Analytic Evaluation of Four-Particle Integrals with Complex Parameters

The method for analytic evaluation of four-particle integrals, proposed by Fromm and Hill, is generalized to include complex exponential parameters. An original procedure of numerical branch tracking for multiple valued functions is developed. It allows high precision variational solution of the Coulomb four-body problem in a basis of exponential-trigonometric functions of interparticle separations. Numerical results demonstrate high efficiency and versatility of the new method.Comment: 13 pages, 4 figure

SQUID-based microtesla MRI for in vivo relaxometry of the human brain

SQUID-based MRI (magnetic resonance imaging) at microtesla fields has developed significantly over the past few years. Here we describe application of this method for magnetic relaxation measurements in the living human brain. We report values of the longitudinal relaxation time T1 for brain tissues, measured in vivo for the first time at microtesla fields. The experiments were performed at 46 microtesla field using a seven-channel SQUID system designed for microtesla MRI and MEG. Values of T1, measured for different tissues at this field, are found to be close (within 5%) to the corresponding values of the transverse relaxation time T2 at the same field. Implications of this result for imaging contrast in microtesla MRI are discussed.Comment: To appear in Proceedings of 2008 Applied Superconductivity Conferenc

Variational Approximations in a Path-Integral Description of Potential Scattering

Using a recent path integral representation for the T-matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general ansatz quadratic in the velocity variables -- over which one has to integrate functionally -- we obtain variational equations which contain classical elements (trajectories) as well as quantum-mechanical ones (wave spreading).We analyse these equations and solve them numerically by iteration, a procedure best suited at high energy. The first correction to the variational result arising from a cumulant expansion is also evaluated. Comparison is made with exact partial-wave results for scattering from a Gaussian potential and better agreement is found at large scattering angles where the standard eikonal-type approximations fail.Comment: 35 pages, 3 figures, 6 tables, Latex with amsmath, amssymb; v2: 28 pages, EPJ style, misprints corrected, note added about correct treatment of complex Gaussian integrals with the theory of "pencils", matches published versio