Threshold Condition for Forming an Atomic ⁴He Trimer

Abstract

The Rayleigh-Ritz variational principle is used to formulate a rigorous bound on the threshold conditions under which three helium four atoms will form a bound state when their pair interaction is represented by the Lennard-Jones (n, 6) model and their nonadditive interaction is taken to be the Muto-Axilrod-Teller triple-dipole potential. The accepted parameter values of the model with n equal to 12 predict a bound-state trimer. The oversight, that of failing to use the (12, 6) parameter values of Kihara, Midzuno and Shizume in the extensive work on liquid helium, is pointed out.