Solving the eigenvalue problem of the nuclear Yukawa-folded mean-field Hamiltonian

Abstract

The nuclear Hamiltonian with a Yukawa-folded mean-field potential is diagonalized within the basis of a deformed harmonic-oscillator in Cartesian coordinates. The nuclear shape is characterized by the equivalent sharp surface described either by the well known Funny–Hills or the Trentalange–Koonin–Sierk parametrizations. They are both able to describe a very vast variety of nuclear deformations, including necked-in shapes, left–right asymmetry and non-axiality. The only imposed limitation on the nuclear shape is the z-signature symmetry, which corresponds to a symmetry of the shape with respect to a rotation by an angle π around the z-axis. On output, the computer code produces for a given nucleus with mass number A and charge number Z the energy eigenvalues and eigenfunctions of the mean-field Hamiltonian at chosen deformation. Program summaryProgram title: yukawaCatalogue identifier: AEYI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYI_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 78599No. of bytes in distributed program, including test data, etc.: 1551468Distribution format: tar.gzProgramming language: Fortran 77.Computer: Any PC machine.Operating system: Windows or a system based on Linux.RAM: bytes: 0.5 GB or moreClassification: 17.19.Nature of problem: The full single-particle nuclear Hamiltonian composed of the Yukawa-folded central, spin–orbit and Coulomb potentials is generated and diagonalized. The only symmetry of the problem is the so called z-signature symmetry which limits the nuclear shapes to those, being invariant with respect to a rotation by an angle π around the z-axis.Solution method: The mean-field Hamiltonian is expressed in matrix form in the basis of an anisotropic harmonic-oscillator potential written in Cartesian coordinates, where the basis parameters are adjusted to the actual deformed nuclear shape. The eigensolutions of the Hamiltonian are determined by diagonalization of the corresponding matrix.Running time: For a nucleus of spherical shape, with the inclusion of NMAX=14 major oscillator shells and including the option of printing out all the eigenfunctions, one program run takes around 7 s on an average dual-core 2 GHz notebook of 1 GB RAM memory. The same type of calculation for a complicated non-axial left–right asymmetric shape requires around 11 s.