First excited band of a spinor Bose-Einstein condensate

Abstract

The analytical expressions of the fractional parentage coefficients for the total spin states of a spinor $N$-boson system have 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 $^{23}\mathrm{Na}$ has been given as an example.