Precise nonvariational calculation of excited states of helium with the correlation-function hyperspherical-harmonic method

Journal Article · Sun Dec 01 04:00:00 EST 1991 · Physical Review A. General Physics; (United States)

DOI:https://doi.org/10.1103/PhysRevA.44.7158· OSTI ID:5590757

Krivec, R ^[1]; Haftel, M I ^[2]; Mandelzweig, V B ^[3]

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1. Max Planck Institute fuer Kernphysik, Postfach 103980, 6900 Heidelberg (Germany) J. Stefan Institute, P.O. Box 100, Jamova 39, 61111 Ljubjana (Yugoslavia)
2. Code 4651, Naval Research Laboratory, Washington, D.C. 20375 (United States)
3. Max Planck Institute fuer Kernphysik, Postfach 103980, 6900 Heidelberg (Germany) Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742 (United States)

A direct solution of the Schroedinger equation for the 2 {sup 1}{ital S}, 3 {sup 1}{ital S}, 4 {sup 1}{ital S}, and 5 {sup 1}{ital S} states of the helium atom is obtained with the correlation-function hyperspherical-harmonic (CFHH) method. Given the proper correlation function chosen from physical considerations, the method generates wave functions accurate in the whole range of interparticle distances that lead, in turn, to precise estimates of the expectation values of the Hamiltonian and of different functions of interparticle distances. Our results show that even with the simplest correlation function, the accuracy of the CFHH method (which contains no adjustable parameters) for excited states is comparable to that of the ground state. The accuracy is also comparable to that of the most sophisticated variational calculations involving hundreds of variational parameters.

• OSTI ID: 5590757
• Journal Information: Physical Review A. General Physics; (United States), Journal Name: Physical Review A. General Physics; (United States) Vol. 44:11; ISSN 1050-2947; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

664100* -- Theory of Electronic Structure of Atoms & Molecules-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
ASYMPTOTIC SOLUTIONS
ATOMIC RADII
CORRELATION FUNCTIONS
COULOMB FIELD
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
ELEMENTS
ENERGY LEVELS
EQUATIONS
EXCITED STATES
EXPECTATION VALUE
FLUIDS
FUNCTIONS
GASES
GROUND STATES
HAMILTONIANS
HELIUM
LAGUERRE POLYNOMIALS
LAMB SHIFT
MATHEMATICAL OPERATORS
NONMETALS
PARTIAL DIFFERENTIAL EQUATIONS
POLYNOMIALS
QUANTUM OPERATORS
RARE GASES
SCHROEDINGER EQUATION
SPECTRAL SHIFT
WAVE EQUATIONS
WAVE FUNCTIONS