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MNRAS453,810-818 (2015)

Revisited study of the ro-vibrational excitation of H 2 by H: towards a Franc

LOMC - UMR 6294, CNRS-Universit

Accepted 2015 July 22. Received 2015 July 20; in original form 2015 May 14

ABSTRACT

We report nearly exact quantum time-independent calculations of rate coefficients for the ?22 000 K) for Key words:Molecular data-Molecular processes-scattering.

1 INTRODUCTION

Modelling of astrophysical media relies on modelling microscopic processes that may lead to (de-)excitation of atomic and molecular

?20).EvenifH , ...) are absent in the early Universe. Prior to that red shift, Puy

I=1) (hereafter o-H

I=0) (hereafter p-H

+H

E-mail:

2015 The Author

Ro-vibrational excitation of H

2 by H811 v=0, j=0) and o-H v=0,j=1) so that it is not possible to use them in astrophysical modelling of warm media.

T<1500 K). Their results are in very good agreement with the available experimental data. However, in

ab initiopotential energy surface. The paper is organized as follows. Section 2 provides a brief description

2 SCATTERING CALCULATIONS

In our calculations, we use the H

ab initiomethods and proved to be very successful in the calculation of H+D +H

A+BC→A+BC) and reactive (e.g.A+BC→AB+CorAC+B) processes obtained from such wavefunctions (Truhlar

j,k(the rotational angular momentum of the H v(the vibrational quantum number of the H +H v,j)→H+H v ,j →v j ?(E c 2 vj (2j+1) Jkk (2J+1) ?S (E,vjk→v j k 2

S-matrix for the H+H

|S (E,vjk→v j k 2 |S (E,vjk→v j k )-S (E,vjk→v j k 2 ,ifj,j even, |S (E,vjk→v j k )+S (E,vjk→v j k 2 +2|S (E,vjk→v j k 2 ,ifj,j odd, 3|S (E,vjk→v j k 2 ,ifjeven,j odd, |S (E,vjk→v j k 2 ,ifjodd,j even, (2) S andS are the nonreactive and reactiveS-matrix elements, respectively. k denotes the initial wavevector. The calculations were carried out on a grid of total energiesE: E=E c (3) E c vj is the ro-vibrational energy of the H ?15 000 K). This effect can

453,810-818 (2015)

812F. Lique

be more important for differential cross-sections and at very high collisional energies. Hence, the accuracy of our calculations may slightly

vj <22000 K. A large number of closed ro-vibrational channels of the diatomic moiety ?45 000 K and (b) levels

jof the diatomic moiety is greater than 24. Converged integral reactive cross-sections could be obtained by

?36 000 K. →v j ?(E c k →v j ?(T)= 8

πμk

3 T 3 ?1 0 →v j ?(E c E c -Ec/k B T dE c

μis the reduced mass of H

-Handk B

3 RESULTS

We first present the results for the pure rotational excitation. Fig. +D

3.2 Ro-vibrational (de-)excitation

Fig.

?vtransition, the rate coefficients slightly increase with increasing vibrational states. This result is consistent with previous

?vtransitions. This is in

453,810-818 (2015)

Ro-vibrational excitation of H

2 by H813 Figure 1.Temperature dependence of the rate coefficients for the rotational de-excitation of H v,j)tofinallevel(v ,j +H v≥1). v,j=0) molecule will preferentially form a H ?j≥8 can be efficient. Such an effect has already be found by Wrathmall & Flower

3.3 Comparison with previous experimental and theoretical results

It is then interesting to compare our new collisional data with those previously computed. As mentioned in the introduction, the most

453,810-818 (2015)

814F. Lique

Figure 2.Temperature dependence of the rate coefficients for rotational de-excitation of H v,j)to v ,j ?j=2 are mainly responsible for the cooling of the early Universe. ?vof the ro-vibrational transition increases (not

453,810-818 (2015)

Ro-vibrational excitation of H

2 by H815

Figure 3.Temperature dependence of the state-to-state rate coefficients for the ro-vibrational de-excitation of p-H

j=0) induced by collisions with H. From v,j)tofinallevel(v ,j Table 1.Comparison between present rate coefficients and those of v=0→ v

0) to rotationally inelastic transitions. The rates are in units of cm

-1 j=2→j

0j=4→j

0j=3→j

1j=5→j

1 T(K) -14) 6.6(-14) 8.7(-17) 1.0(-16) 2.5(-14) 2.6(-14) 1.3(-16) 1.7(-16) -14) 7.9(-14) 4.5(-16) 6.0(-16) 3.7(-14) 4.1(-14) 6.5(-16) 1.2(-15) -14) 9.1(-14) 1.9(-15) 2.9(-15) 5.8(-14) 6.8(-14) 3.2(-15) 6.6(-15) -13) 2.2(-13) 2.2(-14) 3.1(-14) 2.5(-13) 3.2(-13) 3.5(-14) 7.9(-14) -12) 2.0(-12) 3.8(-13) 4.4(-13) 3.2(-12) 3.7(-12) 6.6(-13) 1.2(-12) -11) 9.1(-12) 2.4(-12) 2.2(-12) 1.8(-11) 1.8(-11) 4.8(-12) 6.5(-12) -11) 1.6(-11) 4.8(-12) 4.0(-12) 3.3(-11) 3.1(-11) 9.9(-12) 1.2(-11) -11) 2.6(-11) 8.1(-12) 6.5(-12) 5.4(-11) 5.1(-11) 1.6(-11) 1.8(-11) +H v=1)→ H+H v

0) process at room temperature. The rotational structure of H

v=1→v

0 vibrational relaxation. Boltzmann averaging was done using partition function

Qof the first nine rotational states (j=0-8) of the H v=1) molecule: k =1→v=0 8 j=0 12 j 0 w (2j+1)e =1,j =1,j→v 0,j Q j (2j+1)e =1j (5)

453,810-818 (2015)

816F. Lique

Figure 4.Comparison between present (solid lines) and v,j)tofinallevel(v ,j

Table 2.Room temperature rate coefficients for H

v=1)+H→H v

0)+H process.

-13 -1

±1.5

=1j is the energy of thev=1,jrotational levels andw j is a degeneracy weight, which is equal to 1 and 3 for para- and ortho-H

453,810-818 (2015)

Ro-vibrational excitation of H

2 by H817

4 DISCUSSIONS AND CONCLUSIONS

ACKNOWLEDGEMENTS

This research was supported by the CNRS national program Physique et Chimie du Milieu Interstellaire. We acknowledge fruitful discussions

REFERENCES

Aoiz F. J., Ba

453,810-818 (2015)

818F. Lique

Neufeld D. A., Lepp S., Melnick G. J., 1995, ApJS, 100, 132

SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

Rates_H_H2.dat

453,810-818 (2015)

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