H2SPEC

Compute the spectral line list and spectrum of H₂ in the vacuum ultraviolet region.

Description

The program h2spec computes a list of allowed optical transitions for the Lyman (B→X) and Werner (C→X) bands of the hydrogen molecule, using available experimental and theoretical data. The generated line list is written to the file, h2lines.dat. h2spec also uses the line list to compute the vacuum ultraviolet spectrum of the H₂ molecule, under specified excitation conditions and spectral resolution. The spectrum is written to the file, h2vuv.dat.

h2spec was used in the research reported in References 1–5. Input data sources for h2spec are described in Appendix I and Appendix II of [5] -- this information is also provided below.

Build

Under Linux, gfortran may be used to build h2spec from source:

$ gfortran -o h2spec h2spec.f

Energy Levels and Transition Oscillator Strengths

Energy levels for the X, B, and C electronic states of H₂ were obtained from the following sources.

X Levels

Energy levels for the X ground electronic state are found in xlevels.dat. Herzberg and Howe [6] list the X, v = 0–14, J = 0 levels. Energies of higher J levels were computed with the expression,

E(v,J) = G₀(v) + B_vJ(J+1) - D_vJ²(J+1)² + H_vJ³(J+1)³

where G₀(v) is the energy of the v, J=0 level, and B_v, D_v, and H_v are constants given in [6].

Recent high-precision theoretical calculations of the X state ro-vibronic level energies are described in [10–11]. An alternative energy level file for the X state, based on the calculations of H2SPECTRE[10–11] is provided in xlevels-h2spectre.dat.

B Levels

Energy levels for the B electronic state are found in blevels.dat. G₀(v) values for v=0 to v=5 were taken from Herzberg and Howe[6]. However, values for v=6 to v=13 were obtained from their wavelength tables for transitions arising from the given v state and the energy levels obtained for the ground state. For J > 0, the energy levels were taken from Crosswhite[7]. A shift of 8.04 cm^-1 had to be added to the B state energy levels from Crosswhite in order to make them consistent with the wavelength measurements of Herzberg and Howe[6]. The v=14, J=0 and v=15, J=0 levels were taken from Monfils[8].

C Levels

Energy levels for the C state in clevels.dat were taken from Crosswhite [7]. Again, a shift of 8.04 cm^-1 was added to the levels reported in this source to place them on a consistent scale with the lower levels.

Oscillator Strengths for B→X and C→X Transitions

The band oscillator strengths in xbf.dat and xcf.dat are reproduced from Allison and Dalgarno [9]. The oscillator strength for an individual rotation-vibration transition is related to the band oscillator strength by

f_v'v''J'J'' = L_J'J''f_v'v'' (2J'' + 1)^-1,

where L_J'J'' is the Hönl-London factor. The double-primed quantities refer to the lower level, and the single-primed quantities refer to the upper level.

References

1. K. Myneni and J. Kielkopf, Excited-state populations of H₂ in the positive column of a glow discharge, J. Phys. B 21, 2871–2878 (1988).
   
2. J. Kielkopf, K. Myneni, and F. Tomkins, Unusual fluorescence from H₂ excited by multiphoton processes, J. Phys. B 23, 251–261 (1990).
   
3. J. F. Kielkopf and N. F. Allard, Satellites on Lyman alpha due to H-H and H-H⁺ collisions, Astrophysical Journal 450:L75–L78 (1995).
   
4. J. F. Kielkopf and N. F. Allard, Observation of the far wing of Lyman α due to neutral atom and ion collisions in a laser-produced plasma, Phys. Rev. A 58, 4416–4425 (1998).
   
5. K. Myneni, Excited State Populations of H₂ in a Glow Discharge, M.S. Thesis, Dept. of Physics, University of Louisville, 1987.
   
6. G. Herzberg and L. L. Howe, The Lyman Bands of Molecular Hydrogen, Can. J. Phys. 37, 636–659 (1959).
   
7. H. M. Crosswhite, The hydrogen molecule wavelength tables of Gerhard Heinrich Dieke, (New York: Wiley-Interscience), 1972.
   
8. A. Monfils, Absorption spectra of molecules H₂, HD, and D₂: VII. Vibrational constants of the B, B', B'', C, D, D', and D'' states, J. Molec. Spec. 25, 513–543 (1968).
   
9. A. C. Allison and A. Dalgarno, Band oscillator strengths and transition probabilities for the Lyman and Werner systems of H₂, HD, and D₂, Atomic Data 1, 289–304 (1969).
   
10. J. Komasa, M. Puchalski, P. Czachorowski, G. Lach, and K. Pachucki, Rovibrational energy levels of the hydrogen molecule through nonadiabatic perturbation theory, Phys. Rev. A 100, 032519 (2019).
    
11. J. Komasa, M. Puchalski, P. Czachorowski, G. Lach, and K. Pachucki, H2SPECTRE developer's version (28.05.2020), https://www.fuw.edu.pl/~krp/ (2020).