Implementing the hardcore concept in the mean field of the Tamm-Dancoff approximation

Abstract

This paper investigates one of the most prominent models in nuclear physics, the Tamm-Dancoff approximation (TDA), for particle-hole excitations. We demonstrate how to incorporate one of the most challenging aspects of nuclear physics, the hardcore, into this model. Following an introduction to the concept and the corresponding mathematical tools, we examine the sample nuclei ¹⁶O and ⁴⁰Ca. A portion of the excitation spectra of these nuclei is reproduced, and the octupole transition in these nuclei along with the TDA sum rule is investigated. The results are calculated and compared in both the well-known version and the new approach. In all cases, the new model exhibits better agreement with experimental data than the well-known model, which employed the harmonic oscillator basis.