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Saratov Fall Meeting: Laser Physics, Photonic Technologies, and Molecular Modeling

On calculations of metastable and Rydberg states of diatomic beryllium molecule and antiprotonic helium atom

Vladimir Leonardovich Derbov, Galmandakh Chuluunbaatar, Alexander A. Gusev, Ochbadrakh Chuluunbaatar, Sergue Il'ich Vinitsky, ANDRZEJ GÓŹDŹ, Pavel M. Krassovitskiy, Alexander V. Mitin

Published Apr 9, 2020• 1 citation

Abstract

The computational scheme and calculation results of bound, metastable and Rydberg states of atomic and molecular systems important for laser spectroscopy are presented. The solution to the problem is performed using the authors' software package (see program libraries of the Computer Physics Communications journal and of the Joint Institute for Nuclear Research) that implement the high-accuracy finite element method. The FORTRAN procedure of matching tabulated potential functions with van der Waals asymptotic potential using interpolation Hermite polynomials which provides continuity of both the function itself and its derivative is presented. The efficiency of the proposed approach is demonstrated by calculated for the first time sharp metastable states with complex eigen-energies in a diatomic beryllium molecule and weakly bound Rydberg states of antiprotonic helium atom.

DOI: 10.1117/12.2565816

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The computational scheme and calculation results of bound, metastable and Rydberg states of atomic and molecular systems important for laser spectroscopy are presented. The solution to the problem is performed using the authors' software package (see program libraries of the Computer Physics Communications journal and of the Joint Institute for Nuclear Research) that implement the high-accuracy finite element method. The FORTRAN procedure of matching tabulated potential functions with van der Waals asymptotic potential using interpolation Hermite polynomials which provides continuity of both the function itself and its derivative is presented. The efficiency of the proposed approach is demonstrated by calculated for the first time sharp metastable states with complex eigen-energies in a diatomic beryllium molecule and weakly bound Rydberg states of antiprotonic helium atom.

A very accurate variational expansion is suggested for calculation of nonrelativistic energies of the metastable antiprotonic helium atoms

{\mathrm{He}}^{+}\overline{p}.

This expansion reflects the dual atomic-molecular nature of the system. Convergence of the results as a function of the increasing sets of basis functions shows an accuracy better than ${10}^{\ensuremath{-}10}\mathrm{a}.\mathrm{u}.,$ two orders of magnitude better than in our previous calculations.

We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two highly efficient computational methods for determining the bound state energies and eigenfunctions of such systems. The perturbed harmonic oscillator problem is characterized by a long asymptotic region beyond the effective range of the interatomic potential. The first method, which is based on quantum defect theory and is an adaptation of a technique developed by one of the authors (G.P.) for highly excited states in a modified Coulomb potential, is very efficient for integrating through this outer region. The second method is a direct numerical solution of the radial Schr\"odinger equation using a discrete variable representation of the kinetic energy operator and a scaled radial coordinate grid. The methods are applied to the case of trapped spin-polarized metastable helium atoms. The calculated eigenvalues agree very closely for the two methods, and with the eigenvalues computed using the generalized self-consistent method.

Along its lowest rotational band, the antiprotonic helium atom undergoes several changes of structure. It evolves from an hydrogenlike atom with broader and broader resonant states, to a quasistable molecularlike structure with narrow resonances, and then to a quasistable Rydberg pseudoatom. The antiprotonic helium atom is studied with high accuracy as a nonrelativistic three-body Coulomb system in the framework of the Lagrange-mesh method. Its metastable states are first determined from

L=0

to

L=80

by searching conditions of calculation for which energies are stationary. Mean values of distances between the particles are then easily deduced. They show the evolution of the structure of the system. Broad resonances are also analyzed with the complex scaling method. Physical interpretations are provided.

We introduce a computational method developed for study of long-range molecular Rydberg states of such systems that can be approximated by two electrons in a model potential of the atomic cores. Only diatomic molecules are considered. The method is based on a two-electron

R

-matrix approach inside a sphere centered on one of the atoms. The wave function is then connected to a Coulomb region outside the sphere via a multichannel version of the Coulomb Green's function. This approach is put into a test by its application to a study of Rydberg states of the hydrogen molecule for internuclear distances

R

from 20 to 400 bohrs and energies corresponding to

n

from 3 to 22. The results are compared with previous quantum chemical calculations (lower quantum numbers

n

) and computations based on contact-potential models (higher quantum numbers

n

).

Recent progress in studies of Rydberg double-well electronic energy states of MeNg (Me = 12-group atom, Ng = noble gas atom) van der Waals (vdW) molecules is presented and analysed. The presentation covers approaches in experimental studies as well as ab initio-calculations of potential energy curves (PECs). The analysis is shown in a broader context of Rydberg states of hetero- and homo-diatomic molecules with PECs possessing complex 'exotic' structure. Laser induced fluorescence (LIF) excitation spectra and dispersed emission spectra employed in the spectroscopical characterization of Rydberg states are presented on the background of the diverse spectroscopic methods for their investigations such as laser vaporization-optical resonance (LV-OR), pump-and-probe methods, and polarization labelling spectroscopy. Important and current state-of-the-art applications of Rydberg states with irregular potentials in photoassociation (PA), vibrational and rotational cooling, molecular clocks, frequency standards, and molecular wave-packet interferometry are highlighted.

A variational calculation is presented of energy levels for the nonrelativistic Hamiltonian of the metastable antiprotonic helium atom

{\overline{p}}^{3, 4}{\mathrm{He}}^{+}

. This calculation is based on a molecular expansion of the wave function. We estimate the precision of the results to be about ${10}^{\ensuremath{-}7}$ a.u.