Application of an extremum principle to the variational determination of the generalized oscillator strengths of helium

Journal Article · Tue Aug 01 04:00:00 EDT 1978 · Phys. Rev., A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.18.344· OSTI ID:6694538

Wadehra, J M; Spruch, L; Shakeshaft, R

Variational Principles have been used extensively for estimating some given functional F (phi,phi), where the functions phi and phi are well defined by a set of differential equations and boundary conditions but cannot be determined exactly. The variational principle for the estimation of a matrix element of an arbitrary Hermitian operator W involves, not only the trial wave functions phi/sub t/, but also trial auxiliary Lagrange functions L/sub t/; the L/sub t/ depend on the phi/sub t/ and on W. To determine the parameters in the L/sub t/ efficiently, a functional M (L/sub t/t) is constructed which is an extremum for L/sub t/t=L/sub t/. The technique was recently used successfully in the variational estimation of two diagonal matrix elements. We here use this technique for the variational estimation of an off-diagonal matrix element, the generalized oscillator strengths of helium for the transition between the ground state, and the excited 2 /sup 1/P state. Two L/sub t/'s must be determined. Our results on helium indicate that variational estimates are a significant improvement over the first-order estimates. The results are also compared with those obtained nonvariationally using more elaborate ground- and excited-state wave functions; the comparison represents a check on the method. It is not yet clear which of the two approaches is more efficient.

• Research Organization: Physics Department, New York University, New York, New York 10003
• OSTI ID: 6694538
• Journal Information: Phys. Rev., A; (United States), Journal Name: Phys. Rev., A; (United States) Vol. 18:2; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
CRYOGENIC FLUIDS
ELEMENTS
ENERGY-LEVEL TRANSITIONS
FLUIDS
HELIUM
MATRIX ELEMENTS
NONMETALS
OSCILLATOR STRENGTHS
RARE GASES
VARIATIONAL METHODS