Weakly parametrized Jastrow ansatz for a strongly correlated Bose system

We consider the Jastrow pair-product wavefunction for the strongly correlated Bose systems, in our case liquid helium-4. An ansatz is proposed for the pair factors which consists of a numeric solution to a modified and parametrized pair scattering equation. We consider a number of such simple one-variable parametrizations. Additionally, we allow for a parametrizeable cutoff of the pair factors and for the addition of a long-range phonon tail. This approach results in the many-body wavefunctions that have between just one and three parameters. Calculation of observables is carried with the Variational Monte Carlo method. We find that such a simple parametrization is sufficient to produce results that are comparable in quality to the best available two-body Jastrow factors for helium. For two-parameter wavefunction, we find variational energies of $-6.04$~K per particle for a system of one thousand particles. It is also shown that short-range two-body correlations are reproduced in detail by two- and three-parameter functions.