Narrow Results

This paper is a mini-review of nucleon-pair approximation to the nuclear shell model, with focus on the progresses along this line in the last two decades. We present the history of the NPA, the latest M-scheme and J-scheme algorithms, and a few applications of the NPA.

A review is given of attempts to describe nuclear properties in terms of neutron–proton pairs that are subsequently replaced by bosons. Some of the standard approaches with low-spin pairs are recalled but the emphasis is on a recently proposed framework with pairs of neutrons and protons with aligned angular momentum. The analysis is carried out for general j and applied to N=Z nuclei in the 1f_7/2 and 1g_9/2 shells.

The entanglement of pure states of the $0p$-, $1s0d$- and $1p0f$-shell nucleon pairs has been studied. The von Neumann entropy of the partial density matrix has been employed to quantify the entanglement of the $0p$-, $1s0d$- and $1p0f$-shell nucleon pairs. The Slater decomposition theorem has been used to verify if any pure state of a nucleon pair is an entangled state. Results of calculations have evidenced that a dominant part of the isospin $T=0,1$ proton–neutron states of the $0p$-, $1s0d$- and $1p0f$-shell nucleon pairs, respectively, are strongly entangled. It is shown that the calculated data are a source of valuable information on the spin quantum numbers of the entangled protons from two-proton decay.