M. K. Al-Sugheir

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.

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.

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.

3He–HeII Mixtures in the Static Approximation

We have applied, for the first time, the so-called static approximation (SA) on the 3He–HeII mixtures to calculate their thermodynamic properties under different conditions. For that, we have first obtained the so-called self-consistent long-range-equation. The essence of this approximation is to replace the true quantum-mechanical spectrum of the local-field operator with a distribution around the expectation value of the local-field operator. The distribution function of the fermionic particles has been found to be almost a step function up to 0.1 K. The chemical potential, pressure, and the mean internal energy per unit volume have been calculated in this temperature range with different values for the volume differential coefficient α and the effective mass m3*. We have found that the thermodynamic properties of this system are temperature independent.

THERMODYNAMIC PROPERTIES OF AN INTERACTING HARD-SPHERE BOSE GAS IN A TRAP USING THE STATIC FLUCTUATION APPROXIMATION

A hard-sphere (HS) Bose gas in a trap is investigated at finite temperatures in the weakly interacting regime and its thermodynamic properties are evaluated using the static fluctuation approximation. The energies are calculated with a second-quantized many-body Hamiltonian and a harmonic oscillator wave function. The specific heat capacity, internal energy, pressure, entropy, and the Bose–Einstein occupation number of the system are determined as functions of temperature and for various values of interaction strength and number of particles. It is found that the number of particles plays a more profound role in the determination of the thermodynamic properties of the system than the HS diameter characterizing the interaction, that the critical temperature drops with the increase of the repulsion between the bosons, and that the fluctuations in the energy are much smaller than the energy itself in the weakly interacting regime.

SPIN-POLARIZED ATOMIC DEUTERIUM (↓D) IN THE STATIC FLUCTUATION APPROXIMATION (SFA)

Spin-polarized atomic deuterium (↓D) is investigated in the static fluctuation approximation with a Morse-type potential. The thermodynamic properties of the system are computed as functions of temperature. In addition, the ground-state energy per atom is calculated for the three species of ↓D: ↓D1, ↓D2, and ↓D3. This is then compared to the corresponding ground-state energy per atom for the ideal gas, and to that obtained by the perturbation theory of the hard sphere model. It is deduced that ↓D is nearly ideal.

Hot nuclear matter in the static fluctuation approximation

In this work, the bulk and thermodynamic properties of nonrelativistic hot nuclear matter--the mean internal energy per unit volume, the saturation density and the corresponding internal energy per nucleon, the pressure, the entropy per unit volume, the heat capacity per unit volume, and the chemical potential--are studied within the static fluctuation approximation (SFA). The basic input is the well-known Reid68 and Reid93 soft-core potentials, with special emphasis on three channels that have different spin and isospin--namely, the {sup 1}S{sub 0}-channel as well as the {sup 3}S{sub 1}-{sup 3}D{sub 1} and {sup 3}P{sub 2}-{sup 3}F{sub 2} coupled channels. Finally, a full-fledged calculation is presented using the Reid93 potential for all channels J{<=}2. Wherever possible, comparisons are made with previous calculations. It is concluded that SFA is valid for hot nuclear matter over a wide range of temperatures ({<=}50 MeV)

Bose-Einstein condensation and heat capacity of two-dimensional spin-polarized atomic hydrogen

The static fluctuation approximation (SFA) is used to study the condensate fraction and the specific heat capacity of finite two-dimensional spin-polarized atomic hydrogen. It is found that Bose-Einstein condensation occurs in this system. The transition temperature at different densities decreases as the number of particles of the system increases. At low density, a sharp peak in the specific heat capacity is observed at the transition temperature. On the other hand, as the density of the system increases, the transition temperature becomes no longer well-defined, and a hump is observed in the specific heat capacity around the transition temperature. A qualitative comparison of our results to published results for finite Bose systems shows good agreement.