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Manuscript Title: Differential cross sections for electric quadrupole Coulomb excitation I.
Authors: S.M. Lea, V. Joshi, A.B. Lopez-Cepero
Program title: DXS1
Catalogue identifier: ABQE_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 3(1972)118
Programming language: Fortran.
Computer: IBM 360/75.
Operating system: OS 360 MVT.
RAM: 35K words
Word size: 32
Keywords: Nuclear physics, Electric quadrupole, Coulomb excitation, Differential Cross section, Inelastic Scattering, Radial, Coulomb integrals, Finite sums.
Classification: 17.13.

Nature of problem:
The program calculates the differential cross section for inelastic scattering of a structureless charged particle through E2 excitation of a point nucleus. It is assumed that all nuclear effects can be ignored.

Solution method:
The numerical calculation closely follows the well-known quantum- mechanical theory of Coulomb excitation in the distorted wave Born approximation. The target and projectile are assumed to be point particles. Radical integrals are calculated in the long wavelength (of the transferred photon) limit.

The calculation is non-relativistic and in the center of mass coordinates. In spite of the program's capability to consider up to 300 partial waves, even that may not provide good results with a combination of very small energy loss and small scattering angles.

Unusual features:
The capacity for considering up to 300 partial waves is necessary to get reliable results for small angle scattering. The spherical harmonics are calculated by a recursion relation that is very stable for high angular momenta, as are the techniques for computing the Clesbch-Gordan and Racah coefficients. The finite-sum method is used for calculating the radial integrals. This method is remarkably fast and stable with respect to errors; at present there are no available codes for Coulomb excitation that incorporate this method.

Running time:
In the IBM 360/75 the program takes about 52 s to compile and the running time depends on the number of partial waves used. Typically for about 60 partial waves it takes about 2 min to calculate the radial integrals and an extra 15 s for each angle. Running time increases significantly with increase in the number of partial waves used.