10.1088/0953-4075/30/20/008
Andrae, Dirk
Dirk
Andrae
Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom
IOP PUBLISHING LTD
1997
2010-04-28T13:22:13Z
2018-07-24T12:57:50Z
journal_article
https://pub.uni-bielefeld.de/record/1627292
https://pub.uni-bielefeld.de/record/1627292.json
An algorithm for the recursive evaluation of expectation values (r(k)) for a given state of the relativistic one-electron atom with a point-like nucleus of charge number Z is proposed. In contrast to previous approaches, the present algorithm is based on only a single recurrence relation, which is a recurrence relation for a special type of generalized hypergeometric F-3(2) series. Two sequences of values of such 3 F-2 series are generated. Finally, the members of these two sequences are assembled to yield the expectation values. The algorithm can be considered as a relativistic analogue of the Kramers-Pasternack recursion for expectation values (r(k)) for states of the non-relativistic hydrogen-like atom. As an application closed-form expressions for (r(k)), -6 less than or equal to k less than or equal to 5, were derived. In addition, numerical values for (r(k)) are given for some representative states of one-electron atoms with Z = 1, 80 and 137.