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 He-4*-He-4* collisions (in Bohr) 152 < (4-4)a < 230 and for He-3*-He-3* collisions 94 < (3-3)a < 113, while a surprising result arises for mixed collisions, He-3*-He-4*, (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.