Symmetry and Supersymmetry in Nuclear Pairing: Exact Solutions

Pairing plays a crucial role in nuclear spectra and attempts to describe it has a long history in nuclear physics. The limiting case in which all single particle states are degenerate, but with different s-wave pairing strengths was only recently solved. In this strong coupling limit the nuclear pairing Hamiltonian also exhibits a supersymmetry. Another solution away from those limits, namely two non-degenerate single particle states with different pairing strengths, was also given. In this contribution these developments are summarized and difficulties with possible generalizations to more single particle states and d-wave pairing are discussed.Comment: 6 pages of LATEX, to be published in the Proceedings of the "10th Int. Spring Seminar on Nuclear Physics: New Quests in Nuclear Structure", Vietri Sul Mare, May 21-25, 201

Supersymmetry and Nuclear Pairing

We show that nuclear pairing Hamiltonian exhibits supersymmetry in the strong-coupling limit. The underlying supersymmetric quantum mechanical structure explains the degeneracies between the energies of the N and Nmax-N+1 pair eigenstates. The supersymmetry transformations connecting these states are given.Comment: 4 pages of REVTEX, one figur

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

Neutrino interactions in astrophysics and the third neutrino mixing angle theta13

The third neutrino mixing angle theta13 is the least known one. In this contribution, after a brief discussion of the current efforts to determine the value of this angle better, various astrophysical implications of a non-zero value of theta13 are summarized.Comment: 6 pages, Proceedings of OMEG10 Symposium, Osaka, Japa

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

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

Overview of Neutrino-Nucleus Interactions

An overview of neutrino-nucleus interactions is presented. After a brief discussion of theory and applications of detector response three examples are discussed: i) Recent work on neutrino-deuteron reactions, ii) Probing strangeness content of the nucleon with neutrinos, and iii) The role of neutrino reactions in supernova dynamics and r-process nucleosynthesis.Comment: 10 pages, 4 figures; proceedings of the Yukawa International Seminar 2001 (YKIS01), Physics of Unstable Nuclei, November 5-10, 2001, Kyoto, Japa

Neutrino Mixing and Oscillations in Astrophysical Environments

A brief review of the current status of neutrino mixing and oscillations in astrophysical environments, with particular emphasis on the Sun and core-collapse supernovae, is given. Implications of the existence of sterile states which mix with the active neutrinos are discussed.Comment: Proceedings of the OMEG12 Conference, Tsukuba, Japa

Symmetries of Neutrino Physics

In this contribution to the proceedings of a conference honoring the career of Francesco Iachello, two applications of symmetry principles to neutrino physics are described. These applications are the connection between fermion pairing in many-body physics and the neutrino mass as well as collective neutrino oscillationsComment: 7 pages, Proceedings of the conference "SYMMETRIES AND ORDER: Algebraic Methods in Many Body Systems