# Properties of the fast fission and the coincident emissions of light charged
particles in 40Ar + 197Au reactions at 30 MeV/u

Xinyue Diao  Department of Physics, Tsinghua University, Beijing 100084, China
Yijie Wang  Department of Physics, Tsinghua University, Beijing 100084, China
Fenhai Guan  Department of Physics, Tsinghua University, Beijing 100084, China
Dawei Si  Department of Physics, Tsinghua University, Beijing 100084, China
Qianghua Wu  Department of Physics, Tsinghua University, Beijing 100084, China
Yan Huang  Department of Physics, Tsinghua University, Beijing 100084, China
Liming Lyu  Department of Physics, Tsinghua University, Beijing 100084, China
Yuhao Qin  Department of Physics, Tsinghua University, Beijing 100084, China
Zhi Qin  Department of Physics, Tsinghua University, Beijing 100084, China
Dong Guo  Department of Physics, Tsinghua University, Beijing 100084, China
Yaopeng Zhang  Department of Physics, Tsinghua University, Beijing 100084,
China  Xuan Zhao  Department of Physics, Tsinghua University, Beijing 100084,
China  Zhen Bai  Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  Fangfang Duan  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China
Limin Duan  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou
730000, China  Zhihao Gao  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  University of Chinese Academy of Sciences,
Beijing 100049, China  Qiang Hu  Institute of Modern Physics, Chinese Academy
of Sciences, Lanzhou 730000, China  Rongjiang Hu  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  Genming Jin  Institute of
Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China  Shuya Jin
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  University of Chinese Academy of Sciences, Beijing 100049, China
Junbing Ma  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou
730000, China  University of Chinese Academy of Sciences, Beijing 100049,
China
Peng Ma  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou
730000, China  Jiansong Wang  School of Science, Huzhou University, Huzhou,
313000, China  Institute of Modern Physics, Chinese Academy of Sciences,
Lanzhou 730000, China  Peng Wang  Institute of Modern Physics, Chinese Academy
of Sciences, Lanzhou 730000, China  University of Chinese Academy of Sciences,
Beijing 100049, China  Yufeng Wang  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  University of Chinese Academy of
Sciences, Beijing 100049, China  Xianglun Wei  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  Herun Yang  Institute of
Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China  Yanyun
Yang  Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou
730000, China  Gongming Yu  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  University of Chinese Academy of Sciences,
Beijing 100049, China  Yuechao Yu  Institute of Modern Physics, Chinese
Academy of Sciences, Lanzhou 730000, China  University of Chinese Academy of
Sciences, Beijing 100049, China  Yapeng Zhang  Institute of Modern Physics,
Chinese Academy of Sciences, Lanzhou 730000, China  Qingwu Zhou  Institute of
Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China  University
of Chinese Academy of Sciences, Beijing 100049, China  Yaofeng Zhang  College
of Nuclear Science and Technology, Beijing Normal University, Beijing 100875,
China  Chunwang Ma  Institute of Particle and Nuclear Physics, Henan Normal
University, Xinxiang 453007, China  Xinrong Hu  University of Chinese Academy
of Sciences, Beijing 100049, China  Shanghai Institute of Applied Physics,
Chinese Academy of Science, Shanghai 201800, China  Hongwei Wang  Shanghai
Institute of Applied Physics, Chinese Academy of Science, Shanghai 201800,
China  Shanghai Advanced Research Institute, Chinese Academy of Science,
Shanghai 201210, China  Artur Dobrowolski  Uniwersytet Marii Curie
Skłodowskiej, Katedra Fizyki Teoretycznej, Lublin 20031, Poland  Krzysztof
Pomorski  Uniwersytet Marii Curie Skłodowskiej, Katedra Fizyki Teoretycznej,
Lublin 20031, Poland  Zhigang Xiao  Department of Physics, Tsinghua
University, Beijing 100084, China

###### Abstract

The experiment of Ar+Au reactions at 30 MeV/u have been performed using the
Compact Spectrometer for Heavy IoN Experiments (CSHINE) in phase I. The light-
charged particles are measured by the silicon stripe telescopes in coincidence
with the fission fragments recorded by the parallel plate avalanche counters.
The distribution properties of the azimuth difference $\Delta\phi$ and the
time-of-flight difference $\Delta TOF$ of the fission fragments are presented
varying the folding angles which represents the linear momentum transfer from
the projectile to the reaction system. The relative abundance of the light
charged particles in the fission events to the inclusive events is compared as
a function of the laboratory angle $\theta_{\rm lab}$ ranging from
$18^{\circ}$ to $60^{\circ}$ in various folding angle windows. The angular
evolution of the yield ratios of p/d and t/d in coincidence with fission
fragments is investigated. In a relative comparison, tritons are more
abundantly emitted at small angles, while protons are more abundant at large
angles. The angular evolution of the neutron richness of the light-charged
particles is consistent with the results obtained in previous inclusive
experiments.

##  I Introduction

Nuclear fission is a large-amplitude collective motion mode involving up to
hundreds of nucleons. Recently the studies on nuclear fission have been
revived for its significance in both nuclear physics and astrophysics. For
instance, the competition brought by fission reduces the possibility of the
formation of superheavy elements Guol2018 . In the stellar environment, the
abundance of the nuclides in $A\approx 160$ region is significantly influenced
by the recycling of the fission products Lorusso2015 ; Nishimura2012 ;
Suzuki2012 . Theoretically, statistical fission has been described well by
microscopical theories and various phenomenological approaches PBR96 ; SCH99 ;
JB2007 ; LB2011 ; Zhanghf2014 ; Tanimura2017 ; TZL17 ; WY2018 ; WY2018-2 .
Taking a few recent studies, for example, by computing the potential energy
surface in the macroscopic-microscopic model with the Lublin-Strasbourg Drop
(LSD) for the macroscopic part and the Yukawa-folded potential for the
microscopic energy corrections, the fission fragment mass distributions are
predicted in a broad mass region ranging from Thorium to the most superheavy
elements, showing rather good consistency with the data if available
Pomorski2021 ; Pavel2021 . Using the time-dependent Hartree-Fock approach, the
reactions 238U+40Ca near the Coulomb barrier have been investigated in terms
of the influences of various ingredients in effective nuclear interaction,
including incompressibility, symmetry energy, effective nucleon mass,
etcZhengh2018 .

When the excitation energy or the angular momentum becomes much high, as
achieved in heavy-ion reactions well above the Coulomb barrier, the fission
barrier tends to vanish. As a consequence, the fission life-time becomes
shorter by a factor of 10 to 100 and the variance of the mass asymmetry
increases significantly (the mass asymmetry $\eta$ of the two fragments can be
larger than 0.6), compared to the statistical fission Greg82 ; Greg82t ; Gla83
; Leray84 ; Zheng84 . In addition, the friction grows with the increasing of
nuclear temperature and the diffusion enhance the fission probability
Ivanyuk1996 ; Usang2016 ; Pomorski2015 . So the process of fast fission is
more complicated and the dynamic feature of the fission process is of
significance. Usually the transport models have been successfully applied to
describe the mass and total kinetic energy distributions and the time scale of
the fission Wen13 ; Russ11 ; Riz11 ; TL09 ; TO11 ; LTQ13 ; TW08 ; LTO13 ; WT11
; Wuqh2019 . Time-dependent Hartree-Fock theory can give an excellent
qualitative and quantitative description of fast fission starting with large
deformationGod2015 .

With the advent of advanced $4\pi$ detectors for heavy-ion reactions at Fermi
energies, fast fission, usually termed as dynamic fission because of its
vanishing fission barrier and short time scale, has recently been investigated
in various systems Bocage2000 ; Filippo2005 ; Filippo2012 ; Pagano2018 ;
Piantelli2020 . In various reactions from 25 to 50 MeV/u, the angular
distribution of the fission axis w.r.t. the separation direction of
projectile-like fragments (PLF) against the target-like fragments (TLF)
exhibits an alignment enhancement at very forward angles Bocage2000 .
Similarly, forward-backward asymmetry in the angular distribution has been
observed for the dynamic fission events in ${\rm{}^{80}Kr+^{48}Ca}$ at 35
MeV/u using part of FAZIA setup Piantelli2020 ; FAZIA2014  and in
${\rm{}^{124}Sn+^{64}Ni}$ at 35 MeV/u using CHIMERA setup Filippo2005 ;
Pagano2001 . Besides, the isospin content of the emitted IMFs in the dynamic
breakup of PLF shows a slight evolution as a function of the rotating angle of
the fissioning PLF Piantelli2020 . The short time scale of the dynamic fission
is also demonstrated by analysis of the correlation functions of IMF-IMF pairs
Pagano2018 .

The topic of fast fission with the simultaneous emission of the particles
deserves further investigations because the fissioning system provides an
appropriate laboratory to probe the density behavior of nuclear symmetry
energy, which is of great interest in both nuclear physics and astrophysics
Liba2021 , particularly after the discovery of the neutron star merging event
GW170817. According to transport model simulations on ${\rm Ar+Au}$ reactions,
the occurrence of fast fission of the heavy target-like fragment (TLF)
enhances the emission of the coalescence-invariant neutrons (CIN) in
comparison to that in the events without fissionWuqh2020 . Such enhancement
can be associated with the presence of neck emission as shown experimentally
Filippo2012 ; WRS2014 . Due to the enriched emission of neutrons, either free
or bounded in clusters, and to the accumulation of the isospin effect in the
long-time process, the relative neutron richness of the emitted particles
provides an effective probe to the symmetry energy. The experimental attempt
to extract the nuclear symmetry energy parameter has been reported in inverse
kinetic reactions ${\rm{}^{124}Sn+^{64}Ni}$, where the dynamic fission of the
heavy PLF has been experimentally investigated by measuring the three bodies
coincidence. It has been found that the intermediate-mass fragments emitted
from the neck region are more neutron-rich. Comparison to stochastic mean-
field (SMF) simulations favors symmetry energy with the slope parameter
$L\approx 80$ MeV Filippo2012 . Later in ${\rm Ar+Au}$ reactions at 30 MeV/u,
the angular evolution of the neutron excess of the emitted light charged
particles (LCPs) has been used to probe the symmetry energy, yielding a softer
symmetry energy $L\approx 47\pm 14$ MeV at 95% confidential level zy2017 .

In this paper, we present the experimental results of the fast fission
following Ar+Au reactions at 30 MeV/u using the Compact Spectrometer for Heavy
Ion Experiment (CSHINE) fenhai2021 ; yijie2021 . The kinetic properties of the
fission fragments have been investigated, and the coincident light charged
particles (LCPs) at midrapidity have been measured. The angular evolution of
the neutron richness of the LCPs is discussed in different linear momentum
transfer windows. The article is arranged as follows: Section II presents the
experimental setup and the detector performance, Section III introduces the
data analysis method on the fission events. The main results are presented in
Section IV, and Section V is the summary.

##  II Experimental Setup and Detector Performance

The experiment was carried out on the Compact Spectrometer for Heavy IoN
Experiments (CSHINE) installed in the large chamber at the final focal plane
of the Radioactive Ion Beam Line I in Lanzhou (RIBLL1), China. The gold target
with a thickness of 1 mg/cm2 was bombarded by the 30 MeV/u 40Ar beam delivered
by the Heavy Ion Research Facility (HIRFL). The beam intensity was about 6 nA.

The CSHINE with complete configuration consists of six silicon strip detector
(SSD) telescopes and three parallel plate avalanche counters (PPACs) for
measuring the light charged particles and the fission fragments (FFs),
respectively fenhai2021 . In phase I, two SSD telescopes and three PPACs were
mounted for the beam experiment, as shown in Fig. 1. The PPACs with an active
area of $240\times 280$ mm2 were installed at the distance of 427.5 mm to the
target, delivering the position and timing information of the FFs. The PPACs
were operated with 4.5 mbar isobutane at 465 V so that the LCPs and
intermediate-mass fragments (IMFs) were suppressed. The main PPAC is
concentrated at $\theta_{\rm lab}=50^{\circ}$ and the other two PPACs are
placed on the other side of the beam at $\theta_{\rm lab}=40^{\circ}$ and 95∘,
respectively. Each SSD telescope consists of two layers of SSDs for energy
loss ($\Delta E$) measurement and one layer of CsI hodoscope with $3\times 3$
units read out by photodiodes (PD) for residual energy $E_{\rm CsI}$
measurement. The first layer of SSD is a 32-strip one-dimensional detector
with a thickness of 65 $\mu$m. The second layer, 1500 $\mu$m in thickness, is
a two-dimensional detector with 32 strips on both sides. The strips are all
1.9 mm wide, and the inter-strip distance is 0.1 mm. The geometry coverage of
the PPACs and the SSD telescopes in the laboratory reference is presented in
Fig. 2. It is shown that the angular range of $\theta_{\rm
lab}=18^{\circ}-60^{\circ}$ is partially covered for the measurement of the
charged particles. In addition, three small silicon telescopes consisting of
two Si (Au) barrier detectors and a CsI unit are placed at large angles to
measure the evaporation LCPs. The geometric parameters, including the distance
from the center of each detector to the target $d$, the polar angle $\theta$,
the azimuth angle $\phi$, and the sensitive area $S$ of the detectors of
CSHINE components are listed in Table 1.

Figure 1: (Color online) Schematic view of the CSHINE detection system in Phase-I. Figure 2: (Color online) The angular coverage of the CSHINE detectors in the laboratory reference. The abscissa is $\phi$ while the ordinate is $\theta$ in the laboratory frame. The PPACs and SSD telescopes are all marked individually. Table 1: Geometric parameters of PPACs, SSD telescopes and small Si(Au) telescopes. Detector | $d(mm)$ | $\theta^{\circ}$ | $\phi^{\circ}$ | $S(mm^{2})$
---|---|---|---|---
SSD-Tel1 | 161.9 | 50.7 | 81.7 | 64$\times$64
SSD-Tel2 | 221.9 | 22.3 | 64.5 | 64$\times$64
PPAC1 | 427.5 | 50 | 0 | 240$\times$280
PPAC2 | 427.5 | 40 | 180 | 240$\times$280
PPAC3 | 427.5 | 95 | 180 | 240$\times$280
Si-Tel1 | 185.5 | 90 | 0 | $16\pi$
Si-Tel2 | 145.5 | 130 | 40 | $16\pi$
Si-Tel3 | 165.5 | 130 | 15 | $16\pi$

PPAC is a multi-wire chamber working in a region of limited proportionality.
The signals induced by the incident fragments on an individual wire of the
anode plane, either X or Y, are transferred through a delay line to both ends.
The time delay of the two signals $X_{1}$ and $X_{2}$ ($Y_{1}$ and $Y_{2}$)
with respect to the signal collected on the cathode plane, which delivers the
timing information, gives the X (Y) position of the hit in the sensitive area.
Fig. 3 (b) shows a two-dimensional histogram of $Y_{1}-Y_{2}$ $vs$
$X_{1}-X_{2}$ for PPAC1 as an example. The projections to X and Y direction
are plotted in Fig. 3 (a) and (c), respectively. A good performance in timing,
corresponding to good position resolution, manifests itself in the sharp
boundary for the two-dimensional distribution and the well-separated
individual peaks on the projections. The distance of the neighboring wires is
4 mm, and there are 61 peaks and 71 peaks in Fig. 3 (a) and (c), respectively.
The time resolution of $\sigma_{\rm T}=300$ ps and the position resolution of
$\sigma_{\rm r}=1.35$ mm can be derived from the data. The mechanical
structure and the overall performance of the PPACs can be found in wei2020 .

Figure 3: (Color online) The performance plots of PPAC1. Panel (b) is a two-
dimensional distribution of $Y_{1}-Y_{2}$ versus $X_{1}-X_{2}$ . The
projection to X1-X2 and Y1-Y2 dimensions are shown in panel (a) and (c),
respectively.

The SSD telescopes are advantageous for their high granularity and high energy
resolution. Owing the 2 mm width strip, one obtains the angular resolution
better than $1^{\circ}$ at the current geometrical positions. The $\Delta
E_{1}$ and $\Delta E_{2}$ silicon strip detectors are calibrated using the
precise pulse generator and the 239Pu $\alpha$ source. After the SSD
calibration is done, the CsI hodoscope can be calibrated for each individual
isotope from $\Delta E_{2}-E_{\rm CsI}$ scattering plot, where the energy
deposit in CsI can be calculated using LISE++ package lise2016 . The total
energy resolution of the SSD telescopes is about 2$\%$ evaluated by the Monte-
Carlo simulation studies reproducing the trend and the width of all isotope
bands on the $\Delta{E_{2}}-E_{\rm CsI}$ plot fenhai2021 . The performance of
the SSD telescopes in CSHINE is summarized in Fig. 4. Panel (a) presents the
$\Delta{E_{2}}$-ECsI scattering plot of one CsI unit in the SSD telescope 2 as
an example. It is shown that the isotopes of hydrogen and helium are clearly
identified. From the width of each band, the mass resolution of the LCPs,
$\Delta M/M=1$, is estimated. Since the high voltage for the first layer of
the SSD telescopes failed for most of the time in the experiment and caused
poor particle identification on $\Delta{E_{1}}-\Delta{E_{2}}$ plots, only the
high-energy LCPs penetrating through $\Delta{E_{2}}$ SSD were analyzed in
current studies. Fig. 4 (b) presents the energy spectra of p, d, t, 3He, and
4He in coincidence with the FFs, respectively. See Ref. fenhai2021  for the
structural framework, performance, and detailed analysis of the SSD
telescopes.

Figure 4: (Color online) SSD telescopes performances in the experiment. (a)
$\Delta{E_{2}}$-ECsI scattering plot of SSD telescope 2. (b) The energy
spectra of p, d, t, 3He and 4He, respectively.

In addition to the inclusive trigger for all detectors, three types of
coincident trigger signals are constructed in this experiment. i) The two-
fission-fragment event in the PPACs, ii) The two-body LCP event in the SSD
telescopes, and iii) One LCP coincided with two FFs in PPACs. For the
measurement of two FFs, while PPAC1 is served as the primary FF detector,
PPAC2 or PPAC3 on the other side of the beamline provides the coincident FF.
The circuit diagram of the trigger electronics in the experiment can be found
in yijie2021 .

In the 120-hour beam experiment, the inclusive event of at least one LCP is
about $1.6\times 10^{7}$ after applying a fraction divide factor 50, the event
of two fission fragments is about $5\times 10^{6}$, and for the event of two
fission fragments plus one light charged particle, the statistics is about
$3.64\times 10^{5}$.

##  III Data Analysis Method

In the picture of incomplete fusion, a heavy target-like fragment (TLF) is
formed by the fusion of part of the projectile and the target nuclei. The
fraction of the total momentum of the projectile transferred to the TLF is
called linear momentum transfer (LMT). With a certain probability depending on
the system’s total angular momentum, the TLF may undergo fission or fast
fission in competition with the emission residue channel. For the fission
events, Fig. 5 presents the kinetic geometry of the TLF fission event. As
shown, the origin point O is the target nuclei in the laboratory system, the
vector OO${}^{{}^{\prime}}$ represents the direction of the beam. The velocity
vectors $\vec{v}_{\rm f_{1}}$ and $\vec{v}_{\rm f_{2}}$ of the two fission
fragments in the laboratory system are represented by OA and OB. $\vec{v}_{\rm
tl}$ is the velocity of the TLF, and the velocities of the two fragments in
the center-of-mass system of the fissioning TLF are represented by
$\vec{v}^{\,{}^{\prime}}_{\rm f_{1}}$ and $\vec{v}^{\,{}^{\prime}}_{\rm
f_{2}}$ sitting back-to-back collinearly. Here, we define plane OAB as the
fission plane, plane OO${}^{{}^{\prime}}$A as the projection plane, and the
reaction plane is defined as plane DOO${}^{{}^{\prime}}$.

Figure 5: The geometric diagram of the velocities of the two TLF-fission
fragments.

In the experiment, the position and energy information of the LCPs can be
measured accurately. For the fission fragments, however, because the start
timing of the reaction can not be measured with sufficient precision, the
absolute time-of-flight (TOF) is not available. Only the difference of TOF
between the two fission fragments can be derived with sub-nanosecond timing
resolution for each detector, which reaches 300 ps in the source test wei2020
. Besides, the direction of the velocity vectors can be precisely determined
by the hit positions recorded by the PPACs.

It is important to assure that the coincident events recorded by PPAC1 with
PPAC2 (marked by ${\rm PPAC1\times 2}$) or with PPAC3 (marked by ${\rm
PPAC1\times 3}$) are the fission fragments (marked by FF-FF) since the two-
body correlation is possibly contaminated by the correlation of the PLF with
TLF (PLF-TLF) or the correlation of the PLF with one of the fission fragments
from the TLF (PLF-FF). First, the high voltage is set that the response of
PPAC to PLF is highly suppressed, given that the energy loss of PLF is lower
than FFs by more than one order of magnitude. Second, the geometric coverage
of the PPACs is out of the angular range of the PLF. In order to verify this
point, we check the angular correlation of the two fragments in comparison
with the prediction of the improved quantum molecular dynamics (ImQMD)
transport model calculations. The details of the ImQMD model can be found in
Wuqh2020 . Fig. 6 presents the experimental correlation between the polar
angles of the two fragments on the scattering plot of
$|\theta_{1}-\theta_{2}|$ vs $\theta_{1}+\theta_{2}$ . It is shown that the
events of ${\rm PPAC1\times 2}$ are well separated from those of ${\rm
PPAC1\times 3}$. For comparison, the results of transport model simulations
are displayed in Fig. 7 (a-c) in the form of $|\theta_{1}-\theta_{2}|$ as a
function of $\theta_{1}+\theta_{2}$. The calculations from central to
peripheral reactions ($b=4-10$ fm) are accumulated according to the
corresponding weights. The experimental coverage of ${\rm PPAC1\times 2}$ and
${\rm PPAC1\times 3}$ are indicated by the red and green dashed polygons.
Panels (a), (b), and (c) represent the PLF-TLF, PLF-FF, and FF-FF correlations
in ImQMD simulations, respectively. It is shown that the angular correlation
of the PLF-TLF events is mostly out of the experimental coverage. For the
reactions undergoing fission, the PLF-FF correlations are partially covered by
the PPAC1 and PPAC2 with a tiny portion, as indicated by the marked area’s
colorful contour compared with the most populated area in panel (b). It
indicates that the coincident events of two heavy fragments are dominated by
the FF-FF events, as confirmed in panel (c).

Figure 6: (Color online) The experimental correlation between
$|\theta_{1}-\theta_{2}|$ vs. $\theta_{1}+\theta_{2}$ of two fission fragments
marked by subscribes 1 and 2, respectively. Figure 7: (Color online) The
correlation between $|\theta_{1}-\theta_{2}|$ vs. $\theta_{1}+\theta_{2}$ of
two fission fragments in ImQMD calculations. Panel (a-c) presents the results
for PLF-TLF events, PLF-FF events and FF-FF events, respectively. The polygons
in the panels indicate the experimental coverage.

Once the events with two FFs are identified, the folding angle method has been
used to measure the LMT of the reaction. As shown in Fig. 5, the folding angle
$\Theta_{\rm FF}$ is defined as the angle $\angle AOC$, spanned by the
projection of the velocity vectors of the FFs on the projection plane.
Clearly, given the relative velocity $\Delta v_{\rm 12}$ of the FFs, the
folding angle depends on the velocity of the TLF $v_{\rm tl}$, i.e., the
larger $v_{\rm tl}$, the smaller $\Theta_{\rm FF}$. Fig. 8 presents the
distribution of the folding angle $\Theta_{\rm FF}$. The coincident events of
${\rm PPAC1\times 2}$ distribute in the range between $60^{\circ}-120^{\circ}$
with the peak situating at about $90^{\circ}$, corresponding to a larger LMT
(red), while the ${\rm PPAC1\times 3}$ events sit in the range of
$110^{\circ}-170^{\circ}$ corresponds to a smaller LMT (blue). The valley
between the two histograms is due to the deficiency caused by the gap between
PPAC2 and PPAC3.

Figure 8: The folding angle distribution of two-body fission events. The red
histogram represents the events of ${\rm PPAC1\times 2}$ and the blue
histogram represents the ${\rm PPAC1\times 3}$ events.

One can further check the energy spectra of LCP from the statistic emission in
the two groups of events to make sure the experimental folding angle is a
measure of the LMT. Model independently, a larger LMT causes higher excitation
energy of the TLF, for which a larger slope temperature parameter of the
emission LCP can be expected. To check this scenario, one can simply survey
the energy spectra of evaporation particles at very large angles, where only
the evaporation source dominates. Figure 9 presents the energy spectra of
protons recorded in the small Si3 installed at $\theta_{\rm lab}=130^{\circ}$
in coincidence with ${\rm PPAC1\times 2}$ (red) and ${\rm PPAC1\times 3}$
(blue) fission events. Because of the low statistics, finer division of the
$\Theta_{\rm FF}$ is not achievable. The descents of the energy spectra are
fitted by a logarithmic function $Y=a\exp{\left(-E/T_{\rm sl}\right)}$ without
taking into account the kinetic energy difference and the Coulomb barrier
difference of these two groups of event, which mainly influence the peak of
the spectra. The slope parameter $T_{\rm sl}=6.2\pm 0.2$ and $5.3\pm 0.2$ MeV
are deduced from the fitting for the two groups of events, respectively.
Evidently, the slope parameter is larger in the group of ${\rm PPAC1\times 2}$
events than that in ${\rm PPAC1\times 3}$. It is consistent with the picture
that the folding angle of the FFs reflects the LMT of the reaction. Namely,
with a smaller folding angle, or larger LMT, the TLF formed in the incomplete
fusion gains higher excitation energy.

Figure 9: The energy spectra of protons in the Small Si-Tel3 in coincidence
with the ${\rm PPAC1\times 2}$ (red) and ${\rm PPAC1\times 3}$ (blue) events.
The straight lines are the logarithmic fitting to the descents of the energy
spectra.

In order to reconstruct the complete kinetics of the fission of TLF, one has
to measure the velocity vectors of the two FFs. It requires to measure both
the time and the distance of flight of the FFs. However, the start timing
signal, which is supposed to be delivered by the cyclotron’s radio frequency
(RF) signal, was not available in the experiment. Thus, to obtain the
velocity, one relies on the Viola’s systematics describing the velocity of the
FFs in the center of mass reference of the fissioning nucleus. For symmetric
fission, the kinetic energy of fission fragments is mainly supplied by the
Coulomb energy at the scission point, and the most probable velocity of each
FF is 1.2 cm/ns viola . For the fast fission that occurred in heavy-ion
reactions at Fermi energies, recent simulations with the ImQMD model verify
that the distribution of the relative velocity of the FFs is indeed peaked in
the vicinity of 2.4 cm/ns with a broadening less than 10%. It shows
insignificant dependence on the mass asymmetry of the FFs Wuqh2019 . Here we
neglect the influence of highly-aligned events with the fission axis sitting
in parallel with the flying direction of the TLF. These highly-aligned events,
in which the relative velocity may violate the assumption as observed at
higher beam energyBocage2000 , are anyway out of the geometrical reach in the
current experimental setup. Following the Viola systematics, we first assume
that relative velocity between the two FFs is fixed at 2.4 cm/ns. Under this
assumption, applying cosine theorem to the velocity vector triangle $\Delta
OAB$ as shown in Fig. 5, one writes

$v_{\rm f_{1}}^{2}+v_{\rm f_{2}}^{2}-2v_{\rm f_{1}}v_{\rm
f_{2}}\cos\theta=(v_{\rm f_{1}}^{\prime}+v_{\rm f_{2}}^{\prime})^{2}~{},$ (1)

where $\theta$ is the angle met by the two velocity vectors $\vec{v}_{\rm
f_{1}}$ and $\vec{v}_{\rm f_{2}}$. Using the TOF difference $\Delta TOF$ and
the hit position information on PPACs, one gets

$\frac{L_{1}}{v_{\rm f_{1}}}-\frac{L_{2}}{v_{\rm f_{2}}}=\Delta TOF~{},$ (2)

where $L_{1}$ and $L_{2}$ represent the flight distances of the two FFs
deduced by the distance from the hit positions on PPACs to the target for the
two FFs, respectively. The Viola systematics reads

$|v_{\rm f_{1}}^{\prime}+v_{\rm f_{2}}^{\prime}|=2.4~{}{\rm cm/ns}~{}.$ (3)

With equations $(1-3)$, one can readily reconstruct the velocity of the two
FFs numerically. If only the fragments following the fission of TLF are
recorded, the distribution of both velocities will exhibit a one-component
feature.

Fig. 10 presents the correlation of the velocity $v_{\rm f_{1}}$ and $v_{\rm
f_{2}}$ of the two FFs in laboratory for the ${\rm PPAC}1\times 2$ fission
events. Panels (a-e) represents the correlations in five windows of the
folding angle $\Theta_{\rm
FF}=75^{\circ}-85^{\circ},~{}85^{\circ}-95^{\circ},~{}95^{\circ}-105^{\circ},~{}105^{\circ}-115^{\circ}$
and $115^{\circ}-125^{\circ}$, respectively. Panel (f) is the sum of all the
events. Except for the lowest $\Theta_{\rm FF}=75^{\circ}-85^{\circ}$ window,
where two components are seemingly presented indicating that they are
originating from different sources, the anti-correlation is well visible in
all other windows, and the kinetic feature of the two FFs exhibits
insignificant difference. The velocity correlation for the ${\rm PPAC1\times
3}$ fission events, which are not presented here, does not show a two-
component feature.

Figure 10: The velocity correlation for ${\rm PPAC1\times 2}$ fission events.
The abscissa is the velocity of the FF firing PPAC1, and the ordinate is the
velocity of the FF firing PPAC2.

Fig. 11 presents the velocity distributions of the two fission fragments after
imposing the union cuts (see Table 2) for both the central collisions (${\rm
PPAC1\times 2}$) and the peripheral collisions (${\rm PPAC1\times 3}$),
respectively. Here, panel (a) presents the velocity $v_{\rm f_{1}}$ of the FF
in PPAC1, while panel (b) is the velocity $v_{\rm f_{2}}$ of the fragment
measured in PPAC2 (red) or PPAC3 (blue), respectively. For $v_{\rm f_{1}}$,
the broadening of the distribution is $0.5-2.5$ cm/ns in central reactions,
larger than the range $0.8-2$ cm/ns as in peripheral reactions. Very
similarly, the width of $v_{\rm f_{2}}$ is larger in PPAC2 than that in PPAC3
because the former (later) corresponds to central (peripheral) reactions,
respectively. It is as expected that the excitation energy of the TLF is
higher in the event group of ${\rm PPAC1\times 2}$ corresponding to larger
LMT, for which a wider distribution of the velocity of the FFs is observed. In
peripheral reactions,in addition, a part of the LMT is converted into exciting
the collective rotation of the TLF. Detailed analysis on the variance of the
velocity will be discussed in the next section.

Figure 11: The velocity distribution of the two FFs in the central (red) and
peripheral (blue) reactions. Panel (a) presents $v_{f_{1}}$ recorded in PPAC1
and panel (b) presents $v_{f_{2}}$ recorded in PPAC2 (red) or PPAC3 (blue).

As long as the velocities of the FFs are reconstructed using the Viola
systematics, the velocity of the TLF in the center of mass frame can be
calculated if the mass ratio of the two FFs is known. However, the momentum
conservation criteria is already used in equation (2), in order to calculate
the $v_{\rm tl}$ and further LMT, one can fix the direction of $\vec{v}_{\rm
tl}$ by relying on the second assumption that the TLF undergoes symmetric
fission. Fig. 12 presents the velocity of the TLF (left) and the LMT (right),
respectively. Again, the red and blue curves represent the central and
peripheral reactions, where the LMT distribution peaks at ${\rm LMT}=0.81$ and
0.27, respectively. Fig. 13 presents the correlation between the LMT and the
folding angle $\Theta_{\rm FF}$. It is evident that these two quantities are
reversely correlated, i.e., the LMT decreases with increasing the folding
angle. This correlation exists as a general feature without relying on the
symmetric fission assumption, although the details of the correlations may
change if this assumption is released. Nevertheless, to minimize the effect of
the symmetric fission assumption, we will use the folding angle as a
measurement of the reaction violence in the following discussions.

Figure 12: (Color online) The velocity of the TLF (a) and the LMT calculated
under the assumption of symmetric fission for ${\rm PPAC1\times 2}$(red) and
${\rm PPAC1\times 3}$fission events (blue). Figure 13:  (Color online) The
correlation between LMT and folding angle $\Theta_{\rm FF}$.

Finally, to eliminate the influence of the events located at each quantity’s
outer border, we impose four loose cut conditions on the experimental data. i)
On the TOF distribution, $-40<\Delta TOF<40$ ns and $-50<\Delta TOF<30$ ns are
applied for ${\rm PPAC1\times 2}$ and ${\rm PPAC1\times 3}$ events,
respectively, ii) on the folding angle, the cut of $\Theta_{\rm
FF}>85^{\circ}$ is used to minimized the contamination from the FF
correlation, and more importantly iii), the third and fourth cuts are
introduced to confine the planarity of the fission events. Recalling Fig 5, it
can be comprehended that the $\angle BOC$ reflects the deviation of the
projection plane from the fission plane, while the $\angle{DOO^{{}^{\prime}}}$
denotes how much the $\vec{v}_{\rm tl}$ deviates from the beam. If the fission
of the rotating TLF occurs ideally in the reaction plane without being
recoiled by particle emission, the two angles are zero. Fig. 14 presents the
distributions of $\angle BOC$ and $\angle{DOO^{{}^{\prime}}}$. It is shown
that both angles drop rapidly from $0^{\circ}$, indicating that the planarity
is kept well. We set two cuts as $\angle BOC<20^{\circ}$ and
$\angle{DOO^{{}^{\prime}}}<20^{\circ}$, which help to remove some multi-body
events with the emission of undetected massive fragments causing the
degradation of the planarity of the two-body fission process. Table 2
summarizes the cut conditions on the data analysis.

Figure 14: (Color online) The distributions of the planarity angles $\angle BOC$ (a) and $\angle{DOO^{{}^{\prime}}}$ (b), recalling the definition of the angles in 5. Table 2: The sum of value range in the experiment. [0.65pt] Physical quantity | Cut range
---|---
$\Delta TOF$ | $[-40,+40],~{}[-50,+30]$
$\Theta_{\rm FF}$ | $>85^{\circ}$
$\Delta\phi$ | $[160^{\circ},200^{\circ}]$
$\angle{BOC}$ | $<20^{\circ}$
$\angle{DOO^{{}^{\prime}}}$ | $<20^{\circ}$

##  IV Results and Discussions

###  IV.1 Fission Distributions

To view the fission distribution properties, we start with the azimuth
correlation of the two FFs. Fig. 15 presents the correlation between the
azimuthal angle difference $\Delta\phi$ and the folding angle $\Theta_{\rm
FF}$. It is clearly shown that for the FFs from both the central and
peripheral reactions, the most probable value situates at
$\Delta\phi=180^{\circ}$ following the picture that the system undergoes a
binary decay. Here we note that the $\Delta\phi$ is a directly measurable
quantity relying on no assumption. In addition, the distribution of
$\Delta\phi$ exhibits a certain broadening which depnds on the folding angle,
what suggests that the emission of LCP or IMF may change the flight direction
of the FF and smear the back-to-back feature of the fission event.

Figure 15: (Color online) The scattering plot of the azimuthal difference
$\Delta\phi$ $vs$ the folding angle $\Theta_{\rm FF}$ in of the FFs.

In order to further quantify the variation of the azimuthal difference, the
standard deviation $\sigma(\Delta\phi)$ of $\Delta\phi$ is extracted in each
$\Theta_{\rm FF}$ bin of 10∘. The results are summarized in Fig. 16 for the
${\rm PPAC1\times 2}$ (red) and ${\rm PPAC1\times 3}$ (blue) fission events.
It is shown that $\sigma(\Delta\phi)$ decreases with the folding angle in the
whole range. To exclude the possible reason that this trend originates from
the asymmetry of the geometrical locations of the PPACs, we restrict further
the analysis on the events with the two FFs flying symmetrically to the beam
direction, i.e., with the condition of $\theta_{1}=\theta_{2}$, where
$\theta_{i}$ is the polar angle of the $i^{\rm th}$ fragment. The result is
depicted by the black squares, where the bin width of each $\Theta_{\rm FF}$
is $\pm 3^{\circ}$. This condition is applicable only for the ${\rm
PPAC1\times 2}$ fission events because these two PPACs are placed in
approximate left-right symmetry with respect to the beamline. It is shown
clearly that $\sigma(\Delta\phi)$ decreases with the folding angle in the same
manner with the only exceptional point on the very edge of the PPAC2. It is
concluded that the decreasing trend of $\sigma(\Delta\phi)$ as function of
$\Theta_{\rm FF}$ is truly due to the reaction violence. Since the post-
scission particle emission changes the velocity of the FF due recoil effect,
the trend suggests that in the fission following the intermediate energy
heavy-ion reactions, there is sufficient excitation energy left at the
scission point depending on LMT. In the reactions with larger LMT, more
excitation energy is left and released through the particle emission in the
post-scission stage. It is consistent with the picture of fast fission,
instead of statistic fission in which the excitation energy is nearly depleted
at the scission point.

Figure 16: The standard deviation of $\sigma(\Delta\phi)$ of the azimuthal
difference as a function of folding angle. The red (blue) symbols represent
the ${\rm PPAC1\times 2}$ (${\rm PPAC1\times 3}$) events, while the black
symbols represent the events in ${\rm PPAC1\times 2}$ with an additional
condition that the flight paths of the two FFs are geometrically symmetric
with $\theta_{1}=\theta_{2}$.

Next, we investigate the other directly measurable quantity in the experiment,
the TOF difference of the two FFs. In the current scheme with Eq. (2) and the
current geometrical configuration that the central detector-target distances
are the same for three PPACs, the TOF difference $\Delta TOF$ between the FFs
originates mainly from the velocity difference $\Delta v$ of the FFs, which
indirectly reflects the mass asymmetry of the FFs. From Eq. (2) and assuming
$\Delta v/v<<1$, one writes

$\frac{\Delta v}{v}\approx\frac{v}{L}\Delta TOF+\frac{\Delta
L}{L}\approx\frac{v}{L}\Delta TOF$ (4)

where the $\Delta L$ is the difference of the flight length $L$.

Fig. 17 presents the correlation between $\Delta{TOF}$ and the folding angle
$\Theta_{\rm FF}$. The 1-dimensional distribution of $\Delta{TOF}$ is shown in
the inset. Moving from small $\Theta_{\rm FF}$ area to large values, the
broadening of $\Delta{TOF}$ decreases, showing a similar trend as
$\Delta\phi$.

Fig. 18 further presents the standard deviation of the $\Delta TOF$
distribution as a function of folding angle $\Theta_{\rm FF}$ for the ${\rm
PPAC1\times 2}$ (red) and ${\rm PPAC1\times 3}$ (blue) fission events. Again,
to minimize the possible effect of the variation of geometric conditions, we
restrict the analysis to the events with symmetric geometry, i.e.,
$\theta_{1}=\theta_{2}$ in the ${\rm PPAC1\times 2}$ fission events, as
depicted by the black squares in the figure. With this geometrically symmetric
condition, a non-zero TOF suggests that the masses of the two fragments are
not equal since the distance of the two PPACs to the target is the same. The
decreasing trend of the black squares for the conditional events means that
the mass asymmetry of the fission fragments decreases with increasing
(decreasing) the folding angle (LMT). Moreover, in the overlapped region, the
data points situate on top of each other with and without the geometrically
symmetric condition, suggesting that the geometrical asymmetry is not the main
reason for the variation of $\Delta TOF$. The overall descent trend of $\Delta
TOF$ with $\Theta_{\rm FF}$ suggests that the mass asymmetry of the fast
fission increases with the LMT of the reactions. We note that the result is
independent of the assumption of Viola systematics of Eq. (3) since only the
original timing information directly from the experiment is used here.

Figure 17: (Color online) The scattering plot of the TOF difference
$\Delta{TOF}$ $vs$ the folding angle $\Theta_{\rm FF}$ in two-body fission
events. Figure 18: (Color online) The standard deviation of $\sigma(\Delta
TOF)$ of the TOF difference as a function of folding angle. The red (blue)
symbols represent the ${\rm PPAC1\times 2}$ (${\rm PPAC1\times 3}$) events,
while the black symbols represent the events in ${\rm PPAC1\times 2}$ with an
additional condition that the flight paths of the two FFs are geometrically
symmetric with $\theta_{1}=\theta_{2}$.

Further, we present in Fig. 19 the average (a) and the standard deviation (b)
of the reconstructed velocities of the FFs recorded in the two PPACs as a
function of folding angle. Here Eq. (1-3) are used. From panel (a), it can be
seen that the average velocity value $\left<v_{\rm f}\right>$ of the fragments
measured in PPAC 1 and PPAC 2 show an insignificant difference, while in
PPAC3, the average velocity $\left<v_{\rm f}\right>$ is systematically smaller
in PPAC3 because this PPACs is located at a much larger angle and the velocity
of the FF is counteracted mainly by the recoil TLF which is moving forward in
the laboratory frame. Panel (b) presents the standard deviation of the
velocity, and it is also clear that the broadening of the velocity of the FFs
decreases with the folding angle.

Figure 19:  (Color online) The average value of velocity distribution (a) and
its standard deviation (b) as a function of the folding angle. The blue, red,
and black legends correspond to the fission fragments recorded in PPAC1,
PPAC2, and PPAC3, respectively.

The distribution properties of $\sigma(\Delta\phi)$ and $\sigma(\Delta TOF)$
as a function of folding angle reflects part of the dynamic feature of fast
fission that the scission point is early reached when the excitation energy of
the TLF is still high. Thus the post-scission emission of particles may change
the direction of the FFs. In addition, due to the incomplete de-excitation at
the scission point, the statistical fluctuation enhances the variance of the
masses and the velocity of the FF. This is consistent with the earlier
experimental observation in ${\rm Ar+^{209}Bi}$ reactions at 25 MeV/u zjw1999
. The other important feature of fast fission, the time scale $\tau_{\rm f}$,
is not measured and calls for further experimental efforts in two directions:
i) By securing the first layer of the SSD telescope to measure the whole
energy spectra, one can fit the spectra by including the post-scission source
and derive the fission time constant $\tau_{\rm f}$ from the pre-, and post-
scission particle multiplicity in statistical decay model zjw1999-2 , ii)
Alternatively, one can also secure the start timing information from the RF of
the machine to measure the velocity of FFs without introducing the two
mentioned assumptions. Furthermore, in this case, the rotation of the
fissioning system can be reconstructed, and the $\tau_{\rm f}$ can be derived
if is given the rotational angular velocity Casini1993 .

###  IV.2 Results for Light Charged Particles

In this subsection, we investigate the emission of light-charged particles
associated with fission. It is helpful to compare the LCP production with and
without coincidence with the fission fragments to infer fast-fission particle
emission characteristics. Fig. 20 (a) presents the yield ratio of various
species between exclusive events (in coincidence with FFs) and inclusive
events as a function of emission angle in the laboratory frame. The overall
value of the ratios is in the order of a few percent since the PPACs only
cover a small part of the whole space. Nevertheless, it is shown that
generally, in the whole angular range, the ratio decreases with increasing the
mass of the particle. Noticing from the phase space of the LCPs in the
experiment, it suggests that the dynamic emission of lighter particles is
relatively easier than heavier particles in fission events. Alternatively, the
dynamic emission of heavier particles, since it may happen earlier, takes away
more excitation energy and reduces the probability of fast fission
Pomorski2000 .

More specifically, Fig. 20 (b) presents the double ratio of ${\rm t/^{3}He}$
(red) and ${\rm d/^{4}He}$ (blue) between the exclusive events and the
inclusive events, respectively. For the pair of ${\rm t/^{3}He}$, the mass of
the two particles is the same while the neutron richness differs. The value of
the double ratio is larger than unity, indicating that tritons are relatively
easier to be emitted dynamically than ${\rm{}^{3}He}$ in fission events. It is
in qualitative agreement with the prediction of the transport model
simulations Wuqh2020 , namely, the occurrence of fast fission favors the
emission of neutron-rich species. For the pair of ${\rm d/^{4}He}$, the two
particles have the same isospin content but different mass. As shown, with the
increasing of $\theta_{\rm lab}$, the double ratio of d/4He, which is larger
than unity again, exhibits an upward trend. It suggests similarly that the
events with fission favor the production of particles with smaller masses in
accordance with the results in panel (a), particularly at large angles
corresponding to dynamic emissions.

Figure 20: (a) The yield ratio of the LCPs in exclusive and inclusive events
as a function of the angle in laboratory $\theta_{\rm lab}$. Panel(a) is the
analysis of p, d, t, 3He and 4He. (b) shows the double ratio of ${\rm
t/^{3}He}$ (red) and ${\rm d/^{4}He}$ (blue) between the exclusive events and
the inclusive events.

It is of interest to look into the angular distribution of the particle
emission. Since the particle emission occurs in competition with fission, the
angular distribution of the particles w.r.t. the fission axis can be used to
characterize the deformation, and the angular momentum of the fissioning
nuclei before scission point PBR96 ; SCH99 . Similarly, for the dynamic
emission of the LCPs in the fast fission induced by heavy-ion reactions, the
angular distribution of the LCPs w.r.t. the fission axis carries information
of the dynamic evolution of the fission process. In the current experiment,
however, since the derivation of the velocity of the two FFs relies on the
assumptions mentioned in Section 3, the fission axis is not precisely
determined, preventing us from discussing the angular distribution w.r.t. the
fission axis. Nevertheless, we can simply investigate the LCP emissions as a
function of the laboratory angle $\theta_{\rm lab}$, which is in turn
correlated with the angle of LCPs with respect to the fission plane
$\theta_{\rm fp}$ because the PPACs cover very limited range in azimuth. Fig.
21 presents the distribution of $\theta_{\rm lab}$ for the $Z=1$ isotopes. The
results of ${}^{3}{\rm He}$ and ${}^{4}{\rm He}$ are not shown because of the
lower statistics. To view the effect of the reaction violence, we divide the
folding angle into three windows as $85^{\circ}-105^{\circ}$,
$105^{\circ}-135^{\circ}$ and $135^{\circ}-165^{\circ}$, represented by
different colors, respectively. In each folding angle window, the total number
of events are normalized to the same value in order to conveniently compare
the features of all $\Theta_{\rm FF}$ windows. Interestingly, in the small
angular regime with $\theta_{\rm lab}\approx 25^{\circ}$ covered by SSD-Tel 2,
the yield of LCPs with larger folding angle (smaller LMT) is more abundant,
while in the large angular regime with $\theta_{\rm lab}\approx 50^{\circ}$
covered by SSD-Tel 1, the opposite trend is evident. The relative difference
is approximately 50% at large angles. We note here that this difference is not
due to the threshold effect because the threshold of the two SSD telescopes is
very close. It suggests that for the events with large LMT, emissions of light
particles are increasingly enhanced at a large angle. It is consistent with
the picture that the contribution of the intermediate velocity source
increases with increasing the LMT or the violence of the collisions between
the projectile and the target.

Figure 21: The angular distribution in laboratory $\theta_{\rm lab}$ for $Z=1$
isotopes in four windows of the folding angle $\Theta_{\rm FF}$ . The numbers
of events in all windows are normalized.

Fig. 22 (${\rm a-c}$) presents the isotopic yield ratio $R_{I}$ of p/d and t/d
as a function of $\theta_{\rm lab}$ in the same three $\Theta_{\rm FF}$
windows. It is shown that in all $\Theta_{\rm FF}$ windows, the ratio of p/d
increases with $\theta_{\rm lab}$ while that of t/d decreases with
$\theta_{\rm lab}$. The opposite trend for these two ratios suggests that
neutron-rich species tend to be emitted in the forward angle region in the
fast fission event. The difference becomes increasingly enhanced if the
folding angle (LMT) decreases (increases). These results are consistent with
our early experimental results in the same reaction, where the inclusive
production of the light-charged particles are recorded WRS2014 ; zy2017 . The
angular evolution of the neutron excess of the light charged particles in
coincidence with fission fragments provides a novel probe to the density
behavior of nuclear symmetry energy Wuqh2020 ; zy2017 . Compared to the
inclusive measurement, and the exclusive measurement in coincidence with
fission events helps determine the event geometry so that the comparison to
the transport model is better constrained. The theoretical efforts along this
direction are welcomed.

Figure 22: The yield ratio of p/d, t/d as a function of $\theta_{\rm lab}$,
respectively.

##  V Summary

To summarize, the fission fragments and the coincident light charged particles
had been measured in the experiment of 40Ar + 197Au reactions at 30 MeV/u. The
fission fragments are measured using PPACs, and the LCPs are measured using
SSD telescopes. Using the Viola systematics that the most probable value of
the relative velocity between the fission fragments is 2.4 cm/ns, the event
topology can be reconstructed, with the folding angle representing the linear
momentum transfer. The broadening of the azimuthal difference $\Delta\phi$
between the two fission fragments increases with LMT, suggesting the
increasing contribution of the post-scission emission, which smears the back-
to-back feature of the two-body process. The difference of the time-of-flight
between the two fragments also exhibits an increasing width as a function of
LMT, suggesting that the mass distribution of the fission fragments tends to
be broadened if more momentum is transferred to the fissioning system.

The occurrence of fast fission brings some enhancement of the emission of
particles with smaller mass or higher neutron richness, as demonstrated by
comparing the yield of the LCPs in the event groups with and without recording
the fission fragments in coincidence. In the events followed by fast fission,
the emission of LCPs becomes relatively more abundant in the intermediate
angles than the forward angles when the LMT increases, indicating more
contribution of the intermediate velocity source with increasing the violence
of the reaction. Commonly for all LMT windows, the contribution of the
neutron-rich (neutron-deficient) particles is more abundantly emitted at a
smaller (larger) angle in the laboratory frame, according to the results
obtained in the previously inclusive experiment. The exclusive measurement is
more beneficial than future transport model simulations aiming to extract the
nuclear symmetry energy. The studies call for more attention from model
simulations to reveal the isospin dynamics and constrain the nuclear symmetry
energy in heavy ion-induced fission reactions at Fermi energies.

###### Acknowledgements.

This work is supported by the National Natural Science Foundation of China
under Grants Nos. 11961131010 and 11875174, by the Polish National Science
Center under Grant No. 2018/30/Q/ST2/00185. The authors acknowledge the
detector group from IMP, CAS for providing the CsI (TI) crystals and the
machine staff delivering the Argon beam.

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