# Cross Sections for Coherent Elastic and Inelastic Neutrino-Nucleus Scattering

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## Abstract

**:**

## 1. Introduction

## 2. Formalism

#### 2.1. CE$\nu $NS Cross Section

#### 2.2. Inelastic Cross Sections

## 3. Results and Discussion

#### Constraining ${}^{40}$Ar

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Freedman, D.Z. Coherent Neutrino Nucleus Scattering as a Probe of the Weak Neutral Current. Phys. Rev. D
**1974**, 9, 1389. [Google Scholar] [CrossRef] - Akimov, D. et al. [COHERENT Collaboration] Observation of Coherent Elastic Neutrino-Nucleus Scattering. Science
**2017**, 357, 1123. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Akimov, D. et al. [COHERENT Collaboration] COHERENT Collaboration data release from the first observation of coherent elastic neutrino-nucleus scattering. arXiv
**2018**, arXiv:1804.09459. [Google Scholar] - Akimov, D. et al. [COHERENT Collaboration] First Constraint on Coherent Elastic Neutrino-Nucleus Scattering in Argon. Phys. Rev. D
**2019**, 100, 115020. [Google Scholar] [CrossRef] [Green Version] - Akimov, D. et al. [COHERENT Collaboration] First Measurement of Coherent Elastic Neutrino-Nucleus Scattering on Argon. Phys. Rev. Lett.
**2021**, 126, 012002. [Google Scholar] [CrossRef] [PubMed] - Akimov, D. et al. [COHERENT Collaboration] Measurement of the Coherent Elastic Neutrino-Nucleus Scattering Cross Section on CsI by COHERENT. Phys. Rev. Lett.
**2022**, 129, 081801. [Google Scholar] [CrossRef] - Liao, J.; Marfatia, D. Repulsive baryonic interactions and lattice QCD observables at imaginary chemical potential. Phys. Lett. B
**2017**, 775, 47–54. [Google Scholar] [CrossRef] - Dent, J.B.; Dutta, B.; Liao, S.; Newstead, J.L.; Strigari, L.E.; Walker, J.W. Accelerator and reactor complementarity in coherent neutrino-nucleus scattering. Phys. Rev. D
**2018**, 97, 035009. [Google Scholar] [CrossRef] [Green Version] - Aristizabal Sierra, D.; Rojas, N.; Tytgat, M. Neutrino non-standard interactions and dark matter searches with multi-ton scale detectors. J. High Energy Phys.
**2018**, 2018, 197. [Google Scholar] [CrossRef] [Green Version] - Denton, P.B.; Farzan, Y.; Shoemaker, I.M. Testing large non-standard neutrino interactions with arbitrary mediator mass after COHERENT data. J. High Energy Phys.
**2018**, 2018, 37. [Google Scholar] [CrossRef] [Green Version] - Kosmas, T.; Papoulias, D.; Tortola, M.; Valle, J. Probing light sterile neutrino signatures at reactor and Spallation Neutron Source neutrino experiments. Phys. Rev. D
**2017**, 96, 063013. [Google Scholar] [CrossRef] [Green Version] - Blanco, C.; Hooper, D.; Machado, P. Constraining Sterile Neutrino Interpretations of the LSND and MiniBooNE Anomalies with Coherent Neutrino Scattering Experiments. arXiv
**2019**, arXiv:1901.08094. [Google Scholar] [CrossRef] - Aristizabal Sierra, D.; De Romeri, V.; Rojas, N. CP violating effects in coherent elastic neutrino-nucleus scattering processes. J. High Energy Phys.
**2019**, 9, 69. [Google Scholar] [CrossRef] [Green Version] - Cadeddu, M.; Giunti, C.; Li, Y.; Zhang, Y. Average CsI Neutron Density Distribution from COHERENT Data. Phys. Rev. Lett.
**2018**, 120, 072501. [Google Scholar] [CrossRef] [Green Version] - Ciuffoli, E.; Evslin, J.; Fu, Q.; Tang, J. P-wave contributions to B→ψππ decays in the perturbative QCD approach. Phys. Rev. D
**2018**, 97, 113003. [Google Scholar] [CrossRef] [Green Version] - Aristizabal Sierra, D.; Liao, J.; Marfatia, D. Impact of form factor uncertainties on interpretations of coherent elastic neutrino-nucleus scattering data. J. High Energy Phys.
**2019**, 2019, 141. [Google Scholar] [CrossRef] [Green Version] - Papoulias, D.; Kosmas, T.; Sahu, R.; Kota, V.; Hota, M. Constraining nuclear physics parameters with current and future COHERENT data. Phys. Lett. B
**2020**, 800, 135133. [Google Scholar] [CrossRef] - Aguilar-Arevalo, A.A. et al. [CCM Collaboration] First dark matter search results from Coherent CAPTAIN-Mills. Phys. Rev. D
**2022**, 106, 012001. [Google Scholar] [CrossRef] - Coloma, P.; Esteban, I.; Gonzalez-Garcia, M.C.; Menendez, J. Determining the nuclear neutron distribution from Coherent Elastic neutrino-Nucleus Scattering: Current results and future prospects. J. High Energy Phys.
**2020**, 2020, 30. [Google Scholar] [CrossRef] - Aguilar-Arevalo, A.; Bertou, X.; Bonifazi, C.; Butner, M.; Cancelo, G.; Vázquez, A.C.; Vergara, B.C.; Chavez, C.R.; Da Motta, H.; D’Olivo, J.C.; et al. Results of the engineering run of the Coherent Neutrino Nucleus Interaction Experiment (CONNIE). JINST
**2016**, 11, P07024. [Google Scholar] [CrossRef] [Green Version] - Agnolet, G. et al. [MINER Collaboration] Background studies for the MINER Coherent Neutrino Scattering reactor experiment. Nucl. Instrum. Meth. A
**2017**, 853, 53. [Google Scholar] [CrossRef] [Green Version] - Belov, V.; Brudanin, V.; Egorov, V.; Filosofov, D.; Fomina, M.; Gurov, Y.; Korotkova, L.; Lubashevskiy, A.; Medvedev, D.; Pritula, R.; et al. The νGeN experiment at the Kalinin Nuclear Power Plant. J. Instrum.
**2015**, 10, P12011. [Google Scholar] [CrossRef] - Strauss, R.; Rothe, J.; Angloher, G.; Bento, A.; Gütlein, A.; Hauff, D.; Kluck, H.; Mancuso, M.; Oberauer, L.; Petricca, F.; et al. The ν-cleus experiment: A gram-scale fiducial-volume cryogenic detector for the first detection of coherent neutrino-nucleus scattering. Eur. Phys. J. C
**2017**, 77, 506. [Google Scholar] [CrossRef] [Green Version] - Billard, J.; Carr, R.; Dawson, J.; Figueroa-Feliciano, E.; Formaggio, J.A.; Gascon, J.; Heine, S.T.; De Jesus, M.; Johnston, J.; Lasserre, T.; et al. Coherent neutrino scattering with low temperature bolometers at Chooz reactor complex. J. Phys. G
**2017**, 44, 105101. [Google Scholar] [CrossRef] [Green Version] - Wong, H.T. Neutrino-nucleus coherent scattering and dark matter searches with sub-keV germanium detector. Nucl. Phys. A
**2010**, 844, 229c–233c. [Google Scholar] [CrossRef] - Choi, J.J.; Jeon, E.J.; Kim, J.Y.; Kim, K.W.; Kim, S.H.; Kim, S.K.; Kim, Y.D.; Ko, Y.J.; Koh, B.C.; Ha, C.; et al. Exploring coherent elastic neutrino-nucleus scattering using reactor electron antineutrinos in the NEON experiment. Eur. Phys. J. C
**2023**, 83, 226. [Google Scholar] [CrossRef] - Akindele, O.A.; Berryman, J.M.; Bowden, N.S.; Carr, R.; Conant, A.J.; Huber, P.; Langford, T.J.; Link, J.M.; Littlejohn, B.R.; Fernandez-Moroni, G.; et al. High Energy Physics Opportunities Using Reactor Antineutrinos. arXiv
**2022**, arXiv:2203.07214. https://arxiv.org/abs/2203.07214. [Google Scholar] - Hofstadter, R. Electron Scattering and Nuclear Structure. Rev. Mod. Phys.
**1956**, 28, 214. [Google Scholar] [CrossRef] - De Vries, H.; De Jager, C.W.; De Vries, C. Nuclear charge-density-distribution parameters from elastic electron scattering. Atom. Data Nucl. Data Tabl.
**1987**, 36, 495. [Google Scholar] [CrossRef] - Fricke, G.; Bernhardt, C.; Heilig, K.; Schaller, L.A.; Schellenberg, L.; Shera, E.B.; de Jager, C.W. Nuclear Ground State Charge Radii from Electromagnetic Interactions. Atom. Data Nucl. Data Tabl.
**1995**, 60, 177. [Google Scholar] [CrossRef] [Green Version] - Angeli, I.; Marinova, K. Table of experimental nuclear ground state charge radii: An update. Atom. Data Nucl. Data Tabl.
**2013**, 99, 69. [Google Scholar] [CrossRef] - Thiel, M.; Sfienti, C.; Piekarewicz, J.; Horowitz, C.; Vanderhaeghen, M. Neutron skins of atomic nuclei: Per aspera ad astra. J. Phys. G
**2019**, 46, 093003. [Google Scholar] [CrossRef] [Green Version] - Donnelly, T.; Dubach, J.; Sick, I. Isospin dependences in parity-violating electron scattering. Nucl. Phys. A
**1989**, 503, 589. [Google Scholar] [CrossRef] - Abrahamyan, S. et al. [PREX Collaboration] New Measurements of the Transverse Beam Asymmetry for Elastic Electron Scattering from Selected Nuclei. Phys. Rev. Lett.
**2012**, 108, 112502. [Google Scholar] - Horowitz, C.J.; Ahmed, Z.; Jen, C.M.; Rakhman, A.; Souder, P.A.; Dalton, M.M.; Liyanage, N.; Paschke, K.D.; Saenboonruang, K.; Silwal, R.; et al. Weak charge form factor and radius of 208Pb through parity violation in electron scattering. Phys. Rev. C
**2012**, 85, 032501. [Google Scholar] [CrossRef] [Green Version] - Kumar, K.S. Electroweak probe of neutron skins of nuclei. Ann. Phys.
**2020**, 412, 168012. [Google Scholar] [CrossRef] - Patton, K.; Engel, J.; McLaughlin, G.C.; Schunck, N. Neutrino-nucleus coherent scattering as a probe of neutron density distributions. Phys. Rev. C
**2012**, 86, 024612. [Google Scholar] [CrossRef] [Green Version] - Klein, S.; Nystrand, J. Exclusive vector meson production in relativistic heavy ion collisions. Phys. Rev. C
**1999**, 60, 014903. [Google Scholar] [CrossRef] [Green Version] - Helm, R.H. Inelastic and Elastic Scattering of 187-Mev Electrons from Selected Even-Even Nuclei. Phys. Rev.
**1956**, 104, 1466. [Google Scholar] [CrossRef] - Payne, C.G.; Bacca, S.; Hagen, G.; Jiang, W.; Papenbrock, T. Coherent elastic neutrino-nucleus scattering on from first principles. Phys. Rev. C
**2019**, 100, 061304. [Google Scholar] [CrossRef] [Green Version] - Yang, J.; Hernandez, J.A.; Piekarewicz, J. Electroweak probes of ground state densities. Phys. Rev. C
**2019**, 100, 054301. [Google Scholar] [CrossRef] [Green Version] - Co’, G.; Anguiano, M.; Lallena, A. Nuclear structure uncertainties in coherent elastic neutrino-nucleus scattering. J. Cosmol. Astropart. Phys.
**2020**, 4, 44. [Google Scholar] - Hoferichter, M.; Menéndez, J.; Schwenk, A. Coherent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses. Phys. Rev. D
**2020**, 102, 074018. [Google Scholar] [CrossRef] - Tomalak, O.; Machado, P.; Pandey, V.; Plestid, R. Flavor-dependent radiative corrections in coherent elastic neutrino-nucleus scattering. J. High Energy Phys.
**2021**, 2021, 097. [Google Scholar] [CrossRef] - Tanabashi, M. et al. [Particle Data Group] Review of Particle Physics. Phys. Rev. D
**2018**, 98, 030001. [Google Scholar] [CrossRef] [Green Version] - Abdullah, M.; Aristizabal Sierra, D.; Dutta, B.; Strigari, L.E. Coherent Elastic Neutrino-Nucleus Scattering with directional detectors. arXiv
**2020**, arXiv:2003.11510. [Google Scholar] [CrossRef] - Van Dessel, N.; Jachowicz, N.; Nikolakopoulos, A. Forbidden transitions in neutral- and charged-current interactions between low-energy neutrinos and argon. Phys. Rev. C
**2019**, 100, 055503. [Google Scholar] [CrossRef] [Green Version] - Ryckebusch, J.; Waroquier, M.; Heyde, K.; Moreau, J.; Ryckbosch, D. An RPA model for the description of one-nucleon emission processes and application to
^{16}O(γ, N) reactions. Nucl. Phys. A**1988**, 476, 237. [Google Scholar] [CrossRef] - Ryckebusch, J.; Heyde, K.; Van Neck, D.; Waroquier, M. Aspects of the final-state interaction and long-range correlations in quasi-elastic (e, e’p) and (e, e’n) reactions. Nucl. Phys. A
**1989**, 503, 694. [Google Scholar] [CrossRef] - Jachowicz, N.; Rombouts, S.; Heyde, K.; Ryckebusch, J. Cross sections for neutral-current neutrino-nucleus interactions: Applications for
^{12}C and^{16}O. Phys. Rev. C**1999**, 59, 3246. [Google Scholar] [CrossRef] [Green Version] - Jachowicz, N.; Heyde, K.; Ryckebusch, J.; Rombouts, S. Continuum random phase approximation approach to charged-current neutrino-nucleus scattering. Phys. Rev. C
**2002**, 65, 025501. [Google Scholar] [CrossRef] - Jachowicz, N.; Heyde, K.; Ryckebusch, J. Cross sections for neutral-current neutrino scattering on 208 Pb. Phys. Rev. C
**2002**, 66, 055501. [Google Scholar] [CrossRef] - Jachowicz, N.; Vantournhout, K.; Ryckebusch, J.; Heyde, K. Identifying Neutrinos and Antineutrinos in Neutral-Current ScatteringReactions. Phys. Rev. Lett.
**2004**, 93, 082501. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Jachowicz, N.; McLaughlin, G. Reconstructing supernova-neutrino spectra using low-energy beta beams. Phys. Rev. Lett.
**2006**, 96, 172301. [Google Scholar] [CrossRef] [Green Version] - Pandey, V.; Jachowicz, N.; Ryckebusch, J.; Van Cuyck, T.; Cosyn, W. Quasielastic contribution to antineutrino-nucleus scattering. Phys. Rev. C
**2014**, 89, 024601. [Google Scholar] [CrossRef] [Green Version] - Pandey, V.; Jachowicz, N.; Van Cuyck, T.; Ryckebusch, J.; Martini, M. Low-energy excitations and quasielastic contribution to electron-nucleus and neutrino-nucleus scattering in the continuum random-phase approximation. Phys. Rev. C
**2015**, 92, 024606. [Google Scholar] [CrossRef] [Green Version] - Pandey, V.; Jachowicz, N.; Martini, M.; González-Jiménez, R.; Ryckebusch, J.; Van Cuyck, T.; Van Dessel, N. Impact of low-energy nuclear excitations on neutrino-nucleus scattering at MiniBooNE and T2K kinematics. Phys. Rev. C
**2016**, 94, 054609. [Google Scholar] [CrossRef] [Green Version] - Van Dessel, N.; Jachowicz, N.; González-Jiménez, R.; Pandey, V.; Van Cuyck, T. A dependence of quasielastic charged-current neutrino-nucleus cross sections. Phys. Rev. C
**2018**, 97, 044616. [Google Scholar] [CrossRef] [Green Version] - Nikolakopoulos, A.; Jachowicz, N.; Van Dessel, N.; Niewczas, K.; González-Jiménez, R.; Udías, J.M.; Pandey, V. Electron versus muon neutrino induced cross sections in charged current quasielastic processes. Phys. Rev. Lett.
**2019**, 123, 052501. [Google Scholar] [CrossRef] - Van Dessel, N.; Nikolakopoulos, A.; Jachowicz, N. Lepton kinematics in low-energy neutrino-argon interactions. Phys. Rev. C
**2020**, 101, 045502. [Google Scholar] [CrossRef] [Green Version] - Nikolakopoulos, A.; Pandey, V.; Spitz, J.; Jachowicz, N. Modeling quasielastic interactions of monoenergetic kaon decay-at-rest neutrinos. arXiv
**2020**, arXiv:2010.05794. [Google Scholar] [CrossRef] - Tohyama, M. Application of extended random-phase approximation with ground-state correlations to collective excitations of 16O. J. Phys. Conf. Ser.
**2014**, 529, 012026. [Google Scholar] [CrossRef] - Papoulias, D.; Kosmas, T.; Kuno, Y. Recent Probes of Standard and Non-standard Neutrino Physics With Nuclei. Front. Phys.
**2019**, 7, 191. [Google Scholar] [CrossRef] - Antonello, M. et al. [MicroBooNE, LAr1-ND and ICARUS-WA104 Collaboration] A Proposal for a Three Detector Short-Baseline Neutrino Oscillation Program in the Fermilab Booster Neutrino Beam. arXiv
**2015**, arXiv:1503.01520. [Google Scholar] - Abi, B. et al. [DUNE Collaboration] Deep Underground Neutrino Experiment (DUNE), Far Detector Technical Design Report, Volume II: DUNE Physics. arXiv
**2020**, arXiv:2002.03005. [Google Scholar] - Amaudruz, P. et al. [DEAP-3600 Collaboration] First Results from the DEAP-3600 Dark Matter Search with Argon at SNOLAB. Phys. Rev. Lett.
**2018**, 121, 071801. [Google Scholar] [CrossRef] [Green Version] - Agnes, P. et al. [DarkSide Collaboration] Low-Mass Dark Matter Search with the DarkSide-50 Experiment. Phys. Rev. Lett.
**2018**, 121, 081307. [Google Scholar] [CrossRef] [Green Version] - Calvo, J. et al. [ArDM Collaboration] Backgrounds and pulse shape discrimination in the ArDM liquid argon TPC. J. Cosmol. Astropart. Phys.
**2017**, 3, 3. [Google Scholar] - Hime, A. [MiniCLEAN Collaboration]. The MiniCLEAN Dark Matter Experiment. arXiv
**2011**, arXiv:1110.1005. [Google Scholar] - Ottermann, C.R.; Schmitt, C.H.; Simon, G.G.; Borkowski, F.; Walther, V.H. Elastic electron scattering from 40Ar. Nucl. Phys. A
**1982**, 379, 396. [Google Scholar] [CrossRef] - Duda, G.; Kemper, A.; Gondolo, P. Model Independent Form Factors for Spin Independent Neutralino-Nucleon Scattering from Elastic Electron Scattering Data. J. Cosmol. Astropart. Phys.
**2007**, 4, 12. [Google Scholar] [CrossRef] - Lewin, J.; Smith, P. Review of mathematics, numerical factors, and corrections for dark matter experiments based on elastic nuclear recoil. Astropart. Phys.
**1996**, 6, 87–112. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**(

**Left**) Diagrammatic representation of the CE$\nu $NS process where a single ${Z}^{0}$ boson is exchanged between neutrino and target nucleus. (

**Right**) Diagrammatic representation of the inelastic neutrino-nucleus scattering where a single ${W}^{+}$ (CC) or ${Z}^{0}$ (NC) boson is exchanged between neutrino and target nucleus.

**Figure 2.**Panels (

**a**,

**b**) represent proton and neutron densities of different nuclei obtained using the HF–SkE2 approach. Panels (

**c**) through (

**d**) represent charge and weak form factors for the different nuclei.

**Figure 3.**The “weak-skin” form factor depicts the difference between the charge and weak form factors.

**Figure 4.**(

**Left**): the charge form factor of ${}^{208}$Pb compared with elastic electron scattering data of Ref. [29]. (

**Right**): the weak form factor of ${}^{208}$Pb along with the single point measured by the PREX collaboration at the momentum transfer of q = 0.475 fm${}^{-1}$ [34,35]. Both form factors are compared with relativistic mean–field predictions of Yang et al. [41].

**Figure 5.**Total CE$\nu $NS cross sections for a set of nuclear targets obtained within the HF–SkE2 approach.

**Figure 6.**CE$\nu $NS cross section strength compared to CCQE and NCQE scattering cross sections for several nuclei, above particle emission threshold.

**Figure 7.**(

**Left**) The ${}^{40}$Ar charge form factor predictions compared to elastic electron scattering data taken from Ref. [70], a comparison is also performed with the coupled–cluster theory predictions of Payne et al. [40] as well as with Klein–Nystrand [38] (standard and adapted) and Helm [39] form factors. (

**Right**) The ${}^{40}$Ar weak form factor predictions compared with calculations of Payne et al. [40], Yang et al. [41], Hoferichter et al. [43] and with the predictions of Klein–Nystrand [38] (standard and adapted) and Helm [39] form factors.

**Figure 11.**(

**Left**) The CE$\nu $NS cross section on ${}^{40}$Ar as a function of neutrino energy, recent flux–folded measurement by the COHERENT collaboration [5] is shown along with the flux-folded HF–SkE2 prediction. (

**Right**) Flux–averaged CE$\nu $NS cross sections as a function of neutron number for the ${}^{12}$C, ${}^{16}$O, ${}^{40}$Ar, ${}^{56}$Fe and ${}^{208}$Pb nuclei. We also show ${}^{40}$Ar data measured by COHERENT [5].

**Figure 12.**Charged-current (

**left**) and neutral-current (

**right**) inelastic cross section: total as a function of neutrino energy shown along with contributions from different multipoles (top panel), differential as a function of excitation energy (middle panel) and as a function of lepton scattering angle (bottom panel) for fixed neutrino energies, ${E}_{\nu}=$ 30 and 50 MeV.

**Table 1.**Single –particle energies in ${}^{40}$Ar, as provided by a HF calculation using the SkE2 interaction.

$\mathit{p}/\mathit{n}$ | i | ${\mathit{n}}_{\mathit{i}},{\mathit{l}}_{\mathit{i}},{\mathit{j}}_{\mathit{i}}$ | ${\mathit{\epsilon}}_{\mathit{i}}$ (MeV) | ${\mathit{v}}_{\mathit{i}}^{2}$ | # N |
---|---|---|---|---|---|

p | 1 | $1{s}_{1/2}$ | −43.7029 | 1.00 | 2 |

p | 2 | $1{p}_{3/2}$ | −31.4496 | 1.00 | 4 |

p | 3 | $1{p}_{1/2}$ | −27.3921 | 1.00 | 2 |

p | 4 | $1{d}_{5/2}$ | −17.7027 | 1.00 | 6 |

p | 5 | $2{s}_{1/2}$ | −12.0822 | 1.00 | 2 |

p | 6 | $1{d}_{3/2}$ | −10.9243 | 0.50 | 2 |

n | 1 | $1{s}_{1/2}$ | −48.3047 | 1.00 | 2 |

n | 2 | $1{p}_{3/2}$ | −35.2020 | 1.00 | 4 |

n | 3 | $1{p}_{1/2}$ | −31.0247 | 1.00 | 2 |

n | 4 | $1{d}_{5/2}$ | −21.1035 | 1.00 | 6 |

n | 5 | $2{s}_{1/2}$ | −16.1116 | 1.00 | 2 |

n | 6 | $1{d}_{3/2}$ | −14.0266 | 1.00 | 4 |

n | 7 | $1{f}_{7/2}$ | −7.2108 | 0.25 | 2 |

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**MDPI and ACS Style**

Van Dessel, N.; Pandey, V.; Ray, H.; Jachowicz, N.
Cross Sections for Coherent Elastic and Inelastic Neutrino-Nucleus Scattering. *Universe* **2023**, *9*, 207.
https://doi.org/10.3390/universe9050207

**AMA Style**

Van Dessel N, Pandey V, Ray H, Jachowicz N.
Cross Sections for Coherent Elastic and Inelastic Neutrino-Nucleus Scattering. *Universe*. 2023; 9(5):207.
https://doi.org/10.3390/universe9050207

**Chicago/Turabian Style**

Van Dessel, Nils, Vishvas Pandey, Heather Ray, and Natalie Jachowicz.
2023. "Cross Sections for Coherent Elastic and Inelastic Neutrino-Nucleus Scattering" *Universe* 9, no. 5: 207.
https://doi.org/10.3390/universe9050207