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K. Kar

Publications and source records attributed to K. Kar.

5 recordsLinked to original sources
arXiv2000

Transition Strength Sums and Quantum Chaos in Shell Model States

For the embedded Gaussian orthogonal ensemble (EGOE) of random matrices, the strength sums generated by a transition operator acting on an eigenstate vary with the excitation energy as the ratio of two Gaussians. This general result is compared to exact shell model calculations, with realistic interactions, of spherical orbit occupancies and Gamow-Teller strength sums in some $(ds)$ and $(fp)$ shell examples. In order to confirm that EGOE operates in the chaotic domain of the shell model spectrum, calculations are carried out using two different interpolating hamiltonians generating order-chaos transitions. Good agreement is obtained in the chaotic domain of the spectrum, and strong deviations are observed as nuclear motion approaches a regular regime (transition strength sums appear to follow the Dyson's $Δ_3$ statistic). More importantly, they shed new light on the newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities (they include strength functions) define the statistical description of these systems and these densities follow from embedded random matrix ensembles; some EGOE calculations to this end are presented.

nucl-th↗
arXiv1999

Electron Capture Rates of Mid-fp Shell Nuclei for Supernova and Stellar Evolution

A detailed model is constructed for the calculation of electron capture rates of some fp-shell nuclei for situations prevailing in pre-supernova and collapse phases of the evolution of the core of massive stars leading to supernova explosion. The model uses explicitly the Gamow-Teller strength function obtained through (n,p) reaction studies wherever available. The rates include contribution from the excited states of the mother as well as from the resonant states in equilibrium with the back reaction i.e. the beta decay of the daughter nucleus. Comparisons are made with the shell model results and the earlier calculations by Aufderheide et al. and Fuller, Fowler and Newman. For the nuclei $^{56}$Fe, $^{55}$Mn and $^{60}$Ni with negative Q-values one observes large contribution from the excited states.

astro-ph↗
arXiv1998

Half-lives and pre-supernova weak interaction rates for nuclei away from the stability line

A detailed model for the calculation of beta decay rates of the $fp$ shell nuclei for situations prevailing in pre-supernova and collapse phases of evolution of the core of massive stars leading to supernova explosion has been extended for electron-capture rates. It can also be used to determine the half-lives of neutron-rich nuclei in the $fp/fpg$ shell. The model uses an averaged Gamow-Teller (GT) strength function. But it can also use the experimental log ft values and GT strength function from $(n,p)$ reaction studies wherever available. The calculated rate includes contributions from each of the low-lying excited states of the mother including some specific resonant states ("back resonance") having large GT matrix elements.

nucl-th↗
arXiv1997

Spectral Distribution Studies of fp shell nuclei with modified Kuo--Brown Interaction

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 shell model studies. Spectral distribution studies avoid explicit diagonalization and hold promise for applications to astrophysics.

nucl-th↗