A Semiclassical Approach to Level Crossing in Supersymmetric Quantum Mechanics

Much use has been made of the techniques of supersymmetric quantum mechanics (SUSY QM) for studying bound-state problems characterized by a superpotential $\phi(x)$. Under the analytic continuation $\phi(x) \to i\phi(x)$, a pair of superpartner bound-state problems is transformed into a two-state level-crossing problem in the continuum. The description of matter-enhanced neutrino flavor oscillations involves a level-crossing problem. We treat this with the techniques of supersymmetric quantum mechanics. For the benefit of those not familiar with neutrino oscillations and their description, enough details are given to make the rest of the paper understandable. Many other level-crossing problems in physics are of exactly the same form. Particular attention is given to the fact that different semiclassical techniques yield different results. The best result is obtained with a uniform approximation that explicitly recognizes the supersymmetric nature of the system.Comment: 15 pages, Latex with lamuphys and psfig macros. Talk by first Author at the UIC "Supersymmetry and Integrable Models Workshop", Chicago, June 12-14, 1997; proceedings to be published in Springer Lecture Notes in Physics, H. Aratyn et al., eds. This paper also available at http://nucth.physics.wisc.edu/preprint

Partition Functions in Statistical Mechanics, Symmetric Functions, and Group Representations

Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation of the partition functions for particles that carry internal quantum numbers. The partition function is shown to be a sum of one or more group characters. The utility of character expansions in calculating the partition functions is explored. Several examples are given to illustrate these techniques.Comment: 16 pages of RevTe

Neutrinos and Symmetries

Three facets of symmetries in neutrino physics are briefly reviewed: i) The SO(5) symmetry of the neutrino mass and and its connection to the see-saw mechanism; ii) Flavor SU(N) symmetries of dense, self-interacting neutrino gases in astrophysical settings; iii) The neutrino mixing angle theta13 and possible CP-violation in the neutrino sector.Comment: 5 pages of LATEX; to appear in the proceedings 4th International Symposium on Symmetries in Subatomic Physics held on June 2-5, 2009 at Department of Physics, National Taiwan University, Taipei, Taiwa

Relations between fusion cross sections and average angular momenta

We study the relations between moments of fusion cross sections and averages of angular momentum. The role of the centrifugal barrier and the target deformation in determining the effective barrier radius are clarified. A simple method for extracting average angular momentum from fusion cross sections is demonstrated using numerical examples as well as actual data.Comment: 16 REVTeX pages plus 8 included Postscript figures (uses the epsf macro); submitted to Phys. Rev. C; also available at http://nucth.physics.wisc.edu/preprint

Coulomb interaction between a spherical and a deformed nuclei

We present analytic expressions of the Coulomb interaction between a spherical and a deformed nuclei which are valid for all separation distance. We demonstrate their significant deviations from commonly used formulae in the region inside the Coulomb radius, and show that they remove various shortcomings of the conventional formulae.Comment: 7 pages 4 figure

Constraints on Neutrino Mixing

We explore the implications of imposing the constraint that two neutrino flavors (which for definiteness we take to be the mu and tau neutrinos) are similarly coupled to the mass basis in addition to the unitarity constraints. We allow three active and an arbitrary number of sterile neutrinos. We show that in this scheme one of the mass eigenstates decouples from the problem, reducing the dimension of the flavor space by one.Comment: 9 page

Radiation correction to astrophysical fusion reactions and the electron screening problem

We discuss the effect of electromagnetic environment on laboratory measurements of the nuclear fusion reactions of astrophysical interest. The radiation field is eliminated using the path integral formalism in order to obtain the influence functional, which we evaluate in the semi-classical approximation. We show that enhancement of the tunneling probability due to the radiation correction is extremely small and does not resolve the longstanding problem that the observed electron screening effect is significantly larger than theoretical predictions.Comment: 9 pages, 1 eps figure

Effects of nuclear structure on average angular momentum in subbarrier fusion

We investigate the effects of nuclear quadrupole and hexadecapole couplings on the average angular momentum in sub-barrier fusion reactions. This quantity could provide a probe for nuclear shapes, distinguishing between prolate vs. oblate quadrupole and positive vs. negative hexadecapole couplings. We describe the data in the O + Sm system and discuss heavier systems where shape effects become more pronounced.Comment: Latex (uses the epsf macro), 10 pages of text, 3 postscript figures included. Full postscript version available by anonymous ftp from wisnuf.physics.wisc.edu:/pub/preprints. MAD-NT-94-0

Algebraic Approach to Shape Invariance

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as strength and range. Shape-invariance algebras, in general, are shown to be infinite-dimensional. The conditions under which they become finite-dimensional are explored.Comment: Submitted to Physical Review A. Latex file, 9 pages. Manuscript is also available at http://nucth.physics.wisc.edu/preprints

Constraints on Neutrino Parameters from Neutral-Current Solar Neutrino Measurements

We generalize the pull approach to define the $\chi^2$ function to the analysis of the data with correlated statistical errors. We apply this method to the analysis of the Sudbury Neutrino Collaboration data obtained in the salt-phase. In the global analysis of all the solar neutrino and KamLAND data we find the best fit (minimum $\chi^2$) values of neutrino parameters to be $\tan^2 \theta_{12} \sim 0.42$ and $\delta m_{12}^2 \sim 7.1 \times 10^{-5}$ eV$^2$. We confirm that the maximal mixing is strongly disfavored while the bounds on $\delta m_{12}^2$ are significantly strengthened.Comment: 6 figures. Some typos are corrected, figures are visually improve