---
res:
bibo_abstract:
- 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.@eng
bibo_authorlist:
- autoren_ansetzung:
- Andrae, Dirk
- Andrae
- Dirk Andrae
- Andrae, D
- Andrae, D.
- D Andrae
- D. Andrae
foaf_Person:
foaf_givenName: Dirk
foaf_name: Andrae, Dirk
foaf_surname: Andrae
foaf_workInfoHomepage: http://www.librecat.org/personId=20327
bibo_doi: 10.1088/0953-4075/30/20/008
bibo_issue: '20'
bibo_volume: '30'
dct_date: 1997^xs_gYear
dct_identifier:
- UT:A1997YD77800008
dct_isPartOf:
- http://id.crossref.org/issn/0953-4075
- http://id.crossref.org/issn/1361-6455
dct_language: eng
dct_publisher: IOP PUBLISHING LTD@
dct_title: Recursive evaluation of expectation values (r(k)) for arbitrary states
of the relativistic one-electron atom@
...