Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




Professor R. K. Bhaduri


For a system of noninteracting fermions in a one-body potential it is possible to derive an expression for the "smooth" part of the energy by finding corrections to the Thomas-Fermi energy. By the "smooth" part of the energy we mean that part which varies smoothly as a function of particle number and deformation. The smooth energy is needed, for example, to find the shell corrections used in conjunction with the Strutinsky energy theorem to obtain nuclear deformation surfaces. In this thesis we find corrections to the Thomas-Fermi energy as a power series in n² using the Wigner-Kirkwood expansion of the one-body partition function. The resultant expression is valid for any potential whose gradients and higher order derivatives exist. The effects of a spin-orbit term in the Hamiltonian are also included. The convergence of the n² series is checked by considering both the harmonic oscillator potential and realistic Woods-Saxon potentials. Expressions are also found for the spatial and kinetic energy densities. Using these expressions the kinetic energy is expressed in terms of the density and gradients of the density.

The formalism is extended to the case of a constrained Hamiltonian. In particular the pushing and cranking models are considered. When corrections are added to the Thomas-Fermi result for the cranking model the moment of inertia is found to depart somewhat from the rigid-body value.

The extended Thomas-Fermi result is used to derive the usual Strutinsky smoothing method and the good agreement between the two methods shown numerically. The n-expansion is also compared to the A-expansion and is found to converge slightly faster than the A-expansion.

The formalism developed for the cranking model can be applied with only minor modifications to the problem of finding the magnetic susceptibility of a system of electrons. This fact is used to investigate surface effects on the magnetic susceptibility.

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