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We calculate the ionization cross sections for H, He or Ne atoms using $\nu_e$ and $\bar \nu_e$ scattering at keV energies. Such cross sections are useful for e.g. $\bar \nu_e$-oscillation experiments using a tritium source. Using realistic atomic wave functions, we find that for $E_\nu \lsim 10 ~\rm keV $ the atomic ionization cross sections, norm...
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Citations
... Of particular interest is the ionization of atoms by neutrinos and antineutrinos. Ionization cross sections calculated for H, He and Ne were found [4] to be smaller than the corresponding free electron cross sections, and the calculations were then extended [5] to the electron spectra for H, He and Ne, and integrated ionization cross sections for H, He, Ne and Xe. ...
... The energy spectra are compared to those for scattering from free electrons, for which [4] dσ ðνÞ dE f ...
... The total cross section for scattering off free electrons is [4] σ ðνÞ ðFreeÞ ¼ ...
The theory of scattering of low energy neutrinos and antineutrinos by atomic electrons has recently been developed [ I. B. Whittingham, Phys. Rev. D 105, 013008 (2022)] using the bound interaction picture in configuration space to fully implement the relationship between the neutrino helicities and the orbital and spin angular momenta of the atomic electrons. The energy spectra of ionization electrons produced by scattering of neutrinos and antineutrinos with energies of 5, 10, 20, and 30 keV by hydrogen, helium and neon were calculated using Dirac screened Coulombic eigenfunctions. This paper reports further applications of this theory, to a new calculation of the energy spectra for neon, as the original calculation used some screening constants which underestimated the effects of screening in the inner subshells, and to scattering by argon. The results are presented as ratios to the corresponding quantities for scattering by Z free electrons. The new spectra ratios for neon are larger than the original ratios by ≈0.03–≈0.14, with the greatest increases occurring for 10 keV neutrinos and antineutrinos. Integrated spectra ratios range from 0.16 to 0.59 for neon, and from 0.15 to 0.48 for argon, as the neutrino energy increases from 5 to 30 keV.
... Of particular interest is the ionization of atoms by neutrinos and antineutrinos. Ionization cross sections calculated for H, He and Ne were found [4] to be smaller than the corresponding free electron cross sections, and the calculations were then extended [5] to the electron spectra for H, He and Ne, and integrated ionization cross sections for H, He, Ne and Xe. ...
... The energy spectra are compared to those for scattering from free electrons, for which [4] ...
... The total cross section for scattering off free electrons is [4] σ (ν) ...
The theory of scattering of low energy neutrinos and antineutrinos by atomic electrons has recently been developed (I. B. Whittingham, Phys. Rev. D 105, 013008 (2022)) using the Bound Interaction Picture in configuration space to fully implement the relationship between the neutrino helicities and the orbital and spin angular momenta of the atomic electrons. The energy spectra of ionization electrons produced by scattering of neutrinos and antineutrinos with energies of 5, 10, 20, and 30 keV by hydrogen, helium and neon were calculated using Dirac screened Coulombic eigenfunctions. This paper reports further applications of this theory, to a new calculation of the energy spectra for neon, as the original calculation used some screening constants which underestimated the effects of screening in the inner subshells, and to scattering by argon. The results are presented as ratios to the corresponding quantities for scattering by $Z$ free electrons. The new spectra ratios for neon are larger than the original ratios by approx 0.03 to approx 0.14, with the greatest increases occurring for 10 keV neutrinos and antineutrinos. Integrated spectra ratios range from 0.16 to 0.59 for neon, and from 0.15 to 0.48 for argon, as the neutrino energy increases from 5 to 30 keV.
... So the atomic effect cannot be neglected in the study of neutrino electromagnetic properties. For example, the ionization effect due to the neutrino scattering with bound electrons is obtained by considering the binding energy and the initial wave function in light atoms [72,73]. Later, the effect of atomic potential on the final-state electron is also taken into consideration when calculating the cross section [74][75][76]. ...
A bstract
The recent XENON1T excess can be explained by the solar active-sterile neutrino conversion with bound electrons via light mediator. Nevertheless, the atomic effects are usually omitted in the solar neutrino explanations. We systematically establish a second quantization formalism for both bound and ionized electrons to account for the atomic effects. This formalism is of great generality to incorporate various interactions for both neutrino and dark matter scatterings. Our calculation shows that the change in the cross section due to atomic effects can have important impact on the differential cross section. It is necessary to include atomic effects in the low-energy electron recoil signal at dark matter direct detection experiments even for energetic solar neutrinos. With the best-fit values to the XENON1T data, we also project the event rate at PandaX-4T, XENONnT, and LZ experiments.
... Subsequently, calculated electron spectra from inelastic scattering of neutrinos by atomic electrons of 19 F and 96 Mo were found [8,9] to differ significantly from scattering by a free electron and were always smaller than the free electron case. Ionization cross sections for scattering by bound electrons in the light atoms H, He and Ne were also found [10] to be smaller than the corresponding free electron cross sections. The calculations were then extended [11] to the electron spectra for H, He and Ne, and integrated ionization cross sections for H, He, Ne and Xe. ...
... The calculations of [10,11] are based upon the assumption of spin-independent nonrelativistic atomic wave functions and consider the scattering to occur from a free electron whose energy E e i is set to the energy of the initial bound electron m e þ ϵ, where ϵ is the binding energy, and whose momentum p e i is determined by the probability amplitude jΨ n i l i m i ðp e i Þj 2 , where Ψ n i l i m i ðp e i Þ is the momentum-space atomic wave function. The bound electron is then described by the effective squared mass ...
... The calculations [10][11][12][13][14] destroy the relationship between the neutrino helicities and the orbital and spin angular momenta of the atomic electrons. Some of these issues are addressed by [16,17], and their approach is closest in spirit to the present calculations. ...
Studies of neutrino mixing and oscillations, solar neutrinos as background in dark matter searches involving electron detection, detection of sterile neutrino warm dark matter, and of possible electromagnetic properties of neutrinos, have generated interest in the low energy O(10 keV) scattering of electron neutrinos and antineutrinos by atomic electrons where the binding of the atomic electron cannot be ignored. Of particular interest is the ionization of atoms by neutrinos and antineutrinos. Most existing calculations are based upon modifications of the free electron differential cross section which destroy the relationship between the neutrino helicities and the orbital and spin angular momenta of the atomic electrons. The present calculations maintain the full collision dynamics by formulating the scattering in configuration space using the bound interaction picture, rather than the usual formulation in the interaction picture in momentum space as appropriate to scattering by free electrons. Energy spectra of ionization electrons produced by scattering of neutrinos and antineutrinos with energies of 5, 10, 20, and 30 keV by hydrogen, helium and neon have been calculated using Dirac central field eigenfunctions, and are presented as ratios to the spectra for scattering by free electrons. Binding effects increase strongly with atomic number, are largest for low neutrino energy and, for each neutrino energy, greatest at the high electron energy end of the spectrum. The most extreme effects of binding are for 5 keV scattering by Ne where the ratios are less than 0.1. The energy spectra have been calculated for both a Coulombic final electron state and a free final electron state. The results indicate that the binding effects from the continuum state of the final electron are significant and can be comparable to those arising from the bound initial electron state.
... Subsequently, calculated electron spectra from inelastic scattering of neutrinos by atomic electrons of 19 F and 96 Mo were found [8,9] to differ significantly from scattering by a free electron and were always smaller than the free electron case. Ionization cross sections for scattering by bound electrons in the light atoms H, He and Ne were also found [10] to be smaller than the corresponding free electron cross sections. The calculations were then extended [11] to the electron spectra for H, He and Ne, and integrated ionization cross sections for H, He, Ne and Xe. ...
... The calculations of [10,11] are based upon the assumption of spin-independent non-relativistic atomic wave functions and consider the scattering to occur from a free electron whose energy E ei is set to the energy of the initial bound electron m e + ǫ, where ǫ is the binding energy, and whose momentum p ei is determined by the probability amplitude |Ψ nilimi (p ei )| 2 , where Ψ nilimi (p ei ) is the momentum-space atomic wave function. The bound electron is then described by the effective squared mass ...
... The weak current operator (14) is expanded in spherical multipoles. The calculations [10][11][12][13][14] destroy the relationship between the neutrino helicities and the orbital and spin angular momenta of the atomic electrons. Some of these issues are addressed by [16], and their approach is closest in spirit to the present calculations but, as we shall see, they neglect the q dependence of the atomic electron system. ...
Studies of neutrino mixing and oscillations, solar neutrinos as background in dark matter searches involving electron detection, detection of sterile neutrino warm dark matter, and of possible electromagnetic properties of neutrinos, have generated interest in the low energy O(10 keV) scattering of electron neutrinos and antineutrinos by atomic electrons where the binding of the atomic electron cannot be ignored. Of particular interest is the ionization of atoms by neutrinos and antineutrinos. Most existing calculations are based on modifications of the free electron differential cross section, which destroy the relationship between the neutrino helicities and the orbital and spin angular momenta of the atomic electrons. The present calculations maintain the full collision dynamics by formulating the scattering in configuration space using the Bound Interaction Picture, rather than the usual formulation in the Interaction Picture in momentum space as appropriate to scattering by free electrons. Energy spectra of ionization electrons produced by scattering of neutrinos and antineutrinos with energies of 5, 10, 20, and 30 keV by hydrogen, helium and neon have been calculated using Dirac central field eigenfunctions and are presented as ratios to the spectra for scattering by free electrons. Binding effects increase strongly with atomic number, are largest for low neutrino energy and, for each neutrino energy, greatest at the high electron energy end of the spectrum. The most extreme effects of binding are for 5 keV scattering by Ne where the ratios are less than 0.1. The energy spectra are calculated for both a Coulombic final electron state and a free final electron state. The results indicate that the binding effects from the continuum state of the final electron are significant and can be comparable to those arising from the bound initial electron state.
... For the first time this problem was addressed in Ref. [37], where a 2-3 times enhancement of the electroweak cross section in the case of ionization from a 1s state of a hydrogen-like atom with nuclear charge Z had been numerically determined at neutrino energies E ν ∼ αZm e c 2 . Subsequent numerical calculations within the relativistic Hartree-Fock method for ionization from inner shells of various atoms showed much lower enhancement (∼ 5 − 10%) of the electroweak contribution [38,39,40,41,42,43]. It was found that in the scattering on realistic atoms, such as germanium, the so-called stepping approximation works with a very good accuracy. ...
An overview of the current theoretical studies on neutrino-atom scattering
processes is presented. The ionization channel of these processes, which is
studied in experiments searching for neutrino magnetic moments, is brought into
focus. Recent developments in the theory of atomic ionization by impact of
reactor antineutrinos are discussed. It is shown that the stepping
approximation is well applicable for the data analysis practically down to the
ionization threshold.
... As the kinematics in neutrino scattering with sub-keV energy transfer starts to overlap with atomic scales, how the atomic binding effects modify the above free scattering formula becomes an essential issue. This problem has recently been intensively re-visited because of a derivation that atomic structure can greatly enhance the magnetic cross section by orders of magnitude over the free scattering formula at low T [15], in contrast to previous studies all showing suppression [16][17][18][19][20]. While latter works [21][22][23][24] justified, with generic arguments and schematic calculations, that atomic binding effects suppress the scattering cross sections and the usability of a simple free electron approximation [17], it remains challenging to obtain a differential cross section formula at low T with a reasonable error estimate. ...
An ab initio calculation of atomic ionization of germanium (Ge) by neutrinos
was carried out in the framework of multiconfiguration relativistic random
phase approximation. The main goal is to provide a more accurate cross section
formula than the conventional one, which is based on the free electron
approximation, for searches of neutrino magnetic moments with Ge detectors
whose threshold is reaching down to the sub-keV regime. Limits derived with
both methods are compared, using reactor neutrino data taken with low threshold
germanium detectors.
With the advent of detectors with sub-keV sensitivities, atomic ionization
has been identified as a promising avenue to probe possible neutrino
electromagnetic properties. The interaction cross-sections induced by
millicharged neutrinos are evaluated with the ab-initio multi-configuration
relativistic random-phase approximation. There is significant enhancement at
atomic binding energies compared to that when the electrons are taken as free
particles. Positive signals would distinctly manifest as peaks at specific
energies with known intensity ratios. Selected reactor neutrino data with
germanium detectors at analysis threshold as low as 300 eV are studied. No such
signatures are observed, and a combined limit on the neutrino charge fraction
of $| \numq | < 1.0 \times 10^{-12}$ at 90% confidence level is derived.
An ab initio calculation of atomic ionization of germanium by neutrinos was carried out in the framework of multiconfiguration relativistic random phase approximation and benchmarked by related atomic structure and photoabsorption data. This improves over the conventional approach based on scattering off free electrons whose validity at sub-keV energy transfer is questionable. Limits on neutrino magnetic moments are derived using reactor neutrino data taken with low threshold germanium detectors. Future applications of these atomic techniques will greatly reduce the atomic uncertainties in low-energy neutrino and dark matter detections.
The purpose of the present paper is to study the neutrino properties as they may appear in the low-energy neutrinos emitted in triton decay: 3 1 H-3 2 He þ e À þ * n e with maximum neutrino energy of 18:6 keV: The technical challenges to this end can be summarized as building a very large Time Projection Counters (TPC) capable of detecting low-energy recoils, down to 100 eV; within the required low background constraints. More specifically we propose the development of a spherical gaseous TPC of about 10-m in radius and a 200 Mcurie triton source in the center of curvature. One can list a number of exciting studies, concerning fundamental physics issues, that could be made using a large-volume TPC and low-energy antineutrinos: (1) The oscillation length involving the small angle d ¼ sin y 13 ; directly measured in our n e disappearance experiment, is fully contained inside the detector. Measuring the counting rate of neutrino–electron elastic scattering as function of the distance of the source will give a precise and unambiguous measurement of the oscillation parameters free of systematic errors. In fact first estimations show that even with a year's of data taking a sensitivity of a few percent for the measurement of the above angle will be achieved. (2) The low-energy detection threshold offers a unique sensitivity for the neutrino magnetic moment which is about two orders of magnitude beyond the current experimental limit of 10 À10 m B : (3) Scattering at such low neutrino energies has never been studied and any departure from the expected behavior may be an indication of new physics beyond the standard model. We present a summary of various theoretical studies and possible measurements, including a precise measurement of the Weinberg angle at very low momentum transfer. r 2004 Elsevier B.V. All rights reserved.
