G. F. Bertsch

A Guide to microscopic models for intermediate-energy heavy ion collisions

Abstract In the last few years heavy ion experiments have addressed key questions regarding the behavior of nuclear matter at high excitation and density. Simultaneous progress in theory has been achieved by the formulation of calculational tools to apply microscopic models to experimental observables. The present review covers a large part of this theoretical development. We provide enough details so that the uninitiated but interested reader can arrive at the present status of the theory and its relationship to current experiments. The energy range of interest here is 50 MeV/n lab to 1 GeV/n lab.

Interactions for inelastic scattering derived from realistic potentials

An effective local interaction for inelastic scattering is derived by fitting the matrix elements of a sum of Yukawas and, for the tensor force, other closely related forms, to three selected sets of G-matrix elements. The ranges were selected to ensure OPEP tails in the relevant channels as well as a short-range part which simulates the “σ-exchange” process. Some of the implications of the various parts of the interaction are discussed in a distorted-wave context.

octopus: a first-principles tool for excited electron-ion dynamics.

We present a computer package aimed at the simulation of the electron–ion dynamics of finite systems, both in one and three dimensions, under the influence of time-dependent electromagnetic fields. The electronic degrees of freedom are treated quantum mechanically within the time-dependent Kohn–Sham formalism, while the ions are handled classically. All quantities are expanded in a regular mesh in real space, and the simulations are performed in real time. Although not optimized for that purpose, the program is also able to obtain static properties like ground-state geometries, or static polarizabilities. The method employed proved quite reliable and general, and has been successfully used to calculate linear and non-linear absorption spectra, harmonic spectra, laser induced fragmentation, etc. of a variety of systems, from small clusters to medium sized quantum dots.  2002 Elsevier Science B.V. All rights reserved.

A study of the nuclear response function

Abstract We examine the excitation properties of spherical nuclei in the Random Phase Approximation using the Greens function method. The calculations are done with interactions of the Skyrme type for nuclei from 16 O to 208 Pb. Different Skyrme interactions can have the same predictions for ground state Hartree-Fock properties, but give quite different predictions for the dynamic response. Our calculations favor a mild velocity-dependence in the interaction, such as given by Skyrme I. The level of agreement with empirical properties is as follows: energies of low-lying states, ≈25%; positions of giant resonances, ≈10%; transition rates of low states, factor of 2 typical. Inelastic scattering of electrons is reasonably accounted for by the model, but nucleon inelastic scattering has difficulties with the noncollective strength.

Pair correlations near the neutron drip line

Abstract A theory of pairing in weakly bound nuclei is presented. The nucleus is treated as a three-body system consisting of two interacting nucleons together with a structureless core. The pairing interaction is modelled by a density-dependent contact interaction. It is constrained to the free nucleon interaction at low density. Numerically, the Hamiltonian equation is solved by a two-particle Greens function method in coordinate space. Given the single particle resonance energy of 10 Li, the theory reproduces the marginal binding of 11 Li. The large electric dipole stength in 11 Li found experimentally is also accounted for. The nucleus 14 Be is also found to be bound.

NUCLEAR RESPONSE IN THE CONTINUUM

Abstract Continuum effects may be easily treated in the RPA particle-hole theory of excitations, if the calculation is done with the response function formalism. We apply the theory to the low multipolarities in 16 O, 40 Ca, and 208 Pb. We confirm that the width of the giant dipole state in light nuclei is accounted for by the continuum. In heavy nuclei the dipole decay width is relatively small. The giant quadrupole state is predicted to be much narrower than the dipole since it is concentrated in a single state. The 3ħω) octupole state is quite spread out in light nuclei, but has a width of only 1 MeV in 208 Pb.

An effective interaction for inelastic scattering derived from the Paris potential

An effective interaction for inelastic scattering of nucleons from nuclei is derived by fitting oscillator G-matrix elements of the Paris nucleon-nucleon potential to the matrix elements of a sum of Yukawa terms. Except for the singlet-odd channel, these G-matrix elements do not differ in any significant respect from those obtained from the Reid soft-core potential, and give similar results for inelastic proton scattering.

Real-space, real-time method for the dielectric function

We present an algorithm to calculate the linear response of periodic systems in the time-dependent density functional theory, using a real-space representation of the electron wave functions and calculating the dynamics in real time. The real-space formulation increases the efficiency for calculating the interaction, and the real-time treatment decreases storage requirements and allows the entire frequency-dependent dielectric function to be calculated at once. We give as examples the dielectric functions of a simple metal, lithium, and an elemental insulator, diamond.

Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction

A systematic study of low energy nuclear structure at normal deformation is carried out using the Hartree-FockBogoliubov theory extended by the generator coordinate method and mapped onto a five-dimensional collective quadrupole Hamiltonian. Results obtained with the Gogny D1S interaction are presented from drip line to drip line for even-even nuclei with proton numbers Z = 10 to Z = 110 and neutron numbers N 200. The properties calculated for the ground states are their charge radii, two-particle separation energies, correlation energies, and the intrinsic quadrupole shape parameters. For the excited spectroscopy, the observables calculated are the excitation energies and quadrupole as well as monopole transition matrix elements. We examine in this work the yrast levels up to J = 6, the lowest excited 0 + states, and the two next yrare 2 + states. The theory is applicable to more than 90% of the nuclei that have tabulated measurements. We assess its accuracy by comparison with experiments on all applicable nuclei where the systematic tabulations of the data are available. We find that the predicted radii have an accuracy of 0.6%, much better than can be achieved with a smooth phenomenological description. The correlation energy obtained from the collective Hamiltonian gives a significant improvement to the accuracy of the two-particle separation energies and to their differences, the two-particle gaps. Many of the properties depend strongly on the intrinsic deformation and we find that the theory is especially reliable for strongly deformed nuclei. The distribution of values of the collective structure indicator R42 = E(4 + )/E(2 + ) has a very sharp peak at the value 10/3, in agreement with the existing data. On average, the predicted excitation energy and transition strength of the first 2 + excitation are 12% and 22% higher than experiment, respectively, with variances of the order of 40–50%. The theory gives a good qualitative account of the range of variation of the excitation energy of the first excited 0 + state, but the predicted energies are systematically 50% high. The calculated yrare 2 + states show a clear separation between γ and β excitations, and the energies of the 2 + γ vibrations accord well with experiment. The character of the 0 + state is interpreted as shape coexistence or β-vibrational excitations on the basis of relative quadrupole transition strengths. Bands are predicted with the properties of β vibrations for many nuclei having R42 values corresponding to axial rotors, but the shape coexistence phenomenon is more prevalent. The data set of the calculated properties of 1712 even-even nuclei, including spectroscopic properties for 1693 of them, are provided in CEA Web site and EPAPS repository with this article [1].

Production of deuterons and pions in a transport model of energetic heavy-ion reactions

Abstract Green functions are used to derive transport equations with bound-state production and absorption. The equations are valid in the quasiparticle limit and are used to describe deuteron production in heavy-ion induced reactions. The deuterons are produced in three-nucleon collisions in a process that is inverse to deuteron breakup. We also derive rate equations for pion production by resonance formation and decay. Our equations satisfy detailed balance even in the case of wide resonances, unlike previous formulations. The relation widely employed in the cascade and Boltzmann equation models produces an equilibrium with too many pions. We have solved the equations numerically, finding for a number of cases fair agreement with experimental data. The predicted entropy produced in central Nb + Nb collisions at 650 MeV/nucleon exceeds by half a unit the entropy deduced from data. The predicted pion yields in the cascade limit are much closer to the data measured in central Ar + KCl collisions than was found in earlier treatments.