The band structure of the whole spectrum of an N-body cold system containing atoms with arbitrary integer spin and dominated by singlet pairing force

TL;DR

This paper analytically explores the complete energy spectrum of N-boson systems with arbitrary spin, focusing on singlet pairing interactions, revealing detailed spin structures and potential high-density phenomena in high-spin systems.

Contribution

It provides an analytical solution for the eigenstates and energies of N-boson systems with arbitrary spin under singlet pairing, and evaluates effects of other interactions through numerical methods.

Findings

Analytical eigenstates and energies for singlet pairing in N-boson systems.

Identification of spin structure relationships among states.

High level density potential in high-spin systems.

Abstract

The spectra of $N$-boson systems with arbitrary nonzero spin $\mathfrak{f}$ have been studied. Firstly, only the singlet pairing interaction is considered, a set of eigenstates together with the eigenenergies are analytically obtained. The completeness of this set is proved. The analytical expression allows us to see clearly the spin structures of various states different in $N$ and/or $\mathfrak{f}$, and to find out the similarity and relationship lying among them. Secondly, the effect of other interactions is evaluated via exact numerical calculations on the systems with a smaller $N$. Some features and notable phenomena that might emerge in high-$\mathfrak{f}$ systems, say, the ground band might have extremely high level density, have been discussed.