Calculation of moments, potentials, and energies for an arbitrarily shaped diffuse-surface nuclear density distribution

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Abstract
We calculate several quantities of physical interest for an arbitrarily shaped diffuse-surface nuclear density distribution that is made diffuse by folding a short-range function over a uniform sharp-surface distribution of given shape. The quantities calculated include the moment of inertia about an arbitrary axis, generalized multipole moments, Coulomb and nuclear potentials, and Coulomb and nuclear energies. The expressions that are obtained in terms of volume integrals are converted into surface integrals by use of single and double divergence relations; these techniques are discussed for general functions. All of our methods and some of our results apply to arbitrary folding functions, although for definiteness most of our results are specialized to the case of a Yukawa folding function. The diffuseness of the nuclear surface increases the moment of inertia of light nuclei substantially, which increases the critical angular momentum at which compound nuclei can no longer be formed. The diffuseness correction to the Coulomb energy contains a term that is proportional to the surface area; this term increases the effective surface energy by approximately 2% for light nuclei and by approximately 1% for heavy nuclei.