Thermodynamics of the interacting Fermi-system in the Static Fluctuation Approximation

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the frame of the static fluctuation approximation (SFA) method. This method based only on the single and controllable approximation allows to obtain the so-called far-distance equations (FDEs). These equations connecting the quantum states of a Fermi particle with variables of the local field operator contains all necessary information related to calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system considered. The basic expressions for the mean energy and heat capacity for electron gas at low temperatures in the limit of high density were obtained. All expressions are given in the units of r_s,where r_s determines the ratio of a mean distance between electrons to the Bohr radius a_0. In these expressions we calculated the terms of the order r_s and r_s^2, correspondingly. It was shown also that the SFA allows to find the terms related with high orders of the decomposition with respect to the parameter r_s.Comment: 22 pages, 5 figure

Reply to ‘comments on comparison study of bound states for diatomic molecules using kratzer, morse, and modified morse potentials’

Abstract In this reply, I presented clarification for the difference in calculating bound-state energy eigenvalues for HCl obtained using the modified morse potential between our results and the results of Samant et al [Al-Othman and Sandouqa 2022 Phys. Scr. 97 035401]. In their comments, Samant et al [Samant R, Lotliker, and Desai, Phys. Scr.] stated that the reason for this difference is the wrong expression of the parameter used in the modified morse potential. But we found that this difference is a result of using different values of α and β. While we use approximate values of α and β, Samant et al [2] used optimized values of these parameters. Therefore, the results of Samant et al [2] are more accurate.</jats:p

Comparison study of bound states for diatomic molecules using Kratzer, Morse, and modified Morse potentials

Abstract In this paper, the bound-state energy eigenvalues for several diatomic molecules (O2, I2, N2, H2, CO, NO, LiH, HCl) are computed for various quantum numbers using the shifted 1/N expansion method with the Kratzer, Morse and Modified Morse potentials. Numerical results of the energy eigenvalues for the selected diatomic molecules are discussed. Our results for energy eigenvalues agree perfectly with the results obtained in the literature. A comparative study is performed for four diatomic molecules (H2, N2, CO and HCl) in their ground states using the three potentials.</jats:p

Scattering Properties of Argon Gas in the Temperature Range 87.3-120 K

A theoretical model, based on the Galitskii-Migdal-Feynman formalism, is introduced for determining the scattering properties of argon gas, especially the "effective" total, viscosity and average cross-sections. The effective phase shifts are used to compute the quantum second virial coefficient in the temperature range 87.3-120 K. The sole input is the Hartree-Fock dispersion (HFD-B3) potential. The thermophysical properties of the gas are then calculated. The results are in good agreement with experimental data

Weak 3He\text{}^{3}He Pairing in 3He−He(II)\text{}^{3}He-He(II) Mixtures

In this paper a theoretical study of a possible phase transition in dilute $\text{}^3He-He(II)$ mixtures is presented using the Galitskii-Migdal-Feynman formalism. The effective scattering length is calculated from the Galitskii-Migdal-Feynman T-matrix, which is essentially the effective scattering amplitude dependent on the medium. It is found that at very low $\text{}^3He$ concentrations the s-wave effective scattering length for ^3He-He(II) varies discontinuously from positive to negative values at some critical concentration. This indicates a crossover from a regime with dimers to another with the Cooper pairs. The binding energy of the weakly-bound dimers $\text{}^3He_2$ is computed. The effective p-wave scattering lengths are calculated and compared to the effective s-wave scattering lengths at low and high concentrations. It is found that p-scattering has an important effect on the instability of these mixtures at concentrations x > 1%. Finally, the transport coefficients are computed and compared to the theoretical predictions of Fu and Pethick and the experimental results of König and Pobell