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We show that correlated Gaussians with good angular momentum and parityprovide flexible basis functions for specific elongated shape. As itsapplication we study linear-chain states of four-alpha particles invariation-after-projection calculations in which all the matrix elements areevaluated analytically. We find possible chain states for $J=0^+$, $2^+$, $4^+$and perhaps $6^+$ with the bandhead energy being about 33 MeV from the groundstate of $^{16}$O. No chain states with $J\geq 8$ are found. The nature of therotational sequence of the chain states is clarified in contrast to arigid-body rotation. The quadrupole deformation parameters estimated from thechain states increase from 0.59 to 1.07 for $2^+$ to $6^+$. This work suggestsundeveloped fields for the correlated Gaussians beyond those problems whichhave hitherto been solved successfully.

Correlated-Gaussian approach to linear-chain states -Case of four $\alpha$-particles-