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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 tosee clearly the spin structures of various states different in $N$ and/or$\mathfrak{f}$, and to find out the similarity and relationship lying amongthem. Secondly, the effect of other interactions is evaluated via exactnumerical calculations on the systems with a smaller $N$. Some features andnotable phenomena that might emerge in high-$\mathfrak{f}$ systems, say, theground band might have extremely high level density, have been discussed.

physica scripta

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