The threshold anomaly and the effective interaction for nuclear nonelastic scattering

Previously, a dispersion relation has been used to elucidate the energy dependence of one-channel optical potentials, especially the “threshold anomaly” that is observed at low energies. We show that this dispersion relation is also applicable to the elements of the potential matrix which is needed for a coupled-channels treatment. Consequently, the off-diagonal couplings which produce nonelastic transitions may also exhibit such anomalies. We discuss how the energy dependences of the various matrix elements may be related, and provide some arguments that the potential in an excited state is similar to that in the ground state evaluated at a bombarding energy reduced by the excitation energy. We also examine the collective, or deformed potential, model to see whether the way it is commonly applied is consistent with the dispersion relation.     

Analyses of Relativistic Optical Potential for Medium Energy Proton

The influence of the parameters of the relativistic optical potential on the nucleon scattering properties,such as cross sections,angular distributions and spin observables etc.,is studied based on a set of global Dirac phenomenological optical potentials.It is shown that,in contrast with the case at low energies.the total scattering cross sections vary slowly as the energy and weakly depend on the potentials at E_p<200MeV.The differential cross sections and spin observables depend not only on the volume integrals of the optical potentials,but also on their strengths and shapes.The applicability of the relativistic microscopic optical potentia based on Walecka model in the medium energy region is also discussed in this paper.     

INDRA 能区重离子输运过程的系统研究及对称能探测

基于改进的极端相对论量子分子动力学(UrQMD) 输运模型,通过细致考察初始化、状态方程及两体碰撞等系统研究了INDRA 能区重离子碰撞后出射的自由核子及轻粒子的集体流和核阻止本领等观测量。研究发现,一个采用带动量依赖的软的状态方程及动量修正的密度依赖的核子核子弹性散射截面的动力学输运过程能够很好描述INDRA 全能域内实验获得的中心快度区的氢同位素的直接流。利用该套输运系统还研究了直接流平衡能对对称势能密度依赖强度因子的敏感性。发现,出射的自由中子平衡能敏感依赖于对称势能的密度依赖,而自由质子却不会。同时还发现,利用两Sn 同位素系列反应出射的自由中子直接流的平衡能与初始中子/质子比的关系可以很好地探测对称能的密度依赖。The terms of initialization, equation of state (EoS), and two-body collision in the updated ultrarelativistic quantum molecular dynamics (UrQMD) model are examined in details so as to systematically study the collective flows and the nuclear stopping of free nucleons and light clusters from heavy-ion collisions at INDRA energies. It is seen that at INDRA energies the dynamic transport with a soft EoS with momentum dependence and with the momentum-modified density-dependent nucleon-nucleon elastic cross sections describes the directed flow exhibited by hydrogen isotopes (Z= 1) emitted at midrapidity fairly well. The sensitivity of the balance energy (Ebal) of the directed flow to the strength parameter of the density dependence of symmetry potential energy is further studied with the same parameter set. It is found that the Ebal of neutrons from HICs is particularly sensitive to the density dependence of the symmetry potential energy, while that of protons is not. And, the initial neutron/proton ratio dependence of the balance energy of neutrons from Sn isotopes can be taken as a useful probe to constrain the stiffness of the nuclear symmetry energy.     

On the energy dependence of the real part of the heavy-ion optical potential

The energy dependence of the real part of the heavy-ion optical potential is attributed to the J(J + 1) dependence of the-potential which is caused by the rotation induced during the collision. The magnitude and the form of the energy dependence are calculated for several light nucleus-nucleus systems with the use of the distortion potential which is defined by the diagonalization of the coupling interaction. It is shown that the heavy-ion scatterings with the inelastic channels of high and low excitation energies lead to weak and strong energy dependence of the potential, respectively.     

Real part of the optical potential for composite particles

The optical potential for a composite particle is most simply approximated by the sum of the optical potentials of the constituent nucleons. Restricting ourselves to the real parts of the potentials we use this model as a first approximation in a calculation of the potentials for d, ³He, α and ¹²C. We add corrections for (i) the energy dependence of the nucleon potentials, (ii) three-body terms, (iii) the Pauli principle. All corrections can be important and that for the Pauli principle can be very large. We obtain a good explanation of the following phenomena: (a) the deuteron potential is nearly the sum of the neutron and proton potentials, (b) the potential for ³He is about 20 % less than the sum of the potentials of the nucleons in the ³He projectile, (c) the volume integral of the potential for ³He falls at both high and low energies in the energy range 20–100 MeV, (d) shallow potentials with large radii are found for low energy (30 MeV) scattering of α-particles, (e) deeper potentials are found for higher energy α-particle scattering. We predict shallow potentials for ¹²C scattering from light targets but deeper potentials for heavier targets.     

A nuclear structure approach to the nucleon-nucleus optical potential at low energy

An antisymmetrized microscopic calculation of the optical potential for nucleon-⁴⁰Ca elastic scattering is derived. RPA correlations taken into account in the one-particle mass operator are shown to bring a correction to the first-order real potential at low energies and to lead to an imaginary potential. Both are calculated for incident nucleon energies between 10 and 50 MeV. Their general properties are studied in great detail and, after comparison with empirical imaginary potentials, the reliability of such an approach is discussed according to the value of the incident energy.     

Global optical model potentials for symmetrical lithium systems: 6Li+6Li, 7Li+7Li at Elab = 5–40 MeV

Angular distributions of ⁶Li+⁶Li elastic scattering were measured for E_lab = 5–40 MeV. An optical model analysis of these data together with older data of ⁷Li+⁷Li elastic scattering taken at E_lab = 8–17 MeV was performed with the aim to search for a “global” OM potential which describes elastic scattering in both LiLi systems in a broad energy range. Both surface and volume absorbing potentials can be found which fulfill this requirement if a linear energy dependence is assumed of the depths of the real as well as the imaginary potential. These depths, if fitted to individual angular distributions, are found to vary in a correlated manner with the beam energy. This is taken as indication of strong coupling between elastic, inelastic, and reaction channels. This is corroborated by the existence of resonances in reaction channels at these energies where the potential depths are most pronouncedly changing.     

Target excitations and the optical potential for protons scattering from nuclei

We calculate the contributions to the optical potential for 30 MeV protons due to inelastic excitations of the target nucleus. The scattering due to this non-local potential is calculated exactly and some of the results subjected to conventional optical model analysis. When only one excited state is included, a resonant dependence on the excitation energy is observed. Even with ten excited states, the position of a single one can strongly influence the scattering. It is possible to account for about $\text{3}\text{4}$ of the observed absorption in ⁴⁰Ca and ²⁰⁸Pb, but only by postulating unobserved states which exhaust the remainder of the experimental sum rules at somewhat unreasonably low energies. It was not possible to find simple local potentials which gave the same scattering because of the strong L-dependence of the absorption. The constructed potentials concentrate the absorption at too small radii. It is suggested that rearrangement (pick-up) processes contribute a substantial amount of absorption at larger radii, while compound formation will give rise to a volume term in the imaginary potential.     

Radial, sideward and elliptic flow at AGS energies

We study the baryon transverse in-plane (sideward) and elliptic flow from SIS to AGS energies for AuAu collisions in a relativistic dynamical simulation model that includes all baryon resonances up to a mass of 2 GeV as well as string degrees of freedom for the higher mass continuum. There are two factors which dominantly determine the baryon flow at these energies: the momentum dependence of the scalar and vector potentials and the resonance-string degrees of freedom. We fix the explicit momentum dependence of the nucleon-meson couplings of NL3(hard) equation of state (EoS) by the nucleon optical potential up to 1 GeV of kinetic energy. We simultaneously reproduce the sideward flow, the elliptic flow and the radial transverse mass distribution of protons data at AGS energies. In order to study the sensitivity of different mean-field EoS, we use NL2(soft) and NL23(medium) along with NL3(hard) momenta-dependent mean-field EoS. We find that to describe data on both sideward and elliptic flow, NL3 model is better at 2 A·GeV, while NL23 model is at 4–8 A·GeV.     

Rydberg states of HCN observed by electron impact spectroscopy

The electron energy loss spectrum of HCN has been determined in the energy region 8–13.6 eV at impact energies of 100, 50 and 30 eV. It is shown that energy loss spectra of HCN at intermediate impact energies can be satisfactorily analysed unlike the diffuse unassigned optical absorption spectra that have previously been reported. Rydberg series have been assigned using term values and quantum defects together with ionization potentials obtained by photoelectron spectroscopy.     

Pauli exchange effects in the elastic scattering of O + O

The real optical potential for ¹⁶O+¹⁶O system is calculated within a generalized version of the double-folding model with the Pauli knock-on exchange effects between the projectile nucleons and the target nucleons taken into account from first principle. The elastic scattering data at E_lab=350 MeV supplemented by the new measurement at larger angles seem to be the first case in heavy-ion scattering where one can test the reliability of different theoretical heavy-ion optical potentials. Predictions are made for the elastic scattering of ¹⁶O+¹⁶O at laboratory energies of 240–480 MeV to illustrare the energy dependence of the rainbow structure which has been clearly observed in experiment at 350 MeV.     

Dispersive semimicroscopic analysis of nuclear-nuclear collisions on the basis of a corrected folding-model potential

A procedure for correcting the energy dependence determined for the mean-field component of the optical potential on the basis of the double-folding model with allowance for exchange effects in the approximation of single-nucleon exchange knockout is used to calculate the mean field and to analyze data on elastic scattering within the dispersive semimicroscopic optical-potential model. The results of an analysis of all data (including those that were obtained quite recently) on ¹⁶O + ¹²C and ¹⁶O + ¹⁴C interactions at energies of up to 100 MeV per nucleon are presented. The energy dependence of the resulting potentials agrees well with that which was obtained previously within the phenomenological approach. A systematics of the positions of Airy minima in angular distributions versus the reduced mass in the range from 2 to 8 amu is constructed.     

Symmetry energies of nuclear matter and the spin and isospin dependence of the nuclear single-particle potential in the Landau theory

The spin and spin-isospin symmetry energies of nuclear matter and the spin and isospin dependent terms of the nuclear single-particle potential at the Fermi surface are calculated within the frame of the Landau theory of the normal Fermi liquid from the existing sets of the Landau parameters. The possibility of the relation of these parameters to the experimental energies of certain collective nuclear excited states is pointed out. The results are also applied to the calculation of the symmetry and the spin-spin terms in the low energy nuclear optical model potential.     

Computer simulation of solute segregation to a Σ = 5 tilt boundary in Au,Cu and Ni

A Lattice Energy Function that combines a Mie type interatomic potential and a free electron gas volume dependence has been applied to the study of grain boundary energy and structure of a Σ = 5 tilt boundary in Au, Cu and Ni and of solute segregation to the same. Interatomic potentials and volume dependencies of the solvent and solute were adjusted to fit the relative partial molar enthalpy and volume at infinite dilution order to construct a AB type potential and volume dependence. This AB interaction is then applied to calculate the binding energies of solute to various grain boundary sites and the resulting change in grain boundary energy. A relationship between the binding energy and change in grain boundary is derived. The relative values of the grain boundary energy are in agreement with experimental values of the average grain boundary energies. The relative binding energies of the tested solvent-solute systems are in agreemnet with expectations that certain systems should have larger binding energies than others. The behavior of solute binding energies and local relaxations are in agreement with other studies of grain boundary segregation which use different Lattice Energy Functions and relaxation algorithms. The change in grain boundary energy is shown to be directly proportional to the binding energy.     

Isospin-dependent relativistic microscopic optical potential in the Dirac Brueckner-Hartree-Fock method

There is growing evidence to suggest that the binding energy of nucleon in nuclear matter comes from a cancellation between large Lorentz scalar and vector potentials[1,2]. The relativistic approach has been of a great success in describing not only the ground state properties of stable nuclei, but also those of exotic nuclei. In the relativistic frame, the spin-orbit coupling can be deduced automatically, which is usually given by hand in the non-relativistic approach. The relativistic method…     

The 12C+24Mg elastic scattering: An example of anomalous transparency at coulomb barrier energies

Fifteen complete angular distributions of the elastic scattering of ¹²C+²⁴Mg were measured at energies around the Coulomb barrier (E_cm = 10.67–16 MeV). The angular distributions are strongly oscillating and could be well described by an optical potential family, whose real part was determined without continuous ambiguity. The imaginary part of this optical potential is very shallow. At four energies the inelastic scattering angular distributions leading to the 2⁺ state of the ²⁴Mg were also measured and analysed with coupled-channels calculations. The volume integrals of the optical potentials used in the coupled-channels calculations present the threshold anomaly in their energy dependence, with a clear Q-value dependence.     

Solutions of Three-Dimensional Separable Non-Central Potential

We show that a wide class of non-central potentials can be analysed via the improved picture of the Nikiforov- Uvarov method [Physica Scripta 75 （2007） 686]. It has been shown that using the alternative approach, polynomial solutions of three-dimensional separable non-central potential can be obtained.