Schwinger-variational-principle theory of collisions in the presence of multiple potentials

Abstract

A theoretical method for treating collisions in the presence of multiple potentials is developed by employing the Schwinger variational principle. The current treatment agrees with the local (regularized) frame transformation theory and extends its capabilities. Specifically, the Schwinger variational approach gives results without the divergences that need to be regularized in other methods. Furthermore, it provides a framework to identify the origin of these singularities and possibly improve the local frame transformation. We have used the method to obtain the scattering parameters for different confining potentials symmetric in x, y. The method is also used to treat photodetachment processes in the presence of various confining potentials, thereby highlighting effects of the infinitely many closed channels. Two general features predicted are the vanishing of the total photoabsorption probability at every channel threshold and the occurrence of resonances below the channel thresholds for negative scattering lengths. In addition, the case of negative ion photodetachment in the presence of uniform magnetic fields is also considered where unique features emerge at large scattering lengths.

Universal few-body physics and cluster formation

“…That study showed that the motion of the charged particle is bounded in the presence of the magnetic and zero-range potentials whereas in the magnetic free case the zero-range potential can not bind the electron. Another physical system which exhibits similar effects is the negative-ion photodetachment in a uniform magnetic field (Blumberg et al, 1979;Clark, 1983;Crawford, 1988;Greene, 1987;Grozdanov, 1995;Larson and Stoneman, 1985;Robicheaux et al, 2015) where in this particular case the electron-atom interaction is treated as a short-range potential. Note that all these cases are halfcollisions, in the sense that they arise in photofragmentation processes, and only involve an escape to infinity, whereas a full collision involves both an incoming wave and an outgoing wave.…”

“…(67) Therefore, in this Helmholtz region one employs locally the above mentioned frame transformation. The concept of the local frame transformation was introduced by (Fano, 1981a;Harmin, 1982a,b) and extended by (Giannakeas et al, 2016;Granger and Blume, 2004;Greene, 1987;Robicheaux et al, 2015;Wong et al, 1988;Zhang and Greene, 2013).…”

“…In the particular case a Riemann zeta function regularization scheme is used. Note that such techniques are totally avoided in the generalized form of the local frame transformation theory (Giannakeas et al, 2016;Robicheaux et al, 2015). In addition, Eq.…”

“…In addition, (Robicheaux et al, 2015) using ideas related to the Schwinger variational principle provide infinity-free calculations of scattering observables based on physical grounds, and avoids the need for additional regularization schemes which have been previously utilized in the pseudopotential approaches of (Granger and Blume, 2004;Olshanii, 1998;Petrov and Shlyapnikov, 2001). However, in the treatments of (Robicheaux et al, 2015;Zhang and Greene, 2013) the center of mass is coupled with the relative degrees of freedom for particles of finite mass, so they have thus far only been applied in the limit of an infinitely massive particle which is struck by a much lighter one. (Peano et al, 2005) considered the coupling of the center of mass in an arbitrary transversal potential, using the Green's function formalism to solve the corresponding Schrödinger equation directly in the laboratory frame.…”

Generalized local-frame-transformation theory for excited species in external fields

“…Furthermore, the LFT theory gives a compact description of a variety of physical processes such as dielectronic recombination [12], negative-ion photodetachment in magnetic [13] or electric fields [14][15][16] or under generic external confinement [17], or ultracold atomic and/or * pgiannak@purdue.edu † chgreene@purdue.edu ‡ robichf@purdue.edu dipolar collisions in the presence of external trapping potentials [18][19][20][21]. In molecular applications frame transformation theory has been decisive in describing the rich rovibrational Rydberg spectra of diatomic molecules [22], and the dissociative recombination of H + 3 [23,24].…”