Analysis of the structure factor of dense krypton gas: Bridge contributions and many-body effects

The pair-correlation function $g\left(r\right)\mathrm{}$ of the Kr-type model fluid with only pair interactions was calculated using the Rosenfeld-Ashcroft modification of the hypernetted-chain (HNC) equation which includes bridge diagrams, and gave results in excellent agreement with Monte Carlo $g\left(r\right)\mathrm{}$ data. These bridge functions and the known pair potential were used to analyze the neutron-diffraction structure-factor data of Teitsma and Egelstaff, to determine the effective strength of the three-body potential as a function of the density assuming it to be of the Axilrod-Teller (AT) form. The strength of the effective three-body contribution $s=\frac{\nu }{{\nu }_{\mathrm{theor}}}$, where ${\nu }_{\mathrm{theor}}$ is the theoretical value, decreases for higher densities, suggesting that the many-body terms (beyond the Axilrod-Teller form) screen the AT interaction as the density increases. The results are very sensitive to the uncertainties in the structure factor $S\left(k\right)\mathrm{}$ for small $k$ if parameter optimization is used to determine the effective pair potential. However, prediction of the compressibility using $s=1\mathrm{}$ allows us to conclude that ${\nu }_{\mathrm{theor}}$ is consistent with the experimental data for low densities, to within the uncertainties in the presently available pair potentials and in the structure-factor data.