The quasi bound spectrum of H₂

Abstract

We compute the radiative ro-vibrational emission spectrum of H${}_2$ involving quasi-bound states via a simple numerical method of resolution of the Schrödinger equation by introducing a modified effective molecular potential. The comparison of the eigenvalues obtained with our approximation and other theoretical methods based on scattering resonance properties is excellent. Electric quadrupole and magnetic dipole contributions are calculated and we confirm the previous computations of Forrey of the electric quadrupole transition Einstein coefficients. The astrophysical relevance of such quasi-bound levels is emphasized.

GRAPHICAL ABSTRACT

Keywords:

• Molecular Hydrogen
• shape resonance
• infrared

Acknowledgments

We thank the referees for useful comments and for driving our attention on the v = 14, J = 4 level and to the reference [24].

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 A more acccurate value is now available from CODATA21 [26] but we keep the same value as in our previous calculations [27] to preserve the consistency of our results.

2 Fortran source code, 2019, ver7.0, University of Warsaw, Poland; 2019 http://www.qcg.home.amu.edu.pl/qcg/public.html/H2Spectre.html.

3 c is the light velocity = 2.99792458e10 cm/s.

Additional information

Funding

We acknowledge support from the Programme National de Physique et Chimie du Milieu Interstellaire (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES.