Preequilibrium Nucleon Research Articles

Unexpected neutron/proton ratio and isospin effect in low-energy antiproton-induced reactions

The inclusive spectra of preequilibrium nucleons produced in low-energy antiproton-nucleus collisions are thoroughly investigated within the framework of the Lanzhou quantum molecular dynamics model for the first time. All possible reaction channels such as elastic scattering, annihilation, charge exchange and inelastic scattering in antibaryon-baryon, baryon-baryon and meson-baryon collisions have been included in the transport model. The unexpected neutron/proton ratio in comparison to the pion and proton induced reactions is caused from the isospin effects of pion-nucleon collisions and the density dependence of symmetry energy. It is found that the $\pi^{-}$-neutron collisions enhance the neutron emission in the antiproton annihilation in a nucleus. Different to heavy-ion collisions, the isospin effects are pronounced at the low kinetic energies. A soft symmetry energy with the stiffness of $\gamma_{s}=$0.5 at subsaturation densities is constrained from the available data of the neutron/proton spectra.

Pre-equilibrium effects in charge-asymmetric low-energy reactions

We study the pre-equilibrium dipole response in the charge-asymmetric reaction Sn132+Ni58 at Elab=10 MeV/A, within a semi-classical transport model employing effective interactions for the nuclear mean-field. In particular, we adopt the recently introduced SAMi-J Skyrme interactions, whose parameters are specifically tuned to improve the description of spin–isospin properties of nuclei. Within the same framework, we also discuss pre-equilibrium nucleon emission. Our results show that both mechanisms, i.e., pre-equilibrium dipole oscillations and nucleon emission, are sensitive to the symmetry energy below the saturation density ρ0 (in the range 0.6ρ0−ρ0), to the momentum dependence of the mean-field potential and to the nucleon–nucleon cross section. Finally, a correlation analysis is applied to examine the impact of the model parameters on observables of experimental interest.

Probing the momentum dependence of the symmetry potential by the freen/pratio of pre-equilibrium emission

Based on an isospin and momentum-dependent transport model, we studied the effect of momentum-dependent symmetry potential on the free neutron to proton ratio of preequilibrium nucleon emission. It is found that for $^{132}Sn+^{124}Sn$ reaction at 400 MeV/nucleon incident beam energy, free n/p ratio of preequilibrium nucleon emission mainly probe the momentum-dependence of symmetry potential at nucleon momentum around 400 $\sim$ 600 MeV/c. Whereas for 200 MeV/nucleon incident beam energy, this observable mainly probe the momentum-dependence of symmetry potential at nucleon momentum around 200 $\sim$ 400 MeV/c. To probe the symmetry energy/potential using free n/p ratio, not all the details of the momentum-dependence of the symmetry potential are important, the values of symmetry potential at only certain momentum range are crucial for an observable. It is important to input reasonable density- and momentum-dependence of the symmetry potential according to the magnitude of incident beam energy of heavy-ion collisions. The present experimental data on the symmetry potential are not enough for probing the density-dependent symmetry energy. More experimental data (such as nucleon and nuclei's scattering experiments at different nucleonic momenta and densities) on the symmetry potential are therefore needed to pin down the density-dependent symmetry energy.

Disentangling effects of collision geometry and symmetry energy in U+U collisions

Effects of the collision geometry on experimental observables that are known to be sensitive to the high-density behavior of nuclear symmetry energy are examined in U $+$ U collisions at 0.52 GeV/nucleon using an isospin- and momentum-dependent interaction within the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model. It is found that the neutron-proton differential flow in tip-tip collisions and the difference of neutron and proton elliptic flow in body-body collisions are more sensitive to the symmetry energy at suprasaturation densities compared with collisions of spherical nuclei of the same masses. In addition, the $n/p$ ratio of preequilibrium nucleons is found to be slightly more sensitive to the symmetry energy in tip-tip collisions, and the collision geometry affects the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio significantly.

Transverse emission of isospin ratios as a probe of high-density symmetry energy in isotopic nuclear reactions

Transverse emission of preequilibrium nucleons, light clusters (complex particles) and charged pions from the isotopic Sn112,124+Sn112,124 reactions at a beam energy of 400 A MeV, to extract the high-density behavior of nuclear symmetry energy, are investigated within an isospin and momentum-dependent transport model. Specifically, the double ratios of neutron/proton, triton/helium-3 and π−/π+ in the squeeze-out domain are analyzed systematically, which are favorable in reducing the influence of the Coulomb force and less systematic errors. It is found that the transverse momentum distribution of isospin ratios strongly depend on the stiffness of nuclear symmetry energy, which would be a nice observable to extract the high-density symmetry energy. The collision centrality and the mass splitting of neutron and proton in nuclear medium play a significant role on the distribution structure of the ratios, but do not change the influence of symmetry energy on the spectrum.

Description of Nucleon Induced Fission in Intranuclear Cascade -Multiparticle Preequilibrium - Hauser-Feshbach Approach

The MCFx code system for the description of neutron- and proton-induced fission of heavy nu- clei in energy region 20-3000 MeV is presented. The approach integrates the optical model for reaction cross- section calculations, intranuclear cascade for description of fast particle escape, exciton model for multipar- ticle emission of preequilibrium nucleons and Hauser-Feshbach calculations for statistical description of fis- sion/evaporation competition. New results of systematic calculations of fission cross-sections, multiplicities and double-di erential spectra of secondary particles for Pb-Cm targets irradiated by neutrons and protons with en- ergy 20-3000 MeV are discussed.

Fast nucleon emission as a probe of the momentum dependence of the symmetry potential

In this article we investigate the structure of the non-local part of the symmetry term, that leads to a splitting of the effective masses of protons and neutrons in asymmetric matter. Based on microscopic transport simulations we suggest some rather sensitive observables in collisions of neutron-rich (unstable) ions at intermediate ($RIA$) energies. In particular we focus the attention on pre-equilibrium nucleon emissions. We discuss interesting correlations between the N/Z content of the fast emitted particles and their rapidity or transverse momentum, that show a nice dependence on the prescription used for the effective mass splitting.

Effects of in-medium cross sections and optical potential on thermal-source formation inp+Au197reactions at6.2–14.6GeV∕c

Effects of in-medium cross sections and of optical potential on preequilibrium emission and on formation of a thermal source are investigated by comparing the results of transport simulations with experimental results from the $p+^{197}\mathrm{Au}$ reaction at $6.2--14.6\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}∕c$. The employed transport model includes light-composite-particle production and allows for inclusion of in-medium particle-particle cross-section reduction and of momentum dependence in the particle optical potentials. Compared to the past, the model incorporates improved parametrizations of elementary high-energy processes. The simulations indicate that the majority of energy deposition occurs during the first $25\phantom{\rule{0.3em}{0ex}}\mathrm{fm}∕c$ of a reaction. This is followed by a preequilibrium emission and readjustment of system density and momentum distribution toward an equilibrated system. Within different variants of calculations, the best agreement with data, on the $d∕p$ and $t∕p$ yield ratios and on the residue mass and charge numbers, is obtained at the time of about $65\phantom{\rule{0.3em}{0ex}}\mathrm{fm}∕c$ from the start of a reaction, for simulations employing reduced in-medium cross sections and momentum-dependent optical potentials. By that time, the preequilibrium nucleon and cluster emission, as well as mean field readjustments, drive the system to a state of depleted average density, $\ensuremath{\rho}∕{\ensuremath{\rho}}_{0}\ensuremath{\sim}1∕4--1∕3$ for central collisions, and low-to-moderate excitation, i.e., the region of nuclear liquid-gas phase transition.

Lead (Pb) in the C-rich, s-process rich, metal poor subgiant LP625-44

Using isospin-dependent quantum molecular dynamical model, the studies of the isospin effect of preequilibrium nucleon emission in heavy-ion collisions under different entrance channel conditions show that the ratio of preequilibrium neutron number to proton number depends strongly on symmetry potential, beam energy, and the ratio of neutron to proton of the colliding system, but weakly on isospin-dependent in-medium nucleon–nucleon cross sections, impact parameter, Pauli potential, and momentum-dependent interaction in the energy region from 45 MeV/u up to 150 MeV/u where the dynamics is dominated by nucleon–nucleon collisions. In addition, the ratio of preequilibrium neutron number to proton number for a neutron-rich colliding system is larger than the initial value of the ratio of the colliding system, but the ratio for a neutron-deficient system is less than the initial value.

Entrance channel dependence and isospin dependence of preequilibrium nucleon emission in intermediate energy heavy ion collisions

Using isospin-dependent quantum molecular dynamical model, the studies of the isospin effect of preequilibrium nucleon emission in heavy-ion collisions under different entrance channel conditions show that the ratio of preequilibrium neutron number to proton number depends strongly on symmetry potential, beam energy, and the ratio of neutron to proton of the colliding system, but weakly on isospin-dependent in-medium nucleon–nucleon cross sections, impact parameter, Pauli potential, and momentum-dependent interaction in the energy region from 45 MeV/u up to 150 MeV/u where the dynamics is dominated by nucleon–nucleon collisions. In addition, the ratio of preequilibrium neutron number to proton number for a neutron-rich colliding system is larger than the initial value of the ratio of the colliding system, but the ratio for a neutron-deficient system is less than the initial value.

Angular distribution of preequilibrium neutron emissions from heavy-ion reactions

The angular distribution of preequilibrium nucleons emitted in low- and medium-energy heavy-ion reactions is determined from the kinematics of nucleon-nucleon scattering inside the nuclear matter. In calculating the scattering kernels the excitation of the nuclear matter has been taken into account through a finite-temperature Fermi distribution of the nucleons. Neutron angular distribution in ${}^{12}{\mathrm{C}+}^{165}\mathrm{Ho}$ reaction at 300 MeV incident energy and ${}^{20}{\mathrm{N}+}^{165}\mathrm{Ho}$ reaction at 600 MeV is calculated from two-body scattering kinematics and compared with the experimental data. The present calculations reproduce the experimental data fairly well in both cases. It has been found that in heavy-ion reactions the initial distribution of nucleons plays a significant role in determining the angular distributions.

Isospin Physics in Heavy-Ion Collisions at Intermediate Energies

In nuclear collisions induced by stable or radioactive neutron-rich nuclei a transient state of nuclear matter with an appreciable isospin asymmetry as well as thermal and compressional excitation can be created. This offers the possibility to study the properties of nuclear matter in the region between symmetric nuclear matter and pure neutron matter. In this review, we discuss recent theoretical studies of the equation of state of isospin-asymmetric nuclear matter and its relations to the properties of neutron stars and radioactive nuclei. Chemical and mechanical instabilities as well as the liquid-gas phase transition in asymmetric nuclear matter are investigated. The in-medium nucleon-nucleon cross sections at different isospin states are reviewed as they affect significantly the dynamics of heavy ion collisions induced by radioactive beams. We then discuss an isospin-dependent transport model, which includes different mean-field potentials and cross sections for the proton and neutron, and its application to these reactions. Furthermore, we review the comparisons between theoretical predictions and available experimental data. In particular, we discuss the study of nuclear stopping in terms of isospin equilibration, the dependence of nuclear collective flow and balance energy on the isospin-dependent nuclear equation of state and cross sections, the isospin dependence of total nuclear reaction cross sections, and the role of isospin in preequilibrium nucleon emissions and subthreshold pion production.

Nonlocality and polarizability in the fusion of Fermi droplets

The fusion of heavy ions at energies around the barrier is analysed within the framework of semiclassical mean-field transport theory. The paths connecting entrance and exit subbarrier fusion reaction channels are found by incorporating the Wick transformation into the mean-field kinetic equation. The polarization and deformation of nuclei is shown to lower the barrier height at near-barrier energies as compared to the well above barrier collisions. It is demonstrated that preequilibrium nucleon exchange in classically forbidden region gives rise to the nonlocal effects lowering the effective mass of translational motion at smaller relative distances. These effects together show a good fit to 58 Ni+ 58 Ni experimental data.

The isotopic effect as a clock for nuclear fragmentation

Experimental ratios between the emission rates of light fragments (Li, Be, B and C) from 112,(116)Sn and 124Sn targets are compared to predictions from a model which combines the Boltzmann master equation to describe the dynamics and preequilibrium particle emission and the statistical multifragmentation model to describe the final breakup. Since secondary decay and the choice of freeze-out volume affect these ratios very little this comparison can be used to estimate the excitation energy at the instant of fragmentation in a self-consistent way. The preequilibrium nucleon emission governs the time dependence of the excitation energy available for fragment production which is nearly the same for all Sn isotopes. Therefore the yield ratios can be used to estimate the fragmentation time. Data from 1 GeV proton- and 200 MeV 4He induced reactions indicate short fragmentation times - 20-40 fm/c while 32 A MeV 14N induced reactions seems to exhibit much longer times - 300-400 fm/c.

Study of the reactions occurring in the fusion of 12C and 16O with heavy nuclei at incident energies below 10 MeV/nucleon.

The excitation functions for production of many residues in the fusion of $^{12}\mathrm{C}$ with $^{181}\mathrm{Ta}$ and $^{197}\mathrm{Au}$ and of $^{16}\mathrm{O}$ with $^{165}\mathrm{Ho}$ and $^{181}\mathrm{Ta}$ have been measured at incident energies varying from the Coulomb barrier up to about 10 MeV/nucleon. The cross sections for fusion of these ions without fission have been deduced and they show that such a process may only occur for projectile angular momenta smaller than a critical value. The excitation functions for individual reactions provide evidence for the emission of preequilibrium nucleons during the thermalization of the composite nucleus and may be satisfactorily reproduced by a calculation based on the Boltzmann master equation theory.

Quantum molecular dynamics and multistep-direct analyses of multiple preequilibrium emission.

We study multiple preequilibrium emission in nucleon induced reactions at intermediate energies, and compare quantum molecular dynamics (QMD) calculations with multistep-direct Feshbach-Kerman-Koonin results [M. B. Chadwick, P. G. Young, D. C. George, and Y. Watanabe, Phys. Rev. C 50, 996 (1994)]. When the theoretical expressions of this reference are reformulated so that the definitions of primary and multiple emission correspond to those used in QMD, the two theories yield similar results for primary and multiple preequilibrium emission. We use QMD as a tool to determine the multiplicities of fast preequilibrium nucleons as a function of incident energy. For fast particle cross sections to exceed 5% of the inclusive preequilibrium emission cross sections we find that two particles should be included in reactions above 50 MeV, three above about 180 MeV, and four are only needed when the incident energy exceeds about 400 MeV.

Pre-equilibrium nucleon and alpha-particle emission in the alpha-particle-induced reactions on heavy nuclei

Alpha-particle-induced reactions on the target element gold were investigated from 30 to 75 MeV, using stacked-foil activation technique and Ge(Li) gamma-ray spectroscopy method. Six excitation functions for reactions of the type197Au(α,xn),x=1–3,197Au(α, 2pn) and197Au(α, αxn),x=1–3, were studied, of which five new data points and a new reaction were added to the existing data. The experimental cross-section were compared with the predictions of pre-equilibrium hybrid model, as well as the more recent index model using the initial exciton number,n0=4(4p0h). It was observed that both models show better agreement in respect of (α,xn)-type reactions. However, they are equally bad for the reactions emitting protons and alpha-particles, and for which some direct reaction contributions are indicated.

Effects of pre-equilibrium nucleon emission on excitation functions of various reactions in vanadium induced by alpha particles

Excitation functions for the 51V(( alpha ,n), ( alpha ,3n), ( alpha ,p3n), ( alpha ,p6n), ( alpha , alpha 3n), ( alpha , alpha 2pn), ( alpha ,2 alpha ), ( alpha ,2 alpha n) and ( alpha ,2 alpha 3n)) reactions have been measured up to 120 MeV using the stacked foil technique with a view to improving the quality of data, which were measured with poor resolution scintillation and Ge(Li) detectors some 20 years ago. The reaction V( alpha ,p6n) is measured for the first time. The experimental results are compared with calculations considering equilibrium as well as pre-equilibrium reactions according to the hybrid model of Blann(1984). A broad general agreement is observed between the experimental results and theoretical predictions with an initial exciton configuration of n0=(4p0h).

Fast neutrons from annihilation

We analyzed experimental data on fast neutron production in ¯p+64Cu and ¯p+238U annihilation and the ratio of231Th/231Ac isotopes from ¯p+232Th annihilation at rest. The contributions from standard reaction channels are calculated by cascade model. The annihilation pion rescattering and absorption in nuclear medium as well as the preequilibrium nucleon emission were analyzed. The calculation based on the assumption that neutron density distribution ≡uals the proton one multiplied by factor N/Z does not reproduce the experimental data. We discussed the influence of the neutron density distribution on fast neutron and isotope production. It was found that the hypothesis of the neutron halo allows one to get a reasonable description of the experimental data.

Neutron skin effect in preequilibrium nucleon emissions.

The geometry-dependent hybrid model of preequilibrium nuclear reactions is used together with the droplet model description of neutron and proton densities to investigate the effect of excess surface neutrons on the nucleon emission spectra. It is found that in alpha-particle--induced reactions the effect of neutron-skin on nucleon emission spectra is negligible. For nucleon-induced reactions the effect is more significant but not strong enough to remove the discrepancies between calculation and experiment.