Hole-hole contact interaction in the t-J model.

Using an analytical variational approach we calculate the hole-hole contact interaction on the Néel background. Solution of the Bethe-Salpeter equation with this interaction gives bound states in dand p-waves with binding energies close to those obtained by numerical methods. At t/J ≥ 2 − 3 the bound state disappears. In conclusion we discuss the relation between short range and long range interactions and analogy with the problem of pion condensation in nuclear matter.