H. B. Ghassib

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 Schrödinger 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 Levinsons 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.

Liquid Helium-4 in the Static Fluctuation Approximation

In this work liquid helium-4 is studied for the first time within the framework of the so-called static fluctuation approximation. This is based on the replacement of the square of the local-field operator with its mean value. A closed set of nonlinear integral equations is derived for weakly as well as for strongly interacting systems. This set is solved numerically by an iteration method for a realistic interhelium potential. The thermodynamic properties are then obtained for both the weakly interacting system, liquid 4He in Vycor glass, and the strongly interacting system, liquid 4He. It turns out, however, that the present quadratic-fluctuation approximation is valid in the latter, strongly interacting case only in the low-temperature limit (≤0.15 K). Our results are presented in a set of figures. The role of the interaction is emphasized and the functional dependence of key thermodynamic quantities on the temperature is derived for both weakly and strongly interacting 4He systems.

SPIN-POLARIZED ATOMIC HYDROGEN IN THE STATIC FLUCTUATION APPROXIMATION

In this paper we use the so-called static fluctuation approximation (SFA) to calculate the thermodynamic properties of spin-polarized atomic hydrogen. This approximation is based on the replacement of the square of the local-field operator with its mean value. A closed set of nonlinear integral equations is derived for neutral many-bosonic systems. This set is solved numerically by an iteration method for two triplet-state potentials: a Morse- and Silvera-type potentials. It is found that the mean internal energy per unit volume, the pressure, the entropy per unit volume, and the specific heat per unit volume increase with temperature and decrease with spin polarization in the low-temperature region ( 0.1K), and that they are independent of the number density up to 10-3A-3 in the low-temperature region.

A study of liquid 3He in the Brueckner-Goldstone formalism☆

Abstract The two- and three-body correlation energies in liquid 3 He are calculated within the framework of Brueckner-Goldstone theory. Various approximations taken from nuclear matter calculations and used in previous liquid helium studies are examined and improved upon. The dependence of the g -matrix elements on the center of mass momentum of the interacting particles and the question of the self-consistency of the hole spectrum are treated more systematically and extensively than before. The contribution to the three-body energy of relative partial wave interactions with nonzero relative angular momentum is studied in some detail for the first time.

4He n‐mers and Bose–Einstein condensation in He II

A critique is presented of a recent comment by March in which he argues that the Bose–Einstein condensate may not exist in HeII. It is concluded that such a dramatic statement is not warrranted in the light of current evidence.

FERMI PAIRING IN DILUTE 3He-HeII MIXTURES

In this paper the Galitskii–Migdal–Feynman (GMF) formalism is applied to dilute 3He-HeII mixtures. In particular, the effect of the hole-hole scattering on pairing in these systems is investigated. To this end, the relative phase shifts incorporating many-body effects based on both Brueckner–Bethe–Goldstone (BBG) and GMF formalisms are calculated. In the GMF formalism, the S-wave phase shift at zero relative momentum is –π and has a cusp at the Fermi momentum; while in the BBG formalism, this phase shift has zero values up to the Fermi momentum. From these results we conclude that hole-hole scattering plays a crucial role in any possible fermion-fermion pairing in these systems.

Normal Liquid Helium-3 in the Static Fluctuation Approximation

In this paper normal liquid helium-3 is studied for the first time within the framework of the so-called static fluctuation approximation. This is based on the replacement of the square of the local-field operator with its mean value. A closed set of nonlinear integral equations is derived for neutral many-fermionic systems. This set is solved numerically by an iteration method for a realistic interhelium potential. The thermodynamic properties are then obtained for normal liquid helium-3. The quadratic-fluctuation approximation is found to be valid for this system in the low-temperature limit (≤0.25 K). Our results are presented in a set of figures. The role of the interaction is emphasized, and the functional dependence on the temperature of key thermodynamic quantities is derived for normal liquid helium-3.

On dimers and trimers in some helium fluids

Some aspects of dimers and trimers are explored in a unified manner for various helium species. These include3He,4He and6He as well as combinations thereof. The subtle interplay among the central factors involved is delineated carefully. In particular, the dimer problem has been recast in three complementary forms which are based on: (1) the conventional eigenvalua equation in both its Schrödinger and Lippmann-Schwinger versions; (2) the quantum parameter; and (3) the concept of an eigenmass below which no binding occurs for a specific interatomic potential. This framework turns out to be adaptable, in its gross features, to two-dimensional systems and to the liquid phase as well. General implications ofn-merization in several helium liquids, comprising thin films, are examined briefly.

Hole–hole scattering in spin-polarized 3He–HeII mixtures

In this paper the Galitskii–Migdal–Feynman (GMF) formalism is applied to spin-polarized 3He–HeII mixtures with special emphasis on the effect of the magnetic field on hole–hole scattering. For comparison purposes, the relative phase shifts for S- and P-waves, in both GMF and Brueckner–Bethe–Goldstone (BBG) formalisms, are calculated and analysed. Also, the corresponding scattering lengths are evaluated. In polarized mixtures, the S-wave pairing decreases because of the flip of one spin in the pair; whereas the magnetic field has no effect on P-wave pairing.