Why no spin-1 bosons in the Interacting Boson Model of nuclei?

Question

The Interacting Boson Model is a simple approximate model of 'even-even' atomic nuclei: nuclei with an even number of protons and an even number of neutrons.  It treats the nucleus as consisting of bosons, each boson being either a pair of protons or a pair of neutrons (with the members of a pair having opposite spin but other quantum numbers the same).  These bosons are assumed to either have spin 0 ('s-bosons') or spin 2 ('d-bosons'). 

Presumably the spin-2 case comes from the orbital angular momentum of the pair.

Why are these bosons assumed to have spin 0 or spin 2, but not spin 1?  I assume that at some level the answer is "because it works fairly well".   But why does it work fairly well?

I hope the answer is in this book:

• F. Iachello and A. Arima, The Interacting Boson Model, Cambridge University Press, Cambridge, 1987.

but I have not been able to get this book yet.

Answer 1

The interacting boson model is effectively a combination of 

• the dynamical symmetry approach (see, e.g., Section 19.4 of my book A. Neumaier and D. Westra, Algebraic Quantum Physics, Vol. 1: Quantum mechanics via Lie algebras, de Gruyter, Berlin 2024.)
• the much earlier experimental finding (Goldhaber and Sunyar 1951) that the ground state of even-even atoms is an s-state (spin 0), and the first excited state is almost always a d-state (spin 2). For the latter, see
• Scharff-Goldhaber, G. (1953). Excited states of even-even nuclei. Physical Review, 90(4), 587.

A kind of explanation for the spin 2 excited state is given in

• Scharff-Goldhaber, G., & Weneser, J. (1955). System of even-even nuclei. Physical Review, 98(1), 212.

But a proper theoretical explanation would have to come from quantum hadrodynamics. I don't know any result in this direction.

In any case, adding spin 1 would introduce many more parameters in the description, and make the resulting O(9) model hardly predictive.