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Collaborators: University of Ioannina , Greece:

Fourth Annual ENTApP/WP1 Meeting, ‘‘Physics of Massive Neutrinos, 2008’’ Milos, Cyclades, Greece, May 19 th – 23 rd , 2008.

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Collaborators: University of Ioannina , Greece:

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  1. Fourth Annual ENTApP/WP1 Meeting, ‘‘Physics of Massive Neutrinos, 2008’’ Milos, Cyclades, Greece, May 19th – 23rd, 2008 ‘‘Neutrino-nucleus interactions in Nuclear Structure and Astro-nuclear Physics’’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. Chasioti, K. Balasi, V. Tsakstara, G. Karathanou, K. Kosta 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 neutral and charged-current reactions) are needed for various nuclear isotopes • In the modeling of stellar evolution [Janka et al, PR 442(07)38] 16O, Si, 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) Cobra-Experiment : 116Cd (ii) MOON-Experiment : 92,94,95,96,97,98,100Mo

  3. Outline • Introduction Nuclear Structure Calculations for One-body semi-leptonic nuclear processes (standard & exotic) • ν-NucleusCross Section Formalism Walecka-Donnelly-Haxton (multipole expansion) method • Realistic calculations for ν-N reactions 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 neutrinos (solar, SN, etc.) for :16O,56Fe, 92,94,96,98,100Mo,40Ar, 116Cd • Summary - Conclusions- Outlook

  4. 1-body semi-leptonic electroweak processes in nuclei Walecka-Donnely-Haxtonmethod provides a unified description of semi-leptonic 1-body processes in nuclei 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 like contributions 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) 2). Scattering of Cold Dark Matter particles off nuclei (Direct detection) Χ + (Α, Ζ) χ’ + (Α,Ζ)*

  6. LSP-nucleus elastic (+ inelestic) scattering The Content of the universe: Dark Energy ≈ 74%,Cold Dark Matter ≈ 22%( Atoms ≈ 4% 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. Experimental ambitions for Recoils

  8. 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)

  9. 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

  10. 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-dependentform factors: Fi, i=1, 2, A, as 4. Static parameters, q=0, for nucleon form factors (i) Polar-Vector (i) Axial-Vector

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

  12. 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)

  13. Compact expressions for the 7 basic reduced ME For H.O. bases w-fs, all basic reduced ME take the compact forms The Polynomials of even terms in q have constant coefficients as V.Chasioti,TSK, Czech.J.Phys. 52 (2002)467 Advantages of the above Formalism : • The coefficients PJ are calculated once (reduction of computer time) • They can be used for phenomenological description of ME • They are useful for other bases sets (expansion in HO wave-functions)

  14. RESULTS H.O.size-parameter, b, model space and pairing parameters, n, p pairs for 16O ,40Ar,56Fe,98Mo Particle-hole, gph, and particle-particle gppparameters for16O ,40Ar,56Fe,98Mo

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

  16. State-by-state calculations of multipole contributions to dσ/dΩ 56Fe

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

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

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

  20. 98Mo Angular dependence of the differential cross section for the excited states J=2+, J=3-

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

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

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

  24. Coherent and Incoherent 98Mo

  25. Nuclear response to SN-ν The SN-νspectra spread in an energy of few MeV < Eν< few tenths of MeV) This is the region of nuclear excitations whereG-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)

  26. 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

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

  28. Concluding Remarks • UsingQRPA, we performed state-by-state calculations for Coherent and Incoherent ν–nucleus NC 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 of some nuclei to solar neutrinos and ofthe even-even Mo-isotopesto SN-ν spectra (for the MOON experiment) in the temperature range 2.5 < T < 8 MeV. • Our preliminary results for the CC reaction 56Fe(νe,e-)56Cr are not in good agreement with previous 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.

  29. Reactor-Neutrino Spectra

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

  31. Flux averaged Cross Sectionsfor SN-ν α = 0, 3 2.5 < Τ < 8 (in MeV) A= <σ> V= <σ> 16O

  32. Nuclear response to SN-ν Results of : Toivanen-Kolbe-Langanke-Pinedo-Vogel,Nucl.Phys.A 694(2001)395 2.5 < Τ < 8 α = 0, 3 56Fe

  33. Charged-current reactions (l= e, μ, τ) • Neutral-current reactions Introduction There are four types of ν-nucleus reactions for ν-detection

  34. The seven basic single-particle operators Definite Parity Operators (Normal or Abnormal)

  35. The basic multipole operators The multipole operators, which contain Polar Vector + Axial Vector part, (V – A Theory) are defined as The multipole operators are : Coulomb, Longitudinal, Tranverse-Electric, Transverse-Magnetic for Polar-Vector and Axial-Vector components

  36. Polynomial Coefficients of all basic reduced ME

  37. Multipole Expansion – Tensor Operators The ME of the Effective Hamiltonian reads Apply multipole expansion of Donnely-Walecka[PRC 6 (1972)719, NPA 201(1973)81] in the quantities : For J-projected nuclear states the result is written:

  38. Kinematical factors for neutrino currents Summing over final and averaging over initial spin states gives

  39. Non-relativistic reduction of Hadronic Currents The nuclear current is obtained from that of free nucleons, i.e. The free nucleon currents, in non-relativistic reduction, are written α = + ,-, charged-current processes, 0, neutral-current processes

  40. Detection of WIMPs

  41. Low-lying Nuclear Spectra (up to about 5 MeV) 40Ar experimental theoretical

  42. Coherent and Incoherent 16O

  43. Neutrino energy distribution in Supernova The Energy of emitted neutrinos can be described by Fermi- Dirac type distribution

  44. Convolution of Two Gaussian Functions Convolution of Two Step Functions

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

  46. Total Cross section: Coherent + Incoherent contributions 40Ar

  47. Dominance of Axial-Vector contributions in σ 16O

  48. Dominance of Axial-Vector contributions in σ_tot 40Ar

  49. State-by-state calculations of dσ/dΩ 40Ar

  50. State-by-state calculations of dσ/dΩ 16O

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