Scattering lengths for spin-polarized metastable helium-3 and helium-4

Upper and lower bounds are estimated for the scattering length, a , for the various isotopes of spin-polarized metastable helium. From a previous study involving various large basis sets and two ab initio approaches, and paying special attention to combine them with the accurate long-range potential, we get, for 4 He*– 4 He* collisions (in Bohr) 152 < 4−4 a < 230 and for 3 He*– 3 He* collisions 94 < 3−3 a < 113, while a surprising result arises for mixed collisions, 3 He*– 4 He*, 3−4 a < −488 and 3−4 a > 865. Indeed, the scattering length for this species is very close to the divergence occurring at the binding of a 14th vibrational level. Within these limits, our approach suggests that the values for 4−4 a and 3−3 a are closer to their upper bounds than to their lower bounds, and that the value for 3−4 a is negative and very large (>500) in magnitude. Sympathetic cooling could therefore be very efficient for the mixed species. Cooling-rate coefficients are also evaluated: they are large, of order 10 −9 cm 3 s −1 at mK temperatures for all combinations.