Abstract
A new method is developed for determining the distortions (polarizabilities) induced in electronic distributions by valence electrons and/or crystalline fields and their effect (expressed as Sternheimer shielding factors) on magnetic and electric hyperfine interactions. For illustrative purposes emphasis is placed in this paper on the calculation of Sternheimer antishielding factors (). Working within the framework of the Hartree-Fock self-consistent field formalism, it is shown that the 'angular' excitations are gotten by relaxing the usual restriction that the spatial part of the one-electron functions be separable into a radial function times an angular function; relaxing the restriction that electrons of the same shell but differing in magnetic quantum number (ml) have the same radial function yields the 'radial' excitations. To illustrate the method, calculations are reported for several spherical ions (Cl- and Cu+) in an external field, but the scheme is also applicable to the problem of induced electric quadrupole (and magnetic dipole and higher multipole) distortions of an ion by its own aspherical charge distribution. The problems of orthogonality, exchange, and self-consistency, which have complicated applications of the perturbation method are easily resolved by this approach. Further, since a self-consistent field procedure is followed, the distortions induced in the inner closed shells by the distorted outer shells are included in a natural way and by comparison with the results of the perturbation-variation method (which does not take these into consideration) these additional effects are shown to be significant.
| Original language | English |
|---|---|
| Pages (from-to) | 250-255 |
| Number of pages | 6 |
| Journal | Physical Review |
| Volume | 131 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1963 |
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Electronic Polarizabilities and Sternheimer Shielding Factors. / Watson, R. E.; Freeman, Arthur J.
In: Physical Review, Vol. 131, No. 1, 1963, p. 250-255.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Electronic Polarizabilities and Sternheimer Shielding Factors
AU - Watson, R. E.
AU - Freeman, Arthur J
PY - 1963
Y1 - 1963
N2 - A new method is developed for determining the distortions (polarizabilities) induced in electronic distributions by valence electrons and/or crystalline fields and their effect (expressed as Sternheimer shielding factors) on magnetic and electric hyperfine interactions. For illustrative purposes emphasis is placed in this paper on the calculation of Sternheimer antishielding factors (). Working within the framework of the Hartree-Fock self-consistent field formalism, it is shown that the 'angular' excitations are gotten by relaxing the usual restriction that the spatial part of the one-electron functions be separable into a radial function times an angular function; relaxing the restriction that electrons of the same shell but differing in magnetic quantum number (ml) have the same radial function yields the 'radial' excitations. To illustrate the method, calculations are reported for several spherical ions (Cl- and Cu+) in an external field, but the scheme is also applicable to the problem of induced electric quadrupole (and magnetic dipole and higher multipole) distortions of an ion by its own aspherical charge distribution. The problems of orthogonality, exchange, and self-consistency, which have complicated applications of the perturbation method are easily resolved by this approach. Further, since a self-consistent field procedure is followed, the distortions induced in the inner closed shells by the distorted outer shells are included in a natural way and by comparison with the results of the perturbation-variation method (which does not take these into consideration) these additional effects are shown to be significant.
AB - A new method is developed for determining the distortions (polarizabilities) induced in electronic distributions by valence electrons and/or crystalline fields and their effect (expressed as Sternheimer shielding factors) on magnetic and electric hyperfine interactions. For illustrative purposes emphasis is placed in this paper on the calculation of Sternheimer antishielding factors (). Working within the framework of the Hartree-Fock self-consistent field formalism, it is shown that the 'angular' excitations are gotten by relaxing the usual restriction that the spatial part of the one-electron functions be separable into a radial function times an angular function; relaxing the restriction that electrons of the same shell but differing in magnetic quantum number (ml) have the same radial function yields the 'radial' excitations. To illustrate the method, calculations are reported for several spherical ions (Cl- and Cu+) in an external field, but the scheme is also applicable to the problem of induced electric quadrupole (and magnetic dipole and higher multipole) distortions of an ion by its own aspherical charge distribution. The problems of orthogonality, exchange, and self-consistency, which have complicated applications of the perturbation method are easily resolved by this approach. Further, since a self-consistent field procedure is followed, the distortions induced in the inner closed shells by the distorted outer shells are included in a natural way and by comparison with the results of the perturbation-variation method (which does not take these into consideration) these additional effects are shown to be significant.
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U2 - 10.1103/PhysRev.131.250
DO - 10.1103/PhysRev.131.250
M3 - Article
VL - 131
SP - 250
EP - 255
JO - Physical Review
JF - Physical Review
SN - 0031-899X
IS - 1
ER -