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

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

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

Towards a very precise knowledge of theta13

Recent experimental developments towards obtaining a very precise value of the third neutrino mixing angle, $\theta_{13}$, are summarized. Various implications of the measured value of this angle are briefly discussed.Comment: Proceedings of the CETUP* (Center for Theoretical Underground Physics and Related Areas) 2012 Summer Institut

Solar Neutrino Matter Effects Redux

Following recent low-threshold analysis of the Sudbury Neutrino Observatory and asymmetry measurements of the BOREXINO Collaboration of the solar neutrino flux, we revisit the analysis of the matter effects in the Sun. We show that solar neutrino data constrains the mixing angle $\theta_{13}$ poorly and that subdominant Standard Model effects can mimic the effects of the physics beyond the Standard Model.Comment: 12 pages of LATEX, 8 figure