Related papers: Coefficients of Fractional Parentage for Nuclear S…
We introduce an algorithm to obtain coefficients of fractional parentage for light $p$-shell nuclei. The coefficients enable to use Jacobi coordinates in no-core shell model calculations separating off the center-of-mass motion. Fully…
Analytical expressions of the total number of $J$ levels for three and four fermions in a nuclear $j^n$ shell are provided. The formulas were derived using a combination of sum rules for coefficients of fractional parentage, and "unusual"…
For each of the (9/2), (11/2) and (13/2) single j shells we have only one state with J=j V=3 for a five particle system. For four identical particles there can be more than one state of seniority four. We note some ``ratio'' relations for…
The feasibility of shell-model calculations is radically extended by the Quantum Monte Carlo Diagonalization method with various essential improvements. The major improvements are made in the sampling for the generation of shell-model basis…
A new statistical method for systematizing the nuclei fission fragments, investigation of their mass and charge spectra and neutron fission parameters has been suggested. In proposed method, the mass and charge yields of nucleons are…
We present a theoretical and computational framework based on fractional calculus for the analysis of the nonlocal static response of cylindrical shell panels. The differ-integral nature of fractional derivatives allows an efficient and…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
Shell evolution in exotic nuclei is investigated with large-scale shell-model calculations. After presenting that the central and tensor forces produce distinctive ways of shell evolution, we show several recent results: (i) evolution of…
A method of truncating the large shell model basis is outlined. It relies on the order given by the unperturbed energies of the basis states and on the constancy of their spreading widths. Both quantities can be calculated by a simple…
A partial conservation of the seniority quantum number in $j=9/2$ shells has been found recently in a numerical application. In this paper a complete analytic proof for this problem is derived as an extension of the work by Zamick and P.…
The fractional birth and the fractional death processes are more desirable in practice than their classical counterparts as they naturally provide greater flexibility in modeling growing and decreasing systems. In this paper, we propose…
Study of the N ~ Z nuclei in the mass-80 region is not only interesting due to the existence of abundant nuclear structure phenomena, but also important in understanding the nucleosynthesis in the rp-process. It is not feasible to apply a…
Some fundamental Nucleon-Nucleon interactions and their applications to finite nuclei are reviewed. Results for the few-body systems and from Shell-Model calculations are discussed and compared to point out the advantages and disadvantages…
The latest research of the proportionality of atomic weights of chemical elements made it possible to obtain 3 x 3 matrices for the calculation of information coefficients of proportionality Ip that can be used for 3D modeling of the…
Algebraic models are proposed for the description of the shell-like quarteting of the nucleons both on the phenomenologic and on the semimicroscopic levels. In the previous one the quartet is considered as a structureless object, while in…
Low-lying shell model states may be approximated accurately by a sum over products of proton and neutron states. The optimal factors are determined by a variational principle and result from the solution of rather low-dimensional eigenvalue…
The structure of nuclei in the lower half of fp shell is investigated by the spectral distribution method using the modified Kuo-Brown interaction. This interaction recently showed success in reproducing observed properties through detailed…
We review recent advances in the shell model Monte Carlo approach for the microscopic calculation of statistical and collective properties of nuclei. We discuss applications to the calculation of (i) level densities in nickel isotopes,…
The fractional parentage expansion method is extended from $SU(2)_{f}$ nonrelativistic to $SU(3)_{f}$ and relativistic dibaryon calculations. A transformation table between physical bases and symmetry bases for the $SU(3)_{f}$ dibaryon is…
The joint use of counting functions, Hilbert basis and Markov basis allows to define a procedure to generate all the fractions that satisfy a given set of constraints in terms of orthogonality. The general case of mixed level designs,…