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Low Temperature Physics

Interatomic interaction within a 4He−4He dimer with mobile nuclei

Konstantin A. Chishko

Published Jun 1, 2021• 2 citations
Publisher

Abstract

Schrodinger equation for system of two mobile spinless nucleus with Z0 = 2 and four electrons (4He2-dimer) has been solved in the framework of exact diagonalization approach. The spectrum has been obtained with basis of 1134 functions built as direct product of one-particle hydrogen-like functions which are solutions of the exactly solved Sturm-Liouville problem. The asymptotic (Van der Waals) behavior of interaction between two 4He atoms in the limit R0→∞ has been analyzed and discussed. The contribution to the interaction energy from four electronic spins on the 4He–4He bond has been calculated the exact diagonalization procedure.

DOI
10.1063/10.0004975

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Schrodinger equation for system of two mobile spinless nucleus with Z0 = 2 and four electrons (4He2-dimer) has been solved in the framework of exact diagonalization approach. The spectrum has been obtained with basis of 1134 functions built as direct product of one-particle hydrogen-like functions which are solutions of the exactly solved Sturm-Liouville problem. The asymptotic (Van der Waals) behavior of interaction between two 4He atoms in the limit R0→∞ has been analyzed and discussed. The contribution to the interaction energy from four electronic spins on the 4He–4He bond has been calculated the exact diagonalization procedure.
The non-relativistic quantum-mechanical problem on bound states of four interacting spinless electrons moving in the Coulomb field of two attractive point centers with Z0=2 spaced at fixed distance R0 (4He2 dimer within Born–Oppenheimer–Heitler–London approximation) has been solved rigorously through exact diagonalization (expansion on truncated orthonormalized basis) method. The four-spin-conditioned relativistic corrections (of order ∼1/c2) to the ground state level of the dimer have been calculated with exact diagonalization on spin cluster, the spectrum and eigenvectors of the spin problem have been obtained. It is shown that pair spin coupling is antiferromagnetic with exchange constant of 12 K (it provides antisymmetry of the spin-singlet ground-state wave function for isolated 4He atom with two fermions coupled within the unitary spatially symmetric shell), but within four-electron shell of 4He2 dimer this fact yields the quintet ground state of the four-spin cluster totally antisymmetric relative to pair permutations. The exchange within the interatomic bond depends on the interatomic distance, so that there is a coupling between spin and phonon degrees of freedom which leads to renormalization of phonon spectrum in condensed phase as compared to the corresponding spinless medium. This effect can be interpreted as a direct analog of translation-rotation interaction in molecular cryocrystals.
We study the one-dimensional double-exchange model with L localized spins and one mobile electron. We solve the Schrödinger equation analytically and obtain the energies and wave functions for all the eigenstates with spin S = ( L − 1)***/2 exactly. As an application, we compute the single-particle Green's function. We show that, for vanishing exchange interactions between localized spins, the single-particle spectrum is entirely incoherent and the lowest band has an infinite band mass, i.e., the single electron is localized due to its interaction with the spin excitations. The analysis of the wave function gives us a particularly simple ground state.
The interaction potential of three helium atoms in symmetric linear configurations is calculated under the Born–Oppenheimer approximation using an ‘‘exact’’ Green’s function quantum Monte Carlo method. The results are compared with those of ‘‘exact’’ quantum Monte Carlo calculations for the helium dimer and the Axilrod–Teller triple-dipole energy expression. For nearest neighbor separations of 5.6 bohrs, the equilibrium distance for a helium dimer, the corresponding trimer energy is −21.5±1.9 K, compared to −22.3±0.2 K, calculated for pairwise additive behavior. For all internuclear separations in the neighborhood of the van der Waals well (∼5.6 bohrs), the nonadditive contribution is found to be very small.
We present a theoretical study on the potential energy surface and bound states of He–A 2 + complexes, where A is one of the alkali Li or Na atoms. The intermolecular interactions were systematically investigated by high-level ab initio electronic structure computations, and the corresponding raw data were then employed to reproduce accurate analytical expressions of the potential surfaces. In turn, we used these potentials to evaluate bound configurations of the trimers from nuclear quantum calculations and to extract information on the effect of orientational anisotropy of the forces and the interplay between repulsive and attractive interaction within the potential surfaces. The spatial features of the bound states are analyzed and discussed in detail. We found that both systems are going under large amplitude stretching and bending motions with high zero-point energies. Despite the large differences in the potential well-depths, the correct treatment of nuclear quantum effects provides insights on the effect of different strength of the ionic interaction on the spectral structure of such cationic alkali van der Waals complexes, related to the mobility of ions and the formation of cold-molecules in He-controlled environments.
Four-body system of 4He{}^4\mathrm{He}4He atoms: Dimer-dimer scattering
The strong short-range repulsion, characteristic to realistic interatomic potentials, complicates the description of weakly-bound few-body systems such as those of \He atoms. The present work proposes an approach for solving this problem and applies it to a realistic system of four 4He{}^4\mathrm{He}4He atoms. The potential is gradually softened such that rigorous four-body equations for bound and scattering tates can be accurately solved in the momentum-space framework, and the results are extrapolated back to the limit of the original potential. Linear correlations between three- and four body quantities are observed, and the accuracy of the procedure is improved by extrapolating in one of the three-body quantities. Results for the 4He{}^4\mathrm{He}4He tetramer ground and excited state binding energies and atom-trimer scattering agree well with at least some of earlier determinations and shed light on the existing disagreements. An additional case of the Phillips correlation line is established for the dimer-dimer scattering length. The trimer production rate via the ultracold two-dimer collisions is estimated, it exhibits significant finite-range effects despite the weak binding of the dimer.
We investigate the low-energy collision properties of the 4He-4He-X (X = 40K, 85Rb, 133Cs) systems using the R-matrix propagation method within the hyperspherical coordinate framework. The atom-dimer scattering length and atom-molecule collisional exchange rates are derived by solving the three-body Schrödinger equation using a potential energy surface obtained by summing three realistic pairwise potentials. Our results show that the atom-molecule collision exchange rates in the 4He2 + X → 4HeX + 4He process are primarily governed by the 4HeX two-body scattering lengths. Furthermore, when scaled by this parameter, the inelastic cross sections for all three systems collapse onto a single curve, demonstrating universal behavior. These findings provide new insights into the fundamental properties of weakly bound helium-helium-alkali-metal systems and their role in low-energy three-body collisions.