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Four particle harmonic-oscillator transformation brackets and their simplifications for special values of the mass-ratio parameters

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Mickevičius S. , Germanas D. , Kalinauskas R.

tom 10

nr 2

421-428

We present a new independent scheme of SO(3) group transformations suitable for the N particle system, composed of N − 1 and 1 particle subsystems, where N − 1 particles have their own intrinsic clusterization. The simple expressions for corresponding four-particle harmonic-oscillator transformation brackets are presented, as well as their simplifications for the special values of mass ratio parameters d = 0, d → ∞ and d 1 = 0, d 1 → ∞.

Method simplifying calculation of coefficients of fractional parentage for translationally invariant shell-model

100%

Mickevičius S. , Germanas D. , Kalinauskas R.

tom 11

nr 5

568-574

A new procedure for large-scale calculations of the coefficients of fractional parentage (CFP) for many-particle systems is presented. The approach is based on a simple enumeration scheme for antisymmetric N particle states, and we suggest an efficient method for constructing the eigenvectors of two-particle transposition operator $$P_{N_1 ,N}$$ in a subspace where N 1 and N 2 = N − N 1 nucleons basis states are already antisymmetrized. The main result of this paper is that according to permutation operators $$P_{N_1 ,N}$$ eigenvalues we can distinguish totally asymmetrical N particle states from the other states with lower degree of asymmetry.