A One-Particle Generalized Coefficients of Fractional Parentage Calculation Method for Atomic Nucleus Harmonic Oscillator Shell Model

Algirdas Deveikis


A method for the calculation of the one-particle generalized coefficients of fractional parentage for several j-orbits with isospin and an arbitrary number of oscillator quanta (generalized CFPs or GCFPs) is presented. The approach is based on a simple enumeration scheme for antisymmetric many-particle states, an efficient algorithm for calculation of the CFPs for a single j-orbit with isospin, and a general procedure for computation of the angular momentum (isospin) recoupling coefficients describing the transformation between different momentum coupling schemes. The method provides fast calculation of GCFPs for a given particle number and produces results possessing small numerical uncertainties. The introduced GCFPs may be used for calculation of expectation values of one-particle nuclear shell-model operators within the isospin formalism.



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