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

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

Neutrinos and rare isotopes

The close connection between neutrino physics and the physics explored at rare isotope facilities is explored. The duality between the Hamiltonian describing the self-interacting neutrino gas near the proto-neutron star in a core-collapse supernova and the BCS theory of pairing is elucidated. This many neutrino system is unique as it is the only many-body system driven by weak interactions. Its symmetries are discussed.Comment: Proceedings of International Symposium "Exotic Nuclear Structure From Nucleons" (ENSFN 2012

Neutrinos in Astrophysics and Cosmology

Neutrinos play a crucial role in many aspects of astrophysics and cosmology. Since they control the electron fraction, or equivalently neutron-to-proton ratio, neutrino properties impact yields of r-process nucleosynthesis. Similarly the weak decoupling temperature in the Big Bang Nucleosynthesis epoch is exponentially dependent on the neutron-to-proton ratio. In these conference proceedings, I briefly summarize some of the recent work exploring the role of neutrinos in astrophysics and cosmology.Comment: 6 pages, Proceedings of IX International Conference on Interconnections between Particle Physics and Cosmology (PPC2015

Neutrino Propagation in Matter

The enhancement of neutrino oscillations in matter is briefly reviewed. Exact and approximate solutions of the equations describing neutrino oscillations in matter are discussed. The role of stochasticity of the media that the neutrinos propagate through is elucidated.Comment: 17 pages, 5 figures. Expanded version of a talk at the Slansky Memorial Symposium, Los Alamos, May 199

Character Expansions in Physics

Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to generate such expansions and its various applications are briefly reviewed.Comment: To be published in "Symmetries in Nature: Symposium in Memoriam Marcos Moshinsky", August 2010, Cuernavaca, Mexic

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