He-He Interactions Research Articles

Low-energy He-He interactions with phenomenological potentials

The low-energy atom-atom scattering properties are studied for various combinations of He isotopes interacting via a family of semiphenomenological potentials. Some of the potentials bind the (4He)2 molecule and some do not, and it is observed that molecular beam scattering measurements at energies currently accessible cannot resolve the difference between the two types of potentials. Our results are discussed within the framework of possible measurements to resolve this discrepancy. We present a method for solving the Schrodinger equation which is uniformly applicable for both bound and scattering state solutions and which is particularly suited to the types of potentials describing interactions for the rare gas atoms.

A study of the Galitskii-Feynman T matrix for liquid 3He

The Galitskii-Feynman T matrix, which sums the infinite ladder series in a many-fermion system for both particle-particle and hole-hole scattering, is studied in detail for a family of realistic He-He interactions. The structure of the S-wave bound-state singularity, reported previously, and its dependence on the bare interaction are documented at length. Special attention is devoted to the T matrix in the scattering region, where the c.m. energy of the interacting pair is positive. In particular, the on-energy-shell T matrix in this region is parametrized in terms of real “effective” phase shifts incorporating many-body effects. The critical behavior discussed previously in the bound-state region manifests itself clearly in the zero-energy limit of these phase shifts for the S wave. Below (above) a certain critical density, which is a function of both temperature and c.m. momentum, this limit approaches the value 0(−π) radians. A generalized Levinson's theorem relates this behavior to the existence of fermion-fermion pairing. An especially striking feature of these many-body phase shifts is the cusp behavior exhibited at the Fermi surface in the lowtemperature limit, which turns out to arise essentially from the structure of the particle and hole occupation probabilities. Throughout this study the temperature dependence of the T matrix is particularly emphasized.

Superfluidity, ground-state wave function and bose condensation in liquid helium four

Abstract The Bijl-Jastrow product of pairs wave function for the ground-state of He4 leads inevitably to off-diagonal long-range order. Furthermore, if the pair wave function is constructed to yield the Feynman structure factor S(k) = ħk/2Mc, then the occupation number nk of momentum state k diverges as k-1 as k → 0. Re-examination by Jackson of the Mook, Scherm and Wilkinson neutron scattering experiment, and more recent neutron inelastic scattering experiments by Cowley and co-workers on liquid He4 have raised serious doubts as to the existence of a condensate. Superfluidity without a condensate is therefore briefly discussed and appears possible in principle. It is argued here that, if there is no condensate in He4, then the He-He interactions must lead to a ground-state wave function which cannot be built from a product of pairs, but must include fundamentally three-atom correlations (at least). A study of the pressure dependence of S(k) in He4 may be helpful in this connection

A calculation of the interaction between pairs of rare-gas atoms

A recent theory of intermolecular forces is modified by the exclusion of part of the previously estimated exchange energy and the inclusion of the long-range dispersive interaction. This procedure is justified by comparison with the theory of plasma oscillations. Results have been obtained which are in good agreement with experiment in the case of He-He, Ne-Ne, Ar-Ar and Kr-Kr interactions and are in reasonable accord in the case of the unlike-atom pairs.

Theory of helium submonolayers: Formulation of the problem and solution in the zero coverage limit

We are concerned here with the physical adsorption of helium atoms on a crystal surface. A general formulation of the problem is first given, which takes into account both the static periodic potential of a model substrate and He-He interactions. This formulation leads in a natural way to expressions of surface phonon states obtained recently by Jackson. As the first step of carrying out our formalism, we extend an earlier single-particle calculation by Lennard-Jones and Devonshire. A set of basis functions consisting of products of Mathieu functions and eigenfunctions of a Morse Hamiltonian are defined, and a low-order perturbative calculation is performed. While the procedure provides a qualitative description of the energy bands, it appears to be quantitatively inadequate. To facilitate a basis for future work, which will include the effects of correlations between the helium atoms, we carry out variational calculations in this zero-coverage limit, using various combinations of Gaussian and Morse functions. A reasonably single combination results in a ground-state energy which is just 1% higher than that of Ricca, Pisani, and Garrone, who performed elaborate computations to solve a secular equation obtained with harmonic oscillator basis functions.

Quasiparticle Hamiltonian for liquid He3

A quasiparticle Hamiltonian for liquid He 3 is derived from matrix elements computed in the correlated representation using realistic He-He interactions. We outline here a prescription for systematically evaluating the irreducible self-energy parts and vertex parts of Green's functions defined in this representation. These quantities lead directly to a determination of ground state and Fermi liquid properties. Earlier work using the same matrix elements has led to numerical results in good quantitative agreement with experiment. The present reformulation serves to clarify its contents and indicate directions for improvement.