Nuclear level density: Shell-model approach

Abstract

The knowledge of the nuclear level density is necessary for understanding various reactions including those in the stellar environment. Usually the combinatorics of Fermi-gas plus pairing is used for finding the level density. Recently a practical algorithm avoiding diagonalization of huge matrices was developed for calculating the density of many-body nuclear energy levels with certain quantum numbers for a full shell-model Hamiltonian. The underlying physics is that of quantum chaos and intrinsic thermalization in a closed system of interacting particles. We briefly explain this algorithm and, when possible, demonstrate the agreement of the results with those derived from exact diagonalization. The resulting level density is much smoother than that coming from the conventional mean-field combinatorics. We study the role of various components of residual interactions in the process of thermalization, stressing the influence of incoherent collision-like processes. The shell-model results for the traditionally used parameters are also compared with standard phenomenological approaches.

Low energy magnetic radiation enhancement in thef7/2shell

“…By following the procedure of [31], we divide the Hamiltonian into two parts and, keeping the symmetry, let them vary through the numerical coefficients, k 0 and k 1 ,…”

Random matrix theory for transition strengths: Applications and open questions

“…In practical applications to nuclei, J decomposition of the densities is need. This can be carried out either by using exact centroids and variances of I ( m p , m n );J (E) as in [18,19] or by using approximate J projection via spin-cutoff factors as in [16,17].…”

“…In order to apply the EE generated bivariate Gaussian form for the transition strength densities, just as with the level densities [16,18], it is important to partition the m-particle spaces into configuration subspaces and extend the EE theory. We will turn to this now with shell model spherical orbit configuration partitioning.…”

“…As a result, employing the Gaussian form of the strength functions, generated by EE, in configuration subspaces and using the fact that fluctuations follow GOE, interacting particle theory for nuclear level densities is developed (going beyond the conventional non-interacting particle theories) and it is being applied in different parts of the periodic table. The developments here are mainly due to French et al [15,16,17] where spin-cutoff factors are employed for J projection and Zelevinsky et al [18,19] where J is treated exactly along with many other refinements. This theory for level densities is called spectral distribution theory [15] and alternatively it is also called 'statistical shell model theory'for level densities [18].…”

“…The developments here are mainly due to French et al [15,16,17] where spin-cutoff factors are employed for J projection and Zelevinsky et al [18,19] where J is treated exactly along with many other refinements. This theory for level densities is called spectral distribution theory [15] and alternatively it is also called 'statistical shell model theory'for level densities [18]. With this progress, it is natural to develop embedded ensemble theory for transition strengths and apply the same to particle transfer strengths, beta decay, double beta decay and so on.…”