Towards understanding the probability of $0^{+}$ ground states in even-even many-body systems

Abstract

For single-$j$ shells with $j=7/2,9/2$ and 11/2, we relate the large probability of $I^{+}$ ground states to the largest (smallest) coefficients ${\alpha }_{I(v\beta )}^J=<nv\beta I|$ $A^{J†}\cdot A^J|nv\beta I>$, where $n$ is the particle number, $v$ is the seniority, $\beta$ is an additional quantum number, and $I$ is the angular momentum of the state. Interesting regularities of the probabilities of $I^{+}$ ground states are noticed and discussed for 4-particle systems. Several counter examples of the $0^{+}$ ground state (0GS) predominance are noticed for the first time.

Comments: 5 pages, 1 figure. Phys. Rev. C64, in press