Physics – Nuclear Physics – Nuclear Theory
Scientific paper
2009-10-09
Comput.Phys.Commun.180:1013-1040,2009
Physics
Nuclear Physics
Nuclear Theory
55 pages, 9 figures, Computer Physics Communications 180, 1013-1040 (2009)
Scientific paper
10.1016/j.cpc.2008.12.021
We derive a formalism, the separation method, for the efficient and accurate calculation of two-body matrix elements for a Gaussian potential in the cylindrical harmonic-oscillator basis. This formalism is of critical importance for Hartree-Fock and Hartree-Fock-Bogoliubov calculations in deformed nuclei using realistic, finite-range effective interactions between nucleons. The results given here are also relevant for microscopic many-body calculations in atomic and molecular physics, as the formalism can be applied to other types of interactions beyond the Gaussian form. The derivation is presented in great detail to emphasize the methodology, which relies on generating functions. The resulting analytical expressions for the Gaussian matrix elements are checked for speed and accuracy as a function of the number of oscillator shells and against direct numerical integration.
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