# Collective treatment of the isovector pair correlations. Boson representation

## TL;DR

This paper develops a finite boson representation method for the Hamiltonian with pairing forces, successfully describing certain nuclear states but overestimating energies for some N=Z nuclei, indicating areas for further refinement.

## Contribution

It introduces a boson representation technique for pairing Hamiltonians that accounts for isovector monopole pairing in nuclear states.

## Key findings

- Successfully describes pairing vibrational and rotational states in certain nuclei.
- Overestimates energies of pairing rotational states in N=Z nuclei with many nucleons.
- Discusses potential reasons for discrepancies between theory and experiment.

## Abstract

The theoretical approach to consideration of the Hamiltonian with pairing forces using a technique of the finite boson representation is developed. It is shown that a simultaneous description of the pairing vibrational state in $^{56}$Ni and the pairing rotational states with $T$=0 in the neighboring $N=Z$ nuclei is possible if the pairing Hamiltonian takes into account only isovector monopole pairing. However, the calculated energies of the pairing rotational states of $N=Z$ nuclei removed from $^{56}$Ni by 12 and more nucleons exceed significantly the experimental values. The possible reason of this discrepancy is discussed.