Terms Of Second-order Differential Equation Research Articles

Second-order differential equations in the Laguerre–Hahn class

Laguerre–Hahn families on the real line are characterized in terms of second-order differential equations with matrix coefficients for vectors involving the orthogonal polynomials and their associated polynomials, as well as in terms of second-order differential equation for the functions of the second kind. Some characterizations of the classical families are derived.

Relativistic mean-field approach to nuclear surface properties and spin-orbit effects

We treat symmetric semi-infinite nuclear matter in the relativistic mean-field approximation for the scalar-vector field theoretical model. Using special-type Dirac spinors the nucleonic Dirac equation is decoupled into two sets of differential equations for the spin-orientation dependent orbital nucleon Dirac spinors. We also rewrite the Dirac equation in terms of second-order differential equations with the spin-orbit interaction appearing explicitly. These equations can be solved if the spin-orbit part is left out. The spin-orbit effects thus can be isolated, and are shown to reduce the surface energy coefficient a s as well as the surface thickness t in such a way that their ratio remains practically unchanged. For realistic lagrangians — in linear as well as non-linear forms — consistent with the empirical spin-orbit single-partial level splittings, a s is reduced by nearly 10%. We also discuss nuclear surface properties and their relations to bulk properties of nuclei for several parameterizations of lagrangians in current use.