Equations for the Correlation Function in the Bijl—Dingle—Jastrow Description of LiquidHe4at Absolute Zero

Several approximate integral equations for the correlation function $u\left(r\right)\mathrm{}$ are examined for the ground state of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ described by the Bijl—Dingle—Jastrow type of variational wave function. The radial distribution function computed by Schiff and Verlet using a trial form of $u\left(r\right)\mathrm{}$ is used in the present study to calculate approximate values of $u\left(r\right)\mathrm{}$ from the integral equations, and the resulting values of $u\left(r\right)\mathrm{}$ are then used to obtain corresponding energy expectation values. Accuracy of these equations for $u\left(r\right)\mathrm{}$ is estimated by comparing the obtained values of $u\left(r\right)\mathrm{}$ and $〈H〉$ with the exact values which do not involve any approximation for $u\left(r\right)\mathrm{}$.