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

Neutrino Physics and Nuclear Axial Two-Body Interactions

We consider the counter-term describing isoscalar axial two-body currents in the nucleon-nucleon interaction, L1A, in the effective field theory approach. We determine this quantity using the solar neutrino data. We investigate the variation of L1A when different sets of data are used.Comment: 8 pages with 4 figures. To be published in the Proceedings of the Conference "Blueprints For The Nucleus: From First Principles to Collective Motion" held at Feza Gursey Institute, Istanbul, Turkey; May 17 -22, 200

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

Description of Nuclear Structure Effects in Subbarrier Fusion by the Interacting Boson Model

Recent theoretical developments in using the Interacting Boson Model to describe nuclear structure effects in fusion reactions below the Coulomb barrier are reviewed. Methods dealing with linear and all orders coupling between the nuclear excitations and the translational motion are discussed, and the latter is found to lead to a better description of the barrier distribution data. A systematic study of the available data (cross sections, barrier and spin distributions) in rare-earth nuclei is presented.Comment: 9 pages + 2 Figures (in eps form). To be published in the Proceedings of the FUSION97 Conference, South Durras, Australia, March 1997 (J. Phys. G). Full text and figures are also available at http://nucth.physics.wisc.edu/preprints/mad-nt-97-01.abs.htm

Neutrinos in Cosmology and Astrophysics

We briefly review the recent developments in neutrino physics and astrophysics which have import for frontline research in nuclear physics. These developments, we argue, tie nuclear physics to exciting developments in observational cosmology and astrophysics in new ways. Moreover, the behavior of neutrinos in dense matter is itself a fundamental problem in many-body quantum mechanics, in some ways akin to well-known issues in nuclear matter and nuclei, and in some ways radically different, especially because of nonlinearity and quantum de-coherence. The self-interacting neutrino gas is the only many body system driven by the weak interactions.Comment: 7 pages, 1 figur

Impact of the Neutrino Magnetic Moment on the Neutrino Fluxes and the Electron Fraction in core-collapse Supernovae

We explore the effect of the neutrino magnetic moment on neutrino scattering with matter in a core-collapse Supernova. We study the impact both on the neutrino fluxes and on the electron fraction. We find that sizeable modifications require very large magnetic moments both for Dirac and Majorana neutrinos.Comment: 7 pages, 6 figure

Probing anharmonic properties of nuclear surface vibration by heavy-ion fusion reactions

Describing fusion reactions between ^{16}O and ^{154}Dy and, between ^{16}O and ^{144}Sm by the $sd-$ and $sdf-$ interacting boson model, we show that heavy-ion fusion reactions are strongly affected by anharmonic properties of nuclear surface vibrations and nuclear shape, and thus provide a powerful method to study details of nuclear structure and dynamics.Comment: 8 pages, 5 figures, To be published in the Proceedings of the FUSION 97 Conference, South Durras, Australia, March 1997 (J. Phys. G

Majorana Neutrino Magnetic Moment and Neutrino Decoupling in Big Bang Nucleosynthesis

We examine the physics of the early universe when Majorana neutrinos (electron neutrino, muon neutrino, tau neutrino) possess transition magnetic moments. These extra couplings beyond the usual weak interaction couplings alter the way neutrinos decouple from the plasma of electrons/positrons and photons. We calculate how transition magnetic moment couplings modify neutrino decoupling temperatures, and then use a full weak, strong, and electromagnetic reaction network to compute corresponding changes in Big Bang Nucleosynthesis abundance yields. We find that light element abundances and other cosmological parameters are sensitive to magnetic couplings on the order of 10^{-10} Bohr magnetons. Given the recent analysis of sub-MeV Borexino data which constrains Majorana moments to the order of 10^{-11} Bohr magnetons or less, we find that changes in cosmological parameters from magnetic contributions to neutrino decoupling temperatures are below the level of upcoming precision observations.Comment: 19 pages, 9 figure

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