Atomic Distribution in Liquid Argon by Neutron Diffraction and the Cross Sections ofA36andA40

Abstract

The angular distribution of 1.04 A neutrons scattered by liquid argon at 84°K is reported. Small-angle scattering in the pattern is accounted for in terms of isotope incoherence using the same sign for the measured values of the scattering lengths of ${\mathrm{A}}^{40}$ and ${\mathrm{A}}^{36}$. The transmission cross section of ${\mathrm{A}}^{36}$ was measured for 1.04 A neutrons and found to be 77±9 barns corresponding to a scattering cross section of 73±9 barns. The scattering cross section of ${\mathrm{A}}^{40}$ was measured and found to be 0.36 barn. The scattering curve was transformed to the atomic density distribution $4\pi r^2\left[\rho \mathrm{}\right(r)-{\rho }_0]$ for the liquid. The function shows only small oscillations about $-4\mathrm{}\pi r^2{\rho }_0$ for spacings out to 3 A. Beyond this the curve oscillates about zero with an amplitude which decreases with increasing radius. The number of neighbors assigned to the first shell of atoms is ${8.}_2$. From a comparison of the position of the density cutoff and first density maximum with that expected for a Lennard-Jones 12:6 potential, it is concluded that the effective potential in the liquid has a broader bowl than that given by the Lennard-Jones 12:6 potential.