Bound states of a charged particle in a dipole field

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Abstract
A general study has been made of the bound states of a charged particle in a static field which behaves as the dipole form asymptotically. When the field is that of either a point dipole plus a sufficiently repulsive spherical core, or a finite dipole, the existence of bound states of the charged particle depends only on the value of the reduced dipole moment K (equation (5)). It is shown that each symmetry class of states has its own threshold value of K such that states of that symmetry exist if, and only if, K exceeds the critical minimum. There is an infinite number of states of given symmetry when there are any. Critical values of K < 100 are calculated. When the potential has an arbitrary form at short range (but still has the dipole form at long range), the situation remains much the same as above, with the exception that sufficient attraction at short range will allow some states to exist for any value of the dipole moment.