Vibrational excitation

The excitation cross sections from ground vibrational state, , to various final, , vibrational states of are shown in Fig. 7. These compare well with sparse literature data.

The matching of the fully quantal results at low energies with semiclassical, straight-line trajectory

approxi-mation results at higher energies becomes worse at large , as expected.

The role of the particle rearrangements in the excitation process is of particular importance at lowest energies, as can be seen in Fig. 7. Our data contain coherent sum of the direct and arrangement channels. The previous calculations do not include rearrangement channels, under-estimating cross sections at lowest energies.

Total excitation cross sections, summed over all from various initial states of (in collision with proton) and of (in collision with ) are shown in Figs. 8 and 9, respectively. The relevant recommended cross section Figure 5. Charge transfer from vibrationally excited states of H₂⁺(from Ref. [4])

H2

Figure 6. Partial cross sections for charge transfer in excited states of H₂ (from Ref. [4]).

i 0

v = v_f H₂

ν

Figure 7. Vibrational excitation cross sections for collisions of protons on H₂ in the ground state.

f i

v ≠v H₂

H2⁺ H

for of Janev et al. [28] underestimates our curve, due to absence of rearrangement transitions in previous calculations.

5. Dissociation

Dissociation cross sections from various excited states of in collisions by protons and of in collisions with are shown in Figs. 10 and 11, respectively. As shown in Fig. 10, the agreement (matching) of the fully quantal with the TSH results of Ichihara [3] and our semi-classical data is good for higher initial excited states, but deteriorates (overestimate) significantly for lower , as expected from the classical character of the TSH method as well as from the potential insensitivity of the straight-line trajectory approximation.

As shown in Fig. 1(b), the vibrational states separate to two disjunct, uncoupled sets that correspond to the vibrational states of two different Hamiltonians, and .

energy, that belong to the separate dissociative continua, those of and . These states are strongly coupled mutually, thus enabling charge transfer and ”excitation” in the continuum. The coupling of the dissociative states of and with the bound ones can be also realized in indirect way, by CT followed by dissociation. All the processes are accompanied by the reverse processes in either half of the collision. By ”direct” dissociation (DD) we consider the process(es) that lead to the dissociating fragments in the dissociation states of their parent, i.e. of the diatomic molecule that supported the initial vibrational state.

Similarly, charge transfer dissociation (CTD) is process that leads to dissociating fragments of ”charge-transfer”

produced molecule (rather than of parent one). An example of the DD process is dissociation if into by proton impact. An example of CTD process would be the dissociation of into by proton impact.

Obviously, in this latter case the charged projectile will exit the scattering zone as a neutral . These conclusions are also directly supported by the diagrams in Figs. 12(a) and 12(b), showing DD and CTD cross sections for various for and , respectively. It is obvious that the DD is a stronger process than CTD for in Fig. 12(a), but the difference diminishes toward lower . At the contributions of DD and CTD to the total dissociation cross section are almost equal, and for even lower the CTD starts to be a more important process at the higher end of considered energy range. For the dissociation, the conclusions are somewhat opposite: for the higher , CTD dominates the total dissociation by more than a factor 2; this dominance diminishes toward lower , and for the contributions of DDand CTD processes to the total dissoci-ation cross section become practically equal. This consider-ation supports the assertion of the preceding section that DD and CTD are almost equilibrated by the strong mixing in the continuum. The DD process is slightly more intensive from the higher excited states of , while CTD is slightly more

2( _i 0)

H v =

Figure 8. Excitation cross section, summed over all final vibrational states, from various initial states of in collision with

proton ²

H

Figure 9. Excitation cross section, summed over all final vibrational states, from various initial states of in collision

with H ²

Figure 10. Cross section for dissociation from varius excited states of H₂.

In Fig. 13, we present the energy spectra for dissoci-ation fragments of in collision with proton for various CM energies (as values above the dissociation threshold , i.e. ). and for a number of repre-sentative values of . An obvious feature of these spectra is a pronounced cusp at the continuum edge for lower energies of the projectile. This feature is present for all initial states of the target molecule. The spectra extend close to , slowly decreasing with the fragment energy , and then abruptly disappear, as required by the energy conservation.

We have also studied the distribution of dissociated fragments with respect to the angle . In Fig. 14 we show the angular distributions of dissociation fragments from the dissociation (sum of DD and CTD channels) for the initial vibrational states and 11 and a selected number of CM collision energies. The numbers on the concentric

circles indicate the values of dissociationcross section (in units of cm²). For the case, a cosine-type distribution is apparent for the higher energies (7.5 and 9.5 eV), while with decreasing the collision energy the distributions become increasingly more isotropic. In the case of , however, Figure 11. Cross section for dissociation from various excited

states of H₂⁺.

2( )_i H v

EREF

( )_i

W v E_CM^{( )νi} =W v( )_i +E_REF vi

EREF

Ek

γ

H⁺+H2

0 v=

Figure 13. Total dissociation energy spectra for H⁺+ H₂(ν_i) system, for all at representative C.M. collision energies (from [9]).νi

Figure 12. Comparison of the dissociation components, direct and CT dissociation cross sections for different initial vibrational states ν_i of the target, for (a) H⁺+ H₂ (ν_i), and (b) H + H₂⁺(ν_i) collisions (from Ref. [9]).

0 v=

11 v=

the situation is reversed. We conveniently represent the angular spectra of dissociation products in the form

(16)

where α and can be obtained by fitting the cross section data to the above expression. It has been found that the parameter α does not depend on the energy and, to a high accuracy, has the form

(17)

The anisotropy parameter , however, has a very strong energy dependence, as can be seen also from Fig. 14, which for the considered values of has the form

(18)

The angular distributions of fragments from the dissociation have similar features.