Schwinger scattering of twisted neutrons by nuclei

Abstract

Thanks to J. Schwinger, the process of elastic scattering of neutrons by nuclei is known to depend on the interference between a nuclear amplitude and an electromagnetic one for small scattering angles, resulting in spin asymmetries of a cross section or in polarization of the scattered neutrons. While this interference depends on the neutron's transverse polarization and on an imaginary part of the nuclear amplitude, this conclusion holds only for the incident plane-wave neutrons with a definite momentum. Here we show that this scattering is altered when the twisted neutrons, recently obtained experimentally, are used instead -that is, neutrons with an orbital angular momentum. For bulk targets, the angular distributions of the scattered neutrons get modified, while scattering of a superposition of states with the different angular momenta also reveals dependence on the longitudinal polarization. For well-localized targets, the observables develop a dependence on the neutron's helicity and on a real part of the nuclear amplitude, providing full access to its phase already in the Born approximation. We argue that the corresponding spin asymmetries are measurable at existing neutron facilities. Thus, scattering of the twisted neutrons by nuclei can provide means for quantum tomography of the neutron states and become a useful tool for hadronic studies, low-energy nuclear physics, tests of fundamental symmetries, and neutron optics.Introduction. -In 1948 J. Schwinger predicted that in a process of elastic scattering of the non-relativistic neutrons by a nucleus with a charge Ze the final neutrons become spin-polarized, thanks to the spin-orbit coupling [1]. Nowadays such a scattering is well studied, both theoretically [2] and experimentally [3], and the polarized cold and thermal neutrons are needed for a number of standard model test measurements (see, e.g., [4]).

Kinematic surprises in twisted-particle collisions

“…where J is given by (11) or (17). From now on, we deliberately omit the prefactors to stress, as discussed in the section II B, that the figure of merit is not the absolute value of the cross section but its kinematic distribution.…”

“…There is an even larger literature on scattering processes in which only one of the initial particles is twisted, see for instance reviews[4,6] and the recent calculation of twisted neutron scattering on nuclei[11]. Although this collision setting is perhaps easier to achieve experimentally, it does not share the essential novelties offered by two twisted particle collision.…”

Phenomenological extraction of two-photon exchange amplitudes from elastic electron-proton scattering cross section data

“…[13] "Hadronic" where all the proton interme-diate states are accounted for, the partonic model from Ref. [23] which accounts for hard scattering of electrons by quarks embedded in the nucleon through generalized parton distributions "GPD", calculation based on QCD factorization within the SCET approach from Ref. [18] arising from both the soft-spectator "KV-Soft Spectator" and hard-spectator "KV-Hard Spectator" scattering contributions, and calculation based on subtracted dispersion relation formalism applied to the case of a nucleon in the intermediate state from Ref.…”

“…Theoretically, different approaches were adapted to calculate TPE corrections to electron-proton scattering observables such as: the hadronic [9, 12-15, 20, 21, 26, 27, 30-35], partonic models (GPDs) [22,23], dispersion relations (DRs) [19,28], and pQCD [16-18, 29, 39] based calculations. However, calculations of the TPE amplitudes or generalized form factors were done mainly using hadronic-and pQCD-based calculations.…”

“…At high Q 2 values, the hadronic approach becomes inadequate and the TPE corrections are calculated mainly within the framework of GPDs [22,23] and pQCD [16-18, 29, 39]. Afanasev et al [23] calculated TPE corrections to σ R using formalism of GPDs. The authors doubt the applicability of pQCD for the currently existing data.…”