Dynamical equations for clusters involving an open p shell: Basis of allowed states

A harmonic-oscillator basis is used to describe the dynamics of three-cluster systems involving a cluster with an open p shell. General problems arising for nonspherical clusters and additional degrees of freedom characterizing these clusters are discussed. In the Fock-Bargmann space, basis states allowed by the Pauli exclusion principle are constructed as a superposition of hyperharmonics. The coefficients in this superposition are determined as functions of the number of hyperradial quanta, and the contribution of hyperharmonics with additional symmetry indices is also found. The analysis presented here is performed by considering the examples of the 8He=6He+n+n, 10He=8He+n+n, and 11Li=9Li+n+n nuclei