Multi-channel quantum defect theory to dissociative recombination with and without electronic resonance scattering

Abstract

Abstract. The multichannel quantum defect theory (MQDT) of dissociative recombination (DR) is summarized by classifying into two cases whether an electronic resonance state as the dissociative channel exists or not. The DR and dissociative excitation of the isotopes of hydrogen molecular ion are calculated using recent sophisticated MQDT method where the electronic resonance state exists. On the other hand, an adiabatic quantum defect and a mixing matrix of the partial waves in HeH + + e collisions are investigated. These parameters are crucial in MQDT calculation without electronic resonance state. A new approach is proposed by unifying the two cases in a above MQDT treatment. IntroductionThe mechanism of dissociative recombination (DR) has been considered as a capture process of an incident electron into an electronic resonance state and sequential stabilization by molecular dissociation [1]. This mechanism is possible when there is a potential-curve crossing between the resonance state and the target molecular ionic state at the energy lower than the total energy of collision system. The DR cross section had been considered to be quite small unless the molecular system has such a potential-curve crossing. However, large cross section has been confirmed for the DR of HeH + [2], where there is no potential-curve crossing. Hereafter, we abbreviate 'potential-curve crossing' as 'crossing'.There are two kinds of theoretical approaches depending on whether the crossing exists or not. In the crossing case, the resonance state is the main dissociative channel and the Rydberg states contribute to DR through the indirect process [3], where the incident electron is temporally captured into a rotationally and vibrationally excited Rydberg state. In the non-crossing case, the dissociative channels are the Rydberg states. It is well known that the multichannel quantum defect theory (MQDT) can describe the dynamics by the strong non-adiabatic interactions (NAI) among the Rydberg states [4]. We here summarize and investigate MQDT method for DR with and without the crossing. As an extension of these theories, we shall propose a new approach based on MQDT. Examples will be shown for cases both with and without crossings.

Band-stop filter based on tunable Fano resonance and electromagnetically induced transparency in metal-dielectric-metal waveguide coupling systems

“…For example, it can achieve high quality factor [23], high figure of merit [24] and low crosstalk value [25]. Generally speaking, the essence of Fano resonance is the phenomenon of multi-channel quantum defect [26], and its occurrence needs to satisfy the phase matching condition. In MIM waveguide system, SPPs propagating in the waveguide can be coupled into the resonator to produce a narrow discrete state when the phase matching condition is satisfied.…”