A method for the calculation of the one-particle generalized coefficients of fractional parentage for an arbitrary number of 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 the calculation of the CFPs for a single j-orbit with isospin, and a general procedure for the computation of the angular momentum (isospin) coupling 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 make it feasible calculation of expectation values of one-particle nuclear shell-model operators within the isospin formalism.
This paper presents the protons and neutrons distributions in atomic nucleus shells calculation algorithm which may be used for ab initio no-core nuclear shell model computations. The problem of enumeration of many-particle states is formulated on energetic basis instead of application of the traditional scheme for states classification. The algorithm provides calculations of protons and neutrons occupation restrictions for nuclear shells for an arbitrary number of oscillator quanta. The reported results show that the presented algorithm significantly outperforms the traditional approach and may fit the needs of state-of-the-art no-core shell model calculations of atomic nuclei.
Computational modelling of potential and resonant scattering for short range and Coulomb potentials was investigated in this study. The resonant scattering problem is formulated with the short range potential composed of a spherically symmetric square well and spherically symmetric square barrier. An iteration scheme of a continuous analogue of the Newton method for continuous spectral problem with correct asymptotic in uncoupled partial waves has been developed. The nonlinear representation of the scattering problem for the normalized radial Schrödinger equation is solved numerically using the difference sweep technique. The second order accuracy scheme developed allow to find scattering phases and wave functions as well as investigate their numerical evolution. The scattering phases and wave functions dependence on the scattering problem parameters have been studied.