Constrained Molecular Dynamics Model Research Articles

Multinucleon Transfer in 25 MeV/nucleon 86Kr + 64Ni, 124Sn Peripheral Collisions

In this work we investigate multinucleon transfer reaction channels in peripheral collisions between a 86Kr projectile at 25 MeV/nucleon with 64Ni and 124Sn targets. The experimental data of these reactions were obtained with the Momentum Achromat Recoil Separator (MARS) at Texas A&M University in previous works of our group. We extracted and compared experimental mass and momentum per nucleon distributions of ejectiles with a two step model calculation. For the interaction of the projectile with the target, the phenomenological Deep Inelastic Transfer model (DIT) and the microscopic Constrained Molecular Dynamics model (CoMD) were used, both followed by the GEMINI model for the de-excitation of the primary excited projectile-like fragments. Generally, both DIT and CoMD appear to describe the trend of the data for both systems. However, possible further improvements in the models may be necessary. In conjunction with our recent work with a 86Kr beam at 15 MeV/nucleon with a 64Ni target, this study provides further insights into the reaction mechanisms of peripheral collisions in the Fermi energy regime and the production of neutron rich nuclides.

Multinucleon transfer in 48Ti + 48Ti collisions at 11.5 MeV/nucleon

In this work, experimental data of projectile fragment distributions from a preliminary experimental study of the reaction of 11.5 MeV/nucleon 48Ti on 48Ti analyzed with the MARS recoil separator at the Cyclotron Institute of Texas A&M University are presented. Production cross sections, momentum distributions and excitation-energy distributions are extracted and compared with calculations with the Deep Inelastic Transfer (DIT) model and the Constrained Molecular Dynamics model (CoMD). Despite the limited extent of the present dataset, an overall agreement of the models with the data is found pointing at the prevailing nucleon-exchange character of the collisions at this energy.

Nuclear Equation of State and many-body phase-space correlations in the Constrained Molecular Dynamics

Many-body correlations characterizing the Constrained Molecular Dynamics (CoMD) are analyzed in the case of finite and zero-range effective microscopic interactions. The study begins by analyzing the case of infinite nuclear matter at zero temperature. A comparison with the predictions in the mean-field (MF) limit corresponding to different effective masses, highlights non-negligible differences regarding the produced Equation of State (EoS). A procedure is illustrated to determine the necessary corrections of the effective interaction parameters in the CoMD model so to reproduce the chosen EoS. The specific model calculations, the general feature of the discussed correlations gives a wider meaning to the resulting differences, which are in fact strongly related both to the Pauli principle constraint and to the localization effects related to wave-packets dynamics. Moving on to finite systems, preliminary results are shown in relation to the reaction mechanisms in the N64i+48Ca system described by the CoMD model. Therefore, the topic covered illustrates the effects produced by the correlations of the CoMD dynamics on the EoS and on some observables commonly studied in heavy ion collisions.

Momentum Distribution Studies of Projectile Fragments from Peripheral Collisions Below the Fermi Energy

This paper presents our recent studies of multinucleon transfer in peripheral collisions in reactions below the Fermi regime. Our current focus is the study of the mass, angular and momentum distributions of the projectile-like fragments from the reaction of an 86Kr beam at 15 MeV/nucleon with a target of 64Ni. Experimental data from our previous work with the MARS spectrometer at the Cyclotron Institute of Texas A&M University were compared with model calculations. The dynamical stage of the reaction is described with either the Deep-Inelastic Transfer Model (DIT) or with the microscopic Constrained Molecular Dynamics model (CoMD). The de-excitation of the hot projectile-like fragments is performed with the GEMINI model. The momentum distributions are characterized by a quasi-elastic peak and a deep-inelastic peak. Two-body kinematics was employed to extract the total excitation energies of these regions. Through the thorough study of peripheral reactions in the Fermi energy regime we expect to gain valuable information that could lead to the understanding of how the rare isotopes in regions such as the r-process path and the neutron drip line are formed and the reaction mechanism(s) that take place.

Study of Multinucleon Transfer Mechanisms in 86Kr-Induced Peripheral Reactions at 15 and 25 MeV/nucleon

This paper presents our recent studies of the multinucleon transfer in peripheral collisions in reactions near the Fermi regime. Specifically, the reactions of a 86Kr beam at 15 MeV/nucleon with targets of 124Sn ,112Sn, 64Ni and 58Ni and reactions of a 86Kr beam at 25 MeV/nucleon with targets of 124Sn and 112Sn. The experimental data were obtained from the previous work of our group with the MARS spectrometer at the Cyclotron Institute of Texas A&M University. Our current focus is the thorough study of the experimental mass and momentum distributions of the projectile-like fragments. The momentum distributions are characterised by a narrow quasi-elastic peak and a broader deep-inelastic peak. We employed two-body kinematics to characterize the excitation energies of these reactions. We also compared the data with model calculations. The dynamical stage is described with either the Deep-Inelastic Transfer Model (DIT), or with the microscopic Constrained Molecular Dynamics model (CoMD). The de-excitation of the hot projectile-like fragments is performed with the Gemini model. Studying these reactions will provide us with a better understanding as to how the energy of the beam and the different targets affect the mechanism of the multinucleon transfer reactions. With the recent work, our continued efforts in the study of peripheral reactions in the Fermi energy regime delineate new opportunities to elucidate the reaction mechanism(s) of rare isotope production and may effectively contribute to the study of unexplored regions of the nuclear chart toward the r-process and the neutron drip line.

Microscopic dynamical description of multinucleon transfer in 40Ar induced peripheral collisions at 15 MeV/nucleon

This paper deals with heavy-ion peripheral reactions in the Fermi energy region for the production of neutron-rich isotopes. Experimental data of projectile fragments from the reactions of an 40Ar beam at 15 MeV/nucleon with 64Ni and 58Ni targets, collected with the MARS spectrometer at the Cyclotron Institute of Texas A&M University, are considered. Momentum distributions, which provide valuable information on the reaction mechanisms, are extracted and compared with two types of calculations: These are, the Deep Inelastic Transfer (DIT) model and the microscopic Constrained Molecular Dynamics model (CoMD). For the latter, the parameters of the original code were systematically varied in order to achieve an overall satisfactory description of the experimental data. Our results will be discussed.

Microscopic description of proton-induced spallation reactions with the constrained molecular dynamics (CoMD) model

We studied the complete dynamics of the proton-induced spallation process with the microscopic framework of the constrained molecular dynamics (CoMD) model. We performed calculations of proton-induced spallation reactions on 181Ta, 208Pb, and 238U targets with the CoMD model and compared the results with a standard two-step approach based on an intranuclear cascade model followed by a statistical deexcitation model. The calculations were also compared with recent experimental data from the literature. Our calculations showed agreement with some aspects of the experimental data and suggest further improvements in the models. We point out that this CoMD study represents the first complete dynamical description of spallation reactions with a microscopic N-body approach and may lead to advancements in the physics-based modeling of the spallation process.

Rare Isotope Production in peripheral heavy-ion collisions in the energy range 15-25 MeV/nucleon

In this contribution we summarize recent efforts to describe the production of rare isotopes with beams of 15–25 MeV/nucleon expected from low-energy facilities. We first present calculated production cross sections of proton-rich nuclides from collisions of stable beams of mass A∼60–80. Our calculations are performed with the phenomenological deep-inelastic transfer (DIT) model and the microscopic con- strained molecular dynamics model (CoMD). De-excitation of the excited quasipro- jectiles from the dynamical stage of the reaction is performed with the statistical multifragmentation model (SMM). In addition to the efforts on proton-rich nuclides, we investigated the possibility of producing neutron-rich rare isotopes in the mass range A∼180–200, i.e. near the third r-process peak of A=195. We performed calcu- lations for a 208Pb (15MeV/nucleon) beam and find that the multinucleon transfer mechanism leads to very neutron-rich nuclides in this mass range. We believe that our continued progress on the study of multinucleon transfer reactions using heavy- ion beams of 15–25 MeV/nucleon, can provide new opportunities in rare isotope research in the near future, as planned at the KOBRA facility of RISP in Korea.

Microscopic description of neutron-induced fission with the CoMD Model: Preliminary Results

In the present work, we initiated a systematic study of neutron-induced fission reactions using the code CoMD (Constrained Molecular Dynamics) of A. Bonasera and M. Papa [1,2]. The code implements an effective interaction with a nuclear-matter compressibility of K=200 (soft EOS) with several forms of the density-dependence of the nucleon symmetry potential. In addition, CoMD imposes a constraint in the phase space occupation for each nucleon restoring the Pauli principle at each time step of the collision). Proper choice of the surface parameter of the effective interaction has been made to describe fission. In this poster, we presented preliminary results of neutron-indued fission on 235U at neutron energies 5, 10, 15, 25, 50 and 100 MeV. Calculated mass and energy distributions are shown and compared with the recent experimental data of Loveland et al. [3]. It appears that the microscopic code CoMD is able to describe the complicated many-body dynamics of the n-induced fission process. Proper adjustment of the parameters of the effective interaction and further improvements of the code will be implemented to achieve a satisfactory description of the experiment data.

Systematic study of proton-induced spallation reactions with the Constrained Molecular Dynamics (CoMD) model

Proton – induced spallation reactions on 238U, 208Pb, 181Ta and 197Au targets at high energies were studied and investigated using the microscopic Contrained Molecular Dynamics (CoMD) model. Total fission cross sections, the ratio fission cross section to residue cross section, mean kinetic energy of fission fragments, mass yield curves and the number of nucleons emitted, before and after scission, as well as the total nucleon multiplicity were calculated using the CoMD model and compared with experimental data from the literature. Some of our calculations showed satisfactory agreement with available experimental data.The calculations of cross sections and the ratio fission cross section to residue cross section as a function of the proton energy gave us the opportunity to estimate observables for unmeasured nuclides.

Rare Isotope Production in peripheral heavy-ion collisions at beam energy of 15 MeV/nucleon

This paper presents our recent study on the production of neutron-rich rare isotopes with heavy-ion beams in the energy region of 15 MeV/nucleon. We present calculated production cross sections of neutron-rich nuclides from collisions of a 86Kr (15 MeV/nucleon) beam with 238U targets. Our calculations are based on a two-step approach: the dynamical stage of the collision is described with either the phenomenological Deep-Inelastic Transfer model (DIT), or with the microscopic Constrained Molecular Dynamics model (CoMD). The de-excitation of the hot heavy projectile fragments is performed with the Statistical Multifragmentation Model (SMM). We also performed calculations with a radioactive beam of 92Kr (15 MeV/nucleon) with a target of 238U and observed that the multinucleon transfer mechanism leads to very neutron-rich nuclides toward and beyond the astrophysical r-process path. In the future, we plan to experimentally investigate such reactions in the KOBRA spectrometer at the RISP facility in Korea. We conclude that the reaction mechanism at beam energies below the Fermi energy involving periph- eral nucleon exchange, constitutes a novel and effective route to access extremely neutron-rich isotopes toward the r-process path and the neutron drip-line.

Systematic Study of Neutron-Rich Rare Isotope Production in Peripheral Heavy-Ion Collisions at Beam Energies 15–25 MeV/nucleon

The production cross sections of projectile-like fragments from collisions of 86Kr projectiles with 64,58Ni and 124,112Sn targets at 15 and 25 MeV/nucleon are studied systematically with emphasis on the neutron-rich isotopes. Our recent experimental data are compared with calculations for the above collisions employing a hybrid approach. The dynamical stage of the projectile-target interaction was described with either the phenomenological deep-inelastic transfer (DIT) model or with the the microscopic constrained molecular dynamics model (CoMD). Subsequently, for the de-excitation of the projectile-like fragments, the statistical multifragmentation model (SMM) or the binary-decay code GEMINI were employed. An overall good agreement with the experimental results was obtained. We point out that our current understanding of the reaction mechanism at beam energies below the Fermi energy suggests that such nuclear reactions, involving peripheral nucleon exchange, can be exploited as a novel route to access extremely neutron-rich rare isotopes toward the r-process path and the hard-to-reach neutron drip-line. For this purpose, we believe that the use of re-accelerated neutron-rich radioactive beams may offer unique and exciting opportunities toward unexplored regions of the nuclear landscape.

Neutron-rich rare-isotope production from projectile fission of heavy nuclei near 20 MeV/nucleon beam energy

We investigate the possibilities of producing neutron-rich nuclides in projectile fission of heavy beams in the energy range of 20 MeV/nucleon expected from low-energy facilities. We report our efforts to theoretically describe the reaction mechanism of projectile fission following a multinucleon transfer collision at this energy range. Our calculations are mainly based on a two-step approach: the dynamical stage of the collision is described with either the phenomenological Deep-Inelastic Transfer model (DIT), or with the microscopic Constrained Molecular Dynamics model (CoMD). The deexcitation/fission of the hot heavy projectile fragments is performed with the Statistical Mul- tifragmentation Model (SMM). We compared our model calculations with our previous experimental projectile-fission data of 238U (20 MeV/nucleon)+208Pb and 197Au (20 MeV/nucleon)+197Au and found an overall reasonable agreement. Our study suggests that projectile fission following periph- eral heavy-ion collisions at this energy range offers an effective route to access very neutron-rich rare isotopes toward and beyond the astrophysical r-process path.

Symmetry energy dependence of long-timescale isospin transport

Isospin transport occurring within dinuclear projectile-like fragments (PLFs) produced in heavy- ion collisions is explored as a probe of the nuclear symmetry energy. Within the framework of the Constrained Molecular Dynamics model (CoMD), the existence of the long-lived dinuclear PLFs, for up to 800 fm/c, is observed. It is demonstrated that changes in the <N/Z> of the two fragments resulting from the breakup of the dinuclear PLF is due to isospin transport. The rate of the transport between the two fragments is shown to be dependent on the slope of the symmetry energy at saturation density. Comparison of the CoMD calculations with experimental data establish that the evolution of <N/Z> could be used to constrain the density dependence of the symmetry energy.

Systematic study of neutron-rich rare isotope production in peripheral heavy-ion collisions below the Fermi energy

Detailed calculations of the yields of projectilelike fragments (with focus on the neutron-rich isotopes) are presented for the interaction of $^{86}\mathrm{Kr}$ (15 MeV/nucleon) with $^{64}\mathrm{Ni}$, $^{58}\mathrm{Ni}$, and $^{124}\mathrm{Sn}$, $^{112}\mathrm{Sn}$, as well as $^{86}\mathrm{Kr}$ (25 MeV/nucleon) with $^{124}\mathrm{Sn}$ and compared with our recently published experimental data for these reactions. The calculations are based on a two-step approach: the dynamical stage of the collision was described with the microscopic constrained molecular dynamics (CoMD) model, as well as the phenomenological deep-inelastic transfer (DIT) model and its modified (DITm) version. The deexcitation of the hot projectile fragments was performed with the statistical multifragmentation model (SMM) and the binary-decay model gemini, which provided nearly similar results for the neutron-rich products from the reactions studied. An overall good agreement of the calculations with the experimental results, especially for near-projectile isotopes was observed using both the CoMD model and the DITm model for the dynamical stage. The successful description of the production of neutron-rich isotopes with the CoMD model is of particular importance, due to the predictive power of the microscopic approach that essentially does not depend on the reaction dynamics. Our studies to date suggest that peripheral heavy-ion collisions at this energy range (i.e., well above the Coulomb barrier, but below the Fermi energy), if induced by neutron-rich rare-isotope beams of adequate intensity may offer a unique route to access extremely neutron-rich rare isotopes toward the astrophysical $r$-process path and the presently uncharted neutron drip line.

Exploiting neutron-rich radioactive ion beams to constrain the symmetry energy

The Modular Neutron Array (MoNA) and 4 Tm Sweeper magnet were used to measure the free neutrons and heavy charged particles from the radioactive ion beam induced 32Mg + 9Be reaction. The fragmentation reaction was simulated with the Constrained Molecular Dynamics model(CoMD), which demonstrated that the <N/Z> of the heavy fragments and free neutron multiplicities were observables sensitive to the density dependence of the symmetry energy at sub-saturation densities. Through comparison of these simulations with the experimental data constraints on the density dependence of the symmetry energy were extracted. The advantage of radioactive ion beams as a probe of the symmetry energy is demonstrated through examination of CoMD calculations for stable and radioactive beam induced reactions.

Approaching neutron-rich nuclei toward ther-process path in peripheral heavy-ion collisions at 15 MeV/nucleon

The production cross sections of projectilelike fragments from the interaction of 15 MeV/nucleon ${}^{86}$Kr with ${}^{64}$Ni and ${}^{58}$Ni and with ${}^{124}$Sn and ${}^{112}$Sn were measured using a magnetic separator with emphasis on the neutron-rich isotopes. Neutron pickup isotopes (with up to six neutrons picked up from the target) were observed with large cross sections. Calculations involving the the deep-inelastic transfer model as well as the microscopic constrained molecular dynamics model (CoMD) for the primary interaction stage coupled to the statistical deexcitation code gemini were used to describe the gross properties of the product distributions. The present results were also compared with our previous data of the same reactions at 25 MeV/nucleon. The data at 15 MeV/nucleon show enhanced production of neutron-rich isotopes very close to the projectile, relative to the corresponding data at 25 MeV/nucleon. This enhancement in the cross sections is possibly associated with very peripheral collisions and longer interaction times of the neutron-rich ${}^{86}$Kr projectile with the neutron-rich targets. The large cross sections of such reactions well above the Coulomb barrier, but below the Fermi energy, involving peripheral nucleon exchange, suggest that both the $N\text{/}Z$ of the projectile and the $N\text{/}Z$ of the target may properly be exploited in the production of neutron-rich rare isotopes. These reactions offer a novel and attractive route to access extremely neutron-rich rare isotopes toward the the astrophysical $r$-process path and, possibly, the neutron drip-line.

Density and temperature of bosons from quantum fluctuations

A method to determine the density and temperature of a system is proposed based on quantum fluctuations typical of Bosons in the limit where the reached temperature T is close to the critical temperature $T_c$ for a Bose condensate at a given density $\rho$. Quadrupole and particle multiplicity fluctuations relations are derived in terms of $\frac{T}{T_c}$. This method is valid for weakly interacting infinite and finite Boson systems. As an example, we apply it to heavy ion collisions using the Constrained Molecular Dynamics (CoMD) approach which includes the Fermi statistics. The model shows some clusterization into deuteron and ${\alpha}$ clusters which could suggest a Bose condensate. However, our approach demonstrates that in the model there is no Bose condensate but it gives useful informations to be tested experimentally. We stress the differences with methods based on classical approximations. The derived 'quantum' temperatures are systematically higher than the corresponding 'classical' ones. The role of the Coulomb charge of fragments is discussed.