Isospin-dependent Quantum Molecular Dynamics Research Articles

Correlation between magnetic field and nuclear stopping in different rapidity segments during heavy ion collisions

The mid-rapidity zone is a region of crucial scientific interest during heavy ion collisions as it offers deep insight into the complex dynamics and properties of extremely dense nuclear matter. In the framework of the isospin-dependent quantum molecular dynamics model, the mid-rapidity zone (–0.6 ≤ Y c.m./Y beam ≤ 0.6) is segregated into three different regions to discover the intricate correlation between nuclear stopping (〈R p 〉) and the magnetic field eBy(0,0,0) generated due to the nucleons from these rapidity segments. Moreover, study of the time and space evolution of eBy(0,0,0) has been carried out for all the three rapidity bins. The maximum magnetic field intensity eBy(0,0,0)max is observed in the outwardmost region of the mid-rapidity zone due to less nuclear stopping and fewer nucleon–nucleon collisions. Additionally, a fruitful correlation has also been observed between eccentricity and nuclear stopping.

Uncertainties of critical temperatures based on higher-order fluctuations of the largest fragment charge* *Supported by the National Natural Science Foundation of China (11875328, 12075327), the Key Laboratory of Nuclear Data foundation (JCKY2022201C157), and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University (22lgqb39)

The new signature of liquid-gas phase transition has been well indicated by the higher-order fluctuations of the largest fragment charge, but the uncertainties of critical temperatures based on this signature have not been revealed. This study extracts the critical temperatures of liquid-gas phase transition in nuclear reactions and investigates their uncertainties. Utilizing the isospin-dependent quantum molecular dynamics model in conjunction with the statistical model GEMINI enables us to describe the dynamical path from the initial to the final state. An isotope thermometer and a quantum fluctuation thermometer are employed to extract the nuclear temperature. The higher-order fluctuations of the largest fragment charge and critical temperatures are studied in 124Sn + 120Sn collisions ranging from 400 to 1000 MeV/nucleon and 124Sn + AZ collisions at 600 MeV/nucleon. Observations revealed that the pseudo-critical point is robustly indicated by the higher-order fluctuations of the largest fragment charge. The critical temperatures extracted by the isotope thermometer are relatively consistent, with an uncertainty of 15%, while those obtained by the quantum fluctuation thermometer are heavily influenced by the incident energy and mass number of target nuclei. The excitation energy and bound charge are used for event-sorting. These two ensembles represent the statistical properties of the initial and final states of the system, respectively. The initial-final correlations of statistical properties might lead to two phenomena. First, the size distribution of the largest fragment at the pseudo-critical point based on the ensemble is wide, while that based on ensemble exhibits bimodality, which is a typical characteristic in the liquid-gas coexistence of a finite system. Second, the temperature at the pseudo-critical point based on the ensemble is higher than that based on the ensemble. Furthermore, the projectile-like system exhibits a significant dynamical effect in its evolution path from the initial to final state, closely associated with the fluctuation of critical temperature.

Simulation of collective flow of protons and deuterons in Au+Au collisions at Ebeam=1.23A GeV with the isospin-dependent quantum molecular dynamics model

Collective flows of protons and deuterons for $\text{Au}+\text{Au}$ collisions at beam energy ${E}_{\text{beam}}=1.23A \mathrm{GeV}$ were simulated by an isospin-dependent quantum molecular dynamics model. Two coalescence models, namely, naive coalescence and dynamical coalescence models, are compared for the formation of deuterons. After a reasonable agreement of the proton and deuteron rapidity spectra with the high acceptance dielectron spectrometer data is obtained, we apply an event-plane method to calculate the first four order collective flow coefficients and the ratios of $\ensuremath{\langle}{v}_{4}\ensuremath{\rangle}/{\ensuremath{\langle}{v}_{2}\ensuremath{\rangle}}^{2}$ and $\ensuremath{\langle}{v}_{3}\ensuremath{\rangle}/(\ensuremath{\langle}{v}_{1}\ensuremath{\rangle}\ensuremath{\langle}{v}_{2}\ensuremath{\rangle})$ and observe the scaling of the number of constituent nucleons between protons and deuterons. In addition, the dependence of ${\ensuremath{\varepsilon}}_{n}$ versus $\ensuremath{\langle}{v}_{n}\ensuremath{\rangle}$ and the ratio $\ensuremath{\langle}{v}_{n}\ensuremath{\rangle}/{\ensuremath{\varepsilon}}_{n}$ on the centrality is obtained. Finally, the Pearson coefficients $\text{corr}({v}_{n},{v}_{m})$ between the first four harmonic flows for protons and deuterons are studied as a function of rapidity and centrality.

Onset of pressure gradient on collective flow through balance and transition geometry

The impression of mean field and spectator matter has been studied through the collision geometry dependence of reduced flow and elliptical flow in heavy-ion collisions (HICs) at intermediate energies using Isospindependent Quantum Molecular Dynamics (IQMD) model for the reaction of $$_{20}^{50}{\rm{Cu + }}_{20}^{50}{\rm{and}}_{79}^{197}{\rm{Au + }}_{79}^{197}{\rm{Au}}$$ at incident energy between 50 MeV/nucleon and 450 MeV/nucleon. The collision geometry at which the reduced flow and elliptical flow changes its sign is termed as balance geometry $$({\hat b_{bal}})$$ and transition geometry $$({\hat b_{trans}})$$ of flow, respectively. Our study reveals that $$({\hat b_{bal}})$$ and $$({\hat b_{trans}})$$ increases with increase in incident energy. In addition to this, the effect of nuclear charge radius has also been studied by using the isospin-independent as well dependent nuclear charge radii parameterizations.

Production of neutron-deficient nuclei around N = 126 by proton-induced spallation* *Supported by the Open Project of Guangxi Key Laboratory of Nuclear Physics and Nuclear Technology (NLK2020-02), the National Natural Science Foundation of China (11875328, 12075327) and the Fundamental Research Funds for the Central Universities, Sun Yat-Sen University (22qntd1801)

Many isotopes of Np, Pu, Am, and Cm around the N = 126 shell still have not been produced in the laboratory. This study aims to investigate the cross sections and yields of the neutron-deficient nuclei of Np, Pu, Am, and Cm produced in the proton-induced spallations of transuranium elements. The isospin-dependent quantum molecular dynamics (IQMD) model is applied to study the dynamical process of reaction, and the subsequent decay process is simulated by the GEMINI++ model. The IQMD-GEMINI++ model is applied to calculate the cross section, kinetic energy, and angular distribution of the isotopic productions around N = 126. The Lindhand, Scharff, and Schiott theory is applied to calculate the energy loss of different heavy nuclei in the target material. A comparison between the data and the calculations shows that the IQMD-GEMINI++ model can reproduce the production cross sections of the neutron-deficient nuclei in spallation within approximately 1.5 orders of magnitude. The maximum cross section of the undiscovered isotopes of Np, Pu, Am, and Cm is about 10−5 mb, while the kinetic energies of the productions are all less than 16 MeV. The angular distribution shows that the emission direction of production is mostly at a backward angle. The range of production in the target is within the range of 10−7 to 10−5 cm. This range is the effective target thickness for the online identification of undiscovered isotopes. Based on the effective thickness of the target and assuming an intensity of 120 μA for the proton beam, the yields of the undiscovered neutron-deficient nuclei are calculated. Productions of the undiscovered isotopes of Np, Pu, Am, and Cm by the proton-induced spallations of transuranium elements are feasible. However, experimental techniques for online identification of neutron-deficient nuclei produced in proton-induced spallation should be developed.

Correlation between nuclear temperature and symmetry energy in subsaturation nuclear matter density

Herein, a study of the correlation between nuclear temperature and symmetry energy is presented for heavy ion collisions at intermediate energies via the isospin-dependent quantum molecular-dynamics model. It is found that different symmetry energy parameters change the density and kinetic energy distribution of the hot nuclei. More importantly, nuclear temperatures that are based on kinetic energy properties can be used to study symmetry energy information.

Target dependence of isotopic cross sections in the spallation reactions 238U + p, d and 9Be at 1 AGeV * *Supported by the National Natural Science Foundation of China (11875328, 12075327)

The spallation of 238U is an important way to produce rare isotopes. This work aims at studying the cross sections of isotopes produced in 238U + p, d and 9Be reactions at 1 A GeV and their target dependence. (1) A physical model dependent (Bayesian neural network) BNN, which includes the details of IQMD-GEMINI++ model and BNN, was developed for a more accurate evaluation of production cross sections. The isospin-dependent quantum molecular dynamics (IQMD) model is used to study the non-equilibrium thermalization of the 238U nuclei and fragmentation of the hot system. The subsequent decay of the pre-fragments is simulated by the GEMINI++ model. The BNN algorithm is used to improve the prediction accuracy after learning the residual error between experimental data and calculations by the IQMD-GEMINI++ model. It is shown that the IQMD-GEMINI++ model can reproduce the available experimental data (3282 points) within 1.5 orders of magnitude. After being fine tuned by the BNN algorithm, the deviation between calculations and experimental data were reduced to within 0.4 order of magnitude. (2) Based on the predictions by the IQMD-GEMINI++-BNN framework, the target dependence of isotopic cross sections was studied. The cross sections to produce the rare isotopes by the 238U + p, d and 9Be reactions at 1 A GeV are compared. For the generation of neutron-rich fission products, the cross sections for the 238U + 9Be are the largest. For the generation of neutron-deficient nuclei in the region of A = 200–220, the cross sections for 238U + p reaction are the largest. Considering the largest cross sections and the atomic density, the beryllium target is recommended to produce the neutron-rich fission products by the 238U beam at 1 A GeV, while the liquid-hydrogen target is suggested to produce the neutron-deficient nuclei in the region of A = 200–220.

Dissipation of energy and higher-order fluctuations of the largest fragment charge in projectile fragmentation

Abstract The higher-order fluctuations of the largest fragment charge were found to exhibit the signatures of a second-order phase transition in experimental data and simulations of the statistical multifragmentation model recently (Pietrzak et al 2020 Phys. Lett. B 809 135763). This work is devoted to study the dissipation of energy and higher-order fluctuations of the largest fragment charge in projectile fragmentation. The isospin-dependent quantum molecular dynamics (IQMD) model is used to study the non-equilibrium thermalization and fragmentation. The statistical code GEMINI is applied to simulate the second decay of the pre-fragments. To reveal how the incident energy dissipates into the excitation energy of the projectile-like system, the time evolution of the density, collective velocity, and random kinetic energy are displayed. It is found that the competition between the heat conduction and heat flux affects the excitation energy of the projectile-like system, which is the key variable in the fragmenting process. Displaying the mean multiplicity of the intermediate mass fragments and the higher-order fluctuations of the largest fragment charge, it is found that the decay mechanism of the projectile-like system transfers from the multi-fragmentation at mid-peripheral collision into the nucleon-evaporation at peripheral collision. The pseudo-critical point of this transition can be indicated by the zero of third order fluctuation together with the minimum of fourth order fluctuation. The calculations of the pseudo-critical point by the IQMD + GEMINI model agree with that extracted from the experimental data. Finally, the influences of the pseudo-critical point by the second decay, the mass number of the colliding system, and the incident energy are studied.

Azimuthal-sensitive three-dimensional HBT radius in Au–Au collisions at $$E_{beam} = 1.23A$$ GeV by the IQMD model

We used an Isospin dependent Quantum Molecular Dynamics (IQMD) model to simulate Au + Au collisions at beam energy $$E_{beam}$$ = 1.23A GeV, which corresponds to center of mass energy $$\sqrt{s_{NN}} = 2.4$$ GeV. Firstly, we obtained reasonable rapidity and transverse mass spectra of $$\pi ^-$$ and $$\pi ^+$$ as well as “apparent” temperature parameters in comparison with the HADES data. Then by calculating three-dimensional Hanbury Brown and Twiss (HBT) radius of same charged pion-pairs, we obtained the square difference of outward radius and sideward radius, i.e. $$R_{out}^{2}-R_{side}^{2}$$ , as well as the freeze-out volume ( $$V_{fo}$$ ), which were basically consistent with the trend of HADES experimental results. The azimuthal dependence of the HBT radii was also calculated by a matrix method, and corrected by the rotation matrix. In addition, the eccentricities of the xy- and zy- planes of pion-pair emissions were also extracted for different pair transverse momentum and collision centrality, which show that the xy-eccentricity increases with pair transverse momentum as well as centrality but not for zy-eccentricity, indicating a more asymmetric transverse emission of particle-pairs with higher transverse momentum in off-central collisions.

Effects of neutron-skin thickness on direct hard photon emission from reactions induced by the neutron-rich projectile Ca50

Direct hard photon emissions from incoherent proton-neutron bremsstrahlung in collisions of the neutron-rich projectile $^{50}$Ca with $^{12}$C and $^{40}$Ca targets are simulated in the framework of the isospin-dependent quantum molecular dynamics (IQMD) model. By adjusting the diffuseness parameter of neutron density in the droplet model to obtain different neutron skin thicknesses for $^{50}$Ca, the effects of neutron skin thickness on direct hard photon emission are investigated via several probes. The results show that more direct hard photons are produced with increasing neutron skin thickness in peripheral collisions. Meanwhile, we find that the multiplicity yield ratio $R_{cp}(\sigma_{\gamma})$ between central collisions and peripheral collisions as well as the rapidity dependence of multiplicity for direct hard photons are sensitive to neutron skin thickness. The results indicate that direct hard photon emission can be taken as an experimental observable to extract information on neutron skin thickness.

Temperature and density effects on the two-nucleon momentum correlation function from excited single nuclei

Two-nucleon momentum correlation functions are investigated for different single thermal sources at given initial temperature $(T)$ and density $(\rho)$. To this end, the space-time evolutions of various single excited nuclei at $T$ $= 1 - 20$ $MeV$ and $\rho$ = 0.2 - 1.2 $\rho_0$ are simulated by using the thermal isospin-dependent quantum molecular dynamics $(ThIQMD)$ model. Momentum correlation functions of identical proton-pairs ($C_{pp}(q)$) or neutron-pairs ($C_{nn}(q)$) at small relative momenta are calculated by $Lednick\acute{y}$ and $Lyuboshitz$ analytical method. The results illustrate that $C_{pp}(q)$ and $C_{nn}(q)$ are sensitive to the source size ($A$) at lower $T$ or higher $\rho$, but almost not at higher $T$ or lower $\rho$. And the sensitivities become stronger for smaller source. Moreover, the $T$, $\rho$ and $A$ dependencies of the Gaussian source radii are also extracted by fitting the two-proton momentum correlation functions, and the results are consistent with the above conclusions.

Production of high-energy neutrons by interaction of a deuteron beam with matter

Experimental double differential cross section data for neutrons in the high-energy region are still scarce because of the difficulty of producing high-energy neutrons. The present work studies the possibility of producing high-energy neutrons by interaction of a deuteron beam with matter. The Geant4 toolkit is used to simulate the interaction between a deuteron beam and matter. An analytical method is also developed to calculate the neutron yields produced in the interaction of the deuteron beam with matter. The input cross section data are not only taken from the TEDNL-2017 library but are also calculated by the isospin-dependent quantum molecular dynamics model. It is shown that it is possible to produce high-energy neutrons by interaction of a deuteron beam with matter. If one wishes to produce high-energy neutrons, a low-Z target and a small emission angle may be considered. A thin target is a good choice if one wishes to produce neutrons with a smaller energy peak width.

The effects of pre-equilibrium emission and secondary decay on the determination of freeze-out volume at intermediate energies * *Supported by the National Natural Science Foundation of China (11905018) and Scientific and Technological Innovation Programs of Higher Education Institutions of Shanxi Province, China (2019L0908)

The effects of pre-equilibrium emission and secondary decay on the determination of the freeze-out volume are investigated using the isospin-dependent quantum molecular dynamics model accompanied by the statistical decay model GEMINI. Small-mass projectiles and large-mass targets with central collisions are studied at intermediate energies. It is revealed that the proton yields of pre-equilibrium emission are smaller than those of secondary decay. However, the determination of the freeze-out volume from the proton yields is more easily affected by pre-equilibrium emission. Moreover, the percentage of proton yields in the freeze-out stage is found to be approximately 50%.

Interplay of Coulomb and symmetry potential in peak fragment production in asymmetric collisions

Role of the nuclear symmetry potential and Coulomb potential is explored on the peak energy of intermediate mass fragments ([Formula: see text]) and on peak multiplicity ([Formula: see text]) and their dependence on mass asymmetry of the reaction is also investigated. The calculations are done using Isospin-dependent Quantum Molecular Dynamics (IQMD) model. We also showed that the momentum-dependent interactions have uniform effects of [Formula: see text] and these effects are independent of mass asymmetry of the reaction. Further, we see that isospin effects that enter through the Coulomb and symmetry potential show much significant role as one increases the mass asymmetry of reaction. Mass asymmetric reactions thus serve a sensitive tool to investigate the nuclear symmetry energy effects.

Influence of nuclear thermometers and hot nuclei properties on nuclear temperature isospin effect measurement

The influence of nuclear thermometers and hot nuclei properties on nuclear temperature isospin dependence is studied. A systematic study of the nuclear temperature isospin effect is presented for heavy-ion collisions at moderate energy via the isospin-dependent quantum molecular dynamics model in the company of the statistical decay model (GEMINI). It is found that the isospin dependence of nuclear temperatures which is calculated by a momentum quadrupole fluctuation thermometer is more easily affected by hot nuclei mass range. However, the isospin dependence of nuclear temperatures which is calculated by an isotope yields ratio thermometer is more easily affected by neutron-proton ratio range of the hot nuclei. It is also found that the isospin dependence of nuclear temperatures can be changed by hot nuclei properties.

Influence of secondary decay on chemical freeze-out temperature isospin effect measurement

The influence of sequential decay on isospin dependence of isotope yield ratio temperatures is studied and a systematic study of isotope temperatures is presented for heavy-ion collisions at 600 MeV/nucleon via the isospin-dependent quantum molecular dynamics model in the company of the statistical decay model (GEMINI). Calculations show that the isospin dependence of the isotope yield ratio temperature is not affected by secondary decay.

Role of mass asymmetry on the peak energy of intermediate mass fragments production and its influence towards isospin effects

Using the isospin-dependent quantum molecular dynamics model, we study the peak intermediate mass fragments production and corresponding center-of-mass energy in various mass asymmetric reactions. The study is spanned over different mass asymmetries for total system mass 92, 162 and 240. We propose the peak energy as a powerful probe to constrain the low-density behavior of symmetry energy. This peak energy is found to remove the dual dependence of isospin effects in symmetry energy and cross-section.

Determining the temperature in heavy-ion collisions with multiplicity distribution

By relating the charge multiplicity distribution and the temperature of a de-exciting nucleus through a deep neural network, we propose that the charge multiplicity distribution can be used as a thermometer of heavy-ion collisions. Based on an isospin-dependent quantum molecular dynamics model, we study the caloric curve of reaction Pd103 + Be9 with the apparent temperature determined through the charge multiplicity distribution. The caloric curve shows a characteristic signature of nuclear liquid-gas phase transition around the apparent temperature Tap = 6.4MeV, which is consistent with that through a traditional heavy-ion collision thermometer, and indicates the viability of determining the temperature in heavy-ion collisions with multiplicity distribution.

Secondary decay effects of the isospin fractionation in the projectile fragmentation at GeV/nucleon

The isospin fractionations in $$^{124}$$ Sn, $$^{107}$$ Sn + $$^{120}$$ Sn at 600 MeV/nucleon, and $$^{136}$$ Xe, $$^{124}$$ Xe + $$^{208}$$ Pb at 1000 MeV/nucleon are investigated by the isospin-dependent quantum molecular dynamics model coupled with the statistical code GEMINI. The yield ratio as a function of the binding energy difference for light mirror nuclei $$^{3}$$ H/ $$^{3}$$ He, $$^{7}$$ Li/ $$^{7}$$ Be, $$^{11}$$ B/ $$^{11}$$ C, and $$^{15}$$ N/ $$^{15}$$ O is applied to estimate the ratio between neutrons and protons in the gas of the fragmenting system. By comparing the estimated values resulting from the simulations with and without the GEMINI code, it was found that the secondary decay distorts the signal of the isospin fractionation. To minimize the secondary decay effects, the yield ratio of the light mirror nuclei $$^{3}$$ H/ $$^{3}$$ He as well as its double ratio between two systems with different isospin asymmetries of the projectiles is recommended as robust isospin observables.

Azimuthal anisotropy and multiplicities of hard photons and free nucleons in intermediate-energy heavy-ion collisions

Anisotropic flow can offer significant information of evolution dynamics in heavy-ion collisions. A systematic study of the directed flow $v_1$ and elliptic flow $v_2$ of hard photons and free nucleons is performed for $^{40}$Ca+$^{40}$Ca collisions in a framework of isospin dependent quantum molecular dynamics (IQMD) model. The study firstly reveals that thermal photons emitted in intermediate-energy heavy-ion collisions have the behaviors of directed and elliptic flows. The interesting phenomena of incident energy dependence of $v_1$ and $v_2$ for thermal photons in central collisions also confirmed that it can be regarded as a good probe of evolution dynamics. Moreover, the multiplicities of hard photons and free nucleons and their correlation are also investigated. We find that direct photon emission is positively related to free nucleons emission, however, there exists an anti-correlation for thermal photons with free nucleons.