M. Lassaut

Microscopic description of elastic scattering and reaction cross sections of 6Li and 11Li

Abstract An attempt to a consistent description of both 6 Li and 11 Li scattering on 12 C and 28 Si is carried out in an optical model analysis. The optical potential results from a double folding calculation with G-matrix effective nucleon-nucleon interactions. With two renormalization parameters for the real and the imaginary parts of the potential, we describe the 6 Li-scattering and extract the energy dependence of the multiplicative factors. The renormalization procedure provides a satisfactory description of the elastic and reaction cross section for the 11 Li+ 12 C case. A simultaneous description of 11 Li+ 28 Si elastic and reaction cross sections requires a large renormalization of the optical model potential. At small angles, the magnitude and the phase of the 11 Li cross sections on both targets cannot be explained in terms of simple optical model amplitudes.

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.

Model calculations of doubly closed-shell nuclei in the Integro-Differential equation approach

Abstract The binding energies and root mean square radii obtained from the Integro-Differential Equation Approach (IDEA) and from the Weight-Function Approximation (WFA) of the IDEA for an even number of bosons and for 12 C, 16 O and 40 Ca are compared to those recently obtained by the Variational Monte Carlo, Fermi Hypernetted Chain and Coupled Cluster expansion methods with model potentials. The IDEA provides numbers very similar to those obtained by other methods although it takes only two-body correlations into account. The analytical expression of the wave function for the WFA is given for bosons in the ground state when the interacting pair is outside the potential range. Due to its simple structure, the equations of the IDEA can easily be extended to realistic interactions for nuclei as has already been done for the trinucleon and 4 He.

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.

The imaginary part of the local potential equivalent to the non-local α-nucleus optical potential

Abstract A simple expression of the α-nucleus optical potential has been derived from the Feshbach formula by using a closure approximation for summing over the excited states of the target nucleus. It has been shown that the correction to the real folding model potential is small. The imaginary local potential equivalent to the non-local Feshbach potential has been studied in detail for Ca nuclei and shown to reproduce quite well the gross properties of empirical potentials above 100 MeV with, however, a lack of absorption in the surface region. The A-dependence of the imaginary potential volume integral has also been investigated.

Description of α-elastic scattering and (3He, α) reaction at intermediate energy with a microscopic α-nucleus potential

Abstract An attempt is made to describe both the α-elastic scattering and the (3He, α) reaction on 58Ni, 90Zr and 208Pb for energies ranging from 100 to 283 MeV where the phenomenological α-nucleus potentials adjusted on elastic scattering data are unable to reproduce correctly the transfer reaction cross sections. In a first step the real and the imaginary part of the microscopic α-nucleus potential are renormalized by multiplicative constants by fitting the α-elastic scattering data then used to calculate the (3He, α) cross sections within the DWBA approximation. We show that such a potential leads to a satisfactory agreement with experiment in what concerns the shape of the angular distribution of transfer reaction and gives C2S compatible with those determined at low energy from (p, d) and (d, t) reactions. In a second step we show that adding to the microscopic absorptive potential a quite weak surface term is equivalent to the former renormalization of the imaginary potential in the sense that it is sufficient to describe both the α-elastic scattering and the transfer reaction but is, physically, more satisfying.

The global phase of the nucleon-nucleon amplitudes and proton-nucleus scattering

Evidence for a global phase variation of the nucleon-nucleon amplitudes has been investigated at intermediate energies in the elastic scattering of protons, deuterons, 3He and 4He. Extending previous works, we study the influence of this phase variation on the proton-nucleus scattering for heavier systems. As a specific example, calculations have been performed for p-12C elastic and inelastic scattering at 0.8 GeV. The present work being exploratory in nature, we simply used the Kerman, McManus and Thaler approximation(1959) to the optical potential.

l-Dependent local potentials equivalent to a non-local potential

Abstract The Peierls-Vinh Mau local approximation of a non-local potential is revisited for l-waves with l ≠ 0. The approximation is tested numerically on the α-nucleon non-local potential for which the non-locality range is close to its radius.

Microscopic optical-model analysis of α-40Ca elastic scattering at 104 MeV through the near/far decomposition

Abstract The microscopic α- 40 Ca optical potential constructed in previous papers is examined with respect to the near/far components of the α elastic scattering cross section at 104 MeV recently extracted from the experimental data. A renormalization of the real part of the potential by a multiplicative constant allows one to reproduce the position of the oscillations of the farside component. However, their amplitude is too weak and the absolute value of the farside component is overestimated. Adding a very weak surface term to the imaginary potential, which was shown to be sufficient to describe the (α, α) elastic scattering and the ( 3 He, α) transfer reaction beyond 100 MeV, improves the absolute value of the farside component but is insufficient to reproduce the amplitude of the oscillations which is shown to be determined by the strength of the imaginary potential. Once the microscopic imaginary potential is modified at small distances the agreement with “experimental” near/far components is quite satisfactory.