Correlated-Gaussian approach to linear-chain states -Case of four $\hat{I}\pm$-particles-

Abstract

We show that correlated Gaussians with good angular momentum and parity provide flexible basis functions for specific elongated shape. As its application we study linear-chain states of four-alpha particles in variation-after-projection calculations in which all the matrix elements are evaluated analytically. We find possible chain states for $J=0^{+}$, $2^{+}$, $4^{+}$ and perhaps $6^{+}$ with the bandhead energy being about 33 MeV from the ground state of ${}^{16}$O. No chain states with $J\ge 8$ are found. The nature of the rotational sequence of the chain states is clarified in contrast to a rigid-body rotation. The quadrupole deformation parameters estimated from the chain states increase from 0.59 to 1.07 for $2^{+}$ to $6^{+}$. This work suggests undeveloped fields for the correlated Gaussians beyond those problems which have hitherto been solved successfully.

13 pages, 6 figures, accepted for publication in Phys. Rev. C