7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Reexamination of the hydrogen-molecular spectral constants relevant to theFulcher-α band observed in H2 discharge plasma
K. Sunakawa1, K. Suganami1, A. Nezu2 and H. Akatsuka3,1
1 Dept. Elec/Electron Eng., 2 Open Facility Center, 3 Inst. Innovative Research, Tokyo Teche-mail (speaker): hakatsuk@zc.iir.titech.ac.jp
The history of spectroscopic measurement of hydrogenmolecules can be traced back to before 1930, and manystudies have been done so far. In particular, the Fulcher-αband (d 3Πu – a 3Σg+) is in the visible wavelength region
and is convenient to observe spectroscopically. In
general, when measuring the rotational temperature of a
Fulcher-α band, the theoretical calculation of theemission spectrum of this band is applied, and thetemperature is determined as a kind of best-fitting
parameters. The purpose of this research is to re-examineof the spectroscopic constants, especially the rotational
constants, of the hydrogen molecule used in thatcalculation.
Figure 1 shows the experimental setup used in thisresearch. Hydrogen gas with its gas pressure of 1 Torr
was irradiated with microwaves of 600 W and 2.45 GHz,and surface wave hydrogen plasma was generated in aquartz glass tube with an inner diameter of 26 mm, andoptical emission spectrometry was performed. As a resultof previous actinometric measurement experiments, it
has already been found that the degree of dissociation isapproximately 4% [1].
Table 1 shows the spectroscopic constants of the upperand lower levels of the Fulcher-α band, d 3Πu and a 3Σg+levels, respectively, published by Dieke and Blue et al.
[2], together with those proposed to correct by the resultsof the present study based on the best-fitting method forthe spectrum observed experimentally with theoretical
calculation of the Fulcher-α of the hydrogen molecule.
The molecular rotational constants in this study arecalculated by the least-squares method, using thelower-level spectral constant as a variable from theposition of the peak of the spectrum obtained from thetheoretical formula and the experiment. In the course offitting procedure, the systematic discrepancy was foundTable 1. Rotational constants in cm–1of H2 d 3Πu and a3Σ + levels by (a) Dieke and Blue [2], and (b) thegpresent study based on the best fitting of the spectrum
observed experimentally with theoretical calculation.
(a)
(b)
State
d 3Π ua 3Σ g+Stated 3Π ua 3Σ g+Be
30.364 34.261 Be
30.364 33.399
αe
1.545
1.671
αe
1.545
1.515
–––
γe–
0.049
De
0.0191 0.0216 De
0.0191 0.0216
between the observed one and the calculated one, which
was found to be attributed to the rotational constant Bv ofthe lower level a 3Σg+. Regarding the theoretical formulaof the rotational energy for the upper-level d 3Πu, the one
proposed by Kado et al [3] was adopted. Meanwhile, forthe better agreement of the wavelength of thespectral-lines, it was found that the systematic
modification of the constant Bv is necessary fromconventional linear function of v to quadratic one
introducing another parameter γe as follows:# $#𝐵! = 𝐵" − 𝛼" &𝑣 + ) + 𝛾" &𝑣 + ) .
$$Figure 2 shows an example of fitting. This is the casewhen the vibrational quantum numbers of the upper andthe lower levels are both 0. Using the molecularconstants proposed in this study, it was found that themean-square error for the wavelength was improved
from 0.124 to 0.028. Even now, the spectroscopic
constants of H2 molecule adopted so far need to bereexamined.
ExperimentCalculation

Q3

R1

Trot=0.03[eV]
Q1
Q2

R2

Q5
P2

R0

P4

Q4

Figure 2. Example of spectrum fitting of the Fulcher-αband with (𝑣 % , 𝑣′′) = (0,0).

Figure 1. Experimental apparatus to generate
microwave discharge H2 plasma [1].

References[1] Y. Shimizu, Y. Kittaka, A. Nezu, H. Matsuura and H.
Akatsuka, IEEE Trans. Plasma Sci., 43, 1158 (2015).
[2] G.H. Dieke and R.W. Blue, Phys. Rev. 47, 261(1935).
[3] S. Kado, D. Yamasaki, Y. Iida and B. Xiao, J. Plasma