Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2002.02047

Measurability of Coulomb wavepacket scattering effects

Scott E. Hoffmann

Published Feb 6, 2020• 0 citations
arXivHTMLPDF

Abstract

A previous paper [J. Phys. B: At. Mol. Opt. Phys. 50, 215302 (2017)] showed that partial wave analysis becomes applicable to nonrelativistic Coulomb scattering if wavepackets are used. The scattering geometry considered was special: that of a head-on collision between the wavepacket and the centre of the potential. Our results predicted, in this case, a shadow zone of low probability for small angles around the forward direction for the description of alpha scattering from a gold foil. In this paper we generalize the results to the case of a nonzero impact parameter, a displacement of the wavepacket centre perpendicular to the average momentum direction. We predict a large flux in the forward direction from events with large impact parameters. We find a significant probability of scattering into the deviation region for impact parameters of order the spatial width of the wavepacket. Averaging over impact parameters produces predictions in excellent agreement with the Rutherford formula down to lower angles than for the zero impact parameter prediction. We consider issues that would arise in a real experiment and discuss the possibility of measuring a deviation from the Rutherford formula.

DOI
10.48550/arxiv.2002.02047

Related papers

Prediction of deviations from the Rutherford formula for low-energy Coulomb scattering of wavepackets

Scott E. Hoffmann

Abstract We calculate the nonrelativistic scattering of a wavepacket from a Coulomb potential and find deviations from the Rutherford formula in all cases. These generally occur only at low scattering angles, where they would be obscured by the part of the incident beam that emerges essentially unscattered. For a model experiment, the scattering of helium nuclei from a thin gold foil, we find the deviation region is magnified for low incident energies (in the keV range), so that a large shadow zone of low probability around the forward direction is expected to be measurable. From a theoretical perspective, the use of wavepackets makes partial wave analysis applicable to this infinite-range potential. It allows us to calculate the everywhere finite probability for a wavepacket to wavepacket transition and to relate this to the differential cross section. Time delays and advancements in the detection probabilities can be calculated. We investigate the optical theorem as applied to this special case.

arXiv:1704.04305•Journal of Physics B Atomic Molecular and Optical Physics•Sep 19, 2017•3 citations

Wavepacket Scattering Theory for the Coulomb Potential

Scott E. Hoffmann

We treat the nonrelativistic quantum mechanical scattering of a wavepacket (for a single, charged, spinless particle) of well-resolved momentum incident on a fixed Coulomb potential. To implement this, we calculate the incoming and outgoing probability amplitudes for normalized state vectors on the basis of eigenvectors of total momentum magnitude and total angular momentum. We show that the method of partial wave analysis becomes applicable for this long range potential with the use of wavepackets. We find a relation between the finite probability and the differential cross section that is seen to hold sufficiently far from the singularity of the latter in the forward direction. The resulting differential cross section reduces to the familiar Rutherford form for scattering angles sufficiently far from the forward direction. We find that the interaction causes small time shifts in the detection probabilities. For our particular scattering geometry, we see, at low energies, a shadow zone of low probability for small angles around the forward direction, a phenomenon that cannot be predicted by the standard treatment.

•Apr 14, 2017•0 citations

Nonclassical trajectories in head-on collisions

Ankit Kumar, Tanjung Krisnanda, P. Arumugam +1 more

Rutherford scattering is usually described by treating the projectile either classically or as quantum mechanical plane waves. Here we treat them as wave packets and study their head-on collisions with the stationary target nuclei. We simulate the quantum dynamics of this one-dimensional system and study deviations of the average quantum solution from the classical one. These deviations are traced back to the convexity properties of Coulomb potential. Finally, we sketch how these theoretical findings could be tested in experiments looking for the onset of nuclear reactions.

arXiv:2011.06470•Quantum•Jul 19, 2021•1 citation

Effects of quantum mechanical identity in particle scattering: experimental observations (and lack thereof)

Niels Kjærgaard

ABSTRACT On the occasion of the 150th anniversary of Ernest Rutherford's birth I discuss how indistinguishabilty profoundly affects the collisions of identical particles. In the case of a Coulombic interaction this leads to a dramatic modification of Rutherford's famous scattering formula as predicted by Nevill Mott. An even more extreme example is provided by a low‐energy scattering experiment of identical fermions interacting via a short range potential. Here indistinguishability will make or break the observation of scattered particles. This fascinating phenomenon has been observed using a laser‐based collider for ultracold fermionic potassium atoms.

Journal of the Royal Society of New Zealand•Sep 1, 2021•3 citations

Scattering of wave packets on atoms in the Born approximation

Dmitry V. Karlovets, Gleb L. Kotkin, Valeriy G. Serbo

It has recently been demonstrated experimentally that $200\text{--}300$ 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.

arXiv:1508.00026•Physical Review A•Nov 4, 2015•44 citations

Classical and quantum scattering

C. A. Bertulani, Paweł Danielewicz

Figure 1.1 represents schematically a typical scattering experiment, in fact this is the sketch of E. Rutherford experiment in 1910 [ 1 ]. Projectiles (here, α -particles) from a source go through a collimator and collide with a target (gold foil in Rutherford’s experiment). Some projectiles are scattered by the target and reach the detector (here, a fluorescent screen). Rutherford expected them to go straight through with perhaps a minor deflection. Most did go straight through, but to his surprise some particles bounced directly off the gold sheet! What did this mean? Rutherford hypothesized that the positive alpha particles had hit a concentrated mass of positive particles, which he termed the nucleus. We shall describe the Rutherford scattering theoretically later in this chapter.

CRC Press eBooks•Jan 4, 2019•0 citations
A previous paper [J. Phys. B: At. Mol. Opt. Phys. 50, 215302 (2017)] showed that partial wave analysis becomes applicable to nonrelativistic Coulomb scattering if wavepackets are used. The scattering geometry considered was special: that of a head-on collision between the wavepacket and the centre of the potential. Our results predicted, in this case, a shadow zone of low probability for small angles around the forward direction for the description of alpha scattering from a gold foil. In this paper we generalize the results to the case of a nonzero impact parameter, a displacement of the wavepacket centre perpendicular to the average momentum direction. We predict a large flux in the forward direction from events with large impact parameters. We find a significant probability of scattering into the deviation region for impact parameters of order the spatial width of the wavepacket. Averaging over impact parameters produces predictions in excellent agreement with the Rutherford formula down to lower angles than for the zero impact parameter prediction. We consider issues that would arise in a real experiment and discuss the possibility of measuring a deviation from the Rutherford formula.
Abstract We calculate the nonrelativistic scattering of a wavepacket from a Coulomb potential and find deviations from the Rutherford formula in all cases. These generally occur only at low scattering angles, where they would be obscured by the part of the incident beam that emerges essentially unscattered. For a model experiment, the scattering of helium nuclei from a thin gold foil, we find the deviation region is magnified for low incident energies (in the keV range), so that a large shadow zone of low probability around the forward direction is expected to be measurable. From a theoretical perspective, the use of wavepackets makes partial wave analysis applicable to this infinite-range potential. It allows us to calculate the everywhere finite probability for a wavepacket to wavepacket transition and to relate this to the differential cross section. Time delays and advancements in the detection probabilities can be calculated. We investigate the optical theorem as applied to this special case.
We treat the nonrelativistic quantum mechanical scattering of a wavepacket (for a single, charged, spinless particle) of well-resolved momentum incident on a fixed Coulomb potential. To implement this, we calculate the incoming and outgoing probability amplitudes for normalized state vectors on the basis of eigenvectors of total momentum magnitude and total angular momentum. We show that the method of partial wave analysis becomes applicable for this long range potential with the use of wavepackets. We find a relation between the finite probability and the differential cross section that is seen to hold sufficiently far from the singularity of the latter in the forward direction. The resulting differential cross section reduces to the familiar Rutherford form for scattering angles sufficiently far from the forward direction. We find that the interaction causes small time shifts in the detection probabilities. For our particular scattering geometry, we see, at low energies, a shadow zone of low probability for small angles around the forward direction, a phenomenon that cannot be predicted by the standard treatment.
Rutherford scattering is usually described by treating the projectile either classically or as quantum mechanical plane waves. Here we treat them as wave packets and study their head-on collisions with the stationary target nuclei. We simulate the quantum dynamics of this one-dimensional system and study deviations of the average quantum solution from the classical one. These deviations are traced back to the convexity properties of Coulomb potential. Finally, we sketch how these theoretical findings could be tested in experiments looking for the onset of nuclear reactions.
ABSTRACT On the occasion of the 150th anniversary of Ernest Rutherford's birth I discuss how indistinguishabilty profoundly affects the collisions of identical particles. In the case of a Coulombic interaction this leads to a dramatic modification of Rutherford's famous scattering formula as predicted by Nevill Mott. An even more extreme example is provided by a low‐energy scattering experiment of identical fermions interacting via a short range potential. Here indistinguishability will make or break the observation of scattered particles. This fascinating phenomenon has been observed using a laser‐based collider for ultracold fermionic potassium atoms.
It has recently been demonstrated experimentally that 200–300200\text{--}300200–300 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.
Figure 1.1 represents schematically a typical scattering experiment, in fact this is the sketch of E. Rutherford experiment in 1910 [ 1 ]. Projectiles (here, α -particles) from a source go through a collimator and collide with a target (gold foil in Rutherford’s experiment). Some projectiles are scattered by the target and reach the detector (here, a fluorescent screen). Rutherford expected them to go straight through with perhaps a minor deflection. Most did go straight through, but to his surprise some particles bounced directly off the gold sheet! What did this mean? Rutherford hypothesized that the positive alpha particles had hit a concentrated mass of positive particles, which he termed the nucleus. We shall describe the Rutherford scattering theoretically later in this chapter.