Symmetries, Supersymmetries, and Pairing in Nuclei

TL;DR

This paper discusses algebraic methods and symmetries in nuclear physics, including dynamical symmetry, supersymmetry, and quantum mechanics, with applications to pairing, fusion, and neutrino physics.

Contribution

It introduces algebraic techniques and group theoretical foundations for nuclear physics phenomena, highlighting their applications in pairing, fusion, and neutrino problems.

Findings

Group theoretical tools elucidate nuclear pairing mechanisms.

Supersymmetry concepts apply to subbarrier fusion processes.

Symmetries of neutrino mass are analyzed using algebraic methods.

Abstract

These summer school lectures cover the use of algebraic techniques in various subfields of nuclear physics. After a brief description of groups and algebras, concepts of dynamical symmetry, dynamical supersymmetry, and supersymmetric quantum mechanics are introduced. Appropriate tools such as quasiparticles, quasispin, and Bogoliubov transformations are discussed with an emphasis on group theoretical foundations of these tools. To illustrate these concepts three physics applications are worked out in some detail: i) Pairing in nuclear physics; ii) Subbarrier fusion and associated group transformations; and iii) Symmetries of neutrino mass and of a related neutrino many-body problem.