N.Vinh Mau

Temperature dependence of collective states in the random-phase approximation

Abstract We investigate the temperature dependence of collective states in the framework of the random-phase approximation at finite temperature. We show that sum rules can be extended to collective energies at finite temperature. Numerical methods are developed to solve the RPA equations at finite temperature. Results are presented and discussed in the case of 40Ca for isovector dipole and isoscalar octupole vibrations, using oscillator wave functions and a zero-range force. We show that the broadening of giant dipole resonances observed experimentally, appears as a natural consequence of the structure of the RPA equations. Comparison is made with the schematic model for which the temperature dependence of collective states can be worked out analytically.

Optical potential for low-energy neutrons: Imaginary potential for neutron-40Ca elastic scattering

Abstract A derivatio1n of the optical potential from the Green function formalism is achieved including RPA correlations. The imaginary parts of the non-local and equivalent local optical potentials are calculated for low-energy neutron scattering on 40 Ca, using a zero-range effective nucleon-nucleon interaction. We get the potential as a sum of a surface and a volume term, the parameters of which are in qualitative agreement with phenomenological values.

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

Abstract An antisymmetrized microscopic calculation of the optical potential for nucleon- 40 Ca 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.

Antisymmetrization and density-dependent effects within the folding model approach to α-nucleus scattering

Abstract The real α-nucleus interaction is investigated within the framework of the folding model. First the non-local α-nucleon interaction is calculated in the Hartree-Fock approximation and then folded in with the target matter density. The resulting α-nucleus potential is non-local but a local equivalent potential is obtained within the Perey-Saxon approximation. The calculations are performed both with density-independent and density-dependent forces. The rearrangement terms, arising from the density dependence of the force, which are usually neglected, are calculated and found to be significant at small distances. The local density appearing in the density-dependent part of the force is evaluated using a prescription which avoids explicit contradiction of the Pauli principle, in contrast to many earlier calculations where it is calculated as the sum of the densities of the colliding nuclei. However our prescription is expected to underestimate the density-dependent effects. The calculated potentials are used to fit elastic α-particle scattering from 40 Ca at 104 MeV incident energy. Good agreement with experimental data is obtained after renormalizing the theoretical potentials by a factor ranging from 0.6 to 0.9. Finally the E - and A -dependences of the volume integral per nucleon pair of the calculated potentials are investigated and found to be in good qualitative agreement with the available phenomenological results.

Particle-hole and particle-particle RPA ground state correlations and the Green function formalism

Abstract Green function techniques are used to derive the two-particle and particle-hole RPA correlations in the ground state of a closed shell nucleus. The correlation energy and density are calculated with the Tabakin interaction for 16 O and 40 Ca and compared to the second order perturbation theory contributions. The correlation energies are respectively − 12.80 and − 18.78 MeV for 16 O and 40 Ca.

Dispersion relation for microscopic heavy-ion potentials and description of elastic scattering above the coulomb barrier for 32S on 40Ca

Abstract The closure approximation model is used to study the dispersion relation for local potentials when the Green function is calculated for an hermitian and non-hermitian effective hamiltonian. In the same model the angular distributions for elastic scattering of 32 S on 40 Ca are calculated at 90, 100, 110, 120 and 151.5 MeV. Comparison with data shows the ability of the model to describe the imaginary and polarization potentials.

Effect of residual interactions on nuclear level densities

Abstract We calculate the contribution of residual interactions to nuclear level densities in the framework of the random-phase approximation. We first investigate the case of the schematic model for which analytical formulae can be worked out. More realistic calculations are performed numerically for 40 Ca and 56 Ni using oscillator wave functions and a zero-range interaction. In 56 Ni it is found that residual interactions increase level densities significantly in the random-phase approximation, while small corrections are found in 40 Ca. A comparison with the results of second-order perturbation theory is presented.

Closure approximation to the absorptive potential in heavy ion scattering

Abstract We propose a simple model which is based on the Feshbachs theory of the optical potential. The use of closure relation in both nuclei implies that we implicitly include all possible channels, in particular inelastic scattering and one-nucleon transfer processes. The local absorptive potential is calculated at large distances and its energy dependence is studied. The results are compared with other theoretical works and with phenomenological potentials.

A consistent derivation of the real and imaginary parts of the heavy ion potential below and above the Coulomb barrier

Abstract In a model including approximately a large set of non-elastic channels, the real and imaginary potentials are consistently derived. The “anomaly” of the real potential which sharply increases in the vicinity of the Coulomb barrier where the imaginary potential is strongly reduced is studied in 16 O + 40 Ca and 16 O + 208 Pb systems. The results on the imaginary potential are discussed and compared to our previous calculation.

Low-energy nucleon-alpha scattering: Microscopic potentials and phase shifts

Abstract The nucleon-alpha potential is derived in the antisymmetrized folding model from different effective interactions without and with density dependence. Local equivalent potentials are calculated in two different approximations. The phase shifts for energies below 25 MeV obtained with these two sets of potentials are discussed.