Marianne Dufour

Realistic collective nuclear Hamiltonian

The residual part of the realistic forces{emdash}obtained after extracting the monopole terms responsible for bulk properties{emdash}is strongly dominated by pairing and quadrupole interactions, with important {sigma}{tau}{center_dot}{sigma}{tau}, octupole, and hexadecapole contributions. Their forms retain the simplicity of the traditional pairing plus multipole models, while eliminating their flaws through a normalization mechanism dictated by a universal {ital A}{sup {minus}1/3} scaling. Coupling strengths and effective charges are calculated and shown to agree with empirical values. Comparisons between different realistic interactions confirm the claim that they are very similar. {copyright} {ital 1996 The American Physical Society.}

Multicluster description of p-shell nuclei in a microscopic model

Abstract We use the Generator Coordinate Method to investigate some nuclei between A = 12 and A = 16 in a multicluster model. The microscopic wave functions are defined from clluster wave functions, involving three α particles and any s-shell nucleus. The α clusters are located at the apexes of an equilateral triangle, and form the basis of a tetrahedral structure, with the additional s cluster at the top of its height. Optimal configurations are determined for the 12 C, 13 C, 14 C, 15 N and 16 O nuclei. We show that, with respect to the more usual shell-model approach, this multicluster description significantly improves the binding energy and the spectroscopic properties.

The 15N(α,γ)19F and 15O(α,γ)19Ne reactions in a microscopic multicluster model

Abstract We investigate the 15N (α,γ) 19 F and 15O (α,γ) 19 Ne reactions by using a multicluster description of 15N and 15O. The 15N (α,γ) 19 F and 15O (α,γ) 19 Ne wave functions are defined in the Generator Coordinate Method, using α and triton (or 3He) wave functions. The band structure and the E2 transition probabilities are well reproduced by the model, but some resonances, important for astrophysics, are missing. The non-resonant part of the 15N (α,γ) 19 F and 15O (α,γ) 19 Ne capture cross sections is discussed.

Microscopic Cluster Models

We present an overview of microscopic cluster models, by focusing on the Resonating Group Method (RGM) and on the Generator Coordinate Method (GCM). The wave functions of a nuclear system are defined from cluster wave functions, with an exact account of antisymmetrization between all nucleons. For the sake of pedagogy, the formalism is mostly presented in simple conditions, i.e. we essentially assume spinless clusters, and single-channel calculations. Generalizations going beyond these limitations are outlined. We present the GCM in more detail, and show how to compute matrix elements between Slater determinants. Specific examples dealing with \(\alpha\)+nucleus systems are presented. We also discuss some approximations of the RGM, and in particular, the renormalized RGM which has been recently developed. We show that the GCM can be complemented by the microscopic variant of the R-matrix method, which provides a microscopic description of unbound states. Finally, extensions of the GCM to multicluster and multichannel calculations are discussed, and illustrated by typical examples. In particular we compare different three-\(\alpha\) descriptions of \(^{12}\hbox{C}.\)

Nonmicroscopic and microscopic descriptions of condensate states in the 12C and 16O nuclei

12C and 16O nuclei are investigated within nonmicroscopic and microscopic theoretical frameworks, respectively. For the 12C nucleus viewed as a 3? system, 3-body Faddeev equations are solved in configuration space. Positions of the resonant states are obtained through the complex scaling method. We show that the nonlocal potential developed by Z. Papp and S. Moszkowski appears to be well-adapted to study 3? system. In particular, we show evidence for 12C states of positive-parity which share common features with the well-known 0+2 Hoyle state, currently interpreted as a condensate state. For the 16O nucleus, a 12C+? multicluster generator coordinate method is used to solve the 16-nucleon problem. The 16O nucleus is described by four ? cluster. We comment the difficulty to interpret broad resonant states. The phase-shift analysis of the 12C(0+2) + ? channel reveals the existence of two 0+ states located above the 4? threshold which can be interpreted as condensate states.

THEORETICAL INVESTIGATIONS OF THE 12C(α,γ)16OE2 CROSS SECTION

The E2 component of the 12C(α,γ)16O cross section is investigated in three ways: by a microscopic cluster model, by R-matrix fits and by a combination of both. The microscopic calculation leads to an estimate of the S-factor at a typical energy of 300 keV of SE2(300 keV)≈ 50 keV-b for ground-state transitions. Cascade transitions to the and excited states of 16O are also studied. Then the S-factor is analyzed in the phenomenological R-matrix theory. We show that the background term plays a crucial role, and cannot be determined without ambiguity. Consequently only an upper limit on the extrapolated S-factor can be obtained [SE2(300 keV)< 190 keV-b]. Finally, we use the microscopic Asymptotic Normalization Constant (ANC) of the level, well known to be a cluster state to constrain the R-matrix analysis. This procedure strongly reduces the uncertainties on the R-matrix fits, and we end up with a recommended value of SE2(300 keV) = 42 ± 2 keV-b.

Core excitations in exotic nuclei

The role of core excitations in exotic nuclei is discussed in the framework of a microscopic cluster model. This cluster approach is complemented by the R-matrix theory to take account of the long-range part of the wave functions. We briefly describe the model, and present two recent examples: the neutron-rich nucleus 16B, described by a 15B+n structure, and the proton-rich nucleus 17Na, described by a 16Ne+p structure. In both cases core excitations are shown to play an important role.

Microscopic Cluster Models: Application to the structure of the 16B nucleus

General aspects of microscopic cluster models based on the combination of the Generator-Coordinate-Method and of the R-matrix method are presented. The adequacy of such methods to describe the physics of exotic light nuclei is illustrated with the unbound 16B nucleus.

Multichannel analysis of the 16B nucleus

This work is devoted to a Generator-Coordinate-Method investigation of the 16B spectrum with an Extended Two-Cluster Model which includes many 15B+n channels. We find that the narrow peak above the 15B+n threshold seen in the experiments of Kalpachieva et al. and of Lecouey et al. can be assigned to a resonance. Several resonances are obtained near the 15B+n threshold, in particular a state which could be a possible candidate for the 16B ground state. Comparison with Shell Model calculations is performed.

The 12C(α, γ)16O E2 cross section at stellar energies

The E2 component of the 12 C (α, γ) 16 O cross section is investigated by a microscopic cluster model, and by R‐matrix fits. The first approach provides S E2 (300 keV )≈50 keV ‐ b for ground‐state transitions. In the R‐matrix theory, we show that the background term plays a crucial role, and cannot be determined without ambiguity. Only an upper limit on the extrapolated S factor can be obtained [S E2 (300 keV ) keV ‐ b ]. To constrain the R‐matrix analysis, we use the GCM Asymptotic Normalization Constant (ANC) of the 2 1 + level. This procedure strongly reduces the uncertainties on the R‐matrix fit, and we end up with a recommended value of S E2 (300 keV ) =42±2 keV ‐ b . As ANC values derived from indirect methods are not consistent with the 12 C (α, γ) 16 O cascade transitions to the 2 1 + state, we suggest a remeasurement of this cross section.The E2 component of the {sup 12}C({alpha}, {gamma}){sup 16}O cross section is investigated by a microscopic cluster model, and by R-matrix fits. The first approach provides S{sub E2}(300 keV){approx_equal}50 keV-b for ground-state transitions. In the R-matrix theory, we show that the background term plays a crucial role, and cannot be determined without ambiguity. Only an upper limit on the extrapolated S factor can be obtained [S{sub E2}(300 keV)<190 keV-b]. To constrain the R-matrix analysis, we use the GCM Asymptotic Normalization Constant (ANC) of the 2{sub 1}{sup +} level. This procedure strongly reduces the uncertainties on the R-matrix fit, and we end up with a recommended value of S{sub E2}(300 keV) =42{+-}2 keV-b. As ANC values derived from indirect methods are not consistent with the {sup 12}C({alpha}, {gamma}){sup 16}O cascade transitions to the 2{sub 1}{sup +} state, we suggest a remeasurement of this cross section.