF2+, UF${}_{2}^{2+}$). To avoid detector saturation,
attenuators were used to reduce the intensity of the ion beam injected into
the RFQ-cb. This reduced absolute rates of in-trap formation and the formation
efficiency relative to the ion beam intensity extracted from the ion source.
Rates of molecular formation in the ion-trap represent ratios in the regime
below space-charge limitations.

Figure 5: ToF spectrum of A=238 mass-separated ion beams after cooling and
bunching in the ISOLTRAP RFQ-cb, then trapping for 2000 revolutions in the MR-
ToF MS as calculated for 238U. The status of the U resonant laser (on or off)
is indicated. Vertical lines shown in the top panel indicate ToFs expected
from offline calibrations. See text for further details.  Figure 6: ToF
spectra for various storage times (indicated on the left) of A=238 mass-
separated ion beams from the tungsten surface ion source with RILIS for U
after cooling and bunching in the ISOLTRAP RFQ-cb, then trapping for 2000
revolutions in the MR-ToF MS as calculated for 238UO+. Summed counts in each
of the identified peaks are shown as a function of trapping time. See text for
further details.

Notably, the in-trap UOx formation showed an identical response to the storage
time in the RFQ-cb before and after the addition of a liquid nitrogen cold
trap to the buffer gas line, indicating that reaction products enter the ion
trap through diffusion into the vacuum chamber rather than buffer gas
injection.

Figure 7: ToF spectrum of A=181 mass-separated ion beams from the FEBIAD ion
source after bunching in the ISOLTRAP RFQ-cb. Cooling time is indicated.
Vertical lines in the top panel show ToFs expected from the offline
calibration for single-pass operation of the MR-ToF MS.  Figure 8: ToF spectra
of A=276 mass-separated ion beams from a W surface source with CF4 injection
in single-pass operation of the MR-ToF MS with trapping time 200 ms.
Horizontal lines show switching between offline reference beam (85,87Rb+,
133Cs+). Vertical lines show identified non-isobaric actinide molecules from
molecular formation and charge exchange in the ISOLTRAP RFQ-cb.

##  5 Conclusions

For previously irradiated or oxidized targets, UO+ and UO${}_{2}^{+}$
sidebands are on the order of $10^{5}$ ions s-1 at target temperatures above
1600 ∘C. Without further addition of oxygen, the intensity of these
contaminants will decrease over time, with the UO${}_{2}^{+}$ sideband
depleting first, followed by the UO+ sideband. At nominal target temperatures
(2000 ∘C) and above, UC+, UC${}_{2}^{+}$ can similarly reach rates of $10^{4}$
ions s-1 or more. Fragments formed from the dissociation of metastable U and
Ta fluorides arrive as additional non-isobaric contaminants in mass-separated
beams. Fragment ions and their precursor ions can be identified using their
apparent mass (Eq. 1) and anticipated for a given mass-to-charge ratio with
the rates presented here. We present some representative rates of molecular
ions extracted from different ion sources with oxidation, CF4, and target
temperatures noted in Figure 4 and Table 1 as well as some representative
rates for formation of molecular ions in the RFQ-cb with trapping times noted
in Table 2. Rates from the ion source depend very strongly on target and ion
source temperature and CF4 injection rate. Rates from the RFQ-cb depend on
trapping time.

Ion source | Target | Species | Rate
---|---|---|---
| temperature |  | (ions s-1)
| (∘C ) |  |
Re surface | 1600 |  235U+ | 2.5(1) E+3
previously | 1600 |  238U+ | 8.9(6) E+5
irradiated | 1600 |  235U16O+ | 4.0(6) E+3
| 1600 |  238U16O+ | 1.4(2) E+6
| 1600 |  238U18O+ | 2.5(9) E+3
| 1600 |  235U16O${}_{2}^{+}$ | 2.4(1) E+3
| 1600 |  238U16O${}_{2}^{+}$ | 7.9(5) E+5
| 1600 |  238U16O18O+ | 3.5(5) E+3
Re surface | 2100 |  235U+ | 6.3(1) E+5
previously | 2100 |  238U+ | 5(1) E+7
irradiated | 2100 |  235U12C+ | 7(1) E+3
| 2100 |  235U16O+ | 1.24(6) E+4
| 2100 |  238U16O+ | 3.3(2) E+6
| 2100 |  238U18O+ | 8(1) E+3
| 2100 |  235U12C${}_{2}^{+}$ | 4.5(7) E+4
| 2100 |  238U12C${}_{2}^{+}$ | 1.3(2) E+7
| 2100 |  238U12C13C${}_{2}^{+}$ | 3(2) E+5
| 2100 |  238U16O${}_{2}^{+}$ | 7.3(3) E+4
| 2100 |  238U16O18O+ | 7.4(8) E+2
| 2100 |  238U12C${}_{3}^{+}$ | 1.3(4) E+4
FEBIAD | 1818 |  238U16O2+ | 2.8(5) E+7
with | 1818 |  238U16F2+ | 6(1) E+8
CF4 | 1818 |  238U+ | 1.5(1) E+11
| 1818 |  238U16O+ | 3.2(2) E+11
| 1818 |  238U19F+ | 1.7(1) E+11
| 1818 |  238U19F16O+ | 1.3(1) E+10
| 1818 |  238U19F${}_{2}^{+}$ | 1.4(1) E+11
| 1818 |  238U19F16O${}_{2}^{+}$ | 3.0(7) E+7
| 1818 |  238U19F${}_{2}^{16}$O+ | 3.5(5) E+9
| 1818 |  238U19F${}_{3}^{+}$ | 6.8(5) E+11
| 1818 |  238U19F${}_{4}^{+}$ | 4.9(4) E+10
Table 1: Some observed rates of uranium ion beams from a rhenium surface source and from an electron impact ion source with injected CF4, recorded on a Faraday cup after mass separation from the ISOLDE mass separator magnet. Trapping time | Initial ion | Species | Rate
---|---|---|---
(ms) | beam |  | (ions s-1 of
|  |  | injection time)
5 |  234U+ |  234U+ | 8.0(8) E-2
5 |  234U+ |  234UO2H+ | 9(1) E-2
5 |  235U+ |  235U+ | 1.64(5)
5 |  235U+ |  235UO${}_{2}^{+}$ | 5(1) E-2
5 |  238U+ |  238U+ | 4.40(7) E+4
5 |  238U+ |  238UO+ | 5.6(2) E+2
5 |  238U+ |  238UOH+ | 1.5(1) E+2
5 |  235UF+ |  235UF+ | 1.39(3) E+4
5 |  235UF+ |  235UFO+ | 3.6(3) E+2
5 |  235UF+ |  238UFOH+ | 7(1) E+1
100 |  235UF+ |  235UFO+ | 1.16(6) E+4
100 |  235UF+ |  238UFOH+ | 5.2(9) E+2
100 |  238UF+ |  238UF+ | 1.39(8) E+5
100 |  238UF${}_{2}^{+}$ |  238UF${}_{2}^{+}$ | 1.69(3) E+4
100 |  238UF${}_{2}^{+}$ |  238UF2O+ | 7(1) E+1
100 |  238UF${}_{2}^{+}$ |  238UFO2H+ | 1.6(6) E+1
200 |  238UF${}_{2}^{+}$ |  238UF${}_{2}^{+}$ | 1.17(2) E+4
200 |  238UF${}_{2}^{+}$ |  238UF2O+ | 3.4(3) E+2
200 |  238UF${}_{2}^{+}$ |  238UFO2H+ | 9.2(1.4) E+1
200 |  238UF${}_{2}^{+}$ |  238UF2+ | 8.2(9) E+1
200 |  238UF${}_{2}^{+}$ |  238UF${}_{2}^{2+}$ | 2.9(5) E+1
Table 2: Observed rates of ions formed inside the RFQ-cb from initial mass-
separated ion beams extracted from a tungsten surface ion source. Counts per
seconds of initial beam sampling time were recorded on the ISOLTRAP MagneToF
detector after mass separation in the MR-ToF MS. See text for more details.

Production of fluoride molecular ions from the ion source is achieved by
adding CF4. Since many actinide fluorides are stable at temperatures above
1000 ∘C, in-source formation is a promising approach that can use parameters
including target and ion source temperatures and fluorine partial pressure to
control formation rates. To form molecules that may not be stable at high
temperatures, molecular formation in the RFQ ion trap is presented as a
possible approach. Formation of oxides, carbides, and hydroxides from the
mass-separated atomic and molecular ion beams occurs in the ISOLTRAP RFQ-cb in
the presence of residual gases. Trapping time is shown to be a parameter
influencing the formation of molecules in the ion trap. The molecular
formation reported here in the ISOLTRAP RFQ-cb may have implications for other
RFQ-cb ion traps used in beam preparation (e.g. the ISOLDE cooler ISCOOL [2])
which require further investigations.

These studies combined characterize the composition of beams heavier than the
target material and provide information on the process of creating molecular
actinide beams in targets and in ion traps.

##  6 Acknowledgements

The authors gratefully acknowledge support from the ISOLDE operations team,
the ISOLDE targets and ion sources team, and Simone Gilardoni. This project
has received funding from the European Union’s Horizon 2020 Research and
Innovation Program (grant No. 861198 project ‘LISA’ MSC ITN). The authors
acknowledge support from the German Federal Ministry of Education and Research
(BMBF) for ISOLTRAP (grant No. 05P18HGCIA and 05P21HGCI1). L.N. acknowledges
support from the Wolfgang Gentner Program (grant No. 13E18CHA).

## References

  * [1] G. Arrowsmith-Kron, M. Athanasakis-Kaklamanakis, M. Au, J. Ballof, R. Berger, A. Borschevsky, A. A. Breier, F. Buchinger, D. Budker, L. Caldwell, C. Charles, N. Dattani, R. P. de Groote, D. DeMille, T. Dickel, J. Dobaczewski, C. E. Düllmann, E. Eliav, J. Engel, M. Fan, V. Flambaum, K. T. Flanagan, A. Gaiser, R. G. Ruiz, K. Gaul, T. F. Giesen, J. Ginges, A. Gottberg, G. Gwinner, R. Heinke, S. Hoekstra, J. D. Holt, N. R. Hutzler, A. Jayich, J. Karthein, K. G. Leach, K. Madison, S. Malbrunot-Ettenauer, T. Miyagi, I. D. Moore, S. Moroch, P. Navrátil, W. Nazarewicz, G. Neyens, E. Norrgard, N. Nusgart, L. F. Pašteka, A. N. Petrov, W. Plass, R. A. Ready, M. P. Reiter, M. Reponen, S. Rothe, M. Safronova, C. Scheidenberger, A. Shindler, J. T. Singh, L. V. Skripnikov, A. V. Titov, S.-M. Udrescu, S. G. Wilkins, X. Yang, Opportunities for fundamental physics research with radioactive molecules (2023).  doi:10.48550/ARXIV.2302.02165.
URL https://arxiv.org/abs/2302.02165

  * [2] R. Catherall, W. Andreazza, M. Breitenfeldt, A. Dorsival, G. J. Focker, T. P. Gharsa, T. J. Giles, J. L. Grenard, F. Locci, P. Martins, S. Marzari, J. Schipper, A. Shornikov, T. Stora, The ISOLDE facility, Journal of Physics G: Nuclear and Particle Physics 44 (9) (2017).  doi:10.1088/1361-6471/aa7eba.
  * [3] J. Ballof, C. Seiffert, B. Crepieux, C. E. Düllmann, M. Delonca, M. Gai, A. Gottberg, T. Kröll, R. Lica, M. Madurga Flores, Y. Martinez Palenzuela, T. M. Mendonca, M. Owen, J. P. Ramos, S. Rothe, T. Stora, O. Tengblad, F. Wienholtz, Radioactive boron beams produced by isotope online mass separation at CERN-ISOLDE, European Physical Journal A 55 (5) (2019).  doi:10.1140/epja/i2019-12719-1.
  * [4] U. Köster, O. Arndt, E. Bouquerel, V. N. Fedoseyev, H. Frånberg, A. Joinet, C. Jost, I. S. Kerkines, R. Kirchner, Progress in ISOL target–ion source systems, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 266 (19-20) (2008) 4229–4239.  doi:10.1016/J.NIMB.2008.05.152.
  * [5] U. Köster, P. Carbonez, A. Dorsival, J. Dvorak, R. Eichler, S. Fernandes, H. Frånberg, J. Neuhausen, Z. Novackova, R. Wilfinger, A. Yakushev, (Im-)possible ISOL beams, in: European Physical Journal: Special Topics, Vol. 150, Springer-Verlag, 2007, pp. 285–291.  doi:10.1140/epjst/e2007-00326-1.
  * [6] R. Eder, H. Grawe, E. Hagebø, P. Hoff, E. Kugler, H. L. Ravn, K. Steffensen, The production yields of radioactive ion-beams from fluorinated targets at the ISOLDE on-line mass separator, Nuclear Inst. and Methods in Physics Research, B 62 (4) (1992) 535–540.  doi:10.1016/0168-583X(92)95387-7.
  * [7] L. V. Skripnikov, N. S. Mosyagin, A. V. Titov, V. V. Flambaum, Actinide and lanthanide molecules to search for strong CP-violation, Physical Chemistry Chemical Physics 22 (33) (2020) 18374–18380.  arXiv:2003.10885, doi:10.1039/d0cp01989e.
  * [8] M. S. Safronova, D. Budker, D. Demille, D. F. Kimball, A. Derevianko, C. W. Clark, Search for new physics with atoms and molecules, Reviews of Modern Physics 90 (2) (2018).  arXiv:1710.01833, doi:10.1103/RevModPhys.90.025008.
  * [9] T. A. Isaev, S. Hoekstra, R. Berger, Laser-cooled raf as a promising candidate to measure molecular parity violation, Phys. Rev. A 82 (2010) 052521.  doi:10.1103/PhysRevA.82.052521.
URL https://link.aps.org/doi/10.1103/PhysRevA.82.052521

  * [10] L. Penescu, R. Catherall, J. Lettry, T. Stora, Development of high efficiency Versatile Arc Discharge Ion Source at CERN ISOLDE, Review of Scientific Instruments 81 (2) (2010) 1–5.  doi:10.1063/1.3271245.
  * [11] V. Fedosseev, K. Chrysalidis, T. D. Goodacre, B. Marsh, S. Rothe, C. Seiffert, K. Wendt, Ion beam production and study of radioactive isotopes with the laser ion source at ISOLDE, Journal of Physics G: Nuclear and Particle Physics 44 (8) (2017).  doi:10.1088/1361-6471/aa78e0.
  * [12] F. Herfurth, J. Dilling, A. Kellerbauer, G. Bollen, S. Henry, H.-J. Kluge, E. Lamour, D. Lunney, R. Moore, C. Scheidenberger, S. Schwarz, G. Sikler, J. Szerypo, A linear radiofrequency ion trap for accumulation, bunching, and emittance improvement of radioactive ion beams, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 469 (2) (2001) 254–275.  doi:https://doi.org/10.1016/S0168-9002(01)00168-1.
URL https://www.sciencedirect.com/science/article/pii/S0168900201001681

  * [13] R. N. Wolf, F. Wienholtz, D. Atanasov, D. Beck, K. Blaum, C. Borgmann, F. Herfurth, M. Kowalska, S. Kreim, Y. A. Litvinov, D. Lunney, V. Manea, D. Neidherr, M. Rosenbusch, L. Schweikhard, J. Stanja, K. Zuber, ISOLTRAP’s multi-reflection time-of-flight mass separator/spectrometer, International Journal of Mass Spectrometry 349-350 (1) (2013) 123–133.  doi:10.1016/j.ijms.2013.03.020.
  * [14] M. R. Savina, B. H. Isselhardt, R. Trappitsch, Simultaneous Isotopic Analysis of U, Pu, and Am in Spent Nuclear Fuel by Resonance Ionization Mass Spectrometry, Analytical Chemistry 93 (27) (2021) 9505–9512.  doi:10.1021/acs.analchem.1c01360.
  * [15] L. R. Morss, N. . Edelstein, J. Fuger, J. J. Katz, Chemistry of Actinide and Transactinide Elements - Fourth Edition, Springer, 2010.
  * [16] R. A. W. Johnstone, M. E. Rose, Mass Spectrometry for Chemists and Biochemists, Cambridge University Press, 2012, Ch. Metastable ions and mass spectrometry, pp. 232–288.  doi:10.1017/cbo9781139166522.009.
  * [17] F. Wienholtz, D. Beck, K. Blaum, C. Borgmann, M. Breitenfeldt, R. B. Cakirli, S. George, F. Herfurth, J. D. Holt, M. Kowalska, S. Kreim, D. Lunney, V. Manea, J. Menéndez, D. Neidherr, M. Rosenbusch, L. Schweikhard, A. Schwenk, J. Simonis, J. Stanja, R. N. Wolf, K. Zuber, Masses of exotic calcium isotopes pin down nuclear forces, Nature 498 (7454) (2013) 346–349.  doi:10.1038/nature12226.