  The structure of the unnatural parity states of PsH, LiPs, NaPs and KPs are
investigated with the configuration interaction and stochastic variational
methods. The binding energies (in hartree) are found to be 8.17x10-4,
4.42x10-4, 15.14x10-4 and 21.80x10-4 respectively. These states are constructed
by first coupling the two electrons into a configuration which is predominantly
3Pe, and then adding a p-wave positron. All the active particles are in states
in which the relative angular momentum between any pair of particles is at
least L = 1. The LiPs state is Borromean since there are no 3-body bound
subsystems (of the correct symmetry) of the (Li+, e-, e-, e+) particles that
make up the system. The dominant decay mode of these states will be radiative
decay into a configuration that autoionizes or undergoes positron annihilation.
