The Pseudoscalar Interaction and the Beta Spectrum of RaE

It is shown that the theory of forbidden beta transitions, as hitherto used, does not provide a correct treatment of the pseudoscalar interaction. This is demonstrated by the application of a canonical transformation to the Hamiltonian of interacting nucleons and leptons whereby all odd nuclear Dirac operators are eliminated from the theory. When this is done properly it is seen that the pseudoscalar interaction makes a contribution to the _-decay process only by virtue of the fact that the lepton covariants are not constant. The corresponding additional operators introduced in the other three interactions (S is pure even) are examined and it is shown that, except in one case, these make trivial corrections which would not be observed in practice. The exception occurs in second and higher forbidden transitions wherein the spin change (tensor rank, strictly speaking) is lower than the forbiddenness order. By virtue of present knowledge of the beta interaction these must be regarded as small correction terms. The possibility of calculating all nuclear matrix elements using nonrelativistic wave functions based on some coupling model is discussed. The results presented here also show that wherever P and T interactions interfere (spin change zero, first-forbidden transitions) it will be possible to obtain the ratio of coupling coefficients (gP/gT for example) by comparison with the observed spectral shapes. A method of reduction of the _-decay operators is described and it is pointed out that the same procedure is very convenient for obtaining the nuclear matrix elements. In this method the irreducible tensors are obtained automatically and the retardation expansion is a trivial operation performed at the end of the calculation rather than at the beginning. The correction factors for pseudoscalar (P) as well as P-T and P-A mixtures are obtained and the fact that the shape of the correction factor is strongly modified as compared to the customary result is observed. The correction factor is now more strongly Z dependent and this would perhaps account for the appearance of the P interaction only for heavy elements. The results of this investigation are applied to the RaE spectrum. No fit with the assumption of zero spin for RaE can be obtained. It is suggested that the spin of RaE is unity, and other evidence pointing in this direction is cited.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86125/1/PhysRev.93.1315-RKO.pd

Nuclear Matrix Elements in Beta Decay

By using the j-j coupling model, all the _-decay nuclear matrix elements are calculated (in terms of radial integrals) for one- and two-nucleon configurations. The operators in terms of which one can describe the entire theory are of five types. Three of these, involving the nucleon momentum operator, replace the operators which, in the conventional representation of the theory, appeared as odd Dirac operators. The operators in the present representation, which is most naturally expressed in terms of spherical notation and angular momentum eigenfunctions are explicitly related to those which appeared in the older notation as cartesian tensor components. The results for both one- and two-nucleon configurations are expressed in terms of reduced matrix elements which, in turn, can be written in terms of Racah coefficients and other coefficients derived from them. All these coefficients, and thereby the reduced matrix elements, can be written in terms of comparatively simple algebraic formulas which cover all cases of interest. A brief discussion of the implications of these results for spectral shapes and comparative half-lives is given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86124/1/PhysRev.93.1326-RKO.pd

Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential

We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived from non-Hermitian random matrix theory. When comparing these to quenched lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the quark chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class.Comment: 4 pages, 4 figures, minor changes, as published in Phys. Rev. Let

The Transition from Heavy Fermion to Mixed Valence in Ce1-xYxAl3: A Quantitative Comparison with the Anderson Impurity Model

We present a neutron scattering investigation of Ce1-xYxAl3 as a function of chemical pressure, which induces a transition from heavy-fermion behavior in CeAl3 (TK=5 K) to a mixed-valence state at x=0.5 (TK=150 K). The crossover can be modeled accurately on an absolute intensity scale by an increase in the k-f hybridization, Vkf, within the Anderson impurity model. Surprisingly, the principal effect of the increasing Vkf is not to broaden the low-energy components of the dynamic magnetic susceptibility but to transfer spectral weight to high energy.Comment: 4 pages, 5 figure

Stochastic field theory for a Dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white noise potential, the gauge field disorder. Effective supersymmetric non-linear sigma-models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy in QCD. Connections to other low-energy effective theories, in particular the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.Comment: 4 pages, 1 figur

Large harmonic softening of the phonon density of states of uranium

Phonon density-of-states curves were obtained from inelastic neutron scattering spectra from the three crystalline phases of uranium at temperatures from 50 to 1213 K. The alpha -phase showed an unusually large thermal softening of phonon frequencies. Analysis of the vibrational power spectrum showed that this phonon softening originates with the softening of a harmonic solid, as opposed to vibrations in anharmonic potentials. It follows that thermal excitations of electronic states are more significant thermodynamically than are the classical volume effects. For the alpha-beta and beta-gamma phase transitions, vibrational and electronic entropies were comparable