Nuclear volume effects

Abstract uranium isotopes fractionate as a result of nuclear volume effects such that ratios vary as a funotion of uranium oxidation state, being highest in reduced species such as U"" in uraninite. The values of uranium minerals from volcanic-, metasomatic-, unconformity-,... 

This paper reviews progress in the application of atomic isotope shift measurements, together with high precision atomic theory, to the determination of nuclear radii from the nuclear volume effect. The theory involves obtaining essentially exact solutions to the nonrelativistic three- and four-body problems for helium and lithium by variational methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. The results are applied to the calculation of isotope shifts for the short-... 

K. Hirao. Ligand effect on uranium isotope fractionations caused by nuclear volume effects An ab initio relativistic molecular orbital study. /. Chem. Phys.,... 

F. A. Paipia, A. K. Mohanty, E. Qementi. Relativistic calculations for atoms self-consistent treatment of Breit interaction and nuclear volume effect. /. Phys. B At. Mol. Opt. Phys., 25 (1992) 1-16. 

Nuclear volume effects, sometimes referred to as nuclear field shift effects, are believed to be one cause of mass-independent isotope fractionation [46]. Nuclei of isotopes differ from one another only in their number of neutrons. Self-evidently, this provides the isotopes with a different mass, but this may also give rise to differences in the size and shape of the nuclei among the isotopes. The nuclei of nuclides with an odd number of neutrons are often smaller than they should be based on the mass difference relative to those of the neighboring nuclides with an even number of neutrons [47]. These differences in nuclear shape and size, and thus charge density, affect the interaction between the nucleus and the surrounding electron cloud. The resulting difference between the isotopes in terms of density and shape of the electron cloud results in slight differences in the efficiency with which they participate in chemical reactions [48]. 

A variety of experimental techniques have been employed to research the material of this chapter, many of which we shall not even mention. For example, pressure as well as temperature has been used as an experimental variable to study volume effects. Dielectric constants, indices of refraction, and nuclear magnetic resonsance (NMR) spectra are used, as well as mechanical relaxations, to monitor the onset of the glassy state. X-ray, electron, and neutron diffraction are used to elucidate structure along with electron microscopy. It would take us too far afield to trace all these different techniques and the results obtained from each, so we restrict ourselves to discussing only a few types of experimental data. Our failure to mention all sources of data does not imply that these other techniques have not been employed to good advantage in the study of the topics contained herein. 

The electric monopole interaction between a nucleus (with mean square radius k) and its environment is a product of the nuclear charge distribution ZeR and the electronic charge density e il/ 0) at the nucleus, SE = const (4.11). However, nuclei of the same mass and charge but different nuclear states isomers) have different charge distributions ZeR eR ), because the nuclear volume and the mean square radius depend on the state of nuclear excitation R R ). Therefore, the energies of a Mossbauer nucleus in the ground state (g) and in the excited state (e) are shifted by different amounts (5 )e and (5 )g relative to those of a bare nucleus. It was recognized very early that this effect, which is schematically shown in Fig. 4.1, is responsible for the occurrence of the Mossbauer isomer shift [7]. 

For molecules containing light atoms, we accordingly neglect this effect of finite nuclear volume or field shift, but other effects prevent exact application of isotopic ratios that one might expect on the basis of a proportionality with in formula 13 instead of total F. For this reason we supplement term coefficients in formula 8 for a particular isotopic species i with auxiliary coefficients [54],... 

The heaviest elements with observed fractionations of about 3 to 4%c are mercury and thallium. This is surprising because isotope variations due to mass-dependent fractionations should be much smaller. Schauble (2007) demonstrated that isotope variations for the heaviest elements are controlled by nuclear volume, a fractionation effect being negligible for the light elements. Nuclear volume fractionations may... 

Because of the near constancy of the density distributions in the nuclear volume, the separation of shell effects is easier there and part of the methods deviced in the nuclear field are not applicable to electronic structure. 

It is much more difficult to take into account the influence of finite dimensions and form of the nucleus (volume effect) on the atomic energy levels, because we do not know exactly the nuclear volume, or its form, or the character of the distribution of the charge in it. Therefore, in such cases one sometimes finds it by subtracting its part (22.35) from the experimentally measured total isotopic shift. Further on, having the value of the shift caused by the volume effect, we may extract information on the structure and properties of the nucleus itself. For the approximate determination of the isotope shift, connected with the differences dro of the nuclear radii of two isotopes, the following formula may be used [15] ... 

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