Intermediate Energy Heavy Ion Reactions Research Articles

Semirelativistic antisymmetrized molecular dynamics for the production of energetic neutrons in intermediate-energy heavy-ion reactions

Semirelativistic antisymmetrized molecular dynamics for the production of energetic neutrons in intermediate-energy heavy-ion reactions

Principal Component Analysis of azimuthal flow in intermediate-energy heavy-ion reactions

Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event single-particle azimuthal angle distribution matrices in ultra-relativistic heavy-ion collisions at RHIC-LHC energies indicate that the sine and cosine functions chosen a priori in the traditional Fourier analysis are naturally the most optimal basis for azimuthal flow studies according to the data itself. We perform PCA-SVD analyses of mid-central Au+Au collisions at Ebeam/A=1.23 GeV simulated using an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model to address the following two questions: (1) if the principal components of the covariance matrix of nucleon azimuthal angle distributions in heavy-ion reactions around 1 GeV/nucleon are naturally sine and/or cosine functions and (2) what if any advantages the PCA-SVD may have over the traditional flow analysis using the Fourier expansion for studying the EOS of dense nuclear matter. We find that (1) in none of our analyses the principal components come out naturally as sine and/or cosine functions, (2) while both the eigenvectors and eigenvalues of the covariance matrix are appreciably EOS dependent, the PCA-SVD has no apparent advantage over the traditional Fourier analysis for studying the EOS of dense nuclear matter using the azimuthal collective flow in heavy-ion collisions.

Intermediate Energy Reactions Versus Heavy-Ion Fusion: Light Particle Emission and Post-Saddle Friction in the Presence of Deformation Effects**Supported by the National Nature Science Foundation of China under Grant No. 11575044 and the Foundation of Nanjing University of Finance & Economics under Grant No. JGY1859

A decaying nucleus undergoes a change in deformation when it fissions. This affects the particle emission in the fission process. Using the dynamical Langevin model, we investigate the role of deformation in the sensitivity of post-saddle neutrons and light charged particles (LCPs) to the post-saddle friction strength (β) for heavy nuclei 240Am produced with different initial conditions: (i) a low excitation energy E* and a large spin ℓ (provided via a fusion mechanism) and (ii) a high E* and a large ℓ as well as a higher E* but a small ℓ (provided in peripheral and near-central intermediate energy heavy-ion reactions, respectively). It is shown that deformation obviously enhances the sensitivity of post-saddle neutrons to β at intermediate-energy peripheral collisions and that for case (i), the drop of LCPs emission due to deformation makes post-saddle LCPs to be almost insensitive to β, but for case (ii) LCPs still have a significant change with β. Furthermore, we find that post-saddle LCPs display a greater sensitivity to β for near-central collisions than for peripheral collisions. These results suggest that given the deformation effects, to better probe post-saddle dissipation properties with neutrons (LCPs) in experiments, it is best to choose those excited heavy nuclear systems populated in peripheral (near-central) collisions at intermediate energies.

Dynamical effects of spin-dependent interactions in low- and intermediate-energy heavy-ion reactions

It is well known that non-central nuclear forces, such as the spin-orbital coupling and the tensor force, play important roles in understanding many interesting features of nuclear structures. However, their dynamical effects in nuclear reactions are poorly known since only the spin-averaged observables are normally studied both experimentally and theoretically. Realizing that spin-sensitive observables in nuclear reactions may carry useful information about the in-medium properties of non-central nuclear interactions, besides earlier studies using the time-dependent Hartree-Fock approach to understand effects of spin-orbital coupling on the threshold energy and spin polarization in fusion reactions, some efforts have been made recently to explore dynamical effects of non-central nuclear forces in intermediate-energy heavy-ion collisions using transport models. The focuses of these studies have been on investigating signatures of the density and isospin dependence of the form factor in the spin-dependent single-nucleon potential. Interestingly, some useful probes were identified in the model studies while so far there is still no data to compare with. In this brief review, we summarize the main physics motivations as well as the recent progress in understanding the spin dynamics and identifying spin-sensitive observables in heavy-ion reactions at intermediate energies. We hope the interesting, important, and new physics potentials identified in the spin dynamics of heavy-ion collisions will stimulate more experimental work in this direction.

Freezeout concept and dynamical transport model in intermediate-energy heavy-ion reactions

For the central collision events of ${}^{40}\mathrm{Ca}\phantom{\rule{4pt}{0ex}}+{\phantom{\rule{0.16em}{0ex}}}^{40}\mathrm{Ca}$, generated by an antisymmetrized molecular dynamics model in the intermediate energy range of 35 to 300 MeV/nucleon, the density and temperature of a fragmenting source have been extracted using a self-consistent method with the modified Fisher model. Rather flat density values, $\ensuremath{\rho}/{\ensuremath{\rho}}_{0}\ensuremath{\sim}0.65$ to 0.7, are evaluated at the incident energies studied, even though the maximum density of the system achieved during the collisions increases monotonically from $\ensuremath{\rho}/{\ensuremath{\rho}}_{0}\ensuremath{\sim}1.3$ at 35 MeV/nucleon to 1.8 at 300 MeV/nucleon. Flat temperature values of $T\ensuremath{\sim}5.9$ to 6.5 MeV are also extracted in this incident energy range. These extracted values indicate that, in average, intermediate mass fragments are formed at a later stage when the hot nuclear matter reaches at a ``freezeout'' volume by the expansion, which is not assumed in any transport models, but assumed generally in statistical multifragmentation models. This is the first time to demonstrate quantitatively a direct connection between the freezeout concept and transport model simulations in a multifragmenting regime of heavy ion collisions.

On the angular distribution of intermediate-energy heavy-ion reactions based on a simple model

On the angular distribution of intermediate-energy heavy-ion reactions based on a simple model

A direct probe of the in-medium pn scattering cross section

Hard photon production from neutron–proton bremsstrahlung in intermediate energy heavy-ion reactions is examined as a probe of the in-medium pn scattering cross section within a transport model. Uncertainty of photon production probability pn→pnγ is cancelled out by using the ratio of hard photon spectra RC12+C12/p+n(γ) from two reactions. The in medium pn scattering cross section is constrained by using the ratio of hard photon production cross sections of proton-induced reactions p+C12 and p+H2. A reduction factor σpnmedium/σpnfree of about 0.5–0.7 around saturation density is obtained by comparing with the existing experimental data.

Isospin- and momentum-dependent effective interactions for the baryon octet and the properties of hybrid stars

The isospin- and momentum-dependent MDI interaction, which has been extensively used in intermediate-energy heavy-ion reactions to study the properties of asymmetric nuclear matter, is extended to include the nucleon-hyperon and hyperon-hyperon interactions by assuming same density, momentum and isospin dependence as for the nucleon-nucleon interaction. The parameters in these interactions are determined from the empirical hyperon single-particle potentials in symmetric nuclear matter at saturation density. The extended MDI interaction is then used to study in the mean-field approximation the equation of state of hypernuclear matter and also the properties of hybrid stars by including the phase transition from the hypernuclear matter to the quark matter at high densities. In particular, the effects of attractive and repulsive $\Sigma$N interactions and different values of symmetry energies on the hybrid star properties are investigated.

Neutron–proton bremsstrahlung from intermediate energy heavy-ion reactions as a probe of the nuclear symmetry energy?

Hard photons from neutron–proton bremsstrahlung in intermediate energy heavy-ion reactions are examined as a potential probe of the nuclear symmetry energy within a transport model. Effects of the symmetry energy on the yields and spectra of hard photons are found to be generally smaller than those due to the currently existing uncertainties of both the in-medium nucleon–nucleon cross sections and the photon production probability in the elementary process pn→pnγ. Very interestingly, nevertheless, the ratio of hard photon spectra R1/2(γ) from two reactions using isotopes of the same element is not only approximately independent of these uncertainties but also quite sensitive to the symmetry energy. For the head-on reactions of 132Sn + 124Sn and 112Sn + 112Sn at Ebeam/A=50 MeV, for example, the R1/2(γ) displays a rise up to 15% when the symmetry energy is reduced by about 20% at ρ=1.3ρ0 which is the maximum density reached in these reactions.

Nuclear spin polarization following intermediate-energy heavy-ion reactions

Intermediate-energy heavy-ion collisions can produce a spin polarization of the projectile-like species. Spin polarization has been observed for both nucleon removal and nucleon pickup processes. Qualitative agreement with measured spin polarization as a function of the momentum of the projectile-like fragment is found in a kinematic model that considers conservation of linear and angular momentum and assumes peripheral interactions between the fast projectile and target. Better quantitative agreement was reached by including more realistic angular distributions and deorientation caused by {gamma}-ray emission and by correcting for the out-of-plane acceptance. The newly introduced corrections were found to apply to both nucleon removal and nucleon pickup processes.

Equation of state of isospin-asymmetric nuclear matter in relativistic mean-field models with chiral limits

Using in-medium hadron properties according to the Brown–Rho scaling due to the chiral symmetry restoration at high densities and considering naturalness of the coupling constants, we have newly constructed several relativistic mean-field Lagrangians with chiral limits. The model parameters are adjusted such that the symmetric part of the resulting equation of state at supra-normal densities is consistent with that required by the collective flow data from high energy heavy-ion reactions, while the resulting density dependence of the symmetry energy at sub-saturation densities agrees with that extracted from the recent isospin diffusion data from intermediate energy heavy-ion reactions. The resulting equations of state have the special feature of being soft at intermediate densities but stiff at high densities naturally. With these constrained equations of state, it is found that the radius of a 1.4 M ⊙ canonical neutron star is in the range of 11.9 km ⩽ R ⩽ 13.1 km , and the maximum neutron star mass is around 2.0 M ⊙ close to the recent observations.

Isospin effects on two-particle correlation functions in intermediate energy heavy ion reactions

Isospin effects on two-particle correlation functions in intermediate energy heavy ion reactions

Chronology of neutron, proton and deuteron emission in intermediate energy heavy ion reactions

Chronology of neutron, proton and deuteron emission in intermediate energy heavy ion reactions

Chronology of neutron, proton and deuteron emission in intermediate energy heavy ion reactions

The CHIC Collaboration has performed a series of fermion interferometry experiments to study the space-time evolution of the emission sources in intermediate energy heavy ion reactions. Correlation functions of non-identical particles have allowed us to extract model independent information on the sequence of emission (chronology) of the particles. In this contribution, we discus the order of emission of neutrons, protons and deuterons from the E/A = 61 MeV 36Ar + 27Al, 112Sn and P 124Sn reactions.

Isospin effects on two-particle correlation functions in intermediate energy heavy ion reactions

Exclusive data from an intensity interferometry experiment are presented, where, for the first time, the technique of two-nucleon correlation functions is applied to isotopically selected data, with the aim to study the isospin dependence of the nuclear equation of state (EOS). The different correlation function strength, observed for two isotopically separated systems, E/A=61 MeV 36Ar+ 112Sn, 124Sn, is not explainable in terms of system size, and is attributed to the different isospin content. This experimental finding supports theoretical predictions based on isospin dependent transport models, and demonstrates that intensity interferometry is a promising tool to study the isospin dependence of the EOS.

Isospin effects in nuclear fragmentation

The availability of radioactive heavy-ion beams has driven a large interest in studies of nuclear structure of unstable nuclei. Some essential information in this field can come from investigations of charge asymmetry effects on nonequilibrium dynamics. It is therefore very important to understand the properties of the symmetry term in the nuclear matter equation of state. The purpose of this work is to extract valuable information about the symmetry term in the nuclear equation of state by studying the multifragmentation processes occurring during intermediate-energy heavy-ion reactions. We will concentrate on those observables in fragment production that are particularly sensitive to the symmetry term. The calculations are performed within the semiclassical Boltzmann-Uehling-Uhlenbeck approach with the inclusion of nuclear density fluctuations. We consider neutron-poor and neutron-rich Sn + Sn reactions at 50 MeV/A, with the N/Z ratio varying from 1.24 to 1.48. Both central and peripheral collisions are investigated. Some comparison with the experimental data obtained in the National Superconducting Cyclotron Laboratory at Michigan State University is presented.

Particle emission time sequence in intermediate energy heavy ion reactions

The CHIC Collaboration has performed a series of simultaneous pp, np and nn fermion interferometry experiments in order to study the space-time evolution of the emission sources in intermediate energy heavy ion reactions. Furthermore, when correlations of non-identical particles are available, additional model independent information on the emission chronology of the particles is obtained. In this contribution, after reviewing the method to determine the order of emission of non-identical particles, we discuss the emission chronology of neutrons and protons from the E/A = 45 MeV 58Ni + 27Al reaction and from the E/A = 60 MeV 36Ar + 27Al reaction, shown here for the first time.

Spin polarization of 37K produced in a single-proton pickup reaction at intermediate energies.

Spin polarization of 37K nuclei produced via single proton pickup from a 9Be target by a beam of 150 MeV/nucleon 36Ar has been observed. Positive spin polarization with magnitude (8.5+/-0.6)% was deduced near the peak of the 37K momentum distribution. The variation of the spin polarization as a function of outgoing 37K momentum is explained by a classical conservation model, as previously applied to describe the induced spin polarization observed for fragments produced in intermediate-energy heavy-ion reactions, with the condition that the picked-up proton has an average momentum equal to the Fermi momentum and is aligned along the incident beam direction.

Thermal bremsstrahlung photons probing the nuclear caloric curve

Hard-photon ( E γ > 30 MeV) emission from second-chance nucleon–nucleon bremsstrahlung collisions in intermediate energy heavy-ion reactions is studied employing a realistic thermal model. Photon spectra and yields measured in several nucleus–nucleus reactions are consistent with an emission from hot nuclear systems with temperatures T≈4–7 MeV. The corresponding caloric curve in the region of excitation energies ϵ ★≈3 A–8 A MeV shows lower values of T than those expected for a Fermi fluid.

Role of the nuclear surface in the formation of total cross sections for heavy-ion reactions

Within the Glauber-Sitenko approach, a procedure for calculating cross sections for intermediate-energy heavy-ion reactions is developed by using the analytic form of the eikonal phase for the symmetrized Woods-Saxon potential. The differential and total cross sections obtained on this basis comply well with the results derived by numerically solving the wave equation. A clear and instructive model of the phase is constructed, which makes it possible to separate, in total reaction cross sections, the contributions of the internal and the peripheral region of interaction. It is found that the nuclear surface plays an important role in the formation of reaction cross sections, and the effect of the Coulomb field on these cross sections is investigated. The origin of a continuous ambiguity in optical potentials is revealed in interpreting total cross sections.