Ground State Wave Functions in the Hyperspherical Formalism for Nuclei with A > 4

The general formulation of a technically advantageous method to find the ground state solution of the Schrodinger equation in configuration space for systems with a number of particles A greater than 4 is presented. The wave function is expanded in pair correlated hyperspherical harmonics beyond the lowest order approximation and then calculated in the Faddeev approach. A recent efficient recursive method to construct antisymmetric A-particle hyperspherical harmonics is used. The accuracy is tested for the bound state energies of nuclei with A = 6,8,12. The high quality of the obtained results becomes evident from a comparison with other approaches.Comment: 17 pages, 1 figure, Submitted to Nucl. Phys.

Shell model study of the isobaric chains A=50, A=51 and A=52

Shell model calculations in the full pf-shell are carried out for the A=50, 51 and 52 isobars. The most frequently used effective interactions for the pf-shell, KB3 and FPD6 are revisited and their behaviour at the N=28 and Z=28 closures examined. Cures to their -relatively minor- defaults are proposed, and a new mass dependent version called KB3G is released. Energy spectra, electromagnetic transitions and moments as well as beta decay properties are computed and compared with the experiment and with the results of the earlier interactions. A high quality description is achieved. Other miscellaneous topics are addressed; the Coulomb energy differences of the yrast states of the mirror pair 51Mn-51Fe and the systematics of the magnetic moments of the N=28 isotones.Comment: 45 pages, 34 figures, Latex. Submitted for publicatio

State Dependent Effective Interaction for the Hyperspherical Formalism with Noncentral Forces

The recently developed effective interaction method for the hyperspherical harmonic formalism is extended to noncentral forces. Binding energies and radii of three- and four-body nuclei are calculated with AV6 and AV14 NN potentials. Excellent results for the convergence of the expansion are found, particularly for the three-nucleon system. Due to the higher density the convergence rate is a bit slower for the alpha particle. In comparison to central potential models there is only a very slight deterioration of the convergence due the tensor force, while other potential terms have no visible effect on the convergence. The obtained values for binding energy and radii also agree well with the results in the literature obtained with other few-body techniques.Comment: LaTeX, 12 pages, 6 ps figures, Figures in correct order in this replacemen

Unsupervised Classification by Iterative Voting

In the paper we present a simple algorithm for unsupervised classification of given items by a group of agents. The purpose of the algorithm is to provide fast and computationally light solutions of classification tasks by the randomly chosen agents. The algorithm follows basic techniques of plurality voting and combinatorial stable matching and does not use additional assumptions or information about the levels of the agents’ expertise. Performance of the suggested algorithm is illustrated by its application to simulated and real-world datasets, and it was demonstrated that the algorithm provides close to correct classifications. The obtained solutions can be used both separately and as initial classifications in more complicated algorithms

State Dependent Effective Interaction for the Hyperspherical Formalism

The method of effective interaction, traditionally used in the framework of an harmonic oscillator basis, is applied to the hyperspherical formalism of few-body nuclei (A=3-6). The separation of the hyperradial part leads to a state dependent effective potential. Undesirable features of the harmonic oscillator approach associated with the introduction of a spurious confining potential are avoided. It is shown that with the present method one obtains an enormous improvement of the convergence of the hyperspherical harmonics series in calculating ground state properties, excitation energies and transitions to continuum states.Comment: LaTeX, 16 pages, 8 ps figure

Particle-Number Reprojection in the Shell Model Monte Carlo Method: Application to Nuclear Level Densities

We introduce a particle-number reprojection method in the shell model Monte Carlo that enables the calculation of observables for a series of nuclei using a Monte Carlo sampling for a single nucleus. The method is used to calculate nuclear level densities in the complete $(pf+g_{9/2})$-shell using a good-sign Hamiltonian. Level densities of odd-A and odd-odd nuclei are reliably extracted despite an additional sign problem. Both the mass and the $T_z$ dependence of the experimental level densities are well described without any adjustable parameters. The single-particle level density parameter is found to vary smoothly with mass. The odd-even staggering observed in the calculated backshift parameter follows the experimental data more closely than do empirical formulae.Comment: 14 pages, 4 eps figures included, RevTe