# Dependence of total kinetic energy of fission fragments on the excitation
energy of fissioning systems

Kazuya Shimada  Nuclear Engineering Course, Transdisciplinary Science and
Engineering, School of Environment and Society, Tokyo Institute of Technology,
Tokyo, 152-8550 Japan  Chikako Ishizuka<EMAIL_ADDRESS>Institute of Innovative Research, Tokyo Institute of Technology, Tokyo,
152-8550 Japan  Fedir A. Ivanyuk  Institute for Nuclear Research, 03028 Kiev,
Ukraine  Satoshi Chiba  Institute of Innovative Research, Tokyo Institute of
Technology, Tokyo, 152-8550 Japan

###### Abstract

We elucidated the reason why the average total kinetic energy (TKE) of fission
fragments decreases when the excitation energy of the fissioning systems
increase as indicated by experimental data for the neutron-induced fission
events. To explore this problem, we used a method based on the four-
dimensional Langevin equations we have developed. We have calculated the TKE
of fission fragments for fissioning systems 236U∗ and 240Pu∗ excited above
respective fission barriers, and compared the results with experimental data
for n + 235U and n + 239Pu reactions, respectively. From the Langevin-model
analysis, we have found that the shape of the abundant heavy fragments changes
from almost spherical for low excitation domain to highly prolate shape for
high excitation energy, while that of the light fragments does not change
noticeably. The change of the ”shape” of the heavy fragments causes an
increase of a distance between the charge centers of the nascent fragments
just after scission as excitation energy increases. Accordingly, the Coulomb
repulsion between the two fragments decreases with an increase of the
excitation energy, which causes the decrease of the average TKE. In this
manner, we found that the change of the shape of the heavy fragment as a
function of the excitation energy is the key issue for the TKE of fission
fragments to decrease as the excitation energy of the fissioning nuclei
increases. In other words, washing out of the shell effects which affect the
shape of the heavy fragments is the key reason for the decreasing energy
dependence of the average TKE of the fission fragments.

###### pacs:

24.10.-i, 24.60.-k, 24.60.Ky, 24.75.+i, 25.85.-w, 25.85.Ec, 28.41.-i

##  I Introduction

Nuclear fission is the fundamental process both in nuclear energy and fission
recycling during the r-process nucleosynthesis. Therefore, it is necessary to
understand the nuclear fission process in detail to utilize it with a good
accuracy in various fields. In their earlier works just after the discovery of
nuclear fission, Bohr, Wheeler, and Hill Bohr-Wheeler ; Hill-Wheeler  proposed
the basic concepts of nuclear fission such as saddle point, fission barriers,
fissility, and zero-point oscillation of shape parameters based on the liquid-
drop model. They found that each mode may have independent zero-point
oscillation energy Hill-Wheeler . These ideas are still important even today.
However, precise understanding of the nuclear fission process is still
challenging because of its complexity as a large-amplitude collective motion
of quantum systems consisting of a finite number of nucleons Bender .

It is a special feature of nuclear fission that a large amount of energy is
released as the Q-value and that most of this energy turns into the form of
total kinetic energy (TKE) of the fission fragments. According to this, the
sum of the Q value of fission and the initial excitation energy $E^{*}$ is
divided into TKE and other energies. In particular, $Q+E^{*}-\rm{TKE}$ is the
total excitation energy of fission fragments, and this excitation energy
causes the emission of prompt neutrons and $\gamma$ rays Okumura . The number
of prompt neutrons is important for the criticality of nuclear reactors, and
$\gamma$ rays are also one of the heat sources of nuclear reactors.
$\beta$-decay after gamma emission is also a phenomenon that occurs according
to the distribution of nuclides formed by the emission of prompt neutrons.
Therefore, a quantitative understanding of TKE is important to elucidate the
nature of the fission process.

There remain unsolved questions in the study related to the TKE of the fission
process. One of them is the relationship between the excitation energy of
fissioning nuclei and the TKE. Intuitively, it is expected that the TKE
increases as the excitation energy of the fission nucleus increases since the
energy available to any mode increases. In the terminology of the
4-dimensional Langevin theory which we use, $Q+E^{*}$ is shared among 4
collective coordinates and intrinsic energy, one of the collective coordinate
being the elongation of the whole system. Therefore, if the total energy
available increases, there is more chance for the elongation degree-of-freedom
to get more energy so that the translational motion, namely, kinetic energy of
fragments, gets more energy. Therefore, it is a big mystery to know that the
TKE decreases in neutron-induced fission events as the incident neutron energy
increases which lead to an increase of the excitation energy of the compound
nuclei Dyachenko ; Surin ; Akimov ; Duke235U+n ; Duke238U+n ; Duke239Pu+n .
This fact contradicts the above intuitive expectation. Of course, nuclear
fission is a very complex motion of finite number of nucleons, so such a naive
picture may be an oversimplification of the phenomenon. As a matter of fact,
it is expected that friction will increase as the excitation energy increases,
leading to the decrease of pre-scission kinetic energy. Nevertheless, the
effect of friction on TKE reduction is a minor one since the main source of
TKE is Coulomb repulsion between the nascent fragments formed just after
scission.

Various approaches have been proposed to study the fission process and
properties of fission fragments such as mass and TKE distributions. For a
quantitative estimation of TKE, we need a dynamical model that can describe a
process starting from an almost spherical compound nucleus to scission via
fission saddle points. For example, Langevin equations based on the
fluctuation-dissipation theorem have been successfully applied for this
purpose Usang2016 ; Usang2017 ; Ishizuka2017 ; Usang2019 ; Ishizuka2020 . They
have theoretically studied nuclear fission using a three-dimensional Langevin
model with microscopic transport coefficients Usang2016 ; Usang2017  and a
four-dimensional Langevin model with macroscopic transport coefficients
Ishizuka2017 . Our previous studies found that both systematic and anomalous
trends in fission fragment mass distribution and TKE could be understood by a
correlated twin transition Usang2019 . In the same context, we predicted a new
super asymmetric fission mode in a region of superheavy nuclei where the
magicity of 208Pb plays an important role Ishizuka2020 . In the present study,
we apply the same methodology for typical actinide nuclei important for energy
applications to elucidate the relationship between the excitation energy of a
compound nucleus and the TKE of the fission fragments focusing on the “shape”
of the fission fragments.

This paper is organized as follows. Sec. II., the computational method based
on the four-dimensional Langevin model used in this study is explained. In
Sec. III, the calculation results are shown and compared with the experimental
data. Especially, we focus on the deformation of fission fragments and discuss
the relationship between the change of the fragment deformations on excitation
energy and its impact on the TKE. In Sec. IV, the conclusions and future
prospects of this study are stated.

##  II Computational Method

To describe the nuclear shape during fission process, we adopt a shape
parametrization of the so-called two-center shell model Maruhn , which is
basically two oscillators connected smoothly to each other in the region
between them. In this parametrization, the nuclear shape is described by 5
parameters, namely, the elongation $z_{0}$, deformation of the outer tips of
nuclei, $\delta_{1}$ and $\delta_{2}$, mass asymmetry $\alpha$ which is
defined as $(A_{1}-A_{2})/(A_{1}+A_{2})$ where $A_{1}$ and $A_{2}$ are mass
numbers of the two parts of the fissioning system which eventually leads to
two nascent fragments, and the neck parameter $\epsilon$. The parameter
$z_{0}$ corresponds to the distance between centers of the two oscillators
normalized by $R_{0}=1.2\cdot A_{c}^{1/3}$, where $A_{c}=A_{1}+A_{2}$ stands
for mass number of the fissioning nucleus. See ref. Ishizuka2017  for details.
Out of these 5 parameters, we fixed $\epsilon=0.35$, and the other 4
parameters were selected as the dynamical variables whose time evolutions are
described by the Langevin equation. The value of $\epsilon$=0.35 was
determined from our previous analysis for the mass distributions of actinide
nuclei. The four dynamical parameters may be denoted in general as
$\\{q_{\mu}:~{}\mu=1,\cdots,4\\}=\\{z_{0},\delta_{1},\delta_{2},\alpha\\}$,
then, the Langevin equations take the following form:

$\displaystyle\frac{dq_{\mu}}{dt}$ $\displaystyle=$
$\displaystyle(m^{-1})_{\mu\nu}p_{\nu},$ (1)
$\displaystyle\frac{dp_{\mu}}{dt}$ $\displaystyle=$
$\displaystyle-\frac{\partial F(q,T)}{\partial
q_{\mu}}-\frac{1}{2}\frac{\partial(m^{-1})_{\nu\sigma}}{\partial
q_{\mu}}p_{\nu}p_{\sigma}$ (2)
$\displaystyle-\gamma_{\mu\nu}(m^{-1})_{\nu\sigma}p_{\sigma}+g_{\mu\nu}R_{\nu}(t),$

where all Greek letters take values of 1 to 4, and summation for repeated
subscripts is implicitly assumed. We solve the Langevin equations using the
collective inertia tensor $m_{\mu\nu}$ calculated within the Werner-Wheeler
approximation Werner-Wheeler1 ; Werner-Wheeler2  and the friction tensor
$\gamma_{\mu\nu}$ based on the wall-and-window formula wall-and-window . The
symbol $R_{\nu}$ stands for white noise, while $g_{\mu\nu}$ denotes its
strength. The dumping factor $k_{s}$ for the wall-and-window friction was
determined to be 0.27 ffric1  from analysis of the widths of giant resonances
by Nix and Sierk, and we have used this value in our past researches. They
solved the Fokker-Plank equation with a shape parametrization different from
the two center model used here. The value of this dumping factor should depend
on the combination of other parameters, and also on the parametrization and
models to be solved. In this paper, we adjusted this parameter to 0.55 to
reproduce the average TKE value for n + 235U and n + 239Pu reaction at neutron
energy region below 6 MeV. The change of $k_{s}$ from 0.27 to 0.55 gives a
constant shift to average TKE by about 3 to 4 MeV, but does not affect the
dependence of the TKE on excitation energy. Therefore it does not affect the
purpose of this work. We may use a different value of the $k_{s}$ parameter in
future work when different values of other parameters such as $\epsilon$ are
selected to reproduce other observables. Anyway, this work aims to understand
the dependence of the average TKE of fission fragments on excitation energy.
It is not affected by choice of $k_{s}$ as long as we keep it to be a constant
value.

We introduced independent effective temperature for each dynamical variable in
the following manner. The strength of the random force term $g_{\mu\nu}$ is
related to the friction tensor $\gamma_{\mu\nu}$ via a combination of the
Einstein relation and fluctuation-dissipation theorem:

$g_{\mu\sigma}g_{\sigma\nu}=T\gamma_{\mu\nu}$ (3)

where $T$ denotes the thermodynamic temperature or, in other words, intrinsic
temperature of the heat bath. From this equation, it is known that the
strength $g_{\mu\nu}$ depends on the temperature in a manner proportional to
$\sqrt{T}$. This $T$ is derived from the initial excitation energy $E_{x}$ as

$\displaystyle E_{int}$ $\displaystyle=$ $\displaystyle
E_{x}-\frac{1}{2}\left(m^{-1}\right)_{\mu\nu}p_{\mu}p_{\nu}-F(q,T=0)$ (4)
$\displaystyle=$ $\displaystyle aT^{2}\ .$

Here, $F$ and $a$ denote the free energy of the system at $T$=0 and the level
density parameter, respectively. Then, in order to introduce ”effective”
temperature which accounts for quantum correction to each dynamical variable
corresponding to zero-point oscillation, we first solve the above equation (3)
for $T=1$ MeV and obtain a ”pseudo” strength $g^{\prime}$, namely,

$g^{\prime}_{\mu\sigma}g^{\prime}_{\sigma\nu}=\gamma_{\mu\nu}$ (5)

Nextly, we introduce effective temperature $T^{eff}_{\mu}$ffric2 ; ffric3  for
each random variable $q_{\mu}$ by using the zero-point energy
$\frac{1}{2}\hbar\omega_{\mu}$ for each variable as

$T^{eff}_{\mu}=\frac{1}{2}\hbar\omega_{\mu}\coth{\frac{\hbar\omega_{\mu}}{2T}}.$
(6)

Then, the strength $g$ is obtained as
$g_{\mu\nu}=\sqrt{T^{eff}_{\mu}}g^{\prime}_{\mu\nu}$ (do not take sum on
$\mu$). In this paper, we have investigated the reasonable zero-point energy
$\hbar\omega_{\mu}/2$ of oscillators forming the heat bath, for each degree of
freedom. Our previous works Ishizuka2017  estimated the zero-point energy as 1
MeV taking the middle of 0.45 to 2.23 MeV suggested in ref. Bohr-Wheeler ;
Hill-Wheeler . As is already discussed in their pioneering works, the
magnitude of the zero-point energy can be different for different degrees-of-
freedom, since it accounts for the curvature of the potential energy landscape
for each of the independent dynamical variables. Based on the previous study,
we compare two sets of $\\{\hbar\omega_{\mu}\\}=(2,2,2,2)$ MeV and $(1,1,1,2)$
MeV. We found that the width of the mass distribution is somehow sensitive to
$\hbar\omega_{4}$. For example, the distribution becomes too sharp for
$\hbar\omega_{4}=1$ MeV, and the symmetric components of the distribution
become too large for $\hbar\omega_{4}=3$ MeV, while $\hbar\omega_{4}=2$ MeV
can reproduce both the width and peak structure reasonably. Then, we decided
to fix $\hbar\omega_{4}=2$ MeV. The other parameters $\hbar\omega_{i}$
($i=1,2,3$) do not affect much important observables except for a constant
shift in the TKE, which was taken care of by the $k_{s}$ parameter as
described above. We take a set of $\\{\hbar\omega_{\mu}\\}=(1,1,1,2)$ [MeV]
for the calculations below.

##  III Results and discussion

We compare the fission fragment mass distributions (FFMDs) and the dependence
of the averaged total kinetic energies of fission fragments on the incident
neutron energy $E_{n}$, calculated by the present model and experimental data.
In this comparison, we shift the calculated data or experiment by the neutron
separation energy since our calculations were performed for 236U and 240Pu
excited above their fission barriers as compound nuclei, so they are denoted
as 236U∗ and 240Pu∗. In the following, we label the fissioning system by the
compound nuclei, while experimental data were taken from neutron-induced
reactions.

Fig. 1 compares the calculated FFMDs for 236U∗ and 240Pu∗ with those for n +
235U and n + 239Pu reactions for which independent fission yield data were
taken from JENDL/FPY2011JENDLFPY2011 , and those for pre-neutron emission were
taken from Okumura et al.Okumura  and Schillebeeckx et
al.Schillebeeckx240PuFPY . The present calculations reproduce the width and
the peak positions, and peak-to-valley ratio, reasonably well, if not perfect.
Note that the present results are given for pre-neutron emission, thus keep a
perfect mirror symmetry around $A_{c}/2$, while data from JENDL/FPY2011 are
for post-neutron emission. We can adjust model parameters to make agreement of
the calculation with experimental data better, but it must be done not only
looking at the FFMD but also for other quantities including TKE. We will leave
that task for our future work.

Figure 1: (Color online) The mass distribution of fission fragments originated
from the compound nuclei ${}^{236}{\rm{U}}$∗ (left) and ${}^{240}{\rm{Pu}}$∗
(right). The histograms are the results of present 4D Langevin calculation for
excitation energy of 7 MeV, while the open circles are evaluated values of
independent fission yields, namely post-neutron yields, given in
JENDL/FPY-2011JENDLFPY2011  for thermal-neutron induced reactions on 235U and
239Pu. In addition, the $+$ symbols are values given by Okumura et al.Okumura
and Schillebeeckx et al.Schillebeeckx240PuFPY  for thermal-neutron induced
pre-neutron emission yields on 235U and 239Pu, respectively.

Fig. 2 exhibits the average TKE of fission fragments for 236U∗ and 240Pu∗ as a
function of neutron energy for n + 235U and 239Pu reactions. The left and
right panels in Fig. 2 correspond to the average TKE plot for neutron energy
$E_{n}$ below 50 MeV and the enlarged view for $E_{n}\leq 6$ MeV,
respectively. Experimental data Dyachenko ; Surin ; Akimov  are shown with
filled triangles (240Pu∗) and filled circles (236U∗). Results of the present
calculation are given by a line with error bars, which indicates the
statistical fluctuation in Monte-Carlo runs. As we can see, both of the
calculated and measured average TKE show clear decreasing trends as incident
neutron energy (or excitation energy of compound nuclei) increases. This
phenomenon has been recognized in experiments for a long time, but, at first
glance, this is a trend against our intuition. If the neutron energy
increases, the excitation energy should increase. Then, it is natural to
expect that energy to be shared to the kinetic energy of fission fragments
should increase, which makes the average TKE increase. But the experimental
data show the opposite tendency, and our calculation can reproduce such
behaviour in a quite reasonable manner. It is the purpose of this paper to
elucidate the reason for this decreasing trend of the average TKE of fission
fragments as the neutron energy (and hence the excitation energy) increases.
Furthermore, we can recognize that the calculated average TKEs agree well with
the experiments within 1 MeV for neutron energies below several MeV, which
indicates that the agreement is accurate to the order of about 0.6%, which is
quite a good accuracy. For higher neutron energies, however, our calculation
underestimates the measured TKE values. This disagreement is due to the fact
that these data at the higher neutron energies include effects of the
multichance fission, which makes the TKE values larger since it involves
fission events for lower excitation energies. Inclusion of the multichance
fission on average TKE is certainly an important issue, but we did not perform
such a correction since we wish to comprehend in this work the reason why the
average TKE of fission fragments decreases as the neutron energy increases
without the complexity of multichance fission which may dilute the essence of
this phenomena.

Figure 2: (Color online) Average TKE (Total Kinetic Energy) of fission
fragments for fissioning systems of ${}^{236}{\rm{U}}$∗ and
${}^{240}{\rm{Pu}}$∗. Two panels are the overall (the left) and enlarged (the
right) views. The scale of the vertical axis is common in these panels. The
solid lines with error bars denote our calculation, while symbols are
experimental data Dyachenko ; Surin ; Akimov . Note that we omit the
multichance fission effects while the experimental data above several MeV
include its effects.

Fig. 3 shows average shapes of fission fragments just after scission for
${}^{236}{\rm{U}}$∗ (left panel) and ${}^{240}{\rm{Pu}}$∗ (right panel) for
excitation energies of 7 MeV (solid line) and 27 MeV (broken line). These
shapes were obtained by averaging each of the four shape parameters at
scission configuration, which is defined as neck radius, $r_{neck}$, $=$0,
adjusting so that the heavy fragment always stays at the right-hand side. In
each panel, the left and right fragments correspond to light and heavy
fragments, respectively. The volume of each fragment can be obtained by the
integral $\pi\int\rho(z)^{2}dz$, where $\rho(z)$ denotes the value of $\rho$
coordinate corresponding to the nuclear surface as a function of $z$, see Fig.
3. The outer tip of the heavy fragment (right part) is closer to a sphere than
the light fragment (left part), which is deformed well to prolate shapes for
both excitation energies. Moreover, it can be noticed that the light fragment
shape does not depend on excitation energy noticeably. On the other hand, the
heavy fragment shape depends on the excitation energy. When the excitation
energy becomes larger, their shape deforms more to the prolate shape
significantly. This fact is common for both 236U∗ and 240Pu∗ systems.

Figure 3: (Color online) Shapes of fission fragments of ${}^{236}{\rm{U}}$∗
and ${}^{240}{\rm{Pu}}$∗ just afther scission for excitation energies of 7 MeV
(solid lines) and 27 MeV (dash lines).

The scatter plot in fig. 4 shows the distribution of the quadrupole moment
$Q_{20}$ of the fission fragments originated from the compound nuclei 236U∗
and 240Pu∗, at an excitation energy of 10 MeV, as a function of a fragment
mass number. In each panel, the averaged $\langle Q_{20}(A)\rangle$ is shown
by a solid histogram. The distribution of the $Q_{20}$ of the heavy fragments
(A=130-144) is located at around 0 to 5 barns with $\langle
Q_{20}(A)\rangle\simeq 2-3$ barns, while that of their counterpart formed as
light fragments (A=90-110) is located at around 4 to 10 barns with $\langle
Q_{20}(A)\rangle\simeq 7-8$ barns. It indicates that the heavy fragments favor
shapes closer to a sphere due to a strong shell effect around A=132-144
(double shell closure of 132Sn and deformed shell closures around A=144). The
$\langle Q_{20}(A)\rangle$ shows a saw-tooth behaviour similar to the
multiplicity of prompt neutrons. Such features are commonly observed in 236U∗
and 240Pu∗.

Fig. 5 displays how this saw-tooth structure of $\langle Q_{20}(A)\rangle$
depends on excitation energy, starting from 7 MeV to 57 MeV. We notice that,
besides large fluctuation at low excitation energies due to low Monte-Carlo
statistics, the $\langle Q_{20}(A)\rangle$ of lighter fragments ($A\lesssim
126$) are almost independent of the excitation energy, while those of heavier
fragments ($A\gtrsim 126$) clearly depend on it. The $\langle
Q_{20}(A)\rangle$ of heavy fragments exhibits a deep dip at around A=130 at an
excitation energy of 7 to 17 MeV which is obviously caused by the spherical
magicity of 132Sn, but this dip disappears gradually as excitation energy gets
increased. Therefore, the dip, brought by the shell effect, gradually
vanishes, since the heavy fragments can possess more energy as a form of
”deformation energy” as excitation energy of the whole system is increased.
This gradual change of the quadrupole moment of the heavier fragment is a
manifestation of the washing out of the shell effects in nuclear fission. At
excitation energies above 47 MeV, the shape of the heavy as well as light
fragments do not change anymore, indicating that the fission mechanisms are
entering into the domain which can be described by the liquid-drop model. In
this domain, both the light and heavy fragments are deformed to certain
equilibrium prolate shapes.

Figure 4: (Color online) Quadrupole moment ($Q_{20}$) of fission fragments
just after scission for the ${}^{236}{\rm{U}}$∗ (left panel) and
${}^{240}{\rm{Pu}}$∗ (right panel) fissioning systems at excitation energy of
10 MeV. In each panel, the solid histogram shows average of $Q_{20}$ for each
fission fragment mass number, namely, $\langle Q_{20}(A)\rangle$. The scatter
plot shows relative occurrence frequency of $Q_{20}$ by each fission event.
Figure 5: (Color online) Dependence of the $\langle Q_{20}(A)\rangle$ of
fission fragments originated from ${}^{236}{\rm{U}}$∗ (left panel) and
${}^{240}{\rm{Pu}}$∗ (right panel) for excitation energies $E_{x}=7-57$ MeV.
Note that the above results reflect only first chance fission.

Fig. 6 shows a similar dependence as shown in fig. 5 but for the octupole
moment $\langle Q_{30}(A)\rangle$. In Fig.6, we found that the fission
fragments have a noticeable octupole deformation (pear-like shapes). This
result is in good agreement with the microscopic study Scamps  where the
importance of octupole deformation was discussed. The excitation-energy
dependence of $\langle Q_{30}(A)\rangle$ is very similar to that of $\langle
Q_{20}(A)\rangle$, though $\langle Q_{30}(A)\rangle$ increases for a larger
fragment mass number more than $\langle Q_{20}(A)\rangle$ , and saw-tooth
structure is less pronounced for $\langle Q_{30}(A)\rangle$. The $\langle
Q_{30}(A)\rangle$ of lighter fragments is almost independent of the excitation
energy of a compound nuclei, while that of the heavier fragments has a dip at
low excitation energy but this dip is washed out as excitation energy gets
larger. At excitation energy above 47 MeV, the $\langle Q_{30}(A)\rangle$
increases almost linearly as a function of the mass number of the fission
fragments.

Figure 6: (Color online) Dependence of the average octupole moment $\langle
Q_{30}(A)\rangle$ of the fission fragments from ${}^{236}{\rm{U}}$∗ (left
panel) and ${}^{240}{\rm{Pu}}$∗ (right panel) for excitation energies at
$E_{x}=7-57$ MeV. Note that the above results reflect only first chance
fission.  Figure 7: (Color online) Distance between the center of mass
$d_{cm}$ of the nascent fragments just after scission for ${}^{236}{\rm{U}}$∗
(solid line) and ${}^{240}{\rm{Pu}}$∗ (broken line) fissioning systems. Note
that the above results reflect only first chance fission.  Figure 8: (Color
online) Schematic diagrams of shape of fission fragments just after scission
for low excitation energy (upper) and high excitation energy (lower). In each
case, the shape of the light fission nucleus (on the left) is prolate. On the
other hand, the heavy fission fragments (on the right) is nearly sphere at low
excitation energy, which turns out to be prolate at high excitation energy.
Therefore, the distance between the centers of mass $d_{cm}$ between nascent
fragments just after scission is larger at high excitation energy than at low
excitation energy, causing average TKE to decrease to higher excitation
energy.

Based on the above results, we elucidate the reason why the average TKE of
fission fragments decreases as the excitation energy increases. Fig. 7 shows
the averaged distance between centers of mass of 2 nascent fragments just
after the scission, $d_{\rm cm}$. Fluctuation of these lines from smooth ones
is brought about by the Monte-Carlo statistics. Thus only the smooth trend is
of our interest. We can observe that $d_{\rm cm}$ increases as the excitation
energy rises in both compound nuclei 236U∗ and 240Pu∗. This increase is
brought about by changing the shape of the heavier fragments from the near
sphere for low excitation energies to a well deformed prolate shape at higher
excitation energies. This situation is schematically illustrated in fig. 8.
Low excitation energy favors the pair of nearly spherical heavy fragments and
deformed light fragments. When the excitation energy rises, the heavy fragment
will be deformed. Therefore, the distance between centers of mass of two
fragments becomes larger for higher excitation energy. Such an increase in
$d_{\rm cm}$ causes a decrease in TKE at higher excitation/neutron energies,
because the Coulomb repulsion energy between two nascent fragments, which is
the main source of the TKE of fragments, as calculated by

$\displaystyle TKE_{Coulomb}$ $\displaystyle=$
$\displaystyle{\frac{Z_{L}Z_{H}e^{2}}{d_{cm}}}\ ,$ (7)

should decrease as $d_{cm}$ gets increased, where $Z_{L}$ and $Z_{H}$ are
proton numbers of the light and heavy fragments. Then, we can conclude that
the reduction of the average TKE toward higher excitation energies is caused,
at least as an important reason, by the washing out of the shell effect
affecting shape of the heavy fragments to be nearly spherical at low
excitation energy.

##  IV Summary

We have studied the reason why the average total kinetic energy of fission
fragments decreases as the excitation energy of the compound nuclei increases,
as indicated by experimental data of neutron-induced fission. As the typical
examples, we take 236U∗ and 240Pu∗ fissioning systems, or neutron-induced
fission of 235U and 239Pu nuclei. For this sake, we have used a computational
method based on the four-dimensional Langevin equations of nuclear fission
Ishizuka2017 . In this method, Langevin equations for four dynamical variables
representing nuclear shape during the scission process are solved in a Monte
Carlo manner. The free energy, inertia, and friction tensors to be used as
transport coefficients in the Langevin equations were calculated by the two-
center Woods-Saxon model, Werner-Wheeler approximation and Wall-and-Window
formula, respectively. To get a quantitative agreement of the absolute value
of the TKE values with experimental data, the dumping factor $k_{s}$ for the
Wall-and-Window friction was adjusted to $k_{s}$=0.55, and we have introduced
different zero-point energy for each variable, as was originally pointed out
by pioneering works by Bohr-WheelerBohr-Wheeler  and Hill-WheelerHill-Wheeler
. This prescription does not change the dependence of the TKE on excitation
energy, therefore the conclusion of this work.

We have found that calculated values of the average TKE of fission fragments
indeed decrease as the incident neutron energy increases, which is in good
accord with the trends in experimental data. Especially, the calculated TKE
values agree with the data within 1 MeV for neutron energy below 6 MeV, which
is in 0.6% accuracy. However, the calculated TKEs underestimate the
experimental data existing at around $E_{n}=16$ MeV. A reason for this
discrepancy is definitely due to the presence of multichance fission in the
experimental data, which was ignored in the present calculation.

Then, we have elucidated the reason why the average TKE of fission fragments
to decrease as the incident neutron energy (or excitation energy of the
compound nuclei) increases. For this sake, we have calculated the quadrupole
moment $Q_{20}$ of fission fragments just after scission. We have found that
$Q_{20}$’s of light and heavy fragments are distributed in a different manner;
those for the light fragments are larger on the average than those for the
heavy fragments, showing that the shape of the heavy fragments is affected by
the magicity of the spherical 132Sn and deformed one around A=144. We have
also obtained $\langle Q_{20}(A)\rangle$, which shows average of the $Q_{20}$
for each fragment mass number $A$ and found that this quantity shows a clear
saw-tooth structure similar to that of the multiplicity of prompt neutrons for
low excitation energy. However, a valley around $A=130$ in this saw-tooth
structure is washed out as the excitation energy gets larger, and almost
disappears for excitation energy larger than 30 MeV. It indicates that the
shape of the heavy fragments changes from nearly spherical shape at low
excitation energy to a well deformed prolate shape for higher excitation
energy. This causes distance of the center-of-mass of the nascent fragments
just after scission to increase as the incident neutron energy, thus the
excitation energy of the compound nuclei, increases. This causes the Coulomb
repulsion between the nascent fragments to decrease, which results in the
decrease of the average TKE of the fission fragments toward higher excitation
energy.

In the current study, we did not take account of the effects of multichance
fission. Inclusion of the multichance fisssion must make the dependence of the
average TKE on the incident neutron energy smaller. Correction to include this
effect is ongoing, and it will be discussed in detail in the next publication.
Furthermore, agreement of the calculated and evaluated mass distribution of
fission fragments remained to be qualitative rather than quantitative in this
work. We are aware of the fact that this quantity is sensitive to combination
of model parameters. We recognize that making agreement of the mass
distribution with experimental data simultaneously with that of the TKE
observables to a quantitative level is also an important future work, and an
effort in this direction is also already ongoing.

##  V acknowledgement

The authors are grateful to Prof. J. Maruhn of Frankfurt university for an
essential support to carry out this study. This study is supported by Japan
Society for the Promotion of Science (JSPS) KAKENHI Grant No. 18K03642 and
21H01856.

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# X-AMR Annotation Tool

Shafiuddin Rehan Ahmed Jon Z. Cai Martha Palmer James H. Martin
University of Colorado, Boulder, USA
{shah7567<EMAIL_ADDRESS>
###### Abstract

This paper presents a novel Cross-document Abstract Meaning Representation
(X-AMR) annotation tool designed for annotating key corpus-level event
semantics. Leveraging machine assistance through the Prodigy Annotation Tool,
we enhance the user experience, ensuring ease and efficiency in the annotation
process. Through empirical analyses, we demonstrate the effectiveness of our
tool in augmenting an existing event corpus, highlighting its advantages when
integrated with GPT-4. Code and annotations:
github.com/ahmeshaf/gpt_coref111Demo: https://youtu.be/TuirftxciNE 222Live
Link: eacldemo.acl-lawpaper34-demo.site/

##  1 Introduction

Semantic representations of events play a pivotal role in natural language
processing (NLP) tasks, facilitating the understanding and extraction of
meaningful information from text. Among the various approaches to represent
events, Semantic Role Labeling (SRL; Palmer et al. (2005)) and Abstract
Meaning Representation (AMR; Banarescu et al. (2013)) have gained significant
attention. In this paper, we delve into the realm of semantic event
representations, with a particular focus on a method for expanding AMR.

AMR, a graph-based semantic representation, aims to capture the underlying
meaning of sentences by breaking them down into atomic concepts and their
semantic relationships. Each concept in AMR is associated with a unique
identifier, and the relationships between concepts are represented as labeled
edges in a graph. AMR has proven to be versatile, serving as a valuable
resource for a wide range of NLP tasks such as machine translation, question
answering Fu et al. (2021), and summarization Liao et al. (2018). Its ability
to provide a structured, language-independent representation of textual
content makes it an essential tool in the NLP toolkit.

However, despite its many merits, current AMR techniques are not without
limitations. One of the primary challenges lies in linking temporal relations
and entity coreference across sentences and documents. This limitation hinders
the comprehensive understanding of text, as it often fails to capture the
intricate interplay between events and entities that span multiple contexts.
This issue becomes particularly pronounced in scenarios involving cross-
document event coreference, where events mentioned in one document need to be
linked to events in other documents for a coherent understanding of a larger
narrative.

To illustrate the challenge of coreference across documents, consider the
following example: Two news articles discuss a corporate acquisition. In one
article, the event is described as "Company A’s purchase of Company B on July
1st, 2008" while in another article, it is referred to as "In 7/08 Company B
was acquired by Company A." Establishing the coreference relationship between
these two descriptions is non-trivial, yet crucial for creating a
comprehensive representation of the acquisition event.

To specifically address the intricate challenges of cross-document event
coreference resolution, our research introduces two significant contributions.
Firstly, we propose a novel framework X-AMR. This framework is an enhancement
of the existing AMR, specifically designed to overcome the challenges inherent
in linking events and entities across different documents. X-AMR effectively
combines the strengths of AMR with the ability to create a more comprehensive
and coherent depiction of narratives that span multiple sources.

Secondly, the development of a specialized interface is another key
contribution of our work. Utilizing the model-in-the-loop annotation
methodology, we have leveraged the customized Prodigy annotation tool to
augment an existing event coreference dataset, the Event Coref Bank plus
(ECB+; Cybulska and Vossen (2014)). This development has facilitaed the
annotation of X-AMR representations, focusing on the annotation interface and
the enhanced X-AMR dataset. Additionaly, we present an evaluation showcasing
the accuracy and efficiency of our approach. Our research endeavors to
demonstrate the effectiveness of X-AMR in addressing the limitations of
current sentence level AMR, especially in linking temporal relations and
entity coreference across sentences and documents.

##  2 Related Work

AMR is a formalism meticulously crafted to capture the semantic nuances of
natural language expressions with versatile and expressive power. In the field
of Natural Language Processing (NLP), automatic AMR parsing transforms natural
language inputs into formal AMR representations, which have demonstrated
utility in a diverse array of downstream applications such as Summarization
Liao et al. (2018), Dialog systems Bonial et al. (2020); Bai et al. (2021),
Question-Answering Kapanipathi et al. (2021), Machine Translation Li and
Flanigan (2022), Language Modeling Bai et al. (2022), and Fact Checking
Ribeiro et al. (2022).

Formally, AMR are structured as labeled, rooted, directed acyclic graphs,
which capture abstract concepts, predicate-argument relationships, and
entities found in sentences or utterances. They integrate the semantic content
addressed by different representation schemes such as SRL, named entities
recognition (NER; Wang et al. (2022)), and coreference resolution into a
unified representation. For example, for sentence “HP acquired EYPMCS.”, the
corresponding AMR is:

⬇

(d / acquire-01

:ARG0 (c / company

:name (n / name

:op1 "HP"))

:ARG1 (c2 / company

:name (n2 / name

:op1 "EYPMCS"))

The above AMR graph captures concepts such as events such as “acquire”, named
entities such as the HP company, and properties of the entity such as their
names as graph nodes and subgraphs. Their interrelations between concepts and
events are then depicted through labeled edges. Events are denoted using
Propbank rolesets, and semantics relations of the entities and events are
specified through numbered arguments and non-core relations from AMR’s role
inventory. For example, in the above acquisition event, the ARG0 typically
specifies the stereotypical agent of an event and ARG1 typically specifies the
stereotypical patient of an event. Additionaly, AMR graphs formalize local
temporal information, as shown in the provided example.

In the preceding disucssion, we highlighted the expressiveness of AMR.
However, the expressiveness of AMR introduces complexities in AMR annotation,
historically a significant bottleneck for NLP community. The challenge has
been to provide a substantial volume of AMR annotations to the data hunger
statistical machine learning models given the limitations of available tools.
The ISI editor, serving as the first AMR editor, has supported the AMR
community for over a decade. Despite the efficacy of the ISI editor, its
learning curve is notably steep for annotators. To make AMR annotation more
accessible, Cai et al. (2023) developed a new annotation approach. They
introduced an AMR editor based on coding, complemented by a neural network
parser model, to streamline the annotation process.

The remarkable progress in large language model-based coding assistance,
pioneered by OpenAI and Microsoft, is transforming the landscape of program
synthesis in software engineering. These models, trained in both natural
language and programming languages, excel at completing programs by
intelligently integrating code history and human instructions. In a similar
vein, CAMRA leverages these large language models (LLMs) to enhance AMR
annotation. We are pioneering the extension of LLMs’ capabilities, broadening
their application to include more complex tasks such as cross-sentential and
cross-document coreference and event linking. This initiative represents a
significant step forward in harnessing the power of LLMs for even more
sophisticated and long-distance dependent language processing tasks.

Figure 1: The Annotation Methodology of X-AMR. The annotators are presented
with PropBank and are allowed to use external resources, such as Wikipedia and
Google News, during the annotations.

##  3 Annotation Methodology

The annotation workflow, as depicted in Figure 1, comprises of two phases. In
the first phase we annotate the roleset IDs of the event triggers. Then we
specify the arguments of the event incrementally. During these two phases, we
maintain an arguments store and a model-in-the-loop that queries the store and
suggests annotators with the most likely arguments. This store and the model
are updated when new events are annotated.

Next, we discuss the annotation guidelines, the interface, and the model-in-
the-loop in the annotation workflow.

###  3.1 Annotation Guidelines for X-AMR

We aim to annotate key event semantics with four arguments, ARG-0, ARG-1, ARG-
Loc, and ARG-Time, capturing agent, patient (and theme), location, and
temporal information. The selection of these arguments is to circumscribe an
event by its minimal participants Lombard (2019); Guarino et al. (2022). We
use the guidelines presented in the next section to hand annotate the roleset
and argument information for the ECB+ train, development, and test sets using
the standardized split of Cybulska and Vossen (2014). Following the annotation
guidelines, we provide the enriched annotations of the ECB+ corpus by two
Linguistic students. We use a model-in-the-loop annotation methodology with
the prodi.gy annotation tool.

####  3.1.1 PropBank & AMR

Semantic role labeling (SRL) centers on the task of assigning the same
semantic role to an argument across various syntactic constructions. For
example, the window can be the (prototypical) Patient, or thing broken,
whether expressed as syntactic object (The storm broke the window) or
syntactic subject (The window broke in the storm).

The Proposition Bank (PropBank; Palmer et al. (2005); Pradhan et al. (2022))
has over 11,000 Frame Files providing valency information (arguments and their
descriptions) for fine-grained senses of English verbs, eventive nouns, and
adjectives. Figure 2 gives an example Frame File for agree as well as an
instantiated frame for HP has an agreement to acquire EYP.

    agree.01 - agree
     ARG-0: Agreer
     ARG-1: Proposition

    agree.01
     ARG-0: HP
     ARG-1: acquire.01
        ARG-1: EYP

Figure 2: The PropBank roleset definitions of agree.01 and the expected
annotations in X-AMR.

The resulting nested predicate-argument structures from PropBank style-SRL
also form the backbones of AMRs, which in addition includes Named Entity (NE)
tags and Wikipedia links (for ‘HP’ and ‘EYP’ in our example). AMRs also
include explicit variables for each entity and event, consistent with Neo-
Davidsonian event semantics, as well as inter- and intra-sentential
coreference links to form directed, (largely) acyclic graphs that represent
the meaning of an utterance or set of utterances.

Our enhanced X-AMR representation follows AMR closely with respect to NE and
coreference, but stops short of AMR’s additional structuring of noun phrase
modifiers (especially with respect to dates, quantities and organizational
relations), the discourse connectives and the partial treatment of negation
and modality. However, we go further than AMR by allowing for cross-document
coreference as well as multi-sentence coreference. X-AMR thus provides us with
a flexible and expressive event representation with much broader coverage than
standard event annotation datasets such as
ACE333https://www.ldc.upenn.edu/collaborations/past-projects/ace or Maven Wang
et al. (2020).

####  3.1.2 Roleset Sense Annotation

The first step in the annotation process involves identifying the roleset
sense for the target event trigger in the given text. Annotators, using an
embedded PropBank website and the assistance of the tool’s model, select the
most appropriate sense by comparing senses across frame files.

Handling Triggers with No Suitable Roleset: If there is no appropriate roleset
that specifies the event trigger, particularly in cases when the trigger is a
pronoun (it) or proper noun (e.g., Academy Awards), the annotator must then
search for a roleset that defines the appropriate predicate.

Target Mention HP today announced that it has signed a definitive  agreement
EVT to acquire EYP Mission Critical Facilities Inc.

Figure 3: Eventive ARG-1 in the roleset agree.01. The ARG-1 clause is
annotated as the connecting event with roleset ID acquire.01

####  3.1.3 Document-level Arguments Identification

Next, we identify the document and corpus-level ARG-0 and ARG-1 of the
selected roleset. Annotators use the embedded PropBank website as a reference
for the roleset’s definition, ensuring that the ARG-0 (usually the agent) and
ARG-1 (typically the patient) are consistent with the roleset’s constraints.
For arguments that cannot be inferred, the annotators leave those fields
empty.

Within- and Cross-Document Entity Coreference Annotation: Annotators perform
within- and cross-document entity coreference using a drop-down box of
argument suggestions (suggested by the model-in-the-loop), simplifying
coreference link establishment.

Nested ARG-1: In many cases, the ARG-1 may itself be an event. In such cases,
the annotator is tasked with identifying the head predicate of the ARG-1 role
and providing its corresponding roleset ID. We then search for the annotations
for such an ARG-1 and connect it to the target event. Fig 3 has an example of
a mention with an eventive ARG-1. For this, the annotator needs to provide the
roleset for the predicate of the ARG-1 clause (agree.01) as the ARG-1 in this
annotation process.

#####  ARG-Loc & ARG-Time Identification

Annotators may also utilize external resources, such as Wikipedia444Although
we add this in the guidelines, the annotators do not wikify. Our choice is to
use Wikipedia over the more commonly used KB-wikidata because of GPT-friendly
identifiers of the pages. Check out Appendix B., or Google-News, for the
accurate identification of temporal and spatial arguments. This is required
when the document does not explicitly mention the location and time of the
event.

Figure 4: The Annotation Interface Using prodi.gy Annotation Tool

###  3.2 Annotation Interface

The annotation interface, as depicted in Figure 4, comprises four distinct
components: (a) the integrated PropBank website, (b) the document view, (c)
the sentence view, and (d) the event argument forms. This interface is hosted
on a server using Prodigy, with links distributed to individual annotators.

PropBank Website: We adapt the publicly available PropBank website
builder555https://github.com/propbank/propbank-frames to ensure compatibility
within an embedded environment. This interactive website hosts an indexed list
of roleset definitions that annotators refer to.

Target Mention Document: The document containing the current mention is fully
displayed in a scrollable view with the event trigger highlighted upon
interface loading, facilitating easy access to additional context for
annotators.

Target Mention Sentence: This section displays the sentence encompassing the
mention, with the event trigger highlighted in Prodigy’s named entity
recognition (NER) style. Typically, a sentence alone is sufficient to identify
the arguments, and therefore, it is in the field of focus first.

Event Arguments Forms: The event argument forms are located in this section,
enabling annotators to manually input corpus-level arguments for the events.
Each form is equipped with a dropdown list containing previously annotated
arguments, facilitating the annotation process. Figure 5 shows the different
kinds of arguments stored in each of the argument forms. The roleset_id form
stores all the rolesets in PropBank, ARG-0 and ARG-1 the identified agents and
patients up til then, ARG-LOC the locations, and ARG-Time the dates.

###  3.3 Model-in-the-loop

Incorporating a model-in-the-loop approach, our annotation framework utilizes
a straightforward Word2Vec classifier implemented using spaCy. This classifier
ranks sentences containing previously seen arguments in relation to the target
sentence. The dynamic ranking of these sentences is reflected in the dropdown
list, with the highest-ranked sentence positioned at the top. The annotator is
presented with the option to either accept or reject the top-ranked arguments.

Argument Ranking and Selection: Upon loading the annotation interface, the
system ranks the arguments from previously annotated sentences alongside the
target sentence. The highest-ranked argument is selected by default and
presented as the initial choice to the annotator. This ranking is based on the
similarity or relevance of the sentences as determined by the Word2Vec
classifier.

Figure 5: Screenshots

Acceptance and Integration: Should the annotator choose to accept the top-
ranked sentence, it is seamlessly integrated into the set of previous
arguments. This integration enhances the corpus-level annotation by
incorporating contextually relevant information from the selected sentence.

Rejection and New Argument Creation: In the event of rejection, the system
generates new arguments, leveraging the embedding of the rejected sentence.
This adaptive mechanism ensures that even when an annotator rejects the top-
ranked sentence, valuable information is not lost. Instead, it is used to
generate potentially relevant arguments for further annotation.

GPT-in-the-loop:  Finally, yet importantly, we employ a GPT-based methodology
to streamline the extraction of cross-document arguments through a two-step
Retrieval Augmented Generation process. A comprehensive breakdown of our
prompt engineering techniques is provided in Appendix B. The primary objective
of this approach is to establish cross-document entity coreference.

Because of budget constraints, we have limited the execution of this
experiment to a subset of the Dev dataset (Dev-small), encompassing a total of
120 mentions. Corpus statistics and annotation analysis are detailed in
Appendix A.

##  4 Analysis

###  4.1 Model-in-the-loop

We collect X-AMR annotations on the ECB+ dataset, as detailed in Appendix A
(refer to the appendix for specific numerical data and human annotation
analysis). During the annotation process, we collect human annotations along
with predicted rolesets and arguments generated by our model. We assess the
model’s performance by comparing its predictions to human annotations. We
carefully recorded the instances in which annotators made modifications to the
predicted text provided by the model. We count the acceptance ratio of the
predictions, which not only signifies the model’s effectiveness but also
represents the amount of effort saved by annotators.

Our analysis on the train, dev, and test sets of ECB+, as illustrated in
Figure 7, reveals several noteworthy observations: the correct roleset ID
prediction consistently exceeded 80% for both annotators, denoted as A1 and
A2. A1 appeared to be more inclined to accept the model’s argument predictions
compared to A2. This experiment serves as a foundation for future research,
and one potential avenue is to incorporate these findings into downstream
tasks, such as Event Coreference Resolution, to evaluate the quality of
annotations and explore further implications of using model-in-the-loop for
X-AMR annotations.

Figure 6: Accuracy of GPT Predictions of Roleset and ARG based on the gold
standard annotation (adjudicated);  Figure 7: Roleset and ARG Analysis for A1
and A2: “Ax Accept” represents the acceptance rate of the model suggestions
according to Annotator $x$; “Ax Reject” represents the rejection rate of the
model suggestions according to Annotator $x$;

###  4.2 GPT-in-the-loop

In our GPT experiment on Dev-small, we had an adjudicator review 120 mentions
and note when they had to adjust GPT’s predictions. The outcomes of this
evaluation are visually represented in Figure 6, which illustrates the ratio
of mentions requiring modification. The main takeaway here is that GPT
performed well in generating Location and Time arguments but struggled with
predicting roleset IDs and ARG-0, ARG-1 arguments. We believe that integrating
the model-in-the-loop approach could help improve performance compared to just
using GPT.

##  5 Future Work

The next steps include leveraging the X-AMR structures in creating efficient
methods for neuro-symbolic event coreference resolution (ECR). For example,
the X-AMR annotations could help in filtering the most pertinent event pairs
that can be used with more resource intensive methods for estimating
coreference Ahmed et al. (2023a). Another important direction is in the
estimation of the quality and cost savings of our methodology in doing ECR
annotations. Quality measured by the number of ECR links that can be found
with the least amount of pairwise event mention comparisons Ahmed et al.
(2023b).

##  6 Conclusion

In this paper, we have introduced a novel approach for cross-document, corpus-
level semantic event extraction utilizing the X-AMR framework. To facilitate
this process, we have developed a model-in-the-loop annotation tool tailored
for X-AMR annotation, seamlessly integrated with Prodigy. This tool has been
employed to curate X-AMR annotations by enriching an existing event
coreference dataset, with contributions from two annotators. To evaluate the
effectiveness of our approach, we have introduced a comprehensive assessment
of the predictions, incorporating both the model’s output and the assistance
of GPT.

## Limitations

This work has several limitations. Firstly, the annotation tool used is a one-
time paid software, which may restrict its accessibility to some researchers,
although we have made the annotation recipe freely available. Secondly, the
study relies on gold mentions rather than predicted ones, suggesting a need
for future research to incorporate an additional annotation process to
identify event triggers. Lastly, the non-reproducibility of GPT is
acknowledged, and it may have been pre-trained on the corpus. However, we
provide GPT-generated outputs and use them primarily for information
generation rather than prediction, especially in event description generation.
Future work may focus on distilling information into smaller, reproducible
models to address these limitations and enhance the robustness of our
approach.

## Ethics Statement

Recognizing the rigor and tediousness of the annotation process, our research
ensured that all annotators were fairly compensated, given reasonable work
hours, and provided with regular breaks to maintain consistency and quality.
Comprehensive training and clear guidelines were offered, and a robust
communication channel was established to address concerns, ambiguities, and to
encourage feedback. Our team made efforts to involve a diverse group of
annotators to minimize biases.

To alleviate the monotonous nature of the task, we employed user-friendly
tools, rotated tasks, and supported peer discussions. We also acknowledged the
crucial role of annotators in our research, ensuring their contributions were
recognized and valued. Post-task, a summary of our findings was shared with
the annotators, incorporating their feedback into the final manuscript,
underlining our commitment to an inclusive and ethical research approach.

By adhering to the EACL guidelines, we aim to emphasize the ethical
considerations surrounding the involvement of annotators in research projects.
We believe that a humane, respectful, and inclusive approach to data
annotation not only results in superior-quality datasets but also upholds the
dignity and rights of all involved.

## Acknowledgements

The authors would like to thank the reviewers of EACL 2024 System
Demonstrations who helped improve this paper. Part of this work was done
during an internship of one of the authors at ExplosionAI GmbH. We would also
like to thank Ákos Kádár, Matthew Hannibal, and the BoulderNLP group for their
valuable comments on this paper. We gratefully acknowledge the support of
DARPA FA8750-18-2-0016-AIDA – RAMFIS: Representations of vectors and Abstract
Meanings for Information Synthesis and a sub-award from RPI on DARPA KAIROS
Program No. FA8750-19-2-1004. Any opinions, findings, conclusions, or
recommendations expressed in this material are those of the authors and do not
necessarily reflect the views of DARPA or the U.S. government.

## References

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##  Appendix A Dataset Details

The ECB+ corpus is a popular English corpus used to train and evaluate systems
for event coreference resolution. It extends the Event Coref Bank corpus (ECB;
Bejan and Harabagiu (2010)), with annotations from around 500 additional
documents. The corpus includes annotations of text spans that represent
events, as well as information about how those events are related through
coreference. We divide the documents from topics 1 to 35 into the training and
validation sets2 , and those from 36 to 45 into the test set, following the
approach of Cybulska and Vossen (2014).

###  A.1 Annotation Analysis

We have currently annotated all the mentions in the corpus with their Roleset
IDs and 5,287 out of the 6,833 with X-AMR. In the three splits, only the Dev
set has been fully annotated. We calculate the inter-annotator agreement (IAA)
on the common Roleset predictions. The IAA is highest for the Dev set at 0.91,
as depicted in Table 1.

| Train | Dev | Test |  Dev small |
---|---|---|---|---|---
Documents |  | 594 | 196 | 206 | 91 |
Mentions |  | 3808 | 1245 | 1780 | 120 |
Roleset ID Agreement |  | 0.84 | 0.91 | 0.80 | – |
w/ X-AMR |  | 3195∗ | 1245 | 847∗ | 120 |
w/ Nested ARG-1 |  | 1081 | 325 | 220 | 24 |
w/ ARG-Loc |  | 2949 | 1243 | 707 | 120 |
w/ ARG-Time |  | 3192 | 1244 | 805 | 120 |
Table 1:  ECB+ Corpus statistics for event mentions in ECB+ and the mentions
annotated with X-AMR (∗Annotation in Progress). Inter-annotator agreement for
the Roleset ID is highest for the Dev set.

Arguments: Our analysis reveals a significant presence of mentions with nested
ARG-1 annotations, as highlighted in Table 1 (w/ Nested ARG-1). This
underscores the importance of capturing nested event relationships
effectively. Additionally, our annotations for location and time modifiers
successfully capture this information for nearly all mentions (w/ X-AMR),
thanks to the assistance provided by drop-down options and the model-in-the-
loop approach. These tools are particularly valuable in cases where date
references are not explicitly mentioned in the document.

##  Appendix B Prompt Engineering

Our approach for X-AMR extraction with GPT involves a two-step process. In the
initial step, we extract the Event Description along with the document-level
arguments of the event by utilizing prompts such as Instructions A, JSON
Labels A, and Inputs A. Following the generation of individual event
descriptions through this step, we employ another prompt-based technique to
generate corpus-level arguments.

In this secondary method, we introduce an additional instruction into
Instructions A, forming Instructions B. This instruction directs GPT to
identify the most informative Event Description that is coreferent with the
current Event. Subsequently, we provide this identified Event Description
(JSON Labels B) within the context and task GPT with generating missing
information, such as date and location, pertaining to the target event. We
provide the list of informative event descriptions in the topic of the target
event in Inputs B.

The estimated cost of running this experiment is about $15.

Instructions A You are a concise annotator that follows these instructions: 1.
Identify the target event trigger lemma and its correct roleset sense in the
given text. 2. Annotate the document-level ARG-0 and ARG-1 roles using the
PropBank website for the roleset definitions. 3. If the ARG-1 role is an
event, identify the head predicate and provide its roleset ID. 4. Perform
within-document and cross-document anaphora resolution of the ARG-0 and ARG-1
using Wikipedia. 5. Use external resources, such as Wikipedia, to annotate
ARG-Loc and ARG-Time.

JSON Labels A Here are the definitions of the keys in the JSON output: Roleset
ID: The PropBank Roleset ID corresponding to the event trigger ARG-0: The text
in the Document corresponding to the typical agent ARG-0 Coreference: The
reference to the ARG-0 in Wikipedia in the format /wiki/Wikipedia_ID $\vdots$
ARG-1 Roleset ID: If the Event is Nested, provide the Roleset ID for the head
event in ARG-1 clause ARG-Location: The reference to the event location in
Wikipedia ARG-Time: The event time in the format of Month-Day-Year in your
knowledge of the world or the document Event Description: In a single
sentence, summarize the event capturing the Roleset_ID and the names and wiki
links of the Participants, Location and Time

Inputs A Target Mention Document: Entire document with the marked event
trigger Target Mention Sentence: Sentence with the marked event trigger

Instructions B Instructions A 6\. Identify the most informative (having
Wikipedia and complete dates) and best matching Event Description from the
provided list of descriptions.

JSON Labels B JSON Labels A Most Informative Event Description: Pick the most
informative event description from the Event Description List. Choose by
selecting the one that has complete date and Wikipedia links for the arguments
and also is coreferent with the target Event. Hint: choose the one starts
starts with "On DATE"

Inputs B Event Description List: Event descriptions of the three most
informative and similar events in the corpus. Target Event Description: Event
description of the target event Target Mention Sentence: Sentence with the
marked event trigger