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Quasiparticle Random Phase versus the Shell Model and the Double Beta Decay

Quasiparticle Random Phase versus the Shell Model and the Double Beta Decay. Why is VAMPIR better than the Shell Model and QRPA?. K. W. Schmid, Vadim Rodin, Alberto Escuderos and Amand Faessler. O νββ -Decay (forbidden in Standard Model).

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Quasiparticle Random Phase versus the Shell Model and the Double Beta Decay

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  1. Quasiparticle Random Phase versus the Shell Model and the Double Beta Decay Whyis VAMPIR betterthanthe Shell Model and QRPA? K. W. Schmid, Vadim Rodin, Alberto Escuderos and Amand Faessler

  2. Oνββ-Decay (forbidden in Standard Model) only formassive MajoranaNeutrinos  Grand Unified Th. and SUSY ν = νc P P Left ν Phase Space 106x2νββ Left n n NOW Sept. 2008

  3. GRAND UNIFICATION Left-right Symmetric Models SO(10) Majorana Mass: NOW Sept. 2008

  4. Left-Right Symmetric Grand Unified Theory p p e- e- n n L/R l/r W n n P P ν light ν heavy N Neutrinos l/r n l/r n NOW Sept. 2008

  5. Theoretical Description of Nuclei: Vadim Rodin, Fedor Simkovic, Amand Faessler, Saleh Yousef P k 0+ P e2 k 1+ e1 k 2- ν Ek n n Ei 0+ 0+ 0νββ NOW Sept. 2008

  6. The best choice: Quasi-Particle Random Phase Approximation (QRPA) and Shell Model QRPA starts with Pairing: NOW Sept. 2008

  7. Neutrinoless Double Beta- Decay Probability

  8. QRPA and RQRPA with errors from Basis Size, exp. 2-Neutrino Decay, axial Coupling Constant gA = 1.25 and 1.00 and Short Range Correlations ( UCOM + Jastrow) Shell Model Blue points 24 calculations with fit to 2nbb: 3bases*Bonn CD*2gA*2QRPA*2Short RC = 24; Error = highest and lowest value Red triangles: Shell model of Strassburg and Madrid group only 4 to 5 single nucleon levels

  9. Ground State Correlations in QRPAonly Ring Diagrams (0, 4, 8, … q.p.) Time

  10. Excited State in Odd-Odd Nucleus in QRPA only 2, 6, 10, … q.p. States Time

  11. Ground State Correlations in the Shell Model Time

  12. Excited Shell Model States in Odd-Odd Nucleus Time BetaTransition is a One-Body Operator

  13. Shell Model in sd N=2 Oscillator Shell Single Nucleon Oscillator (or Saxon-Woods) Basis States: |i> = ci+ |0> = |p/n, N(ls)jm> = |oscillator nucleon state> Configuration C; JM: 2d 3/2 2s 1/2 2d 5/2 Protons Neutrons

  14. Single Nucleon versus Configuration space • QRPA: large single particle space (five oscillator shells); small configuration space • Shell Model: small single particle space (4 to 5 levels); large configuration space

  15. Shell Model basis: 1f5/2, 2p3/2, 2p1/2, 1g9/2 SM+Spin-Orbit: 1f5/2, 2p3/2, 2p1/2, 1g9/2, 1f7/2, 1g7/2 1f5/2, 2p3/2, 2p1/2, 1g9/2, 1f7/2, 1g7/2, 1d5/2, 1d3/2, 2s1/2 Neutron-Neutron -> Proton-Proton relative

  16. VAMPIR can treat a large Single Nucleon and a large Configuration space. Mister VAMPIR: Karl Wilhelm Schmid Prog. Part. Nucl. Phys. 52(2004) 565-633

  17. Starting point is Hartree-Fock-Bogoliubov i runs over all nucleon states |i> = |p/n; N(ls)jm> : protons, neutrons, different angular momenta, angular momentum projections , different parity.

  18. Restoration of Symmetries: proton number: Z; neutron number: N; total angular momentum: J; projection to the lab axis z: M; (projection to a body fixed axis : K); parity: p ; Determination coefficents A and B and of fK: Min: Projected Hartee-Fock-Bogoliubov

  19. Projection operat. to space orthogonal to F1 , F2 , ….Fm-1 : Solve the Eigenvalue Problem:

  20. TSCM = Truncated Shell Model Strassburg-Madrid: QMCD = Quanten Monte Carlo Diagonalisation of Otsuka about 80 and 160 configurations GCFV = VAMPIR with 2 and 3 configurations (Hjelt, Schmid, Faessler) Exact Shell Model (Poves et al.) with 15 443 648 Configurations in pf-shell (f7/2, p3/2, f5/2, p1/2) NN-force from Alex Brown Single Nucleon Basis: pf Shell

  21. Single particle basis: d5/2, s1/2, d3/2 RV = Real VAMPIR: axial; no p-n mixing; good parity; good T for quasi-particle basis (with real A and B). RM = Real MONSTER = Symmetry projected 2 quasi-particles on 1 determinant VAMPIR (real A,B) CV = Complex (A,B) VAMPIR = single symmetry projected determinant: axial symmetry, good parity, p-n mixing; 1 determinant. 3+: 15 385 GCV = Generalized Complex VAMPIR: no axial symmetry, , no good parity, p/n- mixing; single determinant.

  22. Brückner G matrix of Bonn A nucleon-nucleon force Petrovici, Schmid, Faessler: Nucl. Phys. A665 (2000) 333 74 Kr 74Kr GEV= Generalized Excited VAMPIR. Up to 11 symmetry projected Determinants for each angular momentum. N = 3 and N=4 – (1d3/2 + 2s1/2).

  23. Summary: VAMPIR (Variation After Mean field Projection In Realistic spaces and with realistic forces) allows for a large single particle space like QRPA and for many complicated configurations like the Shell Model. VAMPIR combines the advantages of both for the Double Beta Decay. THE END

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