Virtual states in electron-molecule scattering via modified effective-range theory

Virtual and bound states in low-energy positron scattering by atoms and molecules via modified effective range theory

“…Moreover, MERT allows us to study the effect of long-range polarisation potential (i.e., dipole polarisability) on the S-matrix poles' positions (κ). In particular, we confirmed our recent findings [36], showing that the virtual-state poles are displaced off the negative imaginary axis to the left on the complex momentum plane due to an infinite tail in the interaction potential. Comparison of the currently determined virtual states' positions with the same quantity estimated based on positron annihilation cross-sections shows that the virtual state energy can be calculated using the pole's distance (i.e., the absolute value of the pole's location) from the plane's origin: ε = |κ| 2 /2.…”

“…Except for Xe, all poles are displaced from the negative imaginary k axis, so they do not represent true virtual states as defined for finite-range potentials. This result is consistent with our recent findings for electron scattering from molecules [36]. This shows that a polarisation potential (r −4 ) affects the poles' positions (related to virtual states) similarly to a long-range dipole potential (r −2 ) in polar molecules as reported by Herzenberg and Saha [58].…”

“…Hence, the contribution of this component must be addressed when estimating the poles' positions related to bound and virtual states. Recently, we showed [36] that the virtual states in electron-molecule collisions can be revealed and studied within the frame of MERT using the properties of Mathieu functions, that is, the exact analytical solutions for the Schrödinger equation with pure polarisation potential. We followed the conclusions of Khrebtukov [37], who noted that Mathieu functions can be exploited for the S-matrix continuation into the complex momentum plane.…”

“…Finally, we study the relation between the scattering length and the poles' positions in the presence of long-range polarisation. Recently, we concluded [36] that in the presence of infinitive interactions, the scattering length can not be treated as the reciprocal of the pole's position along the imaginary axis of the complex momentum plane as it is commonly assumed. In the present paper, we analyze this issue more quantitatively.…”