Bound state in positron scattering by allene

We report integral and differential cross sections for positron collisions with allene, calculated with the Schwinger multichannel method. The cross sections were computed in the static-polarization approximation for energies up to 7 eV. We have tested a series of single-particle basis sets and different polarization schemes to improve the description of low-energy positron scattering by the allene molecule. We have found that the use of extra centers with no net charge with additional single-particle $s$- and $p$-type functions centered at them are essential in order to accurately reproduce the polarization potential and, hence, obtain proper scattering cross sections. The choice of the allene molecule was due to the fact that it is a highly symmetric molecule with no permanent dipole moment and would allow several different calculations. Our cross sections are compared to the available experimental data for the total cross section with a reasonable agreement after correcting their results due to the low angular discrimination of their apparatus. Also, a virtual state was observed in the integral cross section that became a bound state when the description of the polarization potential is improved. We also observed a Ramsauer-Townsend minimum in the cross section whose location varies from 2.7 to 3.4 eV, depending on the polarization scheme used in the calculations.

Figure 1

Geometrical structure of allene molecule with the 12 and 16 extra chargeless centers employed in the calculations.

Figure 2

$s$-wave cross section (top) and respective eigenphase (bottom) calculated employing different schemes to account for the polarization effects of the molecular electronic cloud due to the incoming positron. The inset presents the same data within a logarithmic energy scale, in order to highlight their very low-energy behavior.

Figure 3

$A_1$ and $B_2$ components of the integral cross sections for positron scattering by allene, obtained employing different schemes to account for the polarization effects of the molecular electronic cloud due to the incoming positron.

Figure 4

Present integral cross section for elastic positron scattering by allene obtained in the SP-1, SP-3, and SP-4 approximations. The calculated cross sections are compared with the available experimental total cross sections (expt-SCT) [21] for allene, calculated ICSs and experimental TCS for ethene (${\mathrm{C}}_2{\mathrm{H}}_4$) [6], and calculated ICSs for ${\mathrm{C}}_3{\mathrm{H}}_6$ isomers [8]. The vertical line indicates the positronium energy threshold. We also present an estimate for the correction of the experimental TCS (TCS+corr).

Figure 5

Present differential cross section for elastic positron scattering by allene obtained in the SP-1 and SP-4 approximations at 1.0, 2.0, 4.0, and 5.0 eV.