Double-differential cross sections for single ionization of simple polyatomic molecules by proton impact

A theoretical study of double-differential cross sections (DDCSs) for single ionization of ${\text{CH}}_{{}_4}$ and ${\text{NH}}_{{}_3}$ molecules by collision with proton is presented at 0.25, 1, and 2 MeV, respectively. For the final state, we use a continuum distorted wave that contains the product of three-Coulomb distortion due to pairwise Coulombic interactions for which it is called the three-Coulomb wave model. In the entrance channel, the Coulomb distortion between the incoming projectile and the target is taken. In this model, the ground state of the polyatomic molecule is described by means of an accurate one-center molecular wave function, which is a linear combination of atomic orbitals. The contributions of DDCSs for different molecular orbitals of the polyatomic molecules to the spectrum of angular distributions at different electron emission energies have also been analyzed. Generally the preference for ionization depends on the binding energy of the active electron in molecular orbital in the ascending order of loosely bound electrons to more tightly bound electrons. At large ejected electron and projectile energy, the lesser bound electrons in the molecules dominate the DDCS at extreme forward emission angles. The present DDCS results are compared with available experimental and the theoretical findings. In case of ammonia molecules, good agreement is observed at all projectile energies, showing that the present model is sufficient to explain all the experimental data for double-differential cross sections. However, some degree of discrepancy is observed at 2 MeV proton impact for small electron emission angles when ${\text{CH}}_{{}_4}$ molecular target is considered.

Figure 1

DDCS for single ionization of ${\text{CH}}_{{}_4}$ by 250 keV proton impact as a function of electron emission angle for fixed values of electron energy in eV. Solid curve, present 3CW results; dashed curve, CDW-EIS-MO results [25]; dotted curve, CDW-EIS using Bragg's additivity rule [25]; solid circles, experimental results [49].

Figure 2

DDCS for single ionization of ${\text{CH}}_{{}_4}$ by 1 MeV proton impact as a function of electron emission angle and for fixed values of electron energy in eV. Solid curve, present 3CW results; solid circles, experimental results [49].

Figure 3

Same as Fig. 1, but 2 MeV proton impact on ${\text{CH}}_{{}_4}$.

Figure 4

DDCS molecular orbital contributions for the impact of 250 keV proton on ${\text{CH}}_{{}_4}$, as a function of the electron emission angle and for fixed value of the electron emission energy ${\epsilon }_{{}_k}=10\mathrm{eV}$. Solid curve, present results for complete molecule; short dotted curve; CDW-EIS-MO results [25]; short dash-dotted curve, CDW-EIS (Bragg's aditivity rule) [25]; dashed curve, $1A_1$ contribution; dotted curve, $2A_1$ contribution; dash-dot-dotted curve, $1T_{{}_{2x}}$ contribution; short dashed curve, $1T_{{}_{2y}}$ contribution; dash-dotted curve, $1T_{{}_{2z}}$ contribution; solid circles represent experimental results [49].

Figure 5

Same as Fig. 4, but 200 eV electron emission energy.

Figure 6

Same as Fig. 4, but 2 MeV proton impact on ${\text{CH}}_{{}_4}$ for 100 eV electron emission energy.

Figure 7

DDCS for single ionization of ${\text{NH}}_{{}_3}$ by the impact of 250 keV proton, as a function of the emission angle and for different electron emission energies. Solid curve corresponds to present results; dashed curve, DDCS-MT results [24]; filled circles represent experimental results [49].

Figure 8

DDCS for single ionization of ${\text{NH}}_{{}_3}$ by 1 MeV proton impact as a function of electron emission angle for fixed values of electron energy in eV. Solid curve, present 3CW results; solid circles represent experimental results [49].

Figure 9

Same as Fig. 7, but for 2 MeV proton impact on ${\text{NH}}_{{}_3}$.

Figure 10

DDCS molecular orbital contributions for the impact of proton on ${\text{NH}}_{{}_3}$, as a function of the electron emission angle and for fixed value of the electron emission energy, ${\epsilon }_{{}_k}=100\mathrm{eV}$ at 250 keV proton impact. Solid curve, present results for complete molecule; short dotted curve; CDW-EIS-MO results [25]; short dash-dotted curve, CDW-EIS (Bragg's aditivity rule) [25]; dashed curve, $1A_1$ contribution; dotted curve, $2A_1$ contribution; dash-dot-dotted curve, $1E_{{}_x}$ contribution; short dashed curve, $1E_{{}_y}$ contribution; dash-dotted curve, $3A_{{}_1}$ contribution; solid circles represent experimental results [49].

Figure 11

Same as Fig. 10, but for 2 MeV proton impact on ${\text{NH}}_{{}_3}$.