By means of a Monte Carlo cascade method, to account for the rescattering of the outgoing nucleon, we study the charged and neutral current inclusive one nucleon knockout reactions off nuclei induced by neutrinos. The nucleon emission process studied here is a clear signal for neutralcurrent neutrino driven reactions, and can be used in the analysis of future neutrino experiments.Nieves Pamplona,Juan Miguel, Juan.M.Nieves@ific.uv.es ; 

Vicente Vacas, Manuel Jose, Manuel.J.Vicente@ific.uv.e

Nieves Pamplona, Juan Miguel

Valverde Hermosilla, Manuel

Vicente Vacas, Manuel José

Acta Physica Polonica B

arXiv

Presented by J. Nieves at the XX Max Born Symposium “Nuclear Effects in Neutrino
Interactions”, Wrocław, Poland, December 7–10, 2005.By means of a Monte Carlo cascade method, to account for the rescattering of the outgoing nucleon, we study the charged and neutral current inclusive one nucleon knockout reactions off nuclei induced by neutrinos. The nucleon emission process studied here is a clear signal for neutral-current neutrino driven reactions, and can be used in the analysis of future neutrino experiments.This work was supported by DGI and FEDER funds, contracts BFM2005-00810
and BFM2003-00856, by the EU Integrated Infrastructure Initiative Hadron Physics
Project contract RII3-CT-2004-506078 and by the Junta de Andalucía (FQM-225)

Vicente Vacas, M. J.

Institutional Repository of the University of Granada

Charged and neutral current neutrino induced nucleon emission reactions

Repositorio Institucional Universidad de Granada

Vol. 37 (2006) ACTA PHYSICA POLONICA B No 8CHARGED AND NEUTRAL CURRENT NEUTRINOINDUCED NUCLEON EMISSION REACTIONS∗ ∗∗J. Nieves, M. ValverdeDept. de Física Atómica, Molecular y Nuclear, Universidad de Granada18071 Granada, SpainM.J. Vicente VacasDept. de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSICInstitutos de Investigación de PaternaAptdo. 22085, 46071 Valencia, Spain(Received June 19, 2006)By means of a Monte Carlo cascade method, to account for the rescat-tering of the outgoing nucleon, we study the charged and neutral currentinclusive one nucleon knockout reactions off nuclei induced by neutrinos.The nucleon emission process studied here is a clear signal for neutral-current neutrino driven reactions, and can be used in the analysis of futureneutrino experiments.PACS numbers: 25.30.Pt, 13.15.+g, 24.10.Cn, 21.60.Jz1. Introduction and theoretical frameworkRecently an interest in neutrino scattering off nuclei has raised becauseof its implications in the experiments on neutrino oscillations based on largeCerenkov detectors. The presence of neutrinos, being charge-less particles,can only be inferred by detecting the secondary particles they create whencolliding and interacting with matter. Nuclei are often used as neutrinodetectors, thus a trustable interpretation of neutrino oscillation data heavilyrelies on detailed and quantitative knowledge of the features of the neutrino-nucleus interaction [1]. For instance, in the case of neutrino processes drivenby the electroweak Neutral Current (NC), the energy spectrum and angulardistribution of the ejected nucleons are the unique observables. Besides, thestudy of these distributions might also help to improve on our knowledge of∗ Presented by J. Nieves at the XX Max Born Symposium “Nuclear Effects in NeutrinoInteractions”, Wrocław, Poland, December 7–10, 2005.∗∗ This work was supported by DGI and FEDER funds, contracts BFM2005-00810and BFM2003-00856, by the EU Integrated Infrastructure Initiative Hadron PhysicsProject contract RII3-CT-2004-506078 and by the Junta de Andalucía (FQM-225).(2295)2296 J. Nieves, M. Valverde, M.J. Vicente Vacasthe quark and gluon substructure of the nucleon, and in particular on theamount of nucleon spin carried by strange quarks [2].At intermediate energies, above the nuclear giant resonance and belowthe ∆(1232) regions, neutrino–nucleus interactions have been studied withinseveral approaches. Several different Fermi gas, Random Phase Approxima-tion (RPA) and shell model based calculations have been developed dur-ing the last 15 years [3, 14] to compute neutrino or antineutrino inducedsingle-nucleon emission cross sections. Most of the calculations use the planewave and distorted wave impulse approximations (PWIA and DWIA, respec-tively), including or not relativistic effects. The PWIA constitutes a poorapproximation, since it neglects all types of interactions between the ejectednucleon and the residual nuclear system. The DWIA describes the ejectednucleon as a solution of the Dirac or Schrödinger equation with an opticalpotential obtained by fitting elastic proton–nucleus scattering data. Theimaginary part accounts for the absorption into unobserved channels. Thisscheme is incorrect to study nucleon emission processes where the state ofthe final nucleus is totally unobserved, and thus all final nuclear configura-tions, either in the discrete or on the continuum, contribute. The distortionof the nucleon wave function by a complex optical potential removes allevents where the nucleons collide with other nucleons. Thus, in DWIA cal-culations, the nucleons that interact are lost when in the physical processthey simply come off the nucleus with a different energy, angle, and maybecharge, and they should definitely be taken into account. A clear examplewhich illustrates the deficiencies of the DWIA models is the neutron emis-sion process: (νl, l−n). Within the impulse approximation neutrinos onlyinteract via Charged Current (CC) interactions with neutrons and wouldemit protons, and therefore, the DWIA will predict zero cross sections forCC one neutron knock-out reactions. However, the primary protons inter-act strongly with the medium and collide with other nucleons which are alsoejected. As a consequence there is a reduction of the flux of high energyprotons but a large number of secondary nucleons, many of them neutrons,of lower energies appear.In this talk, we present results for the QE (νl, νlN), (νl, l−N), (ν̄l, ν̄lN)and (ν̄l, l+N) reactions in nuclei. We use a Monte Carlo (MC) simulationmethod to account for the rescattering of the outgoing nucleon. The firststep is the gauge boson (W± and Z0 ) absorption in the nucleus, we take thisreaction probability1 from the microscopical many body framework devel-1 It is given by the inclusive QE cross sections d2σ/dΩ′dE′ (Ω′, E′ are the solid angleand energy of the outgoing lepton), for a fixed incoming neutrino or antineutrinolaboratory (LAB) energy. We also compute differential cross sections with respectto d3r. Thus, we also know the point of the nucleus where the gauge boson wasabsorbed, and we can start from there our MC propagation of the ejected nucleon.Charged and Neutral Current Neutrino Induced Nucleon . . . 2297oped in Refs. [15,16] for CC and NC induced reactions. Starting from a LocalFermi Gas (LFG) picture of the nucleus, which automatically accounts forPauli blocking, several nuclear effects are taken into account in that scheme:(i) a correct energy balance, using the experimental Q-values, is enforced,(ii) Coulomb distortion of the charged leptons is implemented by using theso called “modified effective momentum approximation”, (iii) medium polar-ization (RPA), including ∆-hole degrees of freedom and explicit pion and rhoexchanges in the vector–isovector channel of the effective nucleon–nucleonforce, and Short Range Correlation (SRC) effects are computed, and fi-nally (iv) the nucleon propagators are dressed in the nuclear medium, whichamounts to work with a LFG of interacting nucleons and it also accountsfor reaction mechanisms where the gauge boson, W± or Z0, is absorbedby two nucleons. This model is a natural extension of previous studies onelectron [17], photon [18] and pion [19, 20] dynamics in nuclei and predictsQE neutrino–nucleus (differential and integrated) cross sections with an ac-curacy of about 10–15%, at intermediate energies [21, 22].After the absorption of the gauge boson, we follow the path of the ejectednucleon through its way out of the nucleus using a MC simulation methodto account for the secondary collisions. Details on the MC simulation canbe found in [16]. This MC method was designed for single and multi-ple nucleon and pion emission reactions induced by pions [23, 24] and hasbeen successfully employed to describe inclusive (γ, π), (γ,N), (γ,NN), . . . ,(γ,Nπ), . . . [25,26], (e, e′π), (e, e′N), (e, e′NN), . . . , (e, e′Nπ), . . . [27] reac-tions in nuclei or the neutron and proton spectra from the decay of Λ hyper-nuclei [28]. Thus, we are using a quite robust and well tested MC simulator.2. Results and concluding remarksThe nucleon spectra produced by CC processes induced by muon neutri-nos and antineutrinos of 500MeV are shown in Fig. 1 for argon. Of course,neutrinos only interact via CC with neutrons and would emit protons, butthese primary protons interact strongly with the medium and collide withother nucleons which are also ejected. As a consequence there is a reductionof the flux of high energy protons but a large number of secondary nucleons,many of them neutrons, of lower energies appear. Our cascade model doesnot include the collisions of nucleons with kinetic energies below 30MeV.Thus, the results at those low energies are not meaningful and are shownfor illustrative purposes only in Fig. 1.The flux reduction due to the quasielastic NN interaction can be easilyaccommodated in optical potential calculations. However, in those calcula-tions the nucleons that interact are lost when in the physical process theysimply come off the nucleus with a different energy and angle, and may becharge, and they must be taken into account.2298 J. Nieves, M. Valverde, M.J. Vicente Vacasno rescatt.rescatt.Eν = 500 MeVνµ+40Ar → µ− + p + XTp [MeV]1040dσ/dTp[cm2/MeV]4003503002502001501005002520151050no rescatt.rescatt.Eν = 500 MeVνµ+40Ar → µ− + n + XTn [MeV]1040dσ/dTn[cm2/MeV]40035030025020015010050020181614121086420no rescatt.rescatt.Eν = 500 MeVν̄µ+40Ar → µ+ + p + XTp [MeV]1040dσ/dTp[cm2/MeV]40035030025020015010050043.532.521.510.50no rescatt.rescatt.Eν = 500 MeVν̄µ+40Ar → µ+ + n + XTn [MeV]1040dσ/dTn[cm2/MeV]40035030025020015010050076543210Fig. 1. Charged current 40Ar(νµ, µ− + N) (upper panels) and 40Ar(ν̄µ, µ+ + N)(lower panels) cross sections as a function of the kinetic energy of the final nucleonfor an incoming neutrino or antineutrino energy of 500 MeV. Left and right panelscorrespond to the emission of protons and neutrons, respectively. The dashedhistogram shows results without nucleon rescattering; the solid one the full model.no rescatt.rescat.Eν = 500 MeVν+40Ar → ν + p + XTp [MeV]1040dσ/dTp[cm2/MeV]400350300250200150100501.81.61.41.210.80.60.40.20no rescatt.rescat.Eν = 500 MeVν+40Ar → ν + n + XTn [MeV]1040dσ/dTn[cm2/MeV]400350300250200150100502.521.510.50no rescatt.rescat.Eν = 150 MeVν+40Ar → ν + p + XTp [MeV]1040dσ/dTp[cm2/MeV]1401201008060400.350.30.250.20.150.10.050no rescatt.rescat.Eν = 150 MeVν+40Ar → ν + n + XTn [MeV]1040dσ/dTn[cm2/MeV]1401201008060400.40.350.30.250.20.150.10.050Fig. 2. Neutral current 40Ar(ν, ν + N) at 500 MeV (upper panels) and 150 MeV(lower panels) cross sections as a function of the kinetic energy of the final nucleon.Left and right panels correspond to the emission of protons and neutrons, respec-tively. The dashed histogram shows results without rescattering; the solid one thefull model.Charged and Neutral Current Neutrino Induced Nucleon . . . 2299The energy distributions of nucleons emitted after a NC interaction areshown in Figs. 2 and 3. In Fig. 2, we show the results for 40Ar at twodifferent energies. In both cases we find the large effect of the rescatteringof the nucleons. For 500MeV neutrinos the rescattering of the outgoingnucleon produces a depletion of the higher energies side of the spectrum,but the scattered nucleons clearly enhance the low energies region. Forlower neutrino energies, most of the nucleons coming from nucleon nucleoncollisions would show up at energies below the 30MeV cut.no rescatt.rescatt.Eν = 500 MeVν+16O → ν + p + XTp [MeV]1040dσ/dTp[cm2/MeV]400350300250200150100500.80.70.60.50.40.30.20.10no rescatt.rescatt.Eν = 500 MeVν+16O → ν + n + XTn [MeV]1040dσ/dTn[cm2/MeV]400350300250200150100500.80.70.60.50.40.30.20.10no rescatt.rescatt.Eν = 150 MeVν+16O → ν + p + XTp [MeV]1040dσ/dTp[cm2/MeV]1401201008060400.180.160.140.120.10.080.060.040.020no rescatt.rescatt.Eν = 150 MeVν+16O → ν + n + XTn [MeV]1040dσ/dTn[cm2/MeV]1401201008060400.140.120.10.080.060.040.020Fig. 3. Same as Fig. 2 for oxygen.As expected, the rescattering effect is smaller in lighter nuclei as canbe seen in Fig. 3 for oxygen. In all cases the final spectra of protons andneutrons are very similar.no rescatt.rescatt.gsA = 0.0gsA = -0.19Eν = 150 MeVν+40Ar → ν + N + XTN [MeV](dσ/dTp)/(dσ/dTn)9080706050403032.521.510.50no rescatt.rescatt.gsA = 0.0gsA = -0.19Eν = 500 MeVν+40Ar → ν + N + XTN [MeV](dσ/dTp)/(dσ/dTn)300250200150100501.21.110.90.80.70.60.50.40.3Fig. 4. Ratio of dσ/dE for protons over that for neutrons for Eν = 150 MeV andEν = 500 MeV in the reaction ν+40Ar→ ν′ + N + X as a function of the nucleonkinetic energy. Dashed histogram: without nucleon rescattering. Solid histogram:full model.2300 J. Nieves, M. Valverde, M.J. Vicente VacasThe ratio of proton to neutron QE cross section could be very sensitiveto the strange quark axial form factor of the nucleon, and thus to the gsAparameter [3, 4, 6, 11]. The sensitivity to the collisions of the final nucleonsis larger for both heavier nuclei and for larger energies of the neutrinos. InFig. 4, one can clearly appreciate the importance of the secondary nucleonsat the low energies side of the spectrum.REFERENCES[1] Proceedings of the RCCN International Workshop On Sub-dominant Oscilla-tion Effects in Atmospheric Neutrino Experiments Kashiwa, 2004, Eds. T. Ka-jita and K. Okumura, Universal Academy Press, Inc. Tokyo, Japan.[2] FINeSSe Collaboration, L. Bugel et al., hep-ex/0402007; S.F. Pate, Eur.Phys. J. A24S2, 67 (2005).[3] G.T. Garvey, S. Krewald, E. Kolbe, K. Langanke, Phys. Lett. B289, 249(1992); G. Garvey, E. Kolbe, K. Langanke, S. Krewald, Phys. Rev. C48, 1919(1993).[4] C.J. Horowitz, H.C. Kim, D.P. Murdock, S. Pollock, Phys. Rev. C48, 3078(1993).[5] S.L. Mintz, M. Pourkaviani, Nucl. Phys. A594, 346 (1995).[6] W.M. Alberico, M.B. Barbaro, S.M. Bilenky, J.A. Caballero, C. Giunti,C. Maieron, E. Moya de Guerra, J.M. Udías, Nucl. Phys. A623, 471 (1997);Phys. Lett. B438, 9 (1998); Nucl. Phys. A651, 277 (1999).[7] C. Volpe, N. Auerbach, G. Colo, T. Suzuki, N. Van Giai, Phys. Rev. C62,015501 (2000).[8] C. Bleve, G. Co’, I. De Mitri, P. Bernardini, G. Mancarella, D. Martello,A. Surdo, Astropart. Phys. 16, 145 (2001).[9] C. Maieron, M.C. Martinez, J.A. Caballero, J.M. Udias, Phys. Rev. C68,048501 (2003).[10] A. Meucci, C. Giusti, F.D. Pacati, Nucl. Phys. A739, 277 (2004); A. Meucci,C. Giusti, F.D. Pacati, Nucl. Phys. A744, 307 (2004).[11] B.I.S. van der Ventel, J. Piekarewicz, Phys. Rev. C69, 035501 (2004).[12] N. Jachowicz, K. Vantournhout, J. Ryckebusch, K. Heyde, Phys. Rev. Lett.93, 082501 (2004).[13] M.C. Martinez, P. Lava, N. Jachowicz, J. Ryckebusch, K. Vantournhout,J.M. Udias, Phys. Rev. C73, 024607 (2006).[14] K.M. Graczyk, J.T. Sobczyk, Eur. Phys. J. C31, 177 (2003); C. Juszczak,J.A. Nowak, J.T. Sobczyk, Eur. Phys. J. C39, 195 (2005).[15] J. Nieves, J.E. Amaro, M. Valverde, Phys. Rev. C70, 055503 (2004); ErratumPhys. Rev. C72, 019902 (2005).[16] J. Nieves, M. Valverde, M.J. Vicente Vacas, Phys. Rev. C73, 025504 (2006).Charged and Neutral Current Neutrino Induced Nucleon . . . 2301[17] A. Gil, J. Nieves, E. Oset, Nucl. Phys. A627, 543 (1997).[18] R.C. Carrasco, E. Oset, Nucl. Phys. A536, 445 (1992).[19] E. Oset, H. Toki, W. Weise, Phys. Rep. 83, 281 (1982).[20] J. Nieves, E. Oset, C. García-Recio, Nucl. Phys. A554, 509 (1993); Nucl.Phys. A554, 554 (1993); J. Nieves, E. Oset, Phys. Rev. C47, 1478 (1993);E. Oset, P. Fernández de Córdoba, J. Nieves, A. Ramos, L.L. Salcedo, Prog.Theor. Phys. Suppl. 117, 461 (1994); C. Albertus, J.E. Amaro, J. Nieves,Phys. Rev. Lett. 89, 032501 (2002); Phys. Rev. C67, 034604 (2003).[21] M. Valverde, J.E. Amaro, J. Nieves, hep-ph/0604042.[22] J.E. Amaro, A.M. Lallena, J. Nieves, Nucl. Phys. A623, 529 (1997);J.E. Amaro, C. Maieron, J. Nieves, M. Valverde, Eur. Phys. J. A24, 343(2005).[23] L.L. Salcedo, E. Oset, M.J. Vicente Vacas, C. García Recio, Nucl. Phys. A484,557 (1988).[24] M.J. Vicente Vacas, E. Oset, Nucl. Phys. A568, 855 (1994).[25] R.C. Carrasco, E. Oset, L.L. Salcedo, Nucl. Phys. A541, 585 (1992).[26] R.C. Carrasco, M.J. Vicente Vacas, E. Oset, Nucl. Phys. A570, 701 (1994).[27] A. Gil, J. Nieves, E. Oset, Nucl. Phys. A627, 599 (1997).[28] A. Ramos, M.J. Vicente Vacas, E. Oset, Phys. Rev. C55, 735 (1997), ErratumC66, 039903 (2002).

English

By means of a Monte Carlo cascade method, to account for the rescattering of the outgoing nucleon, we study the charged and neutral current inclusive one nucleon knockout reactions off nuclei induced by neutrinos. The nucleon emission process studied here is a clear signal for neutralcurrent neutrino driven reactions, and can be used in the analysis of future neutrino experiments

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

Vol. 37 (2006) ACTA PHYSICA POLONICA B No 8CHARGED AND NEUTRAL CURRENT NEUTRINOINDUCED NUCLEON EMISSION REACTIONS∗ ∗∗J. Nieves, M. ValverdeDept. de Física Atómica, Molecular y Nuclear, Universidad de Granada18071 Granada, SpainM.J. Vicente VacasDept. de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSICInstitutos de Investigación de PaternaAptdo. 22085, 46071 Valencia, Spain(Received June 19, 2006)By means of a Monte Carlo cascade method, to account for the rescat-tering of the outgoing nucleon, we study the charged and neutral currentinclusive one nucleon knockout reactions off nuclei induced by neutrinos.The nucleon emission process studied here is a clear signal for neutral-current neutrino driven reactions, and can be used in the analysis of futureneutrino experiments.PACS numbers: 25.30.Pt, 13.15.+g, 24.10.Cn, 21.60.Jz1. Introduction and theoretical frameworkRecently an interest in neutrino scattering off nuclei has raised becauseof its implications in the experiments on neutrino oscillations based on largeCerenkov detectors. The presence of neutrinos, being charge-less particles,can only be inferred by detecting the secondary particles they create whencolliding and interacting with matter. Nuclei are often used as neutrinodetectors, thus a trustable interpretation of neutrino oscillation data heavilyrelies on detailed and quantitative knowledge of the features of the neutrino-nucleus interaction [1]. For instance, in the case of neutrino processes drivenby the electroweak Neutral Current (NC), the energy spectrum and angulardistribution of the ejected nucleons are the unique observables. Besides, thestudy of these distributions might also help to improve on our knowledge of∗ Presented by J. Nieves at the XX Max Born Symposium “Nuclear Effects in NeutrinoInteractions”, Wrocław, Poland, December 7–10, 2005.∗∗ This work was supported by DGI and FEDER funds, contracts BFM2005-00810and BFM2003-00856, by the EU Integrated Infrastructure Initiative Hadron PhysicsProject contract RII3-CT-2004-506078 and by the Junta de Andalucía (FQM-225).(2295)2296 J. Nieves, M. Valverde, M.J. Vicente Vacasthe quark and gluon substructure of the nucleon, and in particular on theamount of nucleon spin carried by strange quarks [2].At intermediate energies, above the nuclear giant resonance and belowthe ∆(1232) regions, neutrino–nucleus interactions have been studied withinseveral approaches. Several different Fermi gas, Random Phase Approxima-tion (RPA) and shell model based calculations have been developed dur-ing the last 15 years [3, 14] to compute neutrino or antineutrino inducedsingle-nucleon emission cross sections. Most of the calculations use the planewave and distorted wave impulse approximations (PWIA and DWIA, respec-tively), including or not relativistic effects. The PWIA constitutes a poorapproximation, since it neglects all types of interactions between the ejectednucleon and the residual nuclear system. The DWIA describes the ejectednucleon as a solution of the Dirac or Schrödinger equation with an opticalpotential obtained by fitting elastic proton–nucleus scattering data. Theimaginary part accounts for the absorption into unobserved channels. Thisscheme is incorrect to study nucleon emission processes where the state ofthe final nucleus is totally unobserved, and thus all final nuclear configura-tions, either in the discrete or on the continuum, contribute. The distortionof the nucleon wave function by a complex optical potential removes allevents where the nucleons collide with other nucleons. Thus, in DWIA cal-culations, the nucleons that interact are lost when in the physical processthey simply come off the nucleus with a different energy, angle, and maybecharge, and they should definitely be taken into account. A clear examplewhich illustrates the deficiencies of the DWIA models is the neutron emis-sion process: (νl, l−n). Within the impulse approximation neutrinos onlyinteract via Charged Current (CC) interactions with neutrons and wouldemit protons, and therefore, the DWIA will predict zero cross sections forCC one neutron knock-out reactions. However, the primary protons inter-act strongly with the medium and collide with other nucleons which are alsoejected. As a consequence there is a reduction of the flux of high energyprotons but a large number of secondary nucleons, many of them neutrons,of lower energies appear.In this talk, we present results for the QE (νl, νlN), (νl, l−N), (ν¯l, ν¯lN)and (ν¯l, l+N) reactions in nuclei. We use a Monte Carlo (MC) simulationmethod to account for the rescattering of the outgoing nucleon. The firststep is the gauge boson (W± and Z0 ) absorption in the nucleus, we take thisreaction probability1 from the microscopical many body framework devel-1 It is given by the inclusive QE cross sections d2σ/dΩ′dE′ (Ω′, E′ are the solid angleand energy of the outgoing lepton), for a fixed incoming neutrino or antineutrinolaboratory (LAB) energy. We also compute differential cross sections with respectto d3r. Thus, we also know the point of the nucleus where the gauge boson wasabsorbed, and we can start from there our MC propagation of the ejected nucleon.Charged and Neutral Current Neutrino Induced Nucleon . . . 2297oped in Refs. [15,16] for CC and NC induced reactions. Starting from a LocalFermi Gas (LFG) picture of the nucleus, which automatically accounts forPauli blocking, several nuclear effects are taken into account in that scheme:(i) a correct energy balance, using the experimental Q-values, is enforced,(ii) Coulomb distortion of the charged leptons is implemented by using theso called “modified effective momentum approximation”, (iii) medium polar-ization (RPA), including ∆-hole degrees of freedom and explicit pion and rhoexchanges in the vector–isovector channel of the effective nucleon–nucleonforce, and Short Range Correlation (SRC) effects are computed, and fi-nally (iv) the nucleon propagators are dressed in the nuclear medium, whichamounts to work with a LFG of interacting nucleons and it also accountsfor reaction mechanisms where the gauge boson, W± or Z0, is absorbedby two nucleons. This model is a natural extension of previous studies onelectron [17], photon [18] and pion [19, 20] dynamics in nuclei and predictsQE neutrino–nucleus (differential and integrated) cross sections with an ac-curacy of about 10–15%, at intermediate energies [21, 22].After the absorption of the gauge boson, we follow the path of the ejectednucleon through its way out of the nucleus using a MC simulation methodto account for the secondary collisions. Details on the MC simulation canbe found in [16]. This MC method was designed for single and multi-ple nucleon and pion emission reactions induced by pions [23, 24] and hasbeen successfully employed to describe inclusive (γ, pi), (γ,N), (γ,NN), . . . ,(γ,Npi), . . . [25,26], (e, e′pi), (e, e′N), (e, e′NN), . . . , (e, e′Npi), . . . [27] reac-tions in nuclei or the neutron and proton spectra from the decay of Λ hyper-nuclei [28]. Thus, we are using a quite robust and well tested MC simulator.2. Results and concluding remarksThe nucleon spectra produced by CC processes induced by muon neutri-nos and antineutrinos of 500MeV are shown in Fig. 1 for argon. Of course,neutrinos only interact via CC with neutrons and would emit protons, butthese primary protons interact strongly with the medium and collide withother nucleons which are also ejected. As a consequence there is a reductionof the flux of high energy protons but a large number of secondary nucleons,many of them neutrons, of lower energies appear. Our cascade model doesnot include the collisions of nucleons with kinetic energies below 30MeV.Thus, the results at those low energies are not meaningful and are shownfor illustrative purposes only in Fig. 1.The flux reduction due to the quasielastic NN interaction can be easilyaccommodated in optical potential calculations. However, in those calcula-tions the nucleons that interact are lost when in the physical process theysimply come off the nucleus with a different energy and angle, and may becharge, and they must be taken into account.2298 J. Nieves, M. Valverde, M.J. Vicente Vacasno rescatt.rescatt.Eν = 500 MeVνµ+40Ar → µ− + p +XTp [MeV]1040dσ/dTp[cm2/MeV]4003503002502001501005002520151050no rescatt.rescatt.Eν = 500 MeVνµ+40Ar → µ− + n+XTn [MeV]1040dσ/dTn[cm2/MeV]40035030025020015010050020181614121086420no rescatt.rescatt.Eν = 500 MeVν¯µ+40Ar → µ+ + p+XTp [MeV]1040dσ/dTp[cm2/MeV]40035030025020015010050043.532.521.510.50no rescatt.rescatt.Eν = 500 MeVν¯µ+40Ar → µ+ + n+XTn [MeV]1040dσ/dTn[cm2/MeV]40035030025020015010050076543210Fig. 1. Charged current 40Ar(νµ, µ− + N) (upper panels) and 40Ar(ν¯µ, µ+ + N)(lower panels) cross sections as a function of the kinetic energy of the final nucleonfor an incoming neutrino or antineutrino energy of 500MeV. Left and right panelscorrespond to the emission of protons and neutrons, respectively. The dashedhistogram shows results without nucleon rescattering; the solid one the fullmodel.no rescatt.rescat.Eν = 500 MeVν+40Ar → ν + p+XTp [MeV]1040dσ/dTp[cm2/MeV]400350300250200150100501.81.61.41.210.80.60.40.20no rescatt.rescat.Eν = 500 MeVν+40Ar → ν + n+XTn [MeV]1040dσ/dTn[cm2/MeV]400350300250200150100502.521.510.50no rescatt.rescat.Eν = 150 MeVν+40Ar → ν + p+XTp [MeV]1040dσ/dTp[cm2/MeV]1401201008060400.350.30.250.20.150.10.050no rescatt.rescat.Eν = 150 MeVν+40Ar → ν + n +XTn [MeV]1040dσ/dTn[cm2/MeV]1401201008060400.40.350.30.250.20.150.10.050Fig. 2. Neutral current 40Ar(ν, ν + N) at 500MeV (upper panels) and 150MeV(lower panels) cross sections as a function of the kinetic energy of the final nucleon.Left and right panels correspond to the emission of protons and neutrons, respec-tively. The dashed histogram shows results without rescattering; the solid one thefull model.Charged and Neutral Current Neutrino Induced Nucleon . . . 2299The energy distributions of nucleons emitted after a NC interaction areshown in Figs. 2 and 3. In Fig. 2, we show the results for 40Ar at twodifferent energies. In both cases we find the large effect of the rescatteringof the nucleons. For 500MeV neutrinos the rescattering of the outgoingnucleon produces a depletion of the higher energies side of the spectrum,but the scattered nucleons clearly enhance the low energies region. Forlower neutrino energies, most of the nucleons coming from nucleon nucleoncollisions would show up at energies below the 30MeV cut.no rescatt.rescatt.Eν = 500 MeVν+16O → ν + p+XTp [MeV]1040dσ/dTp[cm2/MeV]400350300250200150100500.80.70.60.50.40.30.20.10no rescatt.rescatt.Eν = 500 MeVν+16O → ν + n +XTn [MeV]1040dσ/dTn[cm2/MeV]400350300250200150100500.80.70.60.50.40.30.20.10no rescatt.rescatt.Eν = 150 MeVν+16O → ν + p+XTp [MeV]1040dσ/dTp[cm2/MeV]1401201008060400.180.160.140.120.10.080.060.040.020no rescatt.rescatt.Eν = 150 MeVν+16O → ν + n +XTn [MeV]1040dσ/dTn[cm2/MeV]1401201008060400.140.120.10.080.060.040.020Fig. 3. Same as Fig. 2 for oxygen.As expected, the rescattering effect is smaller in lighter nuclei as canbe seen in Fig. 3 for oxygen. In all cases the final spectra of protons andneutrons are very similar.no rescatt.rescatt.gsA = 0.0gsA = -0.19Eν = 150 MeVν+40Ar → ν +N +XTN [MeV](dσ/dTp)/(dσ/dTn)9080706050403032.521.510.50no rescatt.rescatt.gsA = 0.0gsA = -0.19Eν = 500 MeVν+40Ar → ν +N +XTN [MeV](dσ/dTp)/(dσ/dTn)300250200150100501.21.110.90.80.70.60.50.40.3Fig. 4. Ratio of dσ/dE for protons over that for neutrons for Eν = 150MeV andEν = 500MeV in the reaction ν+40Ar→ ν′ +N +X as a function of the nucleonkinetic energy. Dashed histogram: without nucleon rescattering. Solid histogram:full model.2300 J. Nieves, M. Valverde, M.J. Vicente VacasThe ratio of proton to neutron QE cross section could be very sensitiveto the strange quark axial form factor of the nucleon, and thus to the gsAparameter [3, 4, 6, 11]. The sensitivity to the collisions of the final nucleonsis larger for both heavier nuclei and for larger energies of the neutrinos. 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Charged and neutral current neutrino induced nucleon emission reactions

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