Relativistic Quasiparticle Random Phase Approximation and β -decay in exotic nuclei .

1. Relativistic Quasiparticle Random Phase Approximation and β-decay in exotic nuclei. Peter Ring Technische Universität München E. Litvinova, T. Marketin, T. Nikšić, N. Paar, and D. Vretenar

2. Study of Nucleosynthesis r process

3. e- _ _ _ _ ν ν ν ν (N,Z)→(N-1,Z+1) e- e- p + (N,Z)→(N+1,Z-1) n spin-isospin-wave e- β-decay electron capture

4. Mean field: Eigenfunctions: Interaction: Density functional theory Density functional theory Slater determinant density matrix Extensions: Pairing correlations, Covariance Relativistic Hartree Bogoliubov (RHB)

5. 1.Relativistic mean-field models with medium- dependent meson-nucleon couplings system of Dirac nucleons. Their interactions can be parameterized by effective meson-exchange (finite range) or contact NN-forces (zero-range). Minimal set of spin-isospin channels included in the effective Lagrangian: + γ (J,T)=(0+,0) (J,T)=(1-,0) (J,T)=(1-,1)

6. ENERGY FUNCTIONAL: Density-dependent meson-nucleon couplings:gσ(ρ), gω(ρ), gρ(ρ) MICROSCOPIC: Dirac-Bruecknercalculations of nucleon self-energies in symmetricand asymmetricnuclear matter PHENOMENOLOGICAL: empirical properties of nuclear matter and finite nuclei (binding energies, charge radii and neutron skins)

7. Effective Lagrangians with density-dependent meson-nucleon vertex functions: improved description of nuclear matter, neutron matter, and isovector static and dynamic properties of finite nuclei. Phys. Rev. C 66, 024306 (2002) Phys. Rev. C 71, 024312 (2005)

8. Relativistic Hartree-Bogoliubov calculations: DD-ME2 + Gogny D1S pairing rms error <900 keV for ~ 200 nuclei Absolute deviations of the calculated binding energies from experimental values: Binding energies, charge isotope shifts and quadrupole deformations of isotopic chains in the rare-earth region. Phys. Rev. C 71, 024312 (2005)

9. TDRMF: Eq. 2. Time dependent mean field theory breathing - mode:

10. the same effective interaction determines the Dirac single-particle spectrum and the residual interaction the Dirac sea is properly taken into account Interaction: QRPA-equations based on HB-theory are solved in the canonical basis Full selfconsistency (current conservations, spurious states, sum rules) Relativistic RPA for excited states RRPA drph, drah Small amplitude limit: ground-state density drhp, drha RRPA matrices:

11. Relativistic (Q)RPA calculations of giant resonances Sn isotopes: DD-ME2 effective interaction + Gogny pairing Isovector dipole response protons neutrons Isoscalar monopole response

12. Isoscalar Giant Monopole Resonances in Sn nuclei R(Q)RPA analysis of compression modes and isovector giant dipole resonances: The compressibility and symmetry energy of nuclear matter: Phys. Rev. C 68, 024310 (2003)

13. 3. Charge-exchange: proton-neutron R(Q)RPA Phys. Rev. C 69, 054303 (2004) The particle-hole residual interaction in the PN-RQRPA is derived from the Lagrangian density:

14. IAR-GTR Spin-Isospin Resonances: IAR - GTR Z+1,N-1 Z,N spin flip s isospin flip t p n

15. The isobaric analog resonance Fermi transition operator: PN-RRPA Jπ=0+response functions. The excitations of the IAR are compared with data. RHB plus proton-neutron RQRPA results for the IAR of the sequence of even-even Sn target nuclei.

16. IMPORTANT:include the T=1 proton-neutron pairing interaction! If the pairing interaction is not isospin invariant Fragmentation of the calculated IAS!

17. The Gamov Teller resonance PN-RPA PARAMETERS: The parameter of the zero-range Landau-Migdal force is adjusted to reproduce the excitation energy of the resonance in 208Pb.

18. Ikeda sum rule 3(N-Z) The running sum of the GTR strength for 208Pb. The PN-RRPA strength distribution of discrete Jπ=1- GT- states.

19. Gamow-Teller strength distribution in118Sn,calculated for different values of the strength parameter of theT=0 pairing interaction: calculated centroids of the direct spin-flip GT strenght GTR configuration splitting

20. The isotopic dependence of the energy spacing between the GTR (centroids of the direct spin-flip GT strength) and IAS for the sequence of even-even112 – 124Sntarget nuclei. The energy difference between the GTR and the IAS reflects the magnitude of the effective spin-orbit potential. Phys. Rev. Lett. 91, 262502 (2003)

21. The energy spacing between theGTRand IAR, as function of the calculated differences between the rmsradii of the neutron andproton density distributions of even-even Sn isotopes. The value of rn – rp can be directly determined from the theoretical curve for a given value of EGT –EIAS

22. β- decay half-lives of r-process nuclei Phys. Rev. C 71, 014308 (2005) RMF effective interactions are characterized by low effective nucleon masses: Dirac mass: effective mass: The energy spacings between spin-orbit partner states in finite nuclei, and the nuclear matterbinding and saturation The calculated β half-lives are more than an order of magnitude longer than the empirical values (e.g. 78Ni).

23. Enhance the nucleon effective mass by reducing the vector self-energy, and at the same time enhance the effective spin orbit-potential by including the tensor coupling of the omega-meson to the nucleon: the spin-orbit part of the effective nucleon potential: Effective int. DD-ME1*: Dirac mass mD= m+ΣS= 0.67m, m*=0.76m T=1 pairing: Gogny D1S T=0 pairing

24. N ~ 50 region Proton-neutron RQRPA calculation DD-ME1* + Gogny D1S int. and Landau-Migdal param. g’0=0.62 without T=0 pairing with T=0 pairing By adjusting the strength of the T=0 pairing interactionto one experimental half-life, the PN-QRPA calculation reproduces the data for a chain of isotopes.

25. N ~ 82 region Proton-neutron RQRPA calculation DD-ME1* + Gogny D1S interaction Landau-Migdal parameter g’0=0.62 without T=0 pairing with T=0 pairing A single value of V0, adjusted to the half-life of 130Cd, reproduces the data in the N~82 region.

26. microcopic origin for enhancment effective mass: Energy dependence of the self energy of the nucleons: a) in infinite nuclear matter b) coupling to surface vibrations

27. DD-ME1 D3C EXP D3C* 4-momentum dependent nucleon self-energies neutrons protons meff 0.660,71 0.791.0 Typel, Chossy, Wolter PRC 67, 34002 (2003) Typel, PDC 71, 64301 (2005)

29. Particle-Vibrational Coupling:energy dependent self-energy surface-modes mean field pole part μ + = + μ single particle strength: non-relativistic investigations: Ring, Werner (1973) Hamamoto, Siemens (1976) Perazzo, Reich, Sofia (1980) Bortignon et al (1980) Bernard, Giai (1980) Platonov (1981) Kamerdzhiev, Tselyaev (1986)

30. Single particle spectrum in the Pb region Single particle spectrum 0.71 0.85 1.0 meff 0.76 0.92 1.0 E. Litvinova and P. Ring, PRC 73, 44328 (2006)

31. The full response contains energy dependent parts coming from vibrational couplings. Self energy ph-phonon amplitudes(QRPA) ph interaction amplitude Width of Giant Resonances

32. E1-pb208 Isovector E1 strength in 208Pb

33. Conclusions: -----Open Problems ------ For astrosphysical applications we need: - nuclear matrix elements - in regions, which are hard or impossible to reach in experiment Density functional theory provides a promising tool: - excellent description of ground state properties - and good description of collective excitations Problems with single particle motion - energy dependence of the self energy important - effective mass in nuclear matter - coupling to collective vibrations