Nazakat Ullah
Articles written in Pramana – Journal of Physics
Volume 1 Issue 5 November 1973 pp 209-211 Nuclear And Particles Physics
A study of the variable moment of inertia models
The variable moment of inertia (VMI) model proposed by Holmberg and Lipas has been shown to be a special case of the VMI model of Mariscotti
Volume 7 Issue 5 November 1976 pp 316-318 Nuclear And Particle Physics
Differential equation approach for the energy average of the scattering function
An exact differential equation is given to evaluate the energy average of the scattering function. The advantage of the differential equation as compared to the earlier methods based on series expansion is that one has to evaluate only single sums over the complex poles of the S-matrix. Using Wigner’s semicircle law for the distribution of the real parts of the poles of the scattering matrix, the earlier expression for the energy average of the scattering function is rederived.
Volume 15 Issue 1 July 1980 pp 45-51 Mathematical Physics
On the joint eigenvalue distribution for the matrix ensembles with non zero mean
Exact distributions are given for the two-dimensional case when the mean of the off-diagonal element is non-zero. The joint eigenvalue distribution for the
Volume 18 Issue 2 February 1982 pp 211-214 Nuclear And Particle Physics
An approximation procedure is described to calculate the projected energies from an intrinsic
Volume 20 Issue 2 February 1983 pp 131-135 Mathematical Physics
On an integral over the surface of
An integral which occurs in the new matrix ensembles and the width fluctuation factor is evaluated using a transformation which changes a Gaussian into an exponential. It is expressed in the form of a series whose terms are found using a simple recursion relation. It is shown that the series can be summed in closed form for the two-dimensional case.
Volume 24 Issue 1-2 January 1985 pp 27-29 Quantum Physics
Modified perturbation series for the anharmonic oscillator using linearization technique
The linearization technique of random phase approximation is applied to the anharmonic oscillator to find a modified perturbation series. It is shown that for the anharmonic term
Volume 26 Issue 1 January 1986 pp 9-14 Quantum Mechanics
A determinantal identity is used to calculate the ensemble-averaged traces of the Hamiltonian. Using these averages a general expression is obtained for the Fourier transform of the single eigenvalue probability density function for all the three Gaussian ensembles for the two-dimensional case. It is shown how one can use the familiar step-up operators for the representation of a determinant. The ensemble-averaged traces are also used to derive the Fourier transform of the non-zero mean ensemble.
Volume 28 Issue 6 June 1987 pp 641-644 Nuclear Physics
Density of nucleons in heavy nuclei
A shell model description of heavy nuclei is used to show that the density of nucleons in heavy nuclei is of the form
Volume 30 Issue 4 April 1988 pp 305-307 Nuclear Physics
A note on the mean-internucleon distance in the central region of heavy nuclei
The density distribution of nucleons in a heavy nucleus is used to show that the mean-internucleon distance in the central region of heavy nuclei is 1.99 fm.
Volume 31 Issue 2 August 1988 pp 87-91 Quantum Mechanics
Exact generator coordinate wave functions for some simple hamiltonians
A Gaussian form of the generator coordinate wave function is used to find the exact weight function for the ground state of H-atom using HWG integral equation. Exact pairs of GC wave functions and weight functions are then constructed for other simple Hamiltonians using a simple integral which converts an exponential into a Gaussian. A discussion as to how a GC wave function can be used as a trial variational wave function is also presented.
Volume 35 Issue 3 September 1990 pp 325-328 Research Articles
Density of quarks in heavy spherical nuclei using NRQSM
A nonrelativistic quark shell model (NRQSM) is used to derive an expression for the density of quarks in heavy spherical nuclei. It is shown that quark density is related in a simple way with the probability of finding a nucleon in a nucleus. The quark density is used to determine the ratio of average distance between two quarks to the average distance between two nucleons.
Volume 41 Issue 2 August 1993 pp 1- Comments
It is pointed out that the value of the perturbed energy calculated in the comment by Rath and Pattnayak, is incorrect. When the coupling parameter has the value unity, the energy up to second order of perturbation theory is 0.801 compared to its exact value of 0.804. The suggested split of the Hamiltonian into an unperturbed and perturbed part does not seem to be of any use as the unperturbed part contains anharmonic terms.
Volume 41 Issue 2 August 1993 pp 171-174 Research Articles
Momentum space distribution of electrons in an atom using hydrogenic wave functions
A formulation is developed to derive exact analytic expressions for electron-electron correlation and density of electrons in momentum space using hydrogenic wave functions. It is shown that for large atoms the expression for density of electrons has a simple form.
Volume 42 Issue 6 June 1994 pp 491-494 Brief Report
Quark distribution in light nuclei
The distribution of quarks in light nuclei is given using the quark cluster wave function. An analytic expression for the nucleus^{4}He is obtained. The distribution so obtained is compared with the one obtained using a different theoretical formulation called mapping.
Volume 43 Issue 2 August 1994 pp 165-168
Single nucleon distribution based on shell-model and matrix ensemble theory
An expression for the density of single nucleons in a heavy spherical nucleus is derived using the shell-model and matrix ensembles. It is shown that the theoretical expression gives an excellent fit to the density of nucleons for the nucleus^{197}Au obtained using
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