Eur. Phys. J. Special Topics 229, 2459–2484 (2020)
https://doi.org/10.1140/epjst/e2020-000047-2

Review

Pairing, quasi-spin and seniority

¹ Saha Institute of Nuclear Physics, Kolkata, India
² Homi Bhabha National Institute, Mumbai India
³ University of Malaya, Kuala Lumpur, Malaysia

^a e-mail: sinp.bijay@gmail.com

Received: 23 March 2020
Accepted: 28 August 2020
Published online: 23 October 2020

Abstract

We present our concise notes for the lectures and tutorials on pairing, quasi-spin and seniority delivered at SERB school on Role of Symmetries in Nuclear Physics, AMITY University, 2019. Starting with some generic features of residual nucleon–nucleon interactions, we provide detailed derivation of the matrix elements for the δ-interaction which is the basis for the standard pairing Hamiltonian. The eigen values for standard pairing Hamiltonian are then obtained within the quasi-spin formalism. The algebra involving quasi-spin operators is performed explicitly using the annihilation and creation operators for single nucleon together with the application of Wick’s theorem. These techniques are expected to be helpful in deriving the mean-field equations for the Hartree–Fock, Bardeen–Cooper–Schrieffer and Hartree–Fock Bogoliubov theories.