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 20Ne and the 16(α, γ)20Ne radiative capture reaction are treated as illustrative examples.
The 3He()7Be and 3H()7Li astrophysical S factors are calculated within the no-core shell model with continuum using a renormalized chiral nucleon–nucleon interaction. The 3He()7Be astrophysical S factors agree reasonably well with the experimental data while the 3H()7Li ones are overestimated. The seven-nucleon bound and resonance states and the α + 3He/3H elastic scattering are also studied and compared with experiment. The low-lying resonance properties are rather well reproduced by our approach. At low energies, the s-wave phase shift, which is non-resonant, is overestimated.
We present an -matrix Fortran package to solve coupled-channel problems in nuclear physics. The basis functions are chosen as Lagrange functions, which permits simple calculations of the matrix elements. The main input is the coupling potentials at some nucleus–nucleus distances, specified by the program. The program provides the collision matrix and, optionally, the associated wave function. The present method deals with open and closed channels simultaneously, without numerical instability associated with closed channels. It can also solve coupled-channel problems for non-local potentials. Long-range potentials can be treated with propagation techniques, which significantly speed up the calculations. We first present an overview of the -matrix theory, and of the Lagrange-mesh method. A description of the package and its installation on a UNIX machine is then provided. Finally, five typical examples are discussed.
No. of lines in distributed program, including test data, etc.: 6090
No. of bytes in distributed program, including test data, etc.: 86122
Distribution format: tar.gz
Programming language: Fortran 90.
RAM: Memory usage strongly depends on the nature of the problem (number of channels, size of the basis).
Classification: 17.8.
External routines: If available, the LAPACK library can be used for matrix inversion (faster than the sub-routine included in the package).
Nature of problem: Solving coupled-channel problems for positive energies; the package provides the collision matrix and the associated wave function for given energy, spin and parity.
Solution method: The coupled-channel system is solved with the -matrix method, and Lagrange functions are adopted. Propagation of the -matrix can be performed.
Restrictions: For non-local potentials, the propagation technique cannot be used.
Running time: strongly depends on the nature of the problem. For single-channel calculations, the running type is typically less than 1 s. For large scale calculations (typically more than 100 channels), the running time may increase up to several minutes on a multi-CPU Linux machine.
Three-body continuum states are investigated with the hyperspherical method on a Lagrange mesh. The R-matrix theory is used to treat the asymptotic behaviour of scattering wave functions. The formalism is developed for neutral as well as for charged systems. We point out some specificities of continuum states in the hyperspherical method. The collision matrix can be determined with a good accuracy by using propagation techniques. The method is applied to the 6He () and 6Be () systems, as well as to 14Be (). For 6He, we essentially recover results of the literature. Application to 14Be suggests the existence of an excited state below threshold. The calculated B(E2) value should make this state observable with Coulomb excitation experiments.