Vacancy mobility in crystalline He3
Vacancies that are delocalized at low temperatures in crystalline He3 give rise to indirect exchange, since the circuiting of the vacancy around a closed path is equivalent to a permutation of atoms, and consequently, an important role in the calculation of the energy is played by the symmetry of the wave function, i.e. , its dependence on the spins. Actually the direct exchange in He3 is extremely small, J~10"3 K, whereas the vacancy mobility is quite large. According to various estimates, the corresponding width of the band is Δ~10 K, so that there exists a temperature region where direct exchange can be neglected.