The possibility of existence of a bound state of two 4He atoms is considered by making use of variational method based on asymptotic wave functions at small and large interatomic distances. The result is negative.
Abstract A modification of the Rayleigh—Ritz variational principle is described which makes possible a calculation of the energy, wave function, and pair distribution function f12≡f(x1,x2) of a Bose fluid, such as liquid 4He, at absolute zero. The assumptions made are: (i) two-body interactions with potential Uij, (ii) trial wave functions of the form f12≡f(x1,x2) and (iii) the Kirkwood ‘superposition' approximation. Under these approximations, the expectation energy is E=12n2∫∫d3X1d3X2f12U12−h2m−1(∇18ϕ12)+(∇1ϕ12)2+n∫d3X2f13f23ϕ12⋅∇1ϕ13, where n ≡ N/V. It is shown here that making E stationary with respect to independent variations in f and ɸ corresponds to simultaneously applying the ordinary Rayleigh-Ritz principle and solving the Born-Green-Yvon integral equation for f. The method is illustrated by reproducing Bogolyubov’s results for the case where U is small. The case where U is large must be dealt with numerically, but transformations for simplifying the computations are given here.
The possible existence of bound states in small helium clusters containing atomic and molecular hydrogen has been investigated by means of three completely independent sets of calculations. The first set employs the Jacobi–Davidson filtering procedure recently implemented in the Distributed Gaussian Functions (DGF) approach, the second one is based on the solution of the Faddeev equation by means of the hyperspherical adiabatic expansion method and the third follows the Quantum Monte Carlo approach. The partners within each complex are taken to interact via two-body potentials chosen among the most accurate existing in the literature. All the present quantum treatments show that no bound states are found for H(4He)2 and for D(4He)2 while only one very diffuse bound state is present in T(4He)2, where H, D and T are the three isotopes of hydrogen. The substitution of the atomic dopant with its molecular counterpart, H2, also gives rise to only one bound state whose spatial attributes are reported and analysed, underlining again the ultraweak nature of the interaction forces and the need to implement highly specific tools for the investigation of the ensuing bound states.