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Joint Annual Meeting of N4 IDEA & N6 ENTAaP/WP1 ‘‘Physics of Masive Neutrinos’’ Blaubeuren, Germany, July 1 – 5, 2007. ‘‘Nuclear response to Supernova neutrinos’’ T.S. Kosmas Division of Theoretical Physics, University of Ioannina , Greece. Collaborators:

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  1. Joint Annual Meeting of N4 IDEA & N6 ENTAaP/WP1 ‘‘Physics of Masive Neutrinos’’ Blaubeuren, Germany, July 1 – 5, 2007 ‘‘Nuclear response to Supernova neutrinos’’T.S. KosmasDivision of Theoretical Physics, University of Ioannina, Greece Collaborators: P. Divari, V. Chasioti, K. Balasi, V. Tsakstara, G. Karathanou, K. Kosta

  2. Outline • Introduction • ν-NucleusCross Section Formalism 1. Donnelly-Walecka (multipole expansion) method 2. Effective ν-Nucleus Interaction Hamiltonian • Resultsof Cross Sections 1. Use of Quasi-particle RPA for Nuclear states 2. Differential, integrated, and total cross sections for the nuclei: 16O,56Fe, 98Mo, 40Ar 3. Nuclear response to SN ν (flux averaged cross sections) • Summary - Conclusions- Outlook

  3. Charged-current reactions (l= e, μ, τ) • Neutral-current reactions Introduction There are four types of neutrino-nucleus reactions to be studied :

  4. 1-body semi-leptonic electroweak processes in nuclei Donnely-Walecka method provides a unified description of semi-leptonic 1-body processes in nuclei

  5. Exotic Semi-leptonic Nuclear Processes 1). LF violating process : Conversion of a bound μ-b toe-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 : • (i) PSI best upper limit on 197Au: Rμe < 10-13 • A.van derShaaf, J.Phys.G 29 (2003)1503 • (ii) MECO at Brookhaven on 27Al upper limit Rμe < 2x 10-17Cancelled • W,Molzon, Springer Tracts in Mod. Phys., • (iii) PRIME at PRISM on 48Ti upper limit Rμe < 10-18 • Y.Kuno, AIP Conf.Proc. 542(2000)220 • d) QRPA for nuclear ME Scwienger,TSK,Faessler, PLB 443(1998)7; TSK,NPA 683(2001)443 • E.Deppisch, TSK, JWF.Walle, NPB 752(2006)80 2). LF + L violating process: Conversion of a μ-b toe+in nuclei μ-b+ (Α, Ζ) e+ + (Α,Ζ-2)* 2-body Process (complicated operator) P.Divari,TSK.,Vergados, NPA

  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 part • Dominance of Axial-Vector contributions • Odd-A nuclear targets : 73Ge, 127I, 115In, 129,131Xe • C) Theoretically: MQPM, SM for : 73Ge, 127I, 115In, 81Ga • TSK, J.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. Semi-leptonic Effective Interaction Hamiltonian The effective interaction Hamiltonian reads Matrix Elements between initial and final Nuclear states are needed for obtaining partial transition rates : (leptonic current ME) (momentum transfer)

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

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

  10. Nuclear Matrix Elements - The Nuclear Model The initial and final states, |Ji>, |Jf>, in the ME <Jf ||T(qr)||Ji>2 are determined by using QRPA j1, j2run over all active single-particle levels(coupled to J) D(j1, j2; J)one-body transition densitiesdetermined by our 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)

  11. 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)

  12. 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

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

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

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

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

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

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

  19. Angular dependence of the differential cross-section 56Fe Chasioti,TSK,Divari,,Prog.Part.Nucl.Phys.in press

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

  21. 98Mo Angular dependence of the differential cross section for the excited states J=2+, J=3-

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

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

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

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

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

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

  28. Coherent and Incoherent 16O

  29. Coherent and Incoherent 98Mo

  30. 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 where Gamow-Teller and Fermi Giant Resonances, and isospin and spin isospin Dipole Resonances play crucial role for nuclear responses. For neutral-current processes, importantGR associated with nuclear responses are : Isospin and isospin-spin resonances with Jπ = 1+ , 1-, etc =================================================================== 98Mo as a SN-νdetector 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)

  31. 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

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

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

  34. 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

  35. SUMMARY-CONCLUSIONS-Outlook • UsingQRPA, we performed state-by-state calculations for inelastic ν–nucleus neutral-current processes (J-projected states) for currently interesting nuclei like: 16O , 40Ar,56Fe, 98Mo •The QRPA method has been tested on the reproducibility of : a) the low-lying nuclear spectrum (up to about 5 MeV) b) the nuclear magnetic moments • Total differential cross sections are evaluated by summing-over-partial-rates. For integrated cross-sections we used numerical integration. • Our results are in good agreement with similar calculations (Kolbe-Langanke, case of 56Fe, and Gent-group, 16O). •We have studied the response of 56Fe and16O nuclei in SN-ν spectra for the range of Temperatures: 2.5 < T < 8 MeVand degeneracy-parameter αvalues: α = 0, 3 • Currently we study the response of 98Mo to SN-ν spectra and alsocharged-current ν–nucleus processes. Acknowledgments: I wish to acknowledge financial support from the ΠΕΝΕΔ-03/807, Hellenic GSRT Project, and ILIAS EU project to participate and speak in this meeting.

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