### Abstract

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such electrons do not represent plane waves, the standard Born formula for scattering of them off a potential field is no longer applicable and, hence, needs modification.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.

Original language | English |
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Article number | 052703 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 92 |

Issue number | 5 |

DOIs | |

Publication status | Published - 4 Nov 2015 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*92*(5), [052703]. https://doi.org/10.1103/PhysRevA.92.052703