High precision parallel implementation of four-particle harmonic oscillator transformation brackets for nuclear calculations

Abstract

The microscopic description of nuclear shell model is one of rapidly developing area of modern physics. While solving the Schrödinger's equation, the basis of harmonic oscillator functions has proven to be extremely useful and efficient in describing compact quantum systems, such as nucleons in atomic nuclei and quarks in hadrons. This kind of basis is simple to use, although it has one major disadvantage- it converges quite slow. For this reason the dimensions of matrices becomes very big as the values of quantum numbers, which are describing the elements of matrix. These values are required to find the coefficients for a few particle harmonic oscillator transformation brackets, which are constructed from Clebsh-Gordan, 6j and 9j coefficients. Although the analytical expressions of these coefficients are simple,but big problems arise while doing calculations on the computer. Currently widely used 64 bit (Double) precision is not sufficient for these type of calculations as doing intermediate evaluation of coefficients requires very large factorial values. Therefore calculated coefficients are represented not corectly. Another problem is quite slow calculation, which could be solved by paralleling the computer code and using large computer clusters. This component of multiparticle problem limits its evaluation, so the expansion of limits for algorithms for calculating of harmonic oscillator transformation brackets must be done. Using external parallelization library and mutable precision we created a pack of numerical codes based on the methods of compact expressions of the three and four- particle harmonics oscillator brackets. Program code is written in Fortran 90 programing language. For parallelization of used algorithm MPI parallel communication standard was used. [...]