arXiv subjects

R. F. Snider

Publications and source records attributed to R. F. Snider.

3 recordsLinked to original sources

arXiv2002

An Analytical Formulation of CPMAS

An exact expression for the cross polarization between two spin-1/2 particles is derived from the quantum Liouville equation. This is given in the form of two integrodifferential equations. These can be solved exactly in the static case (no sample spinning) and a powder average performed numerically. With magic angle spinning, the neglect of certain interference terms simplifies the numerical calculation. A further assumption decoupling the calculation of the sidebands gives a very simple formula that is capable of giving a qualitative interpretation of all experimental observations. Examples are given illustrating typical buildup curves and CPMAS matching profiles.

physics.chem-ph↗

arXiv2000

Generalized Faddeev Equations for N-Particle Scattering

A proposal is made for reducing the solution of the N-particle Lippmann-Schwinger equation to that of smaller sets of particles. This consists of first writing the N-particle equation in terms of all possible $N/2$-particle Lippmann-Schwinger equations. (If N is odd this needs a minor modification.) The second step requires a decoupling of the resolvents for the fewer particle systems so that each can be solved separately. This generalization of the Faddeev approach deals only with connected kernels and the homogeneous solution reproduces the N-particle Schrödinger equation. For four particles the proposed method involves only a $3\times3$ matrix whereas other approaches typically require the solution of at least a $7\times7$ matrix equation.

nucl-th↗

arXiv1998

Solvable three boson model with attractive delta function interactions

A one parameter solvable model for three bosons subject to delta function interactions in one-dimension with periodic boundary conditions is studied. The energy levels and wave functions are classified and given explicitly in terms of three momenta. In particular, eigenstates and eigenvalues are described as functions of the model parameter, c. Some of the states are given in terms of complex momenta and represent dimer or trimer configurations for large negative c. The asymptotic behaviour for small and large values of the parameter, and at thresholds between real and complex momenta is provided. The properties of the potential energy are also discussed.

quant-ph↗