Daniel Jean Baye

A compilation of charged-particle induced thermonuclear reaction rates

Low-energy cross section data for 86 charged-particle induced reactions involving light (1 less than or equal to Z less than or equal to 14), mostly stable, nuclei are compiled. The corresponding Maxwellian-averaged thermonuclear reaction rates of relevance in astrophysical plasmas at temperatures in the range from 10(6) K to 10(10) K are calculated. These evaluations assume either that the target nuclei are in their ground state, or that the target states are thermally populated following a Maxwell-Boltzmann distribution, except in some cases involving isomeric states. Adopted values complemented with lower and upper limits of the rates are presented in tabular form. Analytical approximations to the adopted rates, as well as to the inverse/direct rate ratios, are provided

Generalised meshes for quantum mechanical problems

A new method to discretise Schrodinger equations on a mesh is described. This method is based on an accurate approximation of a variational calculation. The regularly spaced mesh and meshes based on the zeros of orthogonal polynomials are studied in detail. It is shown that with each type of mesh is associated a particular kinetic energy operator and an optimal formula for its discretized form. The applications to some simple potential problems show that the method is very accurate as well as very simple. Applications to many-body problems indicate that the accuracy of the results is improved by an order of magnitude with respect to conventional mesh calculations.

Microscopic study of the 7Li(n,γ)8Li and 7Be(p,γ)8B reactions in a multiconfiguration three-cluster model

Abstract The three-cluster generator coordinate method is applied to the 7Li(n, γ)8Li and 7Be(p, γ)8B capture reactions. The 8B (or 8Li) nucleus is defined by a mixing of (α+3He)+p and (α + p) + 3He (or mirror) configurations. We investigate the sensitivity of different observables with respect to the nucleon-nucleon interaction by considering four different Volkov forces. For all of them, the model fairly reproduces most of the experimentally known spectroscopic properties of the 8B and 8Li mirror nuclei. Recent measurements of the quadrupole moments are well explained without a halo structure. The 7Li(n, γ)8Li cross section supports the data of Imhof et al. rather than those of Wiescher et al. At zero energy, the 7Be(p, γ)8B astrophysical S-factors slightly depend on the nucleon-nucleon interaction. They are consistent with the currently accepted value, but contradict lower estimates.

Microscopic R-matrix theory in a generator coordinate basis: (III). Multi-channel scattering

The microscopic R-matrix theory presented in two previous papers is extended to the multichannel scattering case. An antisymmetrized wave function is built in the two-centre harmonic oscillator model. This wave function is proved to be equivalent to the resonating group one even if the nuclei have non-zero spin. The method only requires the calculation of numerical values of matrix elements between Slater determinants. The microscopic R-matrix theory may be applied to study both reactions and inelastic scattering.

Electromagnetic transitions and radiative capture in the generator-coordinate method

Abstract A microscopic study of the electromagnetic properties of nuclei and of radiative capture reactions is presented in the framework of the generator-coordinate method. Fully antisymmetrized wave functions, with a correct asymptotic behaviour, are used to calculate matrix elements of the multipole operators in the long-wavelength approximation. Centre-of-mass corrections are shown to vanish exactly in this approximation. Approximate forms are derived when antisymmetrization is negligible. The E2, E3 and M2 transitions in 20 Ne and the 16 (α, γ) 20 Ne radiative capture reaction are treated as illustrative examples.

Phase-Equivalent Complex Potentials

Potentials providing the same complex phase shifts as a given complex potential but with a shallower real part are constructed with supersymmetric transformations. Successive pairs of transformations eliminate normalizable solutions corresponding to complex eigenvalues of the Schrodinger equation with the full complex potential. With respect to real potentials, a new feature is the occurrence of normalizable solutions with complex energies presenting a positive real part. Removing such solutions provides a way of suppressing narrow resonances but may lead to complicated equivalent potentials with little physical interest. We discuss the singularity of the transformed potential and its relation with the Levinson theorem, the transformation of the Jost function, and the link with the Marchenko approach. The technique is tested with the solvable Poschl-Teller potential. As physical applications, deep optical potentials for the α + 16O and 16O + 16O scatterings are transformed into l-dependent phase-equivalent shallow optical potentials.

The 7Be(p, γ)8B reaction in a microscopic three-cluster model

The 7Be(p, γ)8B reaction is investigated through a microscopic three-cluster model, using the generator coordinate method. The 7Be nucleus is described by an α +3He structure, projected on the 32− and 12− states of 7Be. The model is tested by the calculation of M1 transition probabilities in 8Li and 8B and of the 7Li(n, γ)8Li cross section. At zero energy, we find an S-factor S(0) = 0.030 keV·b, slightly larger than the currently accepted value.

Experimental determination of the 7Be+p scattering lengths

The Be-7 + p elastic cross section has been measured at the Centre de Recherches du Cyclotron RIB facility at Louvain-la-Neuve in the c.m. energy region from 0.3 to 0.75 MeV by bombarding a proton-rich target with a radioactive 7Be beam. The recoil protons have been detected in the angular range theta(c.m.) = 120.2degrees-131.1degrees and theta(c.m.) = 156.6degrees-170.2degrees using the LEDA system. From a R-matrix analysis of the cross section data. we obtain the energy and the width of the I resonance (E-X = 0.77 MeV). The iota = 0 scattering lengths a(01) = 25 +/- 9 fm (channel spin I = 1) and a(02) = -7 +/- 3 fm (channel spin I = 2) have been deduced. They are compared to values expected from charge-symmetry properties. Implications on the low energy S-factor of the Be-7(p,gamma)B-8 reaction are discussed

Constant-step Lagrange meshes for central potentials

The existence conditions of Lagrange meshes, i.e. meshes leading to very accurate results without analytical calculation of potential matrix elements, are studied in relation with sine and cosine bases on a finite interval. For each one of three different types of boundary conditions, three Lagrange meshes are found. A numerical example shows that (i) the Lagrange-mesh calculations nearly reach the same accuracy as a variational calculation involving the same basis in spite of the approximation on the potential matrix elements and (ii) they are much more accurate than mesh calculations which do not satisfy the existence conditions. The striking accuracy of the Gauss quadrature employed in the mesh approximation for the significant eigenvalues remains unexplained in view of the limited accuracy of the same quadrature for individual potential matrix elements.

Antisymmetrization effects in radiative capture reactions

The role played by the Pauli principle in low-energy radiative capture reactions is investigated through a comparison between a microscopic model-the generator coordinate method-and two of its approximations based on an orthogonality condition. The electromagnetic transition matrix element is shown to contain a dominant local term and a smaller residual-antisymmetrization term. The validity of the approximations is studied for the 16O(α, γ) 20Ne reaction under conditions of calculation leading to spectroscopic and elasticscattering properties as close as possible to those of the microscopic model. Nonnegligible differences are found between the three calculations. The local approximation is not significantly less accurate than the more complicated nonlocal one. A simple criterion is proposed to determine the validity of both approximations for other radiative capture reactions. At very low energies, the variation of the astrophysical factor can be well reproduced by the extranuclear capture model. The slope of the S-factor at zero energy is explained qualitatively for different reactions by a simple analytical formula.