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Collaborators: University of Ioannina , Greece:

5 th Annual Meeting ENTApP WP1 ‘‘Neutrinos in Particle, in Nuclear and in Astrophysics’’ Trento, Italy, November 17 th – 20 st , 2008.

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Collaborators: University of Ioannina , Greece:

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  1. 5th Annual Meeting ENTApP WP1 ‘‘Neutrinos in Particle, in Nuclear and in Astrophysics’’ Trento, Italy, November 17th – 20st, 2008 ‘‘Charged-current neutrino-nucleus reactionsand their impact to astrophysics’’T.S. KosmasDivision of Theoretical Physics, University of Ioannina, GR-45110, Greece Collaborators: University of Ioannina, Greece: V. Tsikoudi, J. Sinatkas, P. Divari, Th. Liolios, V. Stavrou K. Balasi, V. Tsakstara, G. Karathanou, P. Giannaka, J. Kardaras Univ. of Jyvaskyla, Finland : Group of J. Suhonen T.Univ. of Darmstadt, Germany: Group of J. Wambach Univ. of Tuebingen, Germany :Group of A. Faessler Univ. of Valencia, Spain : Group of J.W.F. Valle RCNP, Univ. of Osaka, Japan : H. Ejiri (MOON-experiment)

  2. Motivation Reliable ν-Nucleus reaction cross sections (for NC and CC reactions) are needed for various nuclear isotopes • In the modeling of stellar evolution [Janka et al, PR 442(07)38] 16O, 32Si, 56Fe, etc. • In terrestrial experiments [H.Ejiri, Phys.Rep. 338 (00)265] • For solar neutrino-detection experiments(Eν < 20 MeV) 115In, 127I, etc. • Supernova neutrino-detection experiments (Eν < 60 -70MeV) • Neutrinoless double-beta-decay experiments (0νββ-decay) (i) MOON-Experiment: 92,94,95,96,97,98,100Mo (ii)Cobra-Experiment: 116Cd

  3. Outline of the talk • Introduction Nuclear Structure Calculations for One-body semi-leptonic nuclear processes (standard & exotic) non-accelerator physics • ν-NucleusCross Section Formalism Walecka-Donnelly-Haxton (multipole expansion) method • Results of realistic calculations for ν-N reactions CC 1. Use of Quasi-Particle RPA and QPM for Nuclear States 2. Differential, integrated and total ν-N cross sections 3. Nuclear response to Astrophysical ν-spectra (solar, SN) for :16O,56Fe, 92,94,96,98,100Mo,40Ar, 116Cd • Summary - Conclusions- Outlook

  4. 1-body semi-leptonic electroweak processes in nuclei A unified description of semi-leptonic 1-body processes in nuclei has been provided long ago (Walecka-Donnely-Haxton method) Standard (observed) 1-body semi-leptonic electroweak processes in nuclei

  5. Exotic 1-body Semi-leptonic Nuclear Processes 1). LF violating process: Conversion of a bound μ-b to e-in nuclei μ-b+ (Α, Ζ) e- + (Α,Ζ)* • a) Coherent (g.s => g.s.) and Incoherent i> => f> transitions occur • b) Both Fermi and Gammow-Teller type transitions exist • Dominance of Coherent channel, ‘measured’ by experiments : • Best upper limits: (i) PSI 197Au Rμe < 10-13 • (ii) MECO (Brookhaven) 27AlRμe < 2x 10-17(Cancelled) • (iii) PRIME (at PRISM) 48TiRμe < 10-18 • Shaaf, J.Phys.G (2003); Kuno, AIP Conf.Proc. (2000); Molzon, Spr. Trac. Mod. Phys., (2000) • Scwienger,Kosmas,Faessler,PLB (1998);Kosmas,NPA (2001);Deppisch,Kosmas,Valle,NPB (2006)

  6. 2). Scattering of Cold Dark Matter particles off nuclei (Direct detection) LSP-nucleus scattering The Content of the universe: Dark Energy ≈ 74%, Atoms ≈ 4% Cold Dark Matter ≈ 22%( Χ + (Α, Ζ) χ’ + (Α,Ζ)* • Coherent - Incoherent event rates : Vector & Axial-Vector Currents • Dominance of Axial-Vector contributions • (Odd-A nuclear targets : 73Ge, 127I, 115In, 129,131Xe) • C) Theoretical study: SM, MQPM, etc. 73Ge, 127I, 115In, 81Ga • Kosmas & Vergados, PRD 55(97)1752, Korteleinen, TSK, Suhonen, Toivanen, PLB 632(2006)226; Holmlund et. al., PLB 584 (2004) 31; Phys.At.Nuc. 67 (2004)1198.

  7. νμ CC Event νeCC Event NC Event Neutrino-nucleus interactions Neutral current (NC) processes (mediated by Z-bozon) Charged-currents processes (mediated by Z-bozon)

  8. Reactor-Neutrino energy-Spectra

  9. Neutrino Supernova energy-spectra The Energy of neutrinos emitted in a core collapse SN can be described by Fermi- Dirac type distribution

  10. Supernova-neutrino spectra α = Chemical Potential T = Neutrino Temperature

  11. Parametrization of SN-v spectra Recent results showed that the SN neutrino energy spectra can be accurately parametrized with a power- law(PL-distibution) <εν >isthe averaged neutrino energy αistheamount of spectral pinching The parameters n and αallow to adjust the width w

  12. Semi-leptonic Effective Interaction Hamiltonian The effective interaction Hamiltonian reads Matrix Elements between initial and final Nuclear states are needed for partial transition rates : (leptonic current ME) (momentum transfer)

  13. Nucleon-level hadronic current for neutrino processes The effective nucleon level Hamiltonian takes the form For charged-current ν-nucleus processes For neutral-current ν-nucleus processes The form factors, for neutral-current processes, are given by

  14. One-nucleon matrix elements of hadronic current 1). Neglecting second class currents : Polar-Vector current: Axial-Vector current: 2). Assuming CVC theory 3). Use dipole-type q-dependent form factors: Fi, i=1, 2, A, as 4. Static parameters, q=0, for nucleon form factors (i) Polar-Vector (i) Axial-Vector

  15. Neutral-Current ν–Nucleus Cross sections In Walecka-Donnely-Haxton method [PRC 6 (1972)719, NPA 201(1973)81] where The Coulomb-Longitudinal (1st sum), and Transverse (2nd sum) are: ==============================================================================================================

  16. Nuclear Matrix Elements - The Nuclear Model The initial and final states, |Ji>, |Jf>, in the ME <Jf ||T(qr)||Ji>2are determined by using QRPA j1, j2run over all active single-particle levels(coupled to J) D(j1, j2; J)one-body transition densitiesdetermined by the model • 1). Interactions: • Woods-Saxon + Coulomb corrections (as Field) • Bonn-C Potential (as two-body interaction) • 2). Parameters: • In the BCS level: the pairing parameters gnpair , gppair • In the QRPA level: the strength parameters gpp,gph • 3). Testing the reliability of the Method: • Low-lying nuclear excitations (up to about 5 MeV) • magnetic moments(separate spin, orbital contributions)

  17. Low-lying Nuclear Spectra (up to about 5 MeV) 98Mo experimental theoretical

  18. State-by-state calculations of multipole contributions to the differential cross section dσ/dΩ 56Fe

  19. State-by-state calculations of dσ/dΩ 98Mo

  20. Angular dependence of the differential cross-section 56Fe Chasioti,TSK,Divari,,Prog.Part.Nucl.Phys.,59(07)481

  21. Angular dependence of the differential cross-section 98Mo

  22. Dominance of Axial-Vector contributions in σ 56Fe

  23. Dominance of Axial-Vector contributions in σ 98Mo

  24. Total Cross section: Coherent & Incoherent contributions 56Fe g.s.g.s. g.s.f_exc

  25. Coherent and Incoherent 98Mo

  26. Results for C-C ν-nucleus reactions • Total cross sections for the CC56Fe(νe,e-)56Co • B) Comparison with CRPA-results byKolbe-Langanke, PRC 55(97)1752

  27. Nuclear response to SN-ν The SN-νenergies are between few MeV < Eν< few tenths of MeV) This is the region of nuclear excitations where G-T and F Giant Resonances, and isospin and spin-isospin Dipole Resonances play crucial role. For NC processes, importantGR associated with nuclear responses are : Isospin and isospin-spin resonances with Jπ = 1+ , 1-, etc Mo-isotopes as SN-νdetectors H. Ejiri, Phys. Rep. 338 (2000)265; H. Ejiri et a., Phys.Lett. B 530 (02)265; H. Ejiri, Proc. MEDEX-07, Prague, June 11-14, 2007. 100Mo is appropriate for ββ-decay and SN-ν (MOON) 98Mo is appropriate for SN-ν (2-3 MeV < Eν < 40-60 MeV)

  28. Nuclear response to SN-νfor various targets Assuming Fermi-Dirac distribution for the SN-νspectra f(Eν) isnormalized to unity as Using our results, we calculated for various ν–nucleus reaction channels the flux-averaged cross sections F2(α) = Normalisation factor α = degeneracy parameter Τ = Neutrino Temperature Eν = neutrino energy

  29. Flux averaged Cross Sections for SN-ν α = 0, 3 2.5 < Τ < 8 (in MeV) A= <σ>_A V= <σ>_V 56Fe

  30. Folded differential cross sections of 98Mo

  31. W.C.Haxton, Phys. Rev,VOL 36,1987

  32. Concluding Remarks • UsingQRPA, we performed state-by-state calculations for ν–nucleus NC and CC processes (J-projected states) for currently interesting nuclei like: 16O , 40Ar,56Fe, Mo-isotopes (MOON exp.), 116Cd (COBRA exp.) •The QRPA method is tested on the reproducibility of : a) the low-lying nuclear spectrum (up to about 5 MeV) b)the nuclear magnetic moments • From the evaluated Differential and Total cross sections we studied the response to solar and SN-ν spectra (even-even Mo-isotopes, MOON experiment, etc.) in the temperature range 2.5 < T < 8 MeV. The power-law distribution is currently used. • Our results for the CC reaction 56Fe(νe,e-)56Cr and 40Ar(νe,e-)40Kr are in good agreement with recent Continuum RPA calculations. Acknowledgments: I wish to acknowledge financial support from ΠΕΝΕΔ-03/807 (Hellenic G.S.R.T.) projects to participate and speak in the present meeting.

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