Asymptotic form of quantum momentum distributions

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Abstract
The behavior at large momentum, of the first density correction to the momentum distribution of a gas of interacting particles, is investigated for a wide variety of model potentials. The treatment involves neither an expansion in powers of the potential strength VO nor of Planck’s constant h/. As well, the results are valid for all temperatures and include exchange effects. It is shown that slow algebraic decay of the momentum distribution is not peculiar to hard sphere interactions, but also occurs for such smooth interactions as the Yukawa and exponential potential, whose momentum distributions decay as p−8 and p−12, respectively. The pseudopotential gives rise to a p−4 decay, in contrast to the p−6 decay for the hard sphere interaction which it is designed to model. For singular potentials of the form VO(a/r)n, a lower bound is obtained which has (almost) exponential decay.