Isoscaling in central Sn+Sn collisions at 270 MeV/u

During a collision involving heavy-ions at energies well above the Coulomb barrier, nuclear matter is driven through very different configurations. In the early stages, violent collisions between its constituents take place, causing matter to be heated up. If these collisions occur above the production thresholds, sub-atomic particles such as pions, for instance, may be produced StockR_PR_1986_135_259 ; SengerPeter_PPNP_2004_53_1 ; OnoAkira_PPNP_2019_105_139_HIC_dynamics ; IkenoNatsumi_PRC_2016_93_044612_AMD_SnSn300 ; HongJun_PRC_2014_90_024605 . Many particles are ejected in this pre-equilibrium stage XuHM_PRC_1994_50_1659 , carrying away an appreciable amount of energy from the system. At the same time, the relative collective motion between the colliding nuclei leads to the compression of nuclear matter and densities higher than the saturation density found in the core of normal nuclei such as lead IkenoNatsumi_PRC_2016_93_044612_AMD_SnSn300 ; BorderieB_PPNP_2019_105_82_Phase_Transition_Nuclei .

Dynamical treatments WolterHermann_PPNP_2022_125_103962 have been developed to study such early stages. The density, the isospin configuration, and the temperatures attained by the system are sensitive to the physics input parameters employed by the models WolterHermann_PPNP_2022_125_103962 ; XuHM_PRC_1994_50_1659 ; LiBaoAn_PRL_1997_78_1644 ; TanWP_PRC_2001_64_051901 ; JhangG_SpiRIT_PLB_2021_813_136016_pion_ratio . Therefore, important information on the Nuclear Equation of State (EOS) may be provided by these dynamical approaches. Determining the input parameters of the models using experimental observables is of particular interest, as some of them are closely related to the rate of equilibration of the system, providing deeper insight into the dynamics of the collisions.

After pre-equilibrium emission, a freeze-out configuration is reached and many fragments including protons and neutrons are emitted XuHM_PRC_1994_50_1659 . Its behaviors can be described both by dynamical OnoAkira_PPNP_2019_105_139_HIC_dynamics ; WolterHermann_PPNP_2022_125_103962 and statistical models BondorfJP_PR_1995_257_133_SMM ; DasCB_PR_2005_406_1 ; BotvinaAS_EPJA_2006_30_121 ; BorderieB_PPNP_2019_105_82_Phase_Transition_Nuclei . In the former case, it appears as a result of the dynamical path taken by the system. In the case of statistical models, a freeze-out configuration is assumed. In both cases, most of the excited fragments predicted by the models would decay before detection and, therefore, a de-excitation treatment BotvinaAS_NPA_1987_475_663 ; TanWP_PRC_2003_68_034609_ISMM must be applied before comparing theoretical predictions with the experimental data. Consequently, important vestiges of the freeze out configuration may be blurred by the de-excitation process.

In this context, the nuclear isoscaling phenomenon TsangMB_MSU_PRC_2001_64_054615_isoscaling_SMM_EES ; TsangMB_MSU_PRL_2001_86_5023_isoscaling_experiment , first reported in Ref. XuHS_MSU_PRL_2000_85_716_isoscaling for Sn+Sn reactions at 50 MeV/u, is a very useful tool as the ratios of yields from two different reactions (which differ mainly in the isospin composition) is weakly affected by the fragment de-excitation process TsangMB_MSU_PRC_2001_64_054615_isoscaling_SMM_EES , retaining information on the system’s configuration right after the violent stages of the reaction. Particularly, under certain conditions TsangMB_MSU_PRC_2001_64_054615_isoscaling_SMM_EES ; SouzaSR_PRC_2009_80_044606_isoscaling_symmetryenergy ; RamiF_PRL_2000_84_1120_FOPI_Isospin_tracing , it may be related to the symmetry energy, which makes this observable specially relevant to investigations on the nuclear EOS. The isoscaling analysis considers the ratio:

This scaling property can be derived in the framework of the grand-canonical ensemble TsangMB_MSU_PRC_2001_64_054615_isoscaling_SMM_EES . From it, simple relationships between the neutron and proton chemical potentials, $\mu_{n}$ and $\mu_{p}$, respectively, and the scaling parameters are obtained:

Although the formal derivation is based on the grand-canonical ensemble, the isoscaling property is also found in nearly all statistical models TsangMB_MSU_PRC_2001_64_041603_isoscaling_condition , including versions of the Statistical Multifragmentation Model (SMM) which employ the micro-canonical and canonical ensembles SouzaSR_PRC_2009_80_044606_isoscaling_symmetryenergy . It has also been observed in the Antisymmetrized Molecular Dynamics (AMD) model OnoAkira_SpiRIT_PRC_2003_68_051601_isoscaling_AMD . Calculations based on the molecular dynamics approach DorsoCO_PRC_2006_73_044601 seem to indicate that the isoscaling may be observed even when the system has not yet attained thermal equilibrium. Furthermore, recent experimental results suggest that the parameters $\alpha$ and $\beta$ are sensitive to the mechanisms responsible for fragment production. These results call for further investigations on the nuclear isoscaling property.

Many experimental studies GeraciE_LNS_NPA_2004_732_173_isoscaling_experiment ; TrautmannW_2006_nuclex_0603027_isoscaling_ALADIN_INDRA ; FableQ_Arxiv_2022_2202_13850_CaCa_INDRA ; WuenschelS_TAMU_PRC_2009_79_061602_isoscaling_experiment ; YoungsM_TAMU_NPA_2017_962_61_isoscaling_experiment have investigated the isoscaling property in different systems at different bombarding energies. A close relationship between the parameter $\alpha$ and the symmetry energy coefficient $C_{\textrm{sym}}$ has been pointed out in Ref. TsangMB_MSU_PRC_2001_64_054615_isoscaling_SMM_EES . More specifically, denoting by $Z_{i}$ and $A_{i}$ the atomic and mass numbers of the $i$-th source, one has:

In this work, we extend earlier investigations at low incident energies of Sn+Sn reactions to a collision energy (270 MeV/u). We concentrate on central mid-rapidity events, with impact parameters $b<1.5$ fm. The scaling properties are studied as a function of the transverse momentum.

The S$\pi$RIT experiment was performed at the Radioactive Isotope Beam Factory (RIBF) at RIKEN. The primary beams of ²³⁸U and ¹³²Xe impinged on the Be target to produce secondary beams of ${}^{132,124}\textrm{Sn}$ and ${}^{112,108}\textrm{Sn}$ respectively, at 270 MeV/u. The beams bombarded on the isotopically enriched ${}^{124}\textrm{Sn}$ and ${}^{112}\textrm{Sn}$ targets with areal density of $608\,\textrm{mg/cm}^{2}$ and $561\,\textrm{mg/cm}^{2}$, respectively. Four reactions with different neutron-to-proton ratios, $N/Z$, of the total system were measured: ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ $(N/Z=1.56)$, ${}^{108}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ $(N/Z=1.2)$, ${}^{112}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ $(N/Z=1.36)$, and ${}^{124}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ $(N/Z=1.36)$. In this work, we focus mainly on the most $(N/Z=1.56)$ and least $(N/Z=1.2)$ neutron rich systems.

Charged particles produced in the reactions were detected with the SAMURAI Pion Reconstruction and Ion-Tracker Time Projection Chamber (S$\pi$RIT-TPC) ShaneR_SpiRIT_NIMA_2015_784_513_spirittpc ; TangwancharoenS_SpiRIT_NIMA_2017_853_44_TPCGatingGrid ; BarneyJ_SpiRIT_RSI_2021_92_063302_spirittpc installed inside the SAMRURAI dipole magnet OtsuH_NIMB_2016_376_175_SAMURAIMagnet with a magnetic field of 0.5 T. The effective volume of the TPC is 1344 mm $\times$ 864 mm $\times$ 530 mm, and the target was placed at 15 mm upstream of the entrance window, resulting in an angular coverage of $\theta<80^{\circ}$ with respect to the beam axis in the laboratory frame. Description of the associated trigger arrays located on the side and downstream of the TPC used to select central events can be found in Refs. LaskoP_NIMA_2017_856_92_KATANA ; KanekoM_NIMA_2022_1039_167010_KyotoArray . The Generic Electronics for TPCs (GET) was employed to read out the track signals. The analysis software S$\pi$RITROOT JhangGenie_SpiRIT_JKPS_2016_69_144_SpiRITROOT ; LeeJW_SpiRIT_NIMA_2020_965_163840_SpiRITROOT was developed for the track reconstruction of the charged particles. Detailed performance of the TPC and GET electronics as well as the software analysis codes have been published in  BarneyJ_SpiRIT_RSI_2021_92_063302_spirittpc ; JhangGenie_SpiRIT_JKPS_2016_69_144_SpiRITROOT ; IsobeT_SpiRIT_NIMA_2018_899_43_GET_electronics ; LeeJW_SpiRIT_NIMA_2020_965_163840_SpiRITROOT . Other technical issues including space charge correction and extending the dynamic range of the TPC electronics can be found in TsangCY_SpiRIT_NIMA_2020_959_163477_space_charge ; EsteeJ_SpiRIT_NIMA_2019_944_162509_tpcdynamicrange .

The cuboid-shaped S$\pi$RIT TPC lacks the azimuthal symmetry. In this work, we mainly analyze the data at the azimuthal angles, $\phi$, $-30^{\circ}<\phi<20^{\circ}$ and $160^{\circ}<\phi<210^{\circ}$ where the tracks are longest and the track quality is generally much better. The TPC efficiencies arising from the detector performance are determined by the track embedding method AndersonM_NIMA_2003_499_659_STARTPC using events generated from Monte Carlo simulations and GEANT-4. The reconstructed rigidity momentum/charge, $p/Z$ and the mean energy loss per unit length $\left<dE/dx\right>$ were provided for each track. The resolution of the reconstructed momentum and $\left<dE/dx\right>$ for single tracks is 1.6% and 4.6 %, respectively EsteeJustinBrian_phdthesis_MichiganStateUniversity_2020 . The particle identification (PID) is obtained using the correlation plot of magnetic rigidity, $p/Z$, and energy loss, $\left<dE/dx\right>$, of the detected particles, as shown in Fig. 1. Isotopes of $p$, $d$, $t$, ${}^{3}\mathrm{He}$, ⁴He, ${}^{6}\mathrm{He}$, ${}^{6}\mathrm{Li}$, and ${}^{7}\mathrm{Li}$ can be clearly identified. However, below $p/Z<$ 600 MeV/$c$, the $t$ and ${}^{3}\mathrm{He}$ PID lines merge. In this study, we mainly focus on particles in the mid-rapidity range $y_{0}=$ 0 - 0.4 with $y_{0}=y/y_{NN}^{c.m.}-1$ where $y$ is the rapidity of the particle and $y_{NN}^{c.m.}$ is center-of-mass rapidity of the nucleon-nucleon system. Since the mid-rapidity gate eliminates tritons below $p/Z<$ 1000 MeV/$c$, contamination from ${}^{3}\mathrm{He}$ in triton spectra is minimal. On the other hand, contamination from triton in the ³He spectra has to be determined.

Some physics results regarding the symmetry energy constraints from the S$\pi$RIT experiments have been published. Charged pion multiplicities and ratios were published in Ref. JhangG_SpiRIT_PLB_2021_813_136016_pion_ratio and Ref. EsteeJ_SpiRIT_PRL_2021_126_162701_pion_ratio . Ref. KanekoM_SpiRIT_PLB_2021_822_136681_Z1particles_AMD focused on $Z$=1 particles and comparisons of the rapidity distributions with the AMD modelsOnoAkira_PTP_1992_87_1185_AMD ; OnoAkira_PPNP_2019_105_139_HIC_dynamics . This paper provides a more comprehensive study than Ref. KanekoM_SpiRIT_PLB_2021_822_136681_Z1particles_AMD and focuses on the transverse momentum spectra and yield ratios obtained from light charged fragments, specifically $p$, $d$, $t$, ³He and ⁴He.

To select central collisions, we assume the impact parameters increase monotonically with the charged particle multiplicity CavataC_PRC_1990_42_1760_reduced_impact_parameter ; BarneyJonathanElijah_phdthesis_MichiganStateUniversity_2019 . Very central collision events ($b<$ 1.5 fm) similar to those analyzed in Ref. KanekoM_SpiRIT_PLB_2021_822_136681_Z1particles_AMD are chosen for this work. The difference between this work and Ref. KanekoM_SpiRIT_PLB_2021_822_136681_Z1particles_AMD for the rapidity spectra in $y_{0}=$ 0 - 0.4 (Fig. 2) is within 3 %. The charge multiplicity selection in both works is different. Indeed, events with multiplicities equal or more than 57 and 56 charged particles, for ¹³²Sn+¹²⁴Sn and ¹⁰⁸Sn+¹¹²Sn respectively, are chosen in this work, while 56 and 55 are used in Ref. KanekoM_SpiRIT_PLB_2021_822_136681_Z1particles_AMD . In both cases, the impact parameter gates of ($b<$ 1.5 fm) is chosen. In this work, $b_{\mathrm{max}}$ is defined to be the experimental $b_{\mathrm{max}}$ of 7.52 fm in ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and 7.13 fm in ${}^{108}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ while in Ref. KanekoM_SpiRIT_PLB_2021_822_136681_Z1particles_AMD , $b_{\mathrm{max}}$=10 fm is defined by the sum of the radii for the projectile and target. These slight differences in the multiplicity gates do not affect the results of both works. The total statistics is increased as the tracks from both the left and right side of the TPC is used in the present work, whereas only the tracks in the right side of the TPC is used in Ref. KanekoM_SpiRIT_PLB_2021_822_136681_Z1particles_AMD . These are the main reasons for the 3 % discrepancy. In any case, the isocaling ratios are unaffected by the slight discrepancies in the spectra.

Fig. 1 shows a typical PID plot of the charged particles obtained in the ¹³²Sn+¹²⁴Sn collisions. The heavier clusters with A $>$ 5 nuclei such as ${}^{6}\textrm{He}$, ${}^{6}\textrm{Li}$, ${}^{7}\textrm{Li}$ are not included in the current analysis due to lack of statistics. To standardize the PID conditions, the center and width of $\left<dE/dx\right>$ of the PID line for each particle are fitted with the empirical Bethe-Bloch formula with Gaussian widths. Only tracks having PID probability larger than $70\%$ ($50\%$ for ${}^{3}\textrm{He}$) and $2.2\sigma$ width of $\left<dE/dx\right>$ are selected for the analysis.

The overall systematic uncertainties are estimated from the variations of track multiplicity, track quality LeeJW_SpiRIT_NIMA_2020_965_163840_SpiRITROOT and PID quality cuts TsangChunYuen_phdthesis_MichiganStateUniversity_2022 . In the region $p_{T}/A<$ 400 MeV/c, the statistical errors are smaller than systematic errors which are about 5% and 2% for the absolute yield and yield ratios, respectively. Outside of this region the statistic and systematic uncertainties increase with $p_{T}/A$ to exceed 15%. The error bars shown in this work include both the systematic and statistical errors.

The experimental rapidity and transverse momentum spectra for $Z$=1 and 2 particles are shown in Fig. 2 and Fig. 3, respectively, for the neutron rich system ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ $(N/Z=1.56)$ (black circles) and the nearly symmetric system, ${}^{108}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ $(N/Z=1.20)$ (red squares). The data in both left and right panels in each figure are the same. Comparison of the data to the two different parameter sets of the AMD models, shown by solid (left panels) and dashed (right panels) lines, will be discussed in details later.

In all cases, the rapidity spectra show peaking near or at $y_{0}=0$ suggesting high degree of stopping. The slight asymmetry observed around $y_{0}=0$ for all particles is due to the inefficiencies in the TPC to detect target rapidity particles which are generally low in energy and emitted at backward angles in the laboratory frame. In the case of ${}^{3}\mathrm{He}$, the PID contamination from tritons is significant and the spectra peak is located slightly off $y_{0}=0$. For the analysis, we assume the spectra is symmetric at $y_{0}=0$ and only include data in $y_{0}=0$ - $0.4$.

At mid rapidity, except for proton and ${}^{3}\mathrm{He}$ isotopes, more particles, $d$, $t$ and ${}^{4}\mathrm{He}$ are produced in the neutron-rich systems. The same observation is also seen in Fig. 3 for particles with $p_{T}/A<280$ MeV/$c$. On the contrary, more high energy particles including the neutron rich tritons, with $p_{T}/A>400$ MeV/$c$, are produced from the nearly symmetric ${}^{108}\textrm{Sn}+{}^{112}\textrm{Sn}$ system than the neutron-rich one. This is surprising as one would expect that neutron-rich systems would produce more neutron-rich isotopes at all energies. One explanation could be that high energy particles are produced in a dynamical and non-equilibrium environment and that the hot participant zone is rather neutron deficient.

It has been shown that isoscaling occurs only when the two systems have nearly the same temperature TsangMB_MSU_PRC_2001_64_041603_isoscaling_condition . Since the absolute temperature cannot be directly measured, we use the established isotope thermometers based on the double ratio of hydrogen and helium species

We note that the isotope temperature can be derived in the grand-canonical ensemble AlbergoS_INCA_1985_89_1 and it is found to be independent of $N/Z$ ratio of the source in low energy collisions KundeGJ_PLB_1998_416_56_HHeTemperature .

The upper panel of Fig. 4 displays the H-He temperature evaluated from Eq. (7). The $T_{\textrm{H-He}}$ for both neutron rich (solid circles) and the near-symmetric (open squares) systems are nearly the same for low energy particles. The temperatures increases slowly from around 8 MeV to 10 MeV with increasing $p_{T}/A$. Above 280 MeV/$c$, temperatures start to increase dramatically. Furthermore, the temperatures of the two systems begin to differ. Above 400 MeV/$c$ the temperature of the near-symmetric system is higher than that of the neutron rich system. The increasing differences in temperatures with $p_{T}/A$ indicates that the Sn+Sn collisions studied here (with incident energy of 270 MeV/u) do not form fully equilibrated systems.

The increase in H-He temperature as a function of the surface velocity of the particles, has been observed in Refs. WangJ_PRC_2005_72_024603 ; BougaultR_JPG_47_025103 . In previous work, a drop of the temperature is also observed at very high velocity. We do not see the drop. This could be a consequence of the dramatic decrease of the cross-sections for $p_{T}/A$ above 280 MeV/$c$.

Next, we focus on the spectral ratio of isotope yields $R_{21}(N,Z)$ of the $Z$=1 and 2 particles, observed in the ${{}^{132}\textrm{Sn}}+{{}^{124}\textrm{Sn}}$ and ${{}^{108}\textrm{Sn}}+{{}^{112}\textrm{Sn}}$ systems. These are shown in the lower panel of Fig. 4 as a function of $p_{T}/A$. The dotted lines connect data points providing visual guidance to the trends of the data for each particle. The vertical dashed line at $p_{T}/A=280$ MeV/$c$ marks the approximate region when the temperatures of the two systems start to differ.

The isotope ratios plotted to the left of the dashed line show isoscaling characteristics. In each ($N-Z=-1$, 0 and 1) group, $R_{21}(N,Z)$ values are nearly constant as a function of $p_{T}/A$. Moreover, ³He behave like protons ($N-Z=-1$) with ratio value smaller than 1, and ⁴He behave similarly to deuterons ($N-Z=0$) with higher ratio value than protons. The tritons ($N-Z=1$) have the highest ratio values as expected from isoscaling.

The $R_{21}$ ratios for the five particles with $p_{T}/A<$ 280 MeV/$c$ are plotted as a function of $N$ and $Z$, in the left panels of Fig 5. The three parameters $\alpha$, $\beta$ and $C$ are simultaneously fitted and the resulting isoscaling fits are shown as lines in the figure. The two fitted lines of the data for the isotopes with $Z$ = 1 and 2 are shown separately in the top left panel, where the slopes of the lines represent the fit parameter $\alpha$ = 0.29. The three fitted lines for the isotones with $N$ = 0, 1 and 2 are shown on the bottom left panel as a function of $Z$ and the slopes represent the fit parameter $\beta$ = -0.23. In the absence of Coulomb, protons and neutrons should behave similarly and one would expect $\alpha$ and $\beta$ to have similar values but opposite signs. This has been observed in most of the previous studies of isoscaling. In this case, the magnitude of the $\alpha$ value is larger than the $\beta$ value. The isoscaling ratios obtained from these fits are plotted as solid horizontal lines in the bottom panel of Fig. 4 to the left of the vertical dashed line.

In contrast, except for protons, $R_{21}(N,Z)$ for high energy isotopes shown on the right side of the vertical dashed line decreases with $p_{T}/A$. Furthermore, the lines from different isotopes cross over each other. In the case of $N=2$ particles (triton and ⁴He), $R_{21}$ falls off suddenly above $p_{T}/A=$ 280 MeV/$c$ with the largest drop exhibited by tritons. This reflects the sharper drop in the $t$ and ⁴He particle spectra at the high energy. The right panels of Fig. 5 show the ratios $R_{21}$ plotted as a function of $N$ and $Z$ in the range of $p_{T}/A\geq 400$ MeV/$c$. $R_{21}$ values for t, ${}^{3}\mathrm{He}$ and ⁴He have nearly the same values leading to the breakdown of isoscaling. The lines connecting the isotope (upper right panel) and isotone (lower right panel) data points serve only to guide the eye and provide a contrast trends of the $R_{21}$ values between fragments with low (left panels) and high (right panels) transverse momentum.

It is also interesting to note that $R_{21}$ is less than 1 for all high energy isotopes. For isotopes with $p_{T}/A\approx 500$ MeV/$c$, $R_{21}\approx$ 0.5 for t, ³He and ⁴He, i.e. 50% less tritons are produced from the neutron-rich system of ${{}^{132}\textrm{Sn}}+{{}^{124}\textrm{Sn}}$ than that from the ${{}^{108}\textrm{Sn}}+{{}^{112}\textrm{Sn}}$ system. So far there is no explanation for the surprising result.

The isoscaling ratios $R_{21}(N,Z)$ of the $Z$ = 1 and 2 particles, obtained from the experimental yields measured in the ${{}^{132}\textrm{Sn}}+{{}^{124}\textrm{Sn}}$ and ${{}^{108}\textrm{Sn}}+{{}^{112}\textrm{Sn}}$ systems, are shown in Fig. 6. In each panel, data are compared to the models; SMM (horizontal lines in the top panel), AMD${}^{(\textrm{S})}$ and AMD${}^{(\textrm{F})}$ (hatched bands in the middle and bottom pannels, respectively).

In summary, the isoscaling phenomenon of hydrogen and helium isotopes in ${}^{132}\textrm{Sn}+^{124}\textrm{Sn}$ and ${}^{108}\textrm{Sn}+^{112}\textrm{Sn}$ reactions at beam energy of 270 MeV/u is presented as a function of $p_{T}/A$. Isoscaling phenomenon up to $p_{T}/A<280$ MeV/$c$ is found but breaks down for cluster particles with $p_{T}/A>280$ MeV/$c$. The systems are found to form a thermal equilibrium not throughout the system but locally, which is evident from the increasing trend of H-He isotope ratio temperature with increasing $p_{T}/A$. The isoscaling can be qualitatively explained by both the SMM and AMD models. When the yield spectra and isoscaling are compared to the predictions from the dynamical model AMD with two different parameter sets, we do not find any preference in increasing the default values of $\sigma_{NN}$ as observed in earlier study of Z=1 particles. While isoscaling breaks down for $p_{T}/A>280$ MeV/$c$ particles in the data, the isoscaling trend in AMD persist. Most intriguely, the high-momentum clusters are suppressed in the neutron-rich system compared to the more symmetric system suggesting the non-equilibrium nature of the emission process especially for the high energy particles.

The authors would like to thank Prof. Pawel Danielewicz for many fruitful discussions. This work was supported by the U.S. Department of Energy, USA under Grant Nos. DE-SC0021235, DE-NA0003908, DE-FG02-93ER40773, DE-FG02-93ER40773, DE-SC0019209, DE-SC0015266, DE-AC02-05CH11231, U.S. National Science Foundation Grant No. PHY-1565546, the Robert A. Welch Foundation (A-1266 and A-1358), the Japanese MEXT, Japan KAKENHI (Grant-in-Aid for Scientific Research on Innovative Areas) grant No. 24105004, JSPS KAKENHI Grants Nos. JP17K05432, JP19K14709 and JP21K03528, the National Research Foundation of Korea under grant Nos. 2018R1A5A1025563 and 2013M7A1A1075764, the Polish National Science Center(NCN) under contract Nos. UMO-2013/09/B/ST2/04064, UMO-2013/-10/M/ST2/00624, Computing resources were provided by FRIB, the HOKUSAI-Great Wave system at RIKEN, and the Institute for Cyber-Enabled Research at Michigan State University. S.R. Souza acknowledges partial support from CNPq, CAPES, FAPERJ and the use of the supercomputer Lobo Carneiro, where part of the calculations have been carried out. This work has been done as part of the project INCT-Física Nuclear e aplicações, projeto No. 464898/2014-5.

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data can be available on request sent to the corresponding author.]