Effective range theory and many-body perturbation theory applied to electron spin-polarized atomic hydrogen

Accurate scattering lengths and effective ranges for hydrogen atomic collisions are determined from effective range theory. The precise ab initio b3Σsub(u)sup(+) potential energy curve values of H2 calculated by Kolos and Wolniewicz and C6, C8, C10 long-range expansion coefficients are used in obtaining accurate representation of the two-body interaction potential. The s-wave scattering length obtained for this potential (A=1/33455 a0) is used to calculate the zero temperature energy as a function of density of electron spin-polarized ('spin-aligned') atomic hydrogen using previous many-body perturbation theory results for bosons. Neglecting small potential shape dependent terms, one obtains E/N (energy per particle) as a function of density, which may be compared with similar results obtained from Monte-Carlo or variational calculations. The scattering lengths and effective ranges for the other hydrogen isotopic systems are also presented. It is shown that the first bound state for the b3Σsub(u)sup(+) potential (within the Born-Oppenheimer approximation) only exists for a hypothetical isotopic species with mass larger than a value m=3.258176 g/mole (where the scattering length becomes infinite). In terms of the quantum parameter, eta two-body binding occurs in the b3Σsub(u)sup(+) potential only for eta<0.17094. The second order liquid-to-gas transition (corresponding to the onset of infinite-body binding) occurs at the accurately determined critical value of the quantum parameter etasub(CB)=0.43891. This corresponds to zero scattering length