Theoretical interpretation of the vacuum ultraviolet reflectance of liquid helium and of the absorption spectra of helium microbubbles in aluminum

Abstract

The position and width of the helium resonance line $1^{1}S_{0}\ensuremath{\rightarrow}2^{1}P_{1}$ are calculated for a high-density helium fluid. The theory aims at understanding the reflectivity data of Surko et al. for the low-temperature liquid-vapor interface and the absorption data of Rife et al. for room-temperature, high-pressure helium bubbles in aluminum. The theoretical ingredients of the model are (i) the long-range dipole interaction of an excited $2P$ atom with the rest of the fluid and with the metal substrate; (ii) the short-range Pauli pseudorepulsion arising from orthogonalization of the $2p$-electron wave function with the $1s$ ground-state orbital of neighboring atoms; (iii) a statistical treatment of the high-density fluid based either on the experimentally measured radial pair distribution function of low-$T$ liquid He, or on the Percus-Yevick distribution function of hard spheres and the theoretical equation of state of Young et al. for the He fluid in the bubbles; (iv) the standard static line-broadening theory to calculate the effect of Pauli repulsion on the line shapes. The theory provides a reasonably accurate understanding of the observed spectra in both the liquid and high-density gas, and can serve as a sound basis for interpretation of vacuum ultraviolet spectra in other gas-metal combinations.