Jastrow Ansatz

We apply a low density approximation to the Jastrow ansatz and find analytical results for the roton height and position. These low density results compare favorably to a Monte-Carlo quantum (MCQ) calculation of the wavefunction up to e = 0.1. Using the MCQ simulations we find a many-body enhancement of the roton at higher e, leading to a roton peak of almost 8% at e = 0.22. 

This ansatz was first proposed by Boys and Handy (BH) [142] and Schmidt and Moskowitz (SM) later arrived at the same form by considering averaged backflow effects [143], The SMBH form includes both the e-n function (via the m, n, 0 = m, 0, 0 terms) and the homogeneous e-e Jastrow function (via the m, n, 0 = 0, 0, 0 terms). The remaining e-e-n terms modulate the e-e correlation function according to the e-n distances. 

He atoms within a van der Waals cluster must be treated as Fermions, while He atoms in a cluster are Bosons. Rather than the Hartree ansatz of a product of single-mode wavefunctions (as in Eq. (2)), one should employ a determinantal Hartree-Fock ansatz in the case of He atoms. The Hartree-Fock equations for the single-particle orbtials include exchange terms, as in the case of elecfrons in atoms. Other atoms in the cluster should be treated on a Hartree footing. For He clusters, a symmetrical ansatz for the wavefunction should be used, as required for Boson calculations. All these considerations do not affect the Jastrow factor. A formulation of the HF-SCF and Jastrow/HF-SCF for clusters such as Xe( He) Xe( He) will be given in Ref. 18. Calculations we carried out for Xe( He)2, Xe(" He)2 will be briefly discussed in the next section. 

A second orbital-dependent expression, originally introduced for use with the Hartree-Fock scheme, is the Colle-Salvetti (CS) correlation functional [23]. The starting point for the derivation of the CS functional is an approximation for the correlated wavefunction F(ricri,... rjvajv). The ansatz for. .. r aA consists of a product of the HF Slater determinant and Jastrow factors,... 

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