dorsal/arxiv
View SchemaRelativistic recursion relations for transition matrix elements
| Authors | R. P. Martínez-y-Romero, H. N. Núñez-Yépez, A. L. Salas-Brito |
|---|---|
| Categories | |
| ArXiv ID | physics/0402061 |
| URL | https://arxiv.org/abs/physics/0402061 |
Abstract
We review some recent results on recursion relations which help evaluating arbitrary non-diagonal, radial hydrogenic matrix elements of $r^\lambda$ and of $\beta r^\lambda$ ($\beta$ a Dirac matrix) derived in the context of Dirac relativistic quantum mechanics. Similar recursion relations were derived some years ago by Blanchard in the non relativistic limit. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schr\"odinger case. An extension of the relations to the case of two potentials in the so-called unshifted case, but using an arbitrary radial function instead of a power one, is also given. Several important results are obtained as special instances of our recurrence relations, such as a generalization to the relativistic case of the Pasternack-Sternheimer rule. Our results are useful in any atomic or molecular calculation which take into account relativistic corrections.
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"abstract": "We review some recent results on recursion relations which help evaluating\narbitrary non-diagonal, radial hydrogenic matrix elements of $r^\\lambda$ and of\n$\\beta r^\\lambda$ ($\\beta$ a Dirac matrix) derived in the context of Dirac\nrelativistic quantum mechanics. Similar recursion relations were derived some\nyears ago by Blanchard in the non relativistic limit. Our approach is based on\na generalization of the second hypervirial method previously employed in the\nnon-relativistic Schr\\\"odinger case. An extension of the relations to the case\nof two potentials in the so-called unshifted case, but using an arbitrary\nradial function instead of a power one, is also given. Several important\nresults are obtained as special instances of our recurrence relations, such as\na generalization to the relativistic case of the Pasternack-Sternheimer rule.\nOur results are useful in any atomic or molecular calculation which take into\naccount relativistic corrections.",
"arxiv_id": "physics/0402061",
"authors": [
"R. P. Mart\u00ednez-y-Romero",
"H. N. N\u00fa\u00f1ez-Y\u00e9pez",
"A. L. Salas-Brito"
],
"categories": [
"physics.atom-ph",
"physics.atm-clus"
],
"title": "Relativistic recursion relations for transition matrix elements",
"url": "https://arxiv.org/abs/physics/0402061"
},
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