Resonant Tunneling and Resonant Excitation Transfer

Abstract

Issues involved in the tunneling of deuterons in metal deuterides are considered in relation to experimental claims of anomalies in metal deuterides. From earlier studies, screening is thought to be similar to the case of molecular D 2 . Resonant tunneling has been advocated in the literature as a possible mechanism to achieve tunneling enhancements. We develop a two-level system for a piecewise constant potential model for resonant tunneling that matches the energy levels in the vicinity of a level crossing, arguing that such models are applicable for more general potential models. Resonant tunneling effects and dynamics, including acceleration due to coherence, are accounted for in the model. The model is extended to include relaxation effects, and it is found that one would not expect to find coherent effects associated with tunneling in the case of two deuterons in a metal lattice. We present a simple model for the transfer of excitation from a collection of deuterons to a collection of helium nuclei, a model closely related to resonant tunneling and also to new phonon-coupled SU(N) models under development. The excitation transfer models show coherent enhancements as well as collective effects.

Unified Phonon-Coupled Su(n) Models for Anomalies in Metal Deuterides

“…In this case, the mathematical solutions involve Rabi oscillations between the resonant atomic scale and nuclear scale states, with greatly enhanced tunneling. 50 Although there is no stable resonant four nucleon state in vacuum with the right energy (and there is no way to suppress decoherence), we recognize this model as being important nevertheless. It makes clear the difference between tunneling as part of an incoherent process, where the reaction rate is proportional to the square of the matrix element (and the tunneling is proportional to e −2G ); and tunneling as part of a coherent process, where the reaction rate is linear in the matrix element (and the tunneling is proportional to e −G ).…”

“…The dynamics associated with this kind of model behave very differently than for the resonant SU(3) model discussed above. 50 This model describes a new situation in which the collective tunneling transitions at all participating sites of double occupancy interact uniformly with collective balancing transitions among compact states at all of their participating sites. In essence, one population is interacting collectively, as a population, with another population that is responding collectively, also as a population.…”

Lowest-order relativistic interaction between lattice vibrations and internal degrees of freedom of a nucleus

“…The lowest transition energies between ground states and excited nuclear states of stable nuclei are in the keV range; hence, it is not possible to see an excited state decay through the emission of a few phonons since the highest (lattice) phonon energies are less than 1 eV. Because of this, the lowestorder observable processes involving the relativistic phononnuclear coupling involve excitation transfer [24,25]. In resonant excitation transfer, an excited nucleus at one site makes a transition to the ground state, exchanging a phonon in the process; and a ground state nucleus at another site makes a transition to an excited state at the same energy, exchanging a phonon with the same phonon mode.…”