Intensified Tunnel Effect for Complex Particles

Abstract

A quantum-mechanical problem about the penetration through the potentical barrier of two particles in mutual bound state (complex particle) is considered. The account of the internal structure of a complex particle leads to a spreading of the potential barrier which facilitates the penetration through this barrier.The Hamilbonian of the system of two particles interacting with each other by means of the potential v12(x! -x2) and moving in the external field vl(yl) which affects t.he particle 1 (the influence of the external field upon both particles is considered in a similar way) reads: 2m, 2nPWe consider the case when v12 (xl -x2) is an infinite square potential well :Let a potential acting on the first particle be of the form of a rectangular barrier with the hight V, 0 if xi < a and xl> bIn what follows it will be more convenient to use not the coordinates xi and x2 of particles but bhe coordinates of the relative distance of particles e and of their cent.er of mass RIn terms of the coordinates xi and x2 the region in which particles are moving looks like that represented in Fig. 1. The particles cannot go away from each other a t a distance larger than r. Therefore in the plane (xi x2) we shall be interested only in the band which lies between the straight lines A B and CD.In going over to the coordinates R and e the whole picture (Fig. 1) turns and the band ABCD takes the horizantal position (Fig. 2.) 16 Ann. Physik. 7. Folge. Bd. 14

Quantum tunnelling of a complex system: effects of a finite size and intrinsic structure

“…This model allows one to study the limiting cases and shows that the finite size of a tunnelling system may be very important. Similar results for a pair of particles bound in an infinite potential box, while one of the particles encounters a rectangular barrier, were found in the old paper by Zakhariev and Sokolov [7], with the conclusion that the effective barrier is modified which facilitates the penetration. We show also that the electrostatic polarizability of a composite particle adiabatically approaching the Coulomb barrier increases the tunnelling probability.…”

Quantum tunneling and reflection of a molecule with a single bound state

“…We use Crank-Nicholson integration because the method is unconditionally stable and because convergence is second order in time; that is, error is proportional to ( t ) 2 . Conversely, the convergence of Euler methods is only first order in time [i.e., ∝ ( t ) 1 ], and such methods are not unconditionally stable.…”

“…The study of the quantum tunneling of molecules, however, is a relatively new area of research, with most publications appearing since 2005. The first investigation of two particles in a bound state penetrating a potential barrier was made by Zakhariev and Sokolov [1]. The next examination of molecular tunneling did not occur until 1994, with the investigation by Saito and Kayanuma of the resonant tunneling of a pair of bound particles upon a single external barrier [2].…”

Scattering of a composite quasiparticle by an impurity on a lattice

“…Another important problem is tunnelling of composite objects through barriers [5], with applications in nuclear fusion [6], induced decay of false vacuum [7], and tunnelling of Cooper pairs in superconductors and Wannier-Mott excitons in semiconductor heterostructures [8]. It had been shown that the probability of tunnelling of an object possessing an internal degree of freedom -for example, a diatomic molecule -through a barrier may greatly exceed that of a structureless object with similar properties due to appearance of quasi-bound states in the combined scattering and molecular binding potentials [5][6][7]. Furthermore, interaction of a molecule with the ex- * fumika@physics.ubc.ca † litinskaya@gmail.com ‡ unruh@physics.ubc.ca ternal potential can induce transitions between molecular states due to coupling between relative and centre of mass (CM) coordinate degrees of freedom [9,10].…”