• V K B Kota

Articles written in Pramana – Journal of Physics

• Single particle SU(3) parentage coefficients

The single particle SU(3) parentage coefficients are calculated for the case of leading SU(3) representation in the highest orbital symmetry partition, using the method suggested by Hecht. Tabulations are given for all possible cases of identical nucleons in η=3 and η=4 shells.

• Eigenvalue density for ensemble of 2-body random hamiltonians with non-zero mean for matrix elements

We obtain an expression for the ensemble-averaged moments inm-particle space of 2-body random Hamiltonians with same non-zero mean for the matrix elements, in the limit ofN → ∞,m ≫ 2. The eigenvalue density function can then be immediately obtained in terms of the eigenvalue density (a Gaussian whenm ≫ 2) for zero mean ensembles. The results of Monte-Carlo calculations for iso-scalar rotationally invariant 2-body ensembles have also been given.

• Generalized interacting boson model and the collective behaviour in nuclei

The effect of including the high spin bosons on the manifestation of collective behaviour in nuclei is examined by plotting theB(E2; 2+→0+) rates as a function of neutron number for various values ofη, whereη is the highest angular momentum of the bosons included in the calculation.B(E2; 2+→0+) values of a large number of nuclei in various regions of the nuclear periodic table are calculated with a single value for the effective charge in the generalized scheme. Irreducible representations of SU(3) contained in the symmetric partition [N] of U(15) are worked out for integersN uptoN=15, to enable the explicit inclusion of theg boson into calculations. The experimentally observed odd-K bands in234U and184W are described as a direct consequence of theg boson.

• State densities and spectrum fluctuations: information propagation in complex nuclei

At excitation energies in nuclei where the state density is unambiguously defined there is a sharp separation between the smoothed spectrum (which defines the density) and fluctuations about it which have recently been studied with a view to understanding some aspects of quantum chaos. We briefly review these two complementary subjects, paying special attention to: the role of the effective interaction in determining the density; the calculation of interacting-particle state and level densities, and of expectation values of interesting operators; the information about the effective nucleon-nucleon interaction which is carried both by the density and the fluctuations.

• Inverse energy weighted sum-rules

A new derivation of the inverse energy-weighted sum-rules is given by applying the spectral distribution methods to the Rayleigh-Schrodinger perturbation theory. The scalar space result is then extended to the configurations. This is applied to obtain corrections to the ground-state energy estimates when the effective interaction is approximated by a model Hamiltonian obtained by taking linear combinations of various parts of the pairing and the Q.Q operators.

• Spectral distributions in nuclei: General principles and applications

The subject of spectral distribution methods where one derives and applies the locally smoothed forms of observables in nuclei is briefly reviewed. It is well understood that the local forms (with respect to energy) of the level density function, expectation values and strength densities are Gaussian, linear (or ratio of Gaussians) and a bivariate Gaussian respectively. To accomodate symmetries in the above forms, one has to deal with multivariate distributions in general; for example the angular-momentum (J) decomposition leads to a bivariate Gaussian form for the level density. These results extend to indefinitely large spaces by method of partitioning and they generate convolution forms. The origin of these remarkable spectral properties is discussed and shell model examples are given to substantiate their applicability to nuclear systems. Spectral distribution theory is a practical, usable theory because the smoothed forms are defined in terms of traces of low particle-rank operators, and the trace information propagates. Finally we discuss the application of the spectral methods for a wide range of nuclear problems; these include binding energies, orbit occupancies, electromagnetic andβ-decay sum rule quantities, analysis of operators, symmetry breaking, numerical level densities, and determination of bounds on time-reversal non-invariant part of nucleon-nucleon interaction.

• Group theoretical aspects ofUB(6) ⊗UF(20) symmetry limits of IBFM related to theUB(5) andOB(6) limits of IBM

TheUB(6)⊗UF(20) Bose-Fermi dynamical symmetry of interacting boson-fermion model arises when the odd nucleon occupies single particle orbits withj=1/2, 3/2, 5/2, and 7/2. The subgroup structures ofUB(6)⊗UF(20) related to theUB(5) andOB(6) limits of sdIBM (UB(6)) are analysed. Broadly speaking,UB(6)⊗UF(20) admitsUBF(5)⊗UsF(4), SpinBF(5)⊗UkF(5) andUBF(5)⊗UsF(2) limits withUB(5) core and SpinBF(6),OBF(5)⊗UsF(4), SpinBF(6)⊗UkF(5) andOBF(6)⊗UsF(2) limits withOB(6) core respectively. For each of these seven symmetry limits, group chains, quantum numbers labelling the basis states, generators and Casimir operators for the various subgroups and energy formulas are given. Recoupling coefficients (reduced Wigner coefficients) for constructing wavefunctions of low-lying states are tabulated and these will allow (together with sdIBMUB(5) andOB(6) limit results) one to calculateB(E2)’s,B(M1)’s, one and two nucleon transfer strengths etc. in the seven symmetry limits. Experimental examples for theUB(6)⊗UF(20) symmetry limits are briefly discussed.

• # Pramana – Journal of Physics

Current Issue
Volume 93 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019