Effective operators in the nuclear shell model: (II). Phenomenology of E2 operators

doi:10.1016/0375-9474(70)90900-0

Nuclear Physics A

Volume 155, Issue 2, 26 October 1970, Pages 337-361

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Abstract

The coupling operator discussed in paper I is defined in terms of a buffer space and parameterized to fit the observed E2 effective charge in the oxygen region. Variations in the exchange character of the coupling operator resulting from changes in the assumed effective charges are studied. The effect on the E3 effective charge and the magnitude of the two-body E2 operator are discussed.

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Cited by (19)

Neutron and proton polarisation charges from E2 mirror transitions
1985, Nuclear Physics, Section A
Renormalization for collective motion within a truncated space of the spherical shell model. II. Projected frame in a schematic model
1978, Annals of Physics
In paper I, [Ann. Phys. (N.Y.)94 (1975)] the matrix elements of effective operators in an intrinsic frame of the spherical shell model, that were determined by an iterative, renormalization technique, were shown to be analytically equivalent to those from a deformed, unrestricted Hartree-Fock model for the case of ²⁰Ne with a schematic quadrupole-quadrupole Hamiltonian. This paper shows the numerical comparison of the results from the renormalized spherical shell model and the projected, deformed Hartree-Fock model in the laboratory frame with states of definite angular momentum. Good agreement is found for the full iterative, renormalization results and those from the variation-after-projection Hartree-Fock model.
E2 core-polarization charge for nuclei near 16O and 40Ca
1977, Nuclear Physics, Section A
Empirical electric-quadrupole core-polarization charges are extracted from the experimental γ-ray transitions probabilities and quadrupole moments of nuclei near ¹⁶O and ⁴⁰Ca. using Woods-Saxon wave functions which include two-hole excitations of the cores. The results are discussed in terms of microscopic and macroscopic models of the core-polarization charge which are modified to include binding-energy-dependent effects. The empirical results ²⁷A1 deduced levels, J. Enriched target. are e_n = 0.34±0.02 e and e_p = 0.94±0.05 e for A = 18 and e_n = 0.57±0.03 e and e_p = 1.06 ± 0.07 e for A = 42. In both the macroscopic and microscopic models the isoscalar polarization charges imply that some of the isoscalar E2 strength m ¹⁶O and ⁴⁰Ca. lies above √2ħω. The isovector polarization charges are larger than predicted by the microscopic calculations using the Kuo-Brown interaction but are consistent with the macroscopic model where $E(T = 1) = 3.3 h ̵ ω$ .
Magnetic moments and half-lives of isomeric states in polonium isotopes
1976, Nuclear Physics, Section A
We have observed small violations of the additivity rule for isomeric two-proton states in ^{202, 208–210}Po. The g-factors of the 110 ns 8⁺ state in ²⁰²Po and of the 24 ns $132$ ⁻ state in ²⁰⁹Po were measured for the first time. The accuracy of relative g-factors which were previously measured has been considerably improved. The static quadrupole moment of ²⁰⁹Bi g.s. is deduced from three E2 transition probabilities in ²¹⁰Po. The absolute value of Q is ≈ 15% larger than obtained by optical spectroscopy and possible reasons for the discrepancy are discussed.
Lifetime of the 1.89 MeV 2+ level of 18Ne: Two-body contributions to E2 transition rates
1976, Nuclear Physics, Section A
Momentum dependence of polarization charges in electron excitation of nuclei in the oxygen region
1975, Nuclear Physics, Section A
We have considered the polarization effects for monopole and quadrupole electron excitations of nuclei in the oxygen region. A phenomenological method has been used in order to extrapolate empirical values for the polarization charges, from the real photon limit, to higher momentum transfers. We find in most cases polarization charges that are nearly constant, for momentum transfers up to 2 or 3 fm⁻¹. Hence we have provided a justification in the oxygen region for the assumption most frequently made when experiment and theory are compared.

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Nuclear Physics A

Abstract

References (29)

Nucl. Phys.

Nucl. Phys.

Ann. of Phys.

Ann. of Phys.

Rev. Mod. Phys.

Bull. Am. Phys. Soc.

Nucl. Phys.

Phys. Rev.

Report AECL-3366

Phys. Rev.

Enrico Fermi XL Course

Cited by (19)

Neutron and proton polarisation charges from E2 mirror transitions

Renormalization for collective motion within a truncated space of the spherical shell model. II. Projected frame in a schematic model

E2 core-polarization charge for nuclei near <sup>16</sup>O and <sup>40</sup>Ca

Magnetic moments and half-lives of isomeric states in polonium isotopes

Lifetime of the 1.89 MeV 2<sup>+</sup> level of <sup>18</sup>Ne: Two-body contributions to E2 transition rates

Momentum dependence of polarization charges in electron excitation of nuclei in the oxygen region