Bounds for the scattering length of spin-polarized helium from high-accuracy electronic structure calculations

We developed a series of correlation-consistent, polarized multiple zeta basis sets optimized specifically for the energy of the 2 S-3 state of helium atom. These basis sets were subsequently augmented with diffuse functions optimized for the van der Waals constants C-6 through C-14 which determine the asymptotic behavior of the second-order dispersion interaction between 2 S-3 helium atoms at large interatomic separation R. The resulting bases were applied to compute the Born-Oppenheimer (BO) potential for the lowest (5)Sigma(+)(g) state of the helium dimer. The coupled cluster and the full configuration-interaction techniques were employed to account for the electron correlation effects. The cardinal number extrapolation technique was used to obtain the complete-basis-set limit V(R) for the interaction potential and to find its lower V-L(R) and upper V-U(R) bounds. The resulting potentials were fitted to an analytical function containing accurate van der Waals constants C-6 through C-12 (including C-11). We found that the complete-basis-set BO potential has a well depth D-e=1048.24 +/- 0.36 cm(-1). The highest rotationless vibrational level is bound by D-14=90.2 +/- 4.7 MHz, much stronger than the previous most accurate estimation of 15.2 MHz. The error bounds for D-e and D-14 were obtained using the V-L(R) and V-U(R) potentials. The S-wave scattering length computed using the V-L(R), V(R), and V-U(R) potentials (assuming atomic masses) is a(L)=7.41 nm, a=7.54 nm, and a(U)=7.69 nm, respectively. We also computed the adiabatic, relativistic, and quantum electrodynamics (QED) corrections to the BO potential. When these corrections are taken into account the values of D-14 and of a (both computed assuming nuclear masses) are 87.4 +/- 6.7 MHz and 7.64 +/- 0.20 nm; the error bounds reflect now also the uncertainty of the included adiabatic, relativistic, and QED corrections. The value of the scattering length resulting from our investigation lies outside the error bounds of all experimental determinations based on the properties of Bose-Einstein condensate of spin-polarized helium atoms.(c) 2005 American Institute of Physics.