Volume 36, Issue 1
January 1991, pages 1-123
pp 1- January 1991 Rapid Communication
We explain the signature effects in the spectrum of odd mass Yb nuclei in a projected Hartree-Fock calculation without assuming gamma asymmetry. Rotation-alignment of nucleons in largej orbits is responsible for the signature dependence in energy and transition rates.
pp 1-77 January 1991 Review
Spin glass, the travelling salesman problem, neural networks and all that
This paper presents an overview of diverse topics that are seemingly different but interrelated, with strong connections to statistical mechanics on the one hand and spin glass physics on the other. Written primarily for an inter-disciplinary audience, we start with a brief recapitulation of the relevant aspects of statistical mechanics, particularly those needed for understanding the recently-popular simulated-annealing technique used in optimization studies. Then follows a survey of the spin glass problem, with particular attention to the consequences of quenched randomness. The travelling-salesman problem is considered next, as also the impact made on it by the spin glass problem. Several examples are then presented of optimization studies wherein the simulated-annealing concept has been profitably used. Attention is also drawn in this context to the lessons provided by the spin glass problem. Finally, a brief survey of neural networks is made, essentially from a physicist’s point of view. The different learning schemes proposed are discussed, and the relevance of spin models and their statistical mechanics is also discussed.
pp 79-93 January 1991 Research Articles
Estimates of the number of quantal bound states in one and three dimensions
Using the relation between the number of bound states and the number of zeros of the radial eigen-functionψ(r), or equivalently, that ofφ(r)=rψ(r) in the range 0⩽r⩽∞, the upper bounds on the number of bound states generated by potentialV(r) in different angular momentum channels are obtained in three dimension. Using a similar procedure, the upper bound on the number of bound states in one dimension is also deduced. The analysis is restricted to a class of potentials for whichE=0 is the threshold. By taking a number of specific examples, it is demonstrated that both in one and three dimensions, the estimate of the upper bound obtained by this procedure is very close to or equal to the exact number of bound states. The correlation of the present method with the Levison’s theorem and WKB approximation is discussed.
pp 95-103 January 1991 Research Articles
Spherically symmetric static inhomogeneous cosmological models
Spherically symmetric static cosmological models filled with black-body radiation are considered. The models are isotropic about a central observer but inhomogeneous. It is suggested that the energy density of the free gravitational field, which is coupled to the isotropic radiation energy density, might play an important role in generating sufficient field (vacuum) energy (when converted into thermal energy) and initiate processes like inflation. On the central world line the energy density of the free gravitational field vanishes whereas the proper pressure and density of the isotropic black-body radiation are constants. Further, it is shown that the cosmological constant is no more arbitrary but given in terms of the central pressure and density. Also, at its maximum value the energy density of the free gravitational field is proved to be equal to one third of the combined value of radiation pressure and density.
pp 105-114 January 1991 Research Articles
Newby shift ofK=0 rotational bands in odd-odd rare-earths
Alpana Goel A K Jain R W Hoff R K Sheline
A data set of 29 experimentally determined Newby shifts in rare-earth nuclei is examined for the reliability of each values. Using this data set, Newby shifts are obtained which are free from the Coriolis and the particle-particle coupling effects. These new empirical values help resolve the failure of a recently proposed rule for the sign of the Newby shift in the {5/2[413]p − 5/2[642]n} configuration of^{160}Tb and the {5/2[402]p − 5/2[512]n} configuration of^{174}Lu. Also the Newby shifts are significantly modified in two other cases namely the {1/2[411]p − 1/2[521]n} configuration in^{168}Tm and the {1/2[541]p − 1/2[521]n} configuration in^{172}Lu. Only marginal changes are seen in the rest of the cases in the rare-earth nuclei.
pp 115-123 January 1991 Research Articles
Alpha particle induced reactions on copper and tantalum
A V Mohan Rao S Mukherjee J Rama Rao
Alpha particle induced reactions in the target elements copper and tantalum were studied. The excitation functions of^{63}Cu(α, n) +^{65}Cu(α, 3n),^{65}Cu(α, 2n),^{181}Ta(α, 2n) and^{181}Ta(α, 4n) were measured up to 75 MeV.Eight new energy point cross-sections were measured for the first time. The experimental results were compared with the predictions of updated hybrid model (ALICE/85/300) as well as with index model using the initial exciton numbern_{0}=4 (4poh) and level density parameter,a=A/8. A general agreement was found for all the reactions with both the models.
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