4 Results and discussion

Radiative association cross sections are shown in Fig. 5. Comparison of the cross sections for the three species clearly demonstrates the more favorable radiative association process for PH⁺ and SiH⁺, in which the two atomic species approach along an electronically excited state potential curve from which a dipole transition is made, than for SH⁺, in which the entire process takes place within the ground electronic state. This difference is manifested by the two to three orders of magnitude difference in the cross sections. In addition, only the lowest energy region in the vibrational continuum of the SH⁺ ground state contributes to the radiative association process, so the cross section drops off rapidly for collision energies greater than 0.1 eV. The larger cross section for SiH⁺ relative to PH⁺ can be understood by comparing the square of the dipole moments of these two species in the region 2 a.u. < R < 3 a.u.

Figure 5: Radiative association cross sections

In Fig. 6 and Table 3, we present radiative association rate coefficients which were determined by averaging over the cross sections with a Maxwellian velocity distribution. The rate coefficients are fitted to the parametric form

$$\alpha (T) = \sum_i a_i \biggl ({ T \over {300}} \biggl )^{b_i} \exp \biggl ({{-T}\over{c_i}} \biggl )$$ (4)

with the parameters a_i (cm³ s^-1), b_i, and c_i (K) given at the bottom of Table 3. The fits deviate from the computed rate coefficients by less than 20%.

Figure 6: Radiative association rate coefficients

 

 

Table 3: Radiative association rate coefficients $\alpha$ (cm³ s^-1) and fit coefficients for Eq. (4)

$T({\rm K})$	Si+ + H	P+ + H	S+ + H
10	1.75-17	1.70-18	7.32-21
20	1.69-17	1.71-18	8.35-21
50	1.59-17	1.69-18	8.34-21
80	1.50-17	1.62-18	8.20-21
100	1.45-17	1.58-18	8.22-21
200	1.24-17	1.41-18	8.58-21
500	9.79-18	1.17-18	8.70-21
800	8.88-18	1.06-18	8.58-21
1000	8.58-18	1.02-18	8.41-21
2000	8.26-18	9.40-19	6.78-21
5000	9.21-18	1.02-18	3.30-21
10000	9.84-18	1.17-18	1.50-21
a1	1.07-17	1.22-18	9.25-21
b1	-1.83-1	-1.46-1	5.60-2
c1	-1.63+4	-2.14+5	5.27+3

Figure 7: Comparison with the Si+ + H reaction with other Si+ and C+ reactions

Figure 8: Comparison of the P+ + H and S+ + H reactions with other P+ and S+ reactions from Millar et al. ([1997])