Shell model on a random Gaussian basis

Pauli-projected random Gaussians are used as a representation to solve the shell model equations. The elements of the representation are chosen by a variational procedure. This scheme is particularly suited to describe cluster formation and cluster decay in nuclei. It overcomes the basis-size problem of the ordinary shell model and the technical difficulties of the cluster-configuration shell model. The model reproduces the α-decay width of ${}_{}{}^{212}{}_{}{}^{}\mathrm{Po}$ satisfactorily.