22P091-P
Construction of hydrogen molecule collisional-radiative model
水素分子衝突輻射モデルの構築
Shinnosuke Kakura,1 Keiji Sawada,1 Keita Nakane,1 Kento Takeuchi,1 Ryo Idei,1 Naomichi Ezumi2
and Motoshi Goto3
加藏新之輔1，澤田圭司1，中根啓太1，竹内研人1，出井諒1，江角直道2，後藤基志3
1

Graduate school of Sci. and Tec., Shinshu University 4-17-1 Wakasato, Nagano, 380-8533, Japan
2
Nagano National College of Technology 716 Tokuma, Nagano, 381-8550, Japan
3
National Institute for Fusion Science 322-6 Oroshi-cho, Toki, Gifu, 509-5292, Japan1
信州大学大学院工学系研究科 〒380-8533 長野市若里4-17-1
2
長野工業高等専門学校 〒381-8550 長野市徳間716
3
核融合科学研究所 〒509-5292 土岐市下石町322-6

A collisional-radiative model of molecular hydrogen, which includes electronic, vibrational and rotational
states is constructed. Spontaneous transition probabilities for bound and continuum transitions are newly
calculated. Cross sections are estimated from Franck-Condon and Hönl-London factors. Population
density and emission spectra of the molecule are calculated.

1. Introduction
We have been developing collisional-radiativemodels and a neutral-transport code for hydrogenand helium species, which are used to investigatefusion plasmas.
As a revision of the molecular hydrogencollisional-radiative model, which includes
electronic and vibrational states [1, 2], we aredeveloping a model that includes rotational statesin addition. This model will provide more precise
effective reaction rate coefficients of themolecule. Emission line intensities of hydrogenmolecules in plasmas are calculated as a functionof nH2, ne, Te, and Tv, Trot in the ground electronicstate. From observed spectra, these parameters
can be determined.
2. ModelIn the revised model which includes rotational
states, assuming Hund’s (b) case, the levels arelabeled by the principal quantum number of theunited atom n, and Λ , N, and J. The number of
2131 levels for n ≦ 4, listed in Ref. [3], areincluded in the model.
Spontaneoustransition
probabilitiese3Σu+→a3Σg+,d3Πu→a3Σg+,
i3Πg→c3Πu,
j3∆g→c3Πu, I1Πg→C1Πu, and J1∆g→C1Πu in Ref.
[4] are included in the model. The values forother transitions are calculated according to Ref.
[5]. Transition probabilities to continuum states,from a3Σg+ , h3Σg+ , g3Σg+ , i3Πg , r3Πg to b3Σu+, andfrom B1Σu+ , B’1Σu+ , B’’1Σu+ , C1Πu, D1Πu tocontinuum of X1Σg+, are also calculated [8, 9].
The vibrationally resolved excitation crosssection from the electronic ground state to B1Σu+,B’ 1Σu+, B” 1Σu+, C1Πu, D1Πu, D’ 1Πu in Ref. [6]are included in the model; for the excitation toother states, data in Ref. [7, 8] are included.
There is not enough information to derive
vibrationally and rotationally resolved crosssections. For an optically allowed transition, weassume that the rate coefficients are proportional
to Franck-Condon and Hönl-London factors. For
an optically forbidden transition, we use theFranck-Condon factor to obtain vibrationallyresolved data and divide them evenly for
rotational states. Excitation cross sections
between excited states are estimated from united
helium atom cross sections. Reaction rate
coefficients which are essential to determine thevibrational and rotational population of theground electronic state are included in the model.
3. Results and Discussion
We have calculated population of excited statesand emission intensity.
Figure 1 shows
population distribution calculated with nH2=1.0
cm-3, ne=2×1010 cm-3, Te=3.0 eV, and Tv=4200
K, Trot=350 K. Electronic states of the levels arelisted in Table I. Large values in Fig.1 are formetastable triplet c state. Figure 2(a) showsemission line intensity.
Large emission
intensity is seen in vacuum ultraviolet region.
Figure 2(b) is enlarged one of Fig.2(a). Fülcher
band around 600 nm is dominant in visible range.
Continuum emission is seen in the wavelength fromvacuum ultraviolet to around 400 nm.

Fig.1. Calculated population with n H2=1 cm-3, ne=2×1010 cm-3, Te=3.0 eV, and Tv=4200 K, Trot=350 K.
See Table I for levels.
Table I. Electronic states of levels in the model

XE
B
CC+
H
B’
DD+
G
II+
JJ+
O
B’’
D’D’+
P
RR+

1~301
302~333
334~423424~454455~470471~484
485~512513~530531~542543~577578~597598~617618~632633~641642~661662~676677~692693~708709~716717~725726~727

SS+acc+hedd+
gii+
jj+
fkk+
rr+
ss+

728~730731~733734~881882~965969~1049
1050~1093
1094~1243
1244~1372
1373~1438
1439~1523
1524~1598
1599~1661
1662~1724
1725~1784
1785~1810
1811~1912
1913~1930
1931~1999
2000~2062
2063~2098
2099~2131

Fig.2. (a) Calculated emission lines.
one of (a).

(b) Extended

4. Conclusion
A molecular hydrogen collisional-radiativemodel which includes electronic, vibrational androtational states has been constructed. We will
apply this model to RF hydrogen plasmas at
Shinshu University in order to test whether themodel reproduces observed emission intensity.
In the present model, Bolzmann distribution forvibrational and rotational population of theelectronic ground state is assumed. If necessary,
it will be improved.
References[1] K. Sawada and T. Fujimoto, J. Appl. Phys. 78, 2913
(1995).
[2] K. Sawada and T. Fujimoto, Contrib. Plasma Phys.
42, 603 (2002).
[3] H. M. Crosswhite, The Hydrogen Molecule
Wavelength Tables of GERHARD HEINRICH
DIEKE, John Wiley & Sons Inc (1972).
[4] S. A. Astashkevich et al., J. Quant. Spectrosc. Radiat.
Transfer 56, 725 (1996).
[5] James K.G. Watson, Journal of Molecular
Spectroscopy 252, 5 (2008).
[6] R. Celiberto, R. K. Janev et al., Atomic Data andNuclear Data Tables 77, 161 (2001).
[7] R. Janev, D. Reiter, and U. Samm, Report
Forschungszentrum Jülich JUEL 4105, (2003).
[8] T. K. Kwok, S. Guberman, A. Dalgarno and A. Posen,
Phys. Rev. A 34, 1962 (1986)[9] T. L. Stephens and A. Dalgarno, J. Quant. Spectrosc.
Radiat. Transfer 12, 569 (1972)