Unitary group approach to describe interatomic potentials in 3D systems

ABSTRACT

An algebraic approach based on the unitary $U\left(4\right)$ algebra is proposed to describe 3D systems for effective potentials. Our approach is based on the 3D vibron model where the addition of a scalar boson is introduced into the space of a 3D harmonic oscillator. Our approach is based on the mapping between the $U\left(3\right)$ dynamical symmetry and the harmonic oscillator states. A minimisation procedure is used in order to determine the coefficients involved in the algebraic expansions. This allows the kets associated with the different subgroup chains to be linked to energy, coordinate and momentum representations. As an application of this approach the eigensystem of the 3D-Morse potential is analysed in detail. The analyses of inertia moments as well as the dipole moment strengths are also included. To show the convenience of this approach, a comparison with one ab-initio calculation for vibrational and rotational levels for O${}_2$ is presented in the framework of an analytical potential. In addition, a notch test is done to show how the formalism allows to check the sensitivity of the ro-vibrational results as a function of the precise structure of the potential energy surface as a function of r.

GRAPHICAL ABSTRACT

KEYWORDS:

• Algebraic approach
• effective 3D potentials
• Morse potential

Acknowledgments

Authors want to thank Octavio Castaños for useful discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México (DGAPA-UNAM), México, under project IN-227017, by Spanish Consejería de Economía, Inovación, Ciencia y Empleo, Junta de Andalucía [grant number FQM-160], by the Consejería de Conocimiento, Investigación y Universidad, Junta de Andalucía and European Regional Development Fund (ERDF), ref. SOMM17/6105/UGR, and by the Spanish Ministerio de Economía y Competitividad and FEDER funds under projects FIS2017-88410-P and FPA2016-77689-C2-1-R. First author is also grateful for the scholarship (Posgrado en Ciencia e Ingeniería de Materiales) provided by CONACyT, México.