Orthopositronium-orthopositronium scattering at medium energies

The scattering of ortho-positronium $\left(o\text{−}\mathrm{Ps}\right)$ atoms has been investigated using the first Born approximation (FBA) and Born-Oppenheimer (B-O) model at medium energies. The angle integrated total elastic cross sections of $o\text{−}\mathrm{Ps}–o\text{−}\mathrm{Ps}$ scattering have been reported. Apart from this, the inelastic cross sections for discrete excitations (principal quantum number, $n⩽3$) of the single and both the Ps atoms as well as single and double Ps atom ionization have also been obtained. We have also predicted the total cross section of $o\text{−}\mathrm{Ps}–o\text{−}\mathrm{Ps}$ scattering by adding all these partial cross sections. The first Born and B-O scattering amplitudes have also been evaluated using partial wave technique. It has been noticed that odd values of the partial wave B-O amplitude vanishes for even parity transitions and vice versa. To the best of our knowledge, this feature has not been noticed for other systems.

Figure 1

The coordinate system employed here.

Figure 2

Elastic and single Ps excitation cross sections (in units of $\pi a_0^2$) for $o\text{−}\mathrm{Ps}–o\text{−}\mathrm{Ps}$ scattering. Curves: solid, elastic; dash, $\left(1s1s\text{−}1s2s\right)$ transition; dot, $\left(1s1s\text{−}1s2p\right)$ transition; dash-dot, $\left(1s1s\text{−}1s3s\right)$ transition; dash-dot-dot, $\left(1s1s\text{−}1s3p\right)$ transition; short dash, $\left(1s1s\text{−}1s3d\right)$ transition.

Figure 3

Double Ps excitation cross sections (in units of $\pi a_0^2$) for $o\text{−}\mathrm{Ps}–o\text{−}\mathrm{Ps}$ scattering. Curves: solid, $\left(1s1s\text{−}2s2s\right)$ transition; dash, $\left(1s1s\text{−}2s2p\right)$ transition; dot, $\left(1s1s\text{−}2p2p\right)$ transition; dash-dot, $\left(1s1s\text{−}3s3s\right)$ transition; dash-dot-dot, $\left(1s1s\text{−}3s3p\right)$ transition; short dash, $\left(1s1s\text{−}3p3p\right)$ transition.

Figure 4

Single, double, and total Ps ionization cross sections (in units of $\pi a_0^2$) for $o\text{−}\mathrm{Ps}–o\text{−}\mathrm{Ps}$ scattering. Curves: dash, single Ps ionization; dot, double Ps ionization; solid, total ionization.

Figure 5

Elastic, inelastic, and total cross sections (in units of $\pi a_0^2$) for $o\text{−}\mathrm{Ps}–o\text{−}\mathrm{Ps}$ scattering. Curves: dash, elastic; dot, total single excitation (discrete); dash-dot, total double excitation (discrete); dash-dot-dot, total ionization; solid, total Born.