The dependence of the hyperfine interaction on the cellular potential in Li, Na, and K

The effect of including the Hartree field due to the conduction electrons in the cellular potential on the Fermi surface electron wave function is investigated. It is found that the Fermi surface electron density at the nucleus is reduced by 10% to 20% by including this term. Also, an L dependent effective local potential constructed to simulate Hartree–Fock theory is calculated and applied to Li. All calculations are performed using the Wigner–Seitz spherical cellular approximation, and the Schrödinger equation is solved by the Kohn (1954) variational method.

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The dependence of the hyperfine interaction on the cellular potential in Na and K. II

Canadian Journal of Physics ◽

10.1139/p69-170 ◽

1969 ◽

Vol 47 (13) ◽

pp. 1331-1336 ◽

Cited By ~ 11

Author(s):

R. A. Moore ◽

S. H. Vosko

Keyword(s):

Fermi Surface ◽

Electron Density ◽

Wave Functions ◽

Electron Wave ◽

Surface Electron ◽

Conduction Electrons ◽

Hartree Fock ◽

A Value ◽

Dependent Potential ◽

Conduction Electron Density

The dependence of the Fermi surface electron wave functions in Na and K on (i) an L-dependent effective local cellular potential constructed to simulate Hartree-Fock theory and (ii) the inclusion of the Hartree field due to the conduction electrons in the cellular potential is investigated. All calculations are performed using the Wigner–Seitz spherical cellular approximation and the Schrödinger equation is solved by the Kohn variational method. It is found that to ensure a value of the Fermi surface electron density at the nucleus accurate to ~5%, it is necessary to use the L-dependent potential along with the Hartree field due to a realistic conduction electron density.

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"VECTAL" REPRESENTATION OF THE WAVE FUNCTION AND ITS PHYSICAL MEANING

Canadian Journal of Physics ◽

10.1139/p67-308 ◽

1967 ◽

Vol 45 (11) ◽

pp. 3667-3676

Author(s):

C. S. Lin

Keyword(s):

Wave Function ◽

Wave Functions ◽

Electron Wave Function ◽

Electron Wave ◽

Expectation Values ◽

Expectation Value ◽

Hartree Fock ◽

The One ◽

The Relationship ◽

Determinantal Form

A new form of one-electron wave function, "vectal," is introduced. It is shown that an arbitrary CI geminal and a certain class of many-electron wave functions can be represented in a single-determinantal form in terms of the vectal. Eigenvalue equations for the vectal, similar to that of the Hartree–Fock theory, are derived and the vectal representation is shown to enable a formal interpretation of the CI theory in the Hartree–Fock manner. The eigenvalue, vectal energy, is interpreted as the negative of an ionization potential, in Koop-man's sense, of the system described by the CI wave function. It is also shown that the expectation value of any one-electron operator, [Formula: see text], where Ψ is the CI wave function, is expressible in terms of the expectation values of the same operator with respect to the vectals. The vectals are interpreted as the one-electron wave function in the CI space.A possible application of the vectal representation is briefly described, and the relationship between the vectal representation and the "scalar representation" is discussed.

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