Nuclear oblate

In quadrupole splitting, the existence of a nonspherical nuclear charge distribution produces an electric quadrupole moment, Q, which indicates that the charge distribution in the nucleus is prolate, when Q > 0, or oblate, if Q < 0 [137-140],... 

Fig. 1. Nuclear shapes and nuclear quadrupole moments (a) prolate nucleus, I> 1, Q> 0 (b) spherical nucleus, I = 1/2. eQ — 0 (c) oblate nucleus, I> 1, eQ <0...

Extensions to the spherical jellium model have been made to incorporate deviations from sphericality. Clemenger [15] replaced the Woods-Saxon potential with a perturbed harmonic oscillator model, which enables the spherical potential well to undergo prolate and oblate distortions. The expansion of a potential field in terms of spherical harmonics has been used in crystal field theory, and these ideas have been extended to the nuclear configuration in a cluster in the structural jellium model [16]. 

In a 2005 review article, Cwiok, Heenan, and Nazarewicz (2005) present new theoretical results for properties of even-even heavy and SHE element nuclei with 94 < Z < 28 and with 134 < N < 188. They use self-consistent formalism and a modern nuclear energy density functional to formulate the following major conclusions concerning SHEs (1) SHE nuclei around Z= 116 and N= 176 are expected to exhibit coexistence of oblate and prolate shapes,... 

Fig. 1.1. Classical picture of the origin of nuclear electric quadrupole moments through deformation of a (rotating) charged sphere. (A) prolate ellipsoid with eQ positive, (B) oblate ellipsoid with eQ negative...

Nuclear electric quadrupole A parameter which describes the effective shape of the ellipsoid of nuclear charge distribution. A nonzero quadrupole moment Q indicates that the charge distribution is not spherically symmetric. By convention, the value of Q is taken to be positive if the ellipsoid is prolate and negative if it is oblate. 

A table of the microwave spectra of triatomic molecules [1] contains 139 lines for OF2 with frequencies ranging from 8299.51 to 59846.20 MHz, which were taken from the literature, and, in an appendix, 26 additional lines from 84401.810 to 95998.940 MHz and one line at 7803.49 MHz (transitions between rotational levels Jk-,k, with J = total angular momentum quantum number excluding nuclear spin and K", K" = projections of J on the symmetry axis of the limiting prolate or oblate symmetric top). Eight of these known rotational transitions and seven new transitions, belonging to the Vi =1 and Vg = 2 vibrationally excited states, were more recently observed by IR-microwave (MW) double resonance or IR-MW-MW triple resonance [12]. 

Atomic nuclei can be stretched like cigars (prolate shape) or compressed like discs (oblate shape). The deformation is described by the electric quadrii-pole moment Q (prolate Q > 0 oblate Q < 0). The principal interaction is, of course, the normal electrostatic (Coulomb) force on the charged nucleus monopole interaction). The differential interaction, which depends on the structure of the nucleus and on the valuation of the field across its finite extension, is of course very much smaller quadrupole interaction). It gives rise to an electric hyperfine structure. The energy contribution depends on the direction of the nuclear spin in relation to the electric field gradient. For the electric hyperfine interaction one obtains... 

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