Shuichiro Yamasaki

On the Velocity Operator in Many-Boson System

Garrison, Morrison and W ong,l> however, have recently shown that the commutation relation (1) is inconsistent with the nonnegative character of the density operator, and asserted that existence of the velocity operator which satisfies the relation (1) is not admissible. The point of their arguments is essentially equivalent to the wellknown theorem that canonical variables satisfying a canonical commutation relation have as eigenvalues all real numbers from + oo to oo (e.g. see reference 2)). Their assertion is quite correct if one introduces the velocity operator as a canonical conjugate of the density operator itself defined by p(x)=cf;*(x)c{;(x) or by p(x)=(1/N) X2]aJ(x-ra).3l It is however a hasty conclusion to assert non-existence of the velocity operator which satisfies the commutation relation (1). The interacting Bose system enclosed in a cubic box of volume Q is represented by the Hamiltonian h2 H= 2m itk2ak*ak

Interaction of beta-decay and second forbidden spectrum of Cs137

Abstract We discuss the allowed as well as non-unique first forbidden β-spectra, and, in particular, the second forbidden spectrum of Cs 137 taking account of parity non-conservation. Our analysis can be summarized in the following way: 1. (i) From the consideration of Fierz terms in allowed as well as forbidden transitions, we can treat the two combinations STP and VA separately. Though a linear combination of the five interactions is possible, no interference term between STP and VA exists. 2. (ii) In the discussion of non-unique first forbidden transitions the combination VA is more favourable than STP. 3. (iii) From the second forbidden spectrum of Cs 137 we see that where X and Y mean S and T, or V and A.

Multipole Mixing in Odd Mass Spheroidal Nuclei

The multipole mixing and half-lives of gamma transitions of odd mass nuclei are studied in the rare earth region. The relatively large E2/M1 ratios observed in rotational transitions are found to be consistent with the strong coupling model. Many long-life transitions have been found between different rotational families. Some of them are explained by using Nilssons wave functions in spheroidal potential.

Phonon Spectrum of a Degenerate System of Bosons at Finite Temperature

A new set of quasi· particle operators are introduced into the theory of a degenerate system of bosons in which the depletion of the condensate is appreciable. These operators are related by a nonlinear canonical transformation to the density fluctuation operators and their canonical conjugates. T.he quasiparticles have a temperature dependent phonon spectrum. They incorporate the interaction between bbsons with non-zero momenta. In the limit as the density of the condensate approaches zero, tYte proposed theory is reduced to the Hartree-Fock theory for a nondegenerate system.