Quantum reflection by Casimirvan der Waals potential tails
Abstract
We study the reflectivity of Casimirvan der Waals potentials, which behave as C_{4}/r^{4} at large distances and as C_{3}/r^{3} at small distances. The overall behavior of the reflection amplitude R depends crucially on the parameter ρ=(2M)C_{3}/(ħ(C_{4})) which determines the relative importance of the 1/r^{3} and the 1/r^{4} parts of the potential. Near threshold, E=ħ^{2}k^{2}/(2M)>0, the reflectivity is given by \R\~exp(2bk), with b depending on ρ and the shape of the potential at intermediate distances. In the limit of large energies, ln\R\ is proportional to k^{1/3} with a known constant of proportionality depending only on C_{3}. For small values of ρ, the reflectivity behaves as for a homogeneous 1/r^{3} potential in the whole range of energies and does not depend on C_{4} or the shape of the potential beyond the 1/r^{3} region. For moderate and large values of ρ, the reflectivity depends on C_{4} and on the potential shape. For sufficiently large values of ρ, which are ubiquitous in realistic systems, there is a range of energies beyond the nearthreshold region, where the reflectivity shows the highenergy behavior appropriate for a homogeneous 1/r^{4} potential, i.e., ln\R\ is proportional to (k) with a proportionality constant depending only on C_{4}. This conspicuous and modelindependent signature of the Casimir effect is illustrated for the reflectivities of neon atoms scattered off a silicon surface, which were recently measured by Shimizu [Phys. Rev. Lett. 86, 987 (2001)].
 Publication:

Physical Review A
 Pub Date:
 March 2002
 DOI:
 10.1103/PhysRevA.65.032902
 Bibcode:
 2002PhRvA..65c2902F
 Keywords:

 34.50.Dy;
 03.65.w;
 31.30.Jv;
 Interactions of atoms and molecules with surfaces;
 photon and electron emission;
 neutralization of ions;
 Quantum mechanics;
 Relativistic and quantum electrodynamic effects in atoms and molecules