On some integrals arising in mathematical physics

This paper presents in the first section the exact evaluation of three single integrals relating to the dielectric behavior of two-dimensional electron plasmas. In the second section we present a procedure for reducing 3d-dimensional integrals of the form: ∫∫∫dqdpdkD(q)(p+k+q)ƒ(p)[1−ƒ(p+q)]ƒ(k)[1−ƒ(k+q)], where the vectors lie in d-dimensional space and ƒ denotes the Fermi function, to tractable form. The second-order exchange integral for a d-dimensional electron gas is taken as an example and is evaluated in closed form as a function of d.     

Ion heating in the field-reversed configuration by rotating magnetic fields near the ion-cyclotron resonance

The trajectories of ions confined in a field-reversed configuration (FRC) equilibrium magnetic geometry and heated with a small-amplitude, odd-parity rotating magnetic field (RMF) have been studied with a Hamiltonian computer code. When the RMF frequency is in the ion-cyclotron range, explosive heating occurs. Higher-energy ions are found to have betatron-type orbits, preferentially localized near the FRC's midplane. These results are relevant to a compact magnetic-fusion-reactor design.     

The Infinite Square Well with a Singular Perturbation

We study the influence of a singular potential on an infinite square well. Two cases are considered. In the first, the singular potential is centered in the potential well, in the second case it is off-center. We also present a discussion on the self adjointness of the Hamiltonian of some exactly solvable potentials perturbed with singular potentials.     

Moments of Ramanujan?s generalized elliptic integrals and extensions of Catalan?s constant

We undertake a thorough investigation of the moments of Ramanujan?s alternative elliptic integrals and of related hypergeometric functions. Along the way we are able to give some surprising closed forms for Catalan-related constants and various new hypergeometric identities.     

ChemInform Abstract: Relationships Among Ionic Lattice Energies,Molecular (Formula Unit) Volumes,and Thermochemical Radii

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