TY - JOUR

T1 - Scattering of wave packets on atoms in the Born approximation

AU - Karlovets, D. V.

AU - Kotkin, G. L.

AU - Serbo, V. G.

PY - 2015/11/4

Y1 - 2015/11/4

N2 - It has recently been demonstrated experimentally that 200-300 keV electrons with the unusual spatial profiles can be produced and even focused to a subnanometer scale - namely, electrons carrying nonzero orbital angular momentum and also the so-called Airy beams. Since the wave functions of such electrons do not represent plane waves, the standard Born formula for scattering of them off a potential field is no longer applicable and, hence, needs modification. In the present paper, we address the generic problem of elastic scattering of a wave packet of a fast nonrelativistic particle off a potential field. We obtain simple and convenient formulas for a number of events and an effective cross section in such a scattering, which represent generalization of the Born formula for a case when finite sizes and spatial inhomogeneity of the initial packet should be taken into account. As a benchmark, we consider two simple models corresponding to scattering of a Gaussian wave packet on a Gaussian potential and on a hydrogen atom, and perform a detailed analysis of the effects brought about by the limited sizes of the incident beam and by the finite impact parameter between the potential center and the packet's axis.

AB - It has recently been demonstrated experimentally that 200-300 keV electrons with the unusual spatial profiles can be produced and even focused to a subnanometer scale - namely, electrons carrying nonzero orbital angular momentum and also the so-called Airy beams. Since the wave functions of such electrons do not represent plane waves, the standard Born formula for scattering of them off a potential field is no longer applicable and, hence, needs modification. In the present paper, we address the generic problem of elastic scattering of a wave packet of a fast nonrelativistic particle off a potential field. We obtain simple and convenient formulas for a number of events and an effective cross section in such a scattering, which represent generalization of the Born formula for a case when finite sizes and spatial inhomogeneity of the initial packet should be taken into account. As a benchmark, we consider two simple models corresponding to scattering of a Gaussian wave packet on a Gaussian potential and on a hydrogen atom, and perform a detailed analysis of the effects brought about by the limited sizes of the incident beam and by the finite impact parameter between the potential center and the packet's axis.

UR - http://www.scopus.com/inward/record.url?scp=84946779791&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84946779791&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.92.052703

DO - 10.1103/PhysRevA.92.052703

M3 - Article

AN - SCOPUS:84946779791

VL - 92

JO - Physical Review A

JF - Physical Review A

SN - 1050-2947

IS - 5

M1 - 052703

ER -