The heavier even-even W nuclei, on the other hand, have the characteristics of an axial rotor, and hence the negative parity structure of the neighboring odd W isotopes offers the possibility to study the validity of the SU(3) limit. The region of interest thus spans the W-Pt nuclei, and since one prerequisite for an odd-A symmetry is the existence of that same symmetry in the neighboring even-even core nucleus, the odd Pt nuclei around A = 196 offer the obvious testing ground for the 0(6) limit of U(6/12). The fermion is allowed to occupy orbits with j = 1/2, 3/2 and 5/2, so that the assumed single particle space corresponds to the negative parity states available to an odd neutron at the end of the N = 82-126 shell, namely, P/sub 1/2/, p/sub 3/2/ and f/sub 5/2/. Of the structures studied in detail to date, the case of m = 12 is the one with the broadest potential. The ability to construct group chains corresponding to the symmetries SU(5), SU(3) or 0(6) depends on the value of m. The more » group structure of a boson-fermion system is described by U/sup B/(6) x U/sup F/(m) where m specifies the number of states available to the odd fermion, and thus depends on the single particle space assumed. The importance of the recently proposed symmetries in odd-even systems can thus be viewed in the same light, and their role in pointing to a simple prescription for the changing collective structure in odd A nuclei throughout a major shell is likely to prove even more essential, given the much greater complexity of the boson-fermion (IBFM) Hamiltonian. The concept of symmetry in the Interacting Boson Model (IBM) description of even-even nuclei has proved to be one of the model's most important elements, because they provide benchmarks in the formulation of a unified description of a broad range of nuclei. A calculation of the energy spectrum of the odd tungsten isotopes is presented. This model is seen to be very successful in describing nuclei with an odd number of protons or neutrons. Finally, a brief description of the Interacting Boson-Fermion Model is given. This approximation appears to be valid in both the 50-82 and the 82-126 neutron shells whose single-particle levels seem naturally to form two sub-shells. Next, the predictions of a two nondegenerate j-shell approximation are compared with empirical results. In this approximation the valence nucleons are assumed to occupy a single j-shell whose effective j value is chosen so as to reproduce the total occupancy of the valence shell. The predictions of a single j-shell approximation are compared with empirical results. Predictions for the IBM parameters are obtained by constructing the zeroth-order image of the corresponding fermion operator. The structure of the bosons of the IBM is given in terms of correlated fermion pairs. The IBM is then examined from a microscopic point of view, using the generalized seniority scheme. A specific example using the light mercury isotopes and the molybdenum more » isotopes is given. Following the study of the tungsten isotopes an extension of the IBM to describe configuration mixing is presented. The results are seen to agree very well with the experimental data. These observables include transition rates, branching ratios, /rho/(EO) values, quadrupole moments of the first two excited 2+ states, two-neutron separation energies, and isomer and isotope shifts. The basic IBM is then applied to the even tungsten isotopes and compared with experimental observables associated with the low-lying states. = ,Ī review of the principles and phenomenology of the IBM is presented. The importance of an experimental proof of the effect which become a new tool in the research of nuclear structure and a strong test of the validity more » of the hypotheses is emphasized. At the odd-even nuclei the theoretical value of the effect is surely within the reach of atomic spectroscopy, but the specific interest of the phenomenon lies here in the possible study of a pure bound neutron-electron interaction. By considering two particular forms of nuclear potential (harmonic oscillator and infinite square well), it is shown that there exists a very simple relation between the shift and the characteristics of the two nuclear states involved. The general formulas of the shift for odd-even and even-odd nuclei are given. In the case of two characteristic transitions, it is shown that the order of magnitude of the effect does not depend on the shape of nuclear potential. The sign of the shift is generally intimately related to the whole nuclear configuration. Under these assumptions it is shown that except for sign, the effect is a pure single particle effect, given by the optical nucleons. Single-particle transitions, and validity of the Rosenthal-Breit perturbation theory are assumed. Some general theoretical aspects of charge distribution in odd nuclei are studied.
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