QRPA Calculations of Charge Exchange Reactions and Weak Interaction Rates. N. Paar

Transcription

1 Strong, Weak and Electromagnetic Interactions to probe Spin-Isospin Excitations ECT*, Trento, 28 September - 2 October 2009 QRPA Calculations of Charge Exchange Reactions and Weak Interaction Rates N. Paar Physics Department Faculty of Science University of Zagreb Croatia

2 OUTLINE 1. Self-consistent charge-exchange QRPA QRPA based on Skyrme interactions relativistic QRPA based on effective Lagrangians charge-exchange excitations finite temperature RPA 2. Weak interaction rates of lepton absorption in nuclei neutrino induced reactions electron capture muon capture

3 Kolbe, Langanke, Martinez-Pinedo, Phys. Rev. C 60, (1999). SHELL MODEL Strasbourg-Madrid codes by Caurier et al. Gamow-Teller strength (with quenching factor) ( + rescaled by a factor to account finite momentum transfer) Occupation numbers CONTINUUM RPA GROUND STATE: Woods-Saxon potential fitted to single-particle energies forbidden transitions RPA RESIDUAL INTERACTION: G-matrix from Bonn potential or zero-range Landau Migdal force excitations, electron capture, beta decay, neutrino capture,...

4 RELATIVISTIC HARTREE-BOGOLIUBOV MODEL (RHB) + RELATIVISTIC QUASIPARTICLE RPA (RQRPA) BOTH THE GROUND STATE EQUATIONS & RESIDUAL QRPA INTERACTION ARE DERIVED FROM THE SAME EFFECTIVE LAGRANGIAN DENSITY PAIRING CORRELATIONS ARE DESCRIBED BY THE FINITE RANGE GOGNY FORCE excitations, electron capture, beta decay, neutrino capture,...

5 1. SELF-CONSISTENT CHARGE-EXCHANGE QRPA OBJECTIVES: - description of charge-exchange excitations based on quasiparticle random phase approximation (QRPA) - QRPA based on various effective nuclear interactions (Skyrme, RMF,...) - Isobaric analogue resonances, Gamow-Teller resonances,... - excitations in nuclei at finite temperature - FTRPA REFERENCES: N. Paar, T. Niksic, D. Vretenar and P. Ring, Phys. Rev. C 69, (2004) S. Fracasso and G. Colo, Phys. Rev. C 72, (2005) N. Paar, D. Vretenar, E. Khan, and G. Colo, Rep. Prog. Phys. 70, 691 (2007) Y. F. Niu, N. Paar, D. Vretenar, and J. Meng, submitted to Phys. Lett. B (2009) nucl-th/arxiv:

6 Charge-exchange QRPA based on Skyrme interactions Fully self-consistent charge-exchange QRPA S. Fracasso and G. Colo, Phys. Rev. C 72, (2005) Includes pairing correlations QRPA equations

7 Charge-exchange QRPA based on Skyrme interactions Excitation energies of Isobaric analogue resonances in Sn isotope chain QRPA transition strength for the isospin-flip operator (IAR) S. Fracasso and G. Colo, Phys. Rev. C 72, (2005)

8 Charge-exchange QRPA based on Skyrme interactions Gamow-Teller resonances with various Skyrme parameterisations Isotopic dependence of the GTR excitation energy S. Fracasso and G. Colo, Phys. Rev. C 72, (2005)

9 RELATIVISTIC MEAN FIELD THEORY system of Dirac nucleons coupled to the exchange mesons and the photon field through an effective Lagrangian. (J π,t)=(0 +,0) (J π,t)=(1 -,0) (J π,t)=(1 -,1) Sigma-meson: attractive scalar field Omega-meson: shortrange repulsive field Rho-meson: isovector field

10 LAGRANGIAN DENSITY the Lagrangian of the free nucleon: the Lagrangian of the free meson fields and the electromagnetic field: minimal set of interaction terms: with the vertices:

11 MODELS WITH DENSITY DEPENDENT COUPLINGS Model parameters: meson masses + parameters of vertex functions - a mean-field model does not contain explicit correlation effects The parameters are determined from properties of nuclear matter (symmetric and asymmetric) and bulk properties of finite nuclei (binding energies, charge radii, neutron skin, surface thickness ) A least-squares adjustment to empirical nuclear matter properties and experimental data on ground-state properties of spherical nuclei, contains only eight (8) parameters in the general expansion of an effective Lagrangian

12 PROTON-NEUTRON RELATIVISTIC QUASIPARTICLE RPA Derived from the time-dependent RHB equation in the limit of small oscillations around the RHB ground state generalized density

13 PROTON-NEUTRON RELATIVISTIC QUASIPARTICLE RPA

14 ISOBARIC ANALOGUE RESONANCES

15 GAMOW-TELLER RESONANCES WITH PN PAIRING GAMOW-TELLER RESONANCE AND T=0 pn PAIRING direct spin-flip (GTR) core polarisation back spin-flip

16 Gamow-Teller strength distribution for 56 Fe

17 SPIN-ISOSPIN RESONANCES AND NEUTRON SKIN The isotopic dependence of the energy spacings between the GTR and IAS Proton-neutron RQRPA calculation DD-ME1 + Gogny-type pairing Landau-Migdal g 0 =0.55 direct information on the evolution of the neutron skin thickness along the Sn isotopic chain

18 RELATIVISTIC RPA AT FINITE TEMPERATURE The initial nuclear state of hot nucleus is described by the finite temperature RMF Due to finite temperature, some particle states become partially occupied, some hole states too Equation of motion: for states in the Fermi sea for unoccupied states in the Dirac sea Y. F. Niu, N. Paar, D. Vretenar, J. Meng, nucl-th/arxiv: (2009)

19 RELATIVISTIC RPA AT FINITE TEMPERATURE

20 RELATIVISTIC RPA AT FINITE TEMPERATURE the normalization and orthogonality relation the transition strength function the convergence test for the transition strength with number of oscillator shells N f =16-30

21 MONOPOLE AND DIPOLE RESPONSE AT FINITE TEMPERATURE with increased temperature new low-lying transitions appear both in monopole and dipole response Pygmy dipole resonance becomes more distributed toward lower energies

22 ISOVECTOR DIPOLE RESPONSE AT FINITE TEMPERATURE In some cases ( 60 Ni, 62 Ni), new pygmy strength can appear at finite temperature (at energies without any transitions at zero temperature)

23 GAMOW TELLER EXCITATIONS AT FINITE TEMPERATURE FTRRPA SLy5 RELATIVISTIC RPA (DD-ME2) NON-RELATIVISTIC RPA (SLy5)

24 GT + EXCITATIONS AT FINITE TEMPERATURE FTRRPA SLy5 FTRRPA SLy5

25 GAMOW-TELLER EXCITATIONS AT FINITE TEMPERATURE

26 2. WEAK INTERACTION RATES OF LEPTON ABSORPTION IN NUCLEI OBJECTIVES: - description of weak interaction of leptons with nuclei by using self-consistent theory of nuclear structure (based on QRPA) - neutrino-nucleus reactions (exp. & supernova neutrinos), neutrino detectors - muon capture, electron capture and beta decays of relevance for astrophysics, REFERENCES: N. Paar, D. Vretenar, T. Marketin, and P. Ring, Phys. Rev. C 77, (2008) T. Marketin, N. Paar, T. Niksic, and D. Vretenar, Phys. Rev. C 79, (2009) N. Paar, G. Colo, E. Khan, and D. Vretenar, nucl-th/arxiv: (2009)

27 WEAK INTERACTIONS IN NUCLEI Neutrino reactions Charged-lepton capture (muon and electron capture) Relevant input from the theory of nuclear structure ground state and excitations at finite momentum transfer

28 NEUTRINO-NUCLEUS REACTIONS Energy conservation and momentum transfer: neutrino-nucleus cross section Hamiltonian for the weak interaction transition nuclear matrix elements (assuming plane waves for leptons)

29 NEUTRINO-NUCLEUS CROSS SECTIONS Transverse magnetic & Transverse electric multipole operators Coulomb & longitudinal multipole operators Transition matrix elements include the nuclear structure properties (ground state, excitations)

30 Reduced matrix elements for the neutrinonucleus cross section: RQRPA amplitudes RHB occupation probabilities Coulomb correction due to effect of nuclear charge on outgoing lepton: Effective momentum approximation: Fermi function: V c,eff

31 ELECTRON (ANTI)NEUTRINO- 12 C CROSS SECTIONS C! "e [10-40 cm 2 ] (" e,e - ) _ (" e,e + ) E "e [MeV] Weak interaction absorption of neutrino and antineutrino Contributions to the cross sections from excitations of various multipolarity

32 ν e -NUCLEUS CROSS SECTIONS AVERAGED OVER NEUTRINO FLUX ν e FLUX EXP. Experimental flux of neutrinos obtained from µ + decay at rest g A =1.262 g A =1.135

33 IRON TARGET 56 Fe(ν e,e - ) 56 Co <σ>(10-42 cm 2 ) QRPA(SGII) (Lazauskas 2007) 352 PN-RQRPA (g A =1.262) 360 PN-RQRPA (g A =1.135) 330 PN-RQRPA (g A =1.0) 257 EXP. (KARMEN) 256±108±43

34 DISTRIBUTION OF CROSS SECTIONS OVER MULTIPOLARITIES RHB+RQRPA QRPA (Skyrme SIII) Lazauskas, Volpe GT, spin-dipole, and excitations of higher multipolarities are important in neutrinonucleus reactions

35 CROSS SECTIONS FOR SUPERNOVA NEUTRINOS Supernova neutrino flux: Cross section averaged over Supernova neutrino flux

36 SUPERNOVA T=4 MeV, α=0

37 MUON NEUTRINO CAPTURE IN NUCLEI Capture of muon neutrino in 12 C target nuclei EXP. ν µ FLUX (ν µ,µ - ) <σ>(10-40 cm 2 ) QRPA(SGII)(Volpe et al.) CRPA(SkE2)(Jachowicz et al) 23.7 CRPA(Kolbe et al.) PN-RQRPA (DD-ME2) EXP.(LSND) 12.4±0.3±1.8 C. Athanassopoulos et al., PRC 56, 2806 (1997).

38 ELECTRON CAPTURE IN SUPERNOVA COLLAPSE The core of a massive star at the end of hydrostatic burning is stabilized by electron degeneracy pressure, it prevents the star from contracting due to gravitation If the core mass exceeds Chandrasekhar mass, electrons are captured by nuclei, depletion of electron population is crucial to determine the initial collapse phase of a massive star Energy conservation:

39 ELECTRON CAPTURE IN NUCLEI AT FINITE TEMPERATURES Crucial input for the precollapse models are the electron capture cross sections for Fe group nuclei at finite temperatures various Skyrme-type effective interactions

40 ELECTRON CAPTURE IN NUCLEI AT FINITE TEMPERATURES Which multipoles contribute to electron capture cross sections?

41 ELECTRON CAPTURE IN NUCLEI AT FINITE TEMPERATURES Isotopic dependence of electron capture cross sections

42 ELECTRON CAPTURE IN NUCLEI AT FINITE TEMPERATURES Electron capture cross sections at T=0.5, 1.3 and 2.0 MeV

43 ELECTRON CAPTURE IN NUCLEI AT FINITE TEMPERATURES

44 ELECTRON CAPTURE IN NUCLEI AT FINITE TEMPERATURES

45 MUON CAPTURE IN EXOTIC ATOMS Exotic atom is the anologue of a normal atom in which one or more of the electrons are replaced by other negative particles, such as a muon or a pion In muonic atom, bound muon orbit (1s) overlaps with nucleus muon capture in nucleus muon capture rate

46 MUON CAPTURE IN EXOTIC ATOMS Self consistent description of muonic atom Muon wave functions (squared) for 1s 1/2 state Nucleus as point charge Mean-field calculation of Coulomb potentials charge density distribution in nuclei

47 MUON CAPTURE IN EXOTIC ATOMS The role of self-consistent description of muonic wave function Using point charge of nucleus Self-consistent calculations

48 MUON CAPTURE IN EXOTIC ATOMS The role of quenching in axial vector coupling on the muon capture rates Self-consistent, no quenching with quenching

49 BETA DECAYS

50 BETA DECAY RATES BASED ON RELATIVISTIC QRPA