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Canadian Journal of Physics

Binding properties of some alkali metal vapors: specifically lithium-7 (7Li), soduim-23 (23Na), and potassium-39 (39K)

H. B. Ghassib, Anoud H. Al-Aoon, Ayman S. Sandouqa

Published Nov 2, 2023• 1 citation

Abstract

In this work, the binding energy of three alkali metal molecules, namely, lithium-7 (7Li2), sodium-23 (23Na2), and potassium-39 (39K2), is calculated in both free space and the vapor phase. In free space, the Lippmann–Schwinger equation is solved for negative-definite eigenenergies using a highly effective matrix-inversion method with a symmetrized kernel. In the vapor, two medium effects are taken into account: the effective atomic mass, which is somewhat larger than the “bare” mass and therefore enhances the binding; and the effective binary interaction, with less overall attraction than the “bare” interaction. In free space, the binding energies of the respective molecules are, in units of (103 K), 5.304, 2.936, and 2.522. The corresponding experimental results are 6.150 × 103, 4.275 ×103, and 4.275 × 103 K. The results in the vapor phase are by and large somewhat lower than those in free space.

DOI: 10.1139/cjp-2023-0136

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In this work, the binding energy of three alkali metal molecules, namely, lithium-7 (7Li2), sodium-23 (23Na2), and potassium-39 (39K2), is calculated in both free space and the vapor phase. In free space, the Lippmann–Schwinger equation is solved for negative-definite eigenenergies using a highly effective matrix-inversion method with a symmetrized kernel. In the vapor, two medium effects are taken into account: the effective atomic mass, which is somewhat larger than the “bare” mass and therefore enhances the binding; and the effective binary interaction, with less overall attraction than the “bare” interaction. In free space, the binding energies of the respective molecules are, in units of (103 K), 5.304, 2.936, and 2.522. The corresponding experimental results are 6.150 × 103, 4.275 ×103, and 4.275 × 103 K. The results in the vapor phase are by and large somewhat lower than those in free space.

By use of a free-energy model, the properties of a fluid composed of neutral atoms and diatomic molecules, positive ions and molecular ions, and an electron Fermi gas are calculated. The interactions include excluded volume, internal molecular binding, electron-neutral s-wave scattering, and screened Hartree interactions. For rubidium and cesium parametrizations, the vapor-liquid phase transitions with their critical points, the insulator-metal transitions, and the isothermal electrical conductivities and magnetic susceptibilities are obtained.

We present third-order many-body perturbation theory calculations of the Lennard-Jones

{C}_{3}

coefficient for the alkali-metal atoms lithium, sodium, potassium, rubidium, cesium, and francium. All-order singles-doubles calculations of

{C}_{3}

are also presented for lithium, sodium, and potassium. For lithium and sodium the present values of

{C}_{3}

are compared with other theoretical and semiempirical values.

We present ab initio potentials for ground state lithium, sodium, potassium and rubidium atoms interacting with ground state chromium atoms via the 6 Σ + and 8 Σ + states of the corresponding dimers. Each potential is matched to the leading van der Waals dispersion energy − C 6 / R 6 − C 8 / R 8 and an exchange energy; we list the values of C 6 , C 8 and the exchange fitting parameters. We present calculated values from quantal and semi-classical approximations for the s-wave scattering length and effective range and the p-wave scattering volume for collisions of each of the alkali-metal atoms lithium, sodium, potassium and rubidium with 52 chromium atoms and comment on s-wave scattering by 53 chromium atoms.

We report a theoretical calculation of the relativistic corrections to the binding energy of positronic alkali-metal atoms. The ground state for the positronic alkali-metal atom is a loosely bound state with the structure of an alkali-metal ion surrounded by a positronium cloud. The correlation between the valence electron and positron in the field of a residual core ion is taken into account using a three-body model. Relativistic corrections to the binding energy for positronic alkali-metal atoms are evaluated based on the Breit-Pauli perturbation theory up to the second order of the fine structure constant. The relativistic corrections caused by the interaction between the valence electron and core ion was evaluated from the decomposed expectation values of the perturbation Hamiltonian. We found that the importance of relativistic corrections to the binding energy, namely the ratio of the net relativistic correction in the total binding energy, is remarkably enhanced in the loosely bound states of positronic alkali-metal atoms, where the charge of the valence electron is screened by the positron as positronium in the outermost region, while the electron is released from the positron near the nucleus. The results imply that positronic atoms with a dominant positronium can serve as an apt testing ground for relativistic quantum mechanics.

We study the existence of stable bound states of triatomic molecules containing two helium atoms and one alkali atom X (X = Li, Na) and examine the dependence of their binding energies on the mass of the constituent atoms. The three-body systems are solved within the adiabatic approximation in hyperspherical coordinates using the He - He and He - X pair van der Waals interactions that are available in the literature. The binding energies of these systems are shown to be of less than 1 K for some isotope combinations. For the lighter isotopes it is shown that no bound states exist. We found no evidence of the existence of halo states or Efimov states for these systems.