First excited band of a spinor Bose-Einstein condensate

TL;DR

This paper derives analytical fractional parentage coefficients for spinor Bose-Einstein condensates, proposing an S-conserved theory and equations for the first excited band, with numerical results for sodium-23.

Contribution

It introduces a new analytical approach and theoretical framework for describing excited states in spinor Bose-Einstein condensates.

Findings

Derived fractional parentage coefficients for total spin-states.

Proposed an S-conserved theoretical model.

Numerical solutions for $^{23}$Na demonstrated the model's applicability.

Abstract

The analytical expression of the fractional parentage coefficients for the total spin-states of a spinor N-boson system has been derived. Thereby an S-conserved theory for the spinor Bose-Einstein condensation has been proposed. A set of equations has been established to describe the first excited band of the condensates. Numerical solution for $^{23}$Na has been given as an example.