Tapan Kumar Das

Application of supersymmetry to a coupled system of equations: the concept of a superpotential matrix

We apply supersymmetric quantum mechanics (SUSY QM) to multidimensional Schrodinger equations involving nonseparable potentials, which result in a system of coupled differential equations, where instead of the conventional definition of a scalar superpotential we introduce a superpotential matrix and succeed in applying SUSY QM to the coupled system. Finally, we discuss the shape-invariance condition for the potential matrix of such a system.

An approximate many-body calculation for trapped bosons with attractive interaction

The stability of trapped interacting bosons with attractive interactions is studied using an approximate many-body calculation. Instead of using the traditional hyperspherical harmonics expansion method we prescribe a potential harmonics expansion method (PHEM). The justification of the use of PHEM in connection with dilute condensates is presented. The choice of a correlation function is justified as it correctly reproduces the short-range two-body correlation in the wavefunction as also the correct value of the s-wave scattering length (as). Applications to 7Li and 85Rb condensates with the realistic van der Waals interaction give good agreement with the Rice and JILA experiments, respectively. The JILA experiment used controlled collapse of the 85Rb condensate for different values of as. Our calculations agree with the experimental results within the experimental error bars.

Computation of 2+ resonance in 6He: bound state in the continuum

Calculation of the 2+ resonance state of 6He in a three-body model (4He + n + n) is done by adopting a novel theoretical technique. The effective three-body potential for the 2+ state of 6He is obtained using hyperspherical harmonics and it presents a shallow well followed by a low and wide barrier. Numerical diffculties present in the calculation of the resonance energy of such a shallow well–barrier combination are overcome by the construction of a one-parameter (λ) isospectral potential having a bound state in the continuum. This potential develops a deep well followed by a high barrier for small positive values of λ. This effectively traps the system in a sharp resonant state and facilitates calculation of the resonance energy accurately. We obtain the first 2+ resonance at 1.814 MeV with a width of 135 keV. We also get a second 2+ resonance at 4.9 MeV.

Analytic superpotential for Yukawa potential by perturbation of the Riccati equation

Abstract The basic ingredient of supersymmetry is the analytic superpotential, which demands analytic ground state wave function, which does not exist for an arbitrary potential. We present a nice perturbative solution of the Riccati equation leading to an analytic superpotential for any arbitrary potential. Application to Yukawa potential gives excellent results.

Use of correlated potential harmonic basis functions for the description of the 4He trimer and small clusters

A correlated many-body basis function is used to describe the (4)He trimer and small helium clusters ((4)He(N)) with N = 4-9. A realistic helium dimer potential is adopted. The ground state results of the (4)He dimer and trimer are in close agreement with earlier findings. But no evidence is found for the existence of Efimov state in the trimer for the actual (4)He-(4)He interaction. However, decreasing the potential strength we calculate several excited states of the trimer which exhibit Efimov character. We also solve for excited state energies of these clusters which are in good agreement with Monte Carlo hyperspherical description.

Hyperspherical three-body calculation for neutron drip-line nuclei

The hyperspherical harmonics expansion method is applied to a three-body model of two-neutron halo nuclei. Convergence of the expansion has been ensured. A short-range repulsive part is incorporated in the interaction between the core and the extra-core neutron, to simulate the Pauli principle. Two neutron separation energy, rms radii, correlation factor and halo neutron density distributions have been calculated for . It is found that the convergence of the two-neutron separation energy is relatively slow, while other quantities reach convergence quickly.

Calculation of geometrical coupling coefficients for the hyperspherical harmonics approach

An elegant and fast method for the calculation of geometrical structure coefficients needed for an expansion of a few-body wavefunction and interaction in hyperspherical harmonics has been proposed. A sum rule for the GSC has also been derived, which is useful for an independent check of the coefficients. The proposed method of computation is many orders of magnitude faster than conventional methods.

Level-spacing statistics and spectral correlations in diffuse van der Waals clusters

We present a statistical analysis of eigenenergies and discuss several measures of spectral fluctuations and spectral correlations for the van der Waals clusters of different sizes. We show that the clusters become more and more complex with increase in cluster size. We study nearest-neighbour level spacing distribution

Hyperspherical harmonics expansion of the ground state of the Ps− ion

P(s)

Correlated many-body calculation to study characteristics of Shannon information entropy for ultracold trapped interacting bosons

, the level number variance