2012 4 12 16 Nuclear collective vibrations in hot nuclei and electron capture in stellar evolution Yifei Niu Supervisor: Prof. Jie Meng School of Physics, Peking University, China April 12, 2012 Collaborators: Nils Paar: Physics Department, University of Zagreb, Croatia Dario Vretenar: Physics Department, University of Zagreb, Croatia
OUTLINE 1 Introduction 2 Theoretical Framework 3 Results and Discussions 4 Summary & Perspectives
Giant Resonance Giant Resonance: a high-frequency collective excitation of atomic nuclei isoscalar monopole resonance: breathing mode T = 0, L = 0 isovector dipole resonance: all protons oscillate against all neutrons T = 1, L = 1; E 80A 1/3 3. Evolution of low-lying collective modes Paar, Vretenar, Khan, Colò, Rep. Prog. Phys. 70, 1 (2007) Dipole response of neutron-rich nuclei Monopole Dipole Quadrupole E1 srength Energy [MeV] from D. Vretenar
Pygmy Resonance Pygmy Resonance Excitation energy neutron threshold, < 10 MeV. Pygmy dipole resonance In neutron rich nuclei, the weakly bound neutron skin oscillates against the proton-neutron isospin { saturated core. nuclear symmetry energy, neutron skin thickness Importance: Neutron-rich astrophysical nuclei predicted process: occurrence neutron capture of a collective in r-process soft dipole mode (Pygmy Dipole Resonance) E1 srength Energy [MeV] from D. Vretenar
Spin-isospin Resonance Spin-isospin Resonance (N, Z) (N 1, Z ± 1), induced by isospin lowering T and raising T + operators. different modes: a. Isobaric Analog State (IAS): L = S = J = 0 b. Gamow-Teller Resonance (GTR): L = 0, S = J = 1 c. other multipoles one of the central topics in nuclear physics and astrophysics. the spin and isospin properties of the effective nuclear interaction another choice for extracting neutron skin thickness β-decay rates of r-process nuclei, electron capture in stellar evolution
Introduction Electron capture in stellar evolution Collapse of a massive star and a supernova explosion from Langanke 2008, Acta Physica Polonica B,39. Shell-Structured Evolved Massive Star Gravitational Core Collapse Supernova Shock Wave Shock Region Explosive Nucleosynthesis Proto-Neutron Star Neutrino Heating of Shock Region from Inside
Introduction Electron capture in stellar evolution Collapse of a massive star and a supernova explosion from Langanke 2008, Acta Physica Polonica B,39. Shell-Structured Evolved Massive Star Gravitational Core Collapse Supernova Shock Wave { core entropy The dynamics of core-collapse supernova { lepton to baryon ratioy e β decay electron capture dominate! weak interaction processes EC rates: mainly determined by GT Shock Region + Explosive Nucleosynthesis stellar environment: a few hundreds kev to 2 3 MeV Proto-Neutron Star Neutrino Heating of Shock Region from Inside The description of spin isospin resonances at finite temperature is necessary!
Introduction Theoretical description Zero Temperature non-relativistic RPA: Blaizot: 1976, 1977; Random Phase Approximation (RPA) Auerbach: 1981, 1984; Bai: 2009,2010 Quasiparticle RPA (QRPA): Terasaki: 2005; Jun Li: 2008; Giambrone: 2002; Fracasso: 2007; Engel: 1999; Bender: 2002 relativistic with nonlinear meson terms Ring: 2001; Zhongyu Ma: 1997, 2001; Vretenar: 2000; Piekarewicz: 2001 with density dependent meson nucleon couplings RRPA Niksic: 2001; Conti: 1998 QRRPA Paar: 2003, 2004 with Fock terms Haozhao Liang: 2008
Introduction Theoretical description Random Phase Approximation (RPA) Zero Temperature non-relativistic RPA: Blaizot: 1976, 1977; Auerbach: 1981, 1984; Bai: 2009,2010 Quasiparticle RPA (QRPA): Terasaki: 2005; Jun Li: 2008; Giambrone: 2002; Fracasso: 2007; Engel: 1999; Bender: 2002 relativistic with nonlinear meson terms Ring: 2001; Zhongyu Ma: 1997, 2001; Vretenar: 2000; Piekarewicz: 2001 with density dependent meson nucleon couplings RRPA Niksic: 2001; Conti: 1998 QRRPA Paar: 2003, 2004 with Fock terms Haozhao Liang: 2008 Finite Temperature non-relativistic schematic model RPA: Ring: 1983; Vautherin: 1984; Civitarese: 1984; Besold: 1984 QRPA: Sommermann: 1983; Ring: 1984; Tanabe: 1988; Alasia: 1990; Dzhioev: 2010 self-consistent RPA: Sagawa: 1984; Paar: 2009 Continuum QRPA: Khan: 2004 relativistic
Introduction Motivation In this work Purpose To extend the self-consistent RPA for non-charge and charge exchange modes based on relativistic functionals with density dependent meson nucleon couplings to finite temperature To investigate - the low energy excitation of nuclei at finite temperature - the electron capture in stellar evolution
Density Dependent RMF theory at finite temperature The minimization of the thermodynamical potential Ω = E TS µn { hϕi = ɛ i ϕ i, i f i = N, f i = [1 + exp( ɛ i µ kt )] 1 In the density dependent RMF theory, we start from the Lagrangian density L = ψ(iγ µ µ m)ψ + 1 2 µσ µ σ 1 2 m2 σσ 2 1 4 Ω µω µ + 1 2 m2 ωω 2 1 4 R µ R µ + 1 2 m2 ρ ρ 2 1 4 F µf µ g σ ψσψ gω ψγµ ω µ ψ g ρ ψγµ ρ µ τψ e ψγ µ A µ(1 τ 3) ψ 2 with Ω µ µ ω ω µ, R µ µ ρ ρ µ, F µ µ A A µ. Densities ρ s (r) = i ρ v (r) = i f i ϕ i (r)ϕ i (r) f i ϕ i (r)ϕ i(r)
Relativistic RPA at finite temperature The RPA excited state is generated by particle Q = mi X mia ma i mi Y mi a i a m E f RRPA equation at finite temperature ( A B B A ) ( X Y ) = ω ( X Y ) hole The FT-RRPA matrices A and B read ( ) ( (ɛm ɛ A = i )δ ii δ mm (fi f + m )V mi im f i V mi iα (ɛ α ɛ i )δ αα δ ii (f i f m )V αi im f i V αi iα ( (fi f B = m )V mm ii f i V ) mα ii (f i f m )V αm ii f i V. αα ii ), Here, ɛ i < ɛ m. The configuration space includes p-h, p-p, h-h pairs. Occupation probability: f i = [1 + exp( ɛ i µ kt )] 1.
Electron-capture cross section and rate The electron capture on a nucleus A Z X N A ZX N + e A Z 1 X N+1 + e (1) Cross section for a transition followed from Fermi s golden rule reads: dσ dω = 1 (2π) 2V 2 E 2 1 2 lepton spins 1 2J i + 1 M i M f f ĤW i 2. (2) V : the quantization volume; E : energy of outgoing electron neutrino; H W : the Hamiltonian of the weak interaction. Rate λ ec = 1 p π 2 3 e E e σ ec (E e )f (E e, µ e, T )de e (3) E 0 e where E 0 e = max( Q if, m e c 2 ), Q if = E RPA np, and p e = (E 2 e m 2 ec 4 ) 1/2. Electron distribution in stellar environment f (E e, µ e, T ) = 1 exp( E e µ e kt ) + 1 (4)
Evolution of isovector dipole excitations with temperature 132 Sn: pygmy resonance becomes more distributed, and more single particle transitions appear in low energy region. 60 Ni: The pygmy structure, which is absent at T = 0 MeV, appears at finite temperature. Y.F. Niu, N. Paar, D. Vretenar, and J. Meng, Phys. Lett. B681, 315
Evolution of isovector dipole excitations with temperature 60 Ni: The configuration of the pygmy structure at E = 9.71 MeV while T = 2.0 MeV.
Evolution of GT + with temperature G T + G T + 1 0 8 6 4 2 0 1 0 8 6 4 2 0 L S S M e x p. 1 e x p. 2 L S S M e x p. 4 e x p. 2 R Q R P A R R P A T = 1 M e V T = 2 M e V e x p. 3 5 4 F e 0 2 4 6 8 1 0 E (M e V ) 5 6 F e Pairing correlations higher transition energy additional energy is needed to break a proton pair. From T=0 (RQRPA) to T=1: energy pairing collapse. From T=1 to T=2: energy softening of the repulsive residual interaction. T or pairing transition strength partial occupation factor Y. F. Niu, N. Paar, D. Vretenar, N. Paar, Phys. Rev. C 83, 045807 (2011) [1] M. C. Vetterli, et. al. Phys. Rev. C 40, 559, 1989. [2] T. Rönnqvist, et. al. Nucl. Phys. A 563, 225, 1993. [3] S. El-Kateb, et. al. Phys. Rev. C 49, 3128, 1994. [4] D. Frekers, Nucl. Phys. A 752, 580c, 2005.
Electron capture cross section ) 2 ) s (1 0-4 2 c m 2 s (1 0-4 2 c m 1 0 2 1 0 1 1 0 0 1 0-1 1 0-2 1 0-3 1 0 1 1 0 0 1 0-1 1 0-2 1 0-3 5 4 F e D D -M E 2 5 6 F e D D -M E 2 T = 0.0 M e V (R Q R P A ) T = 0.0 M e V T = 1.0 M e V T = 2.0 M e V 0 5 1 0 1 5 2 0 2 5 3 0 E e (M e V ) σ ec E 2 E = E e E RPA NP 0 T threshold energy Low energy: T cross section high energy: T cross section N threshold energies cross sections Y. F. Niu, N. Paar, D. Vretenar, N. Paar, Phys. Rev. C 83, 045807 (2011)
Electron capture rate lo g 1 0 ( l e c ) (s e c -1 ) 6 3 0-3 -6-9 3 0-3 -6-9 lo g 1 0 (r Y e ) = 7 2 4 6 8 1 0 lo g 1 0 (r Y e ) = 8 lo g 1 0 (r Y e ) = 9 lo g 1 0 (r Y e ) = 1 0 5 4 F e 5 6 F e F T R R P A L S S M 2 4 6 8 1 0 2 4 6 8 1 0 2 4 6 8 1 0 Electron capture rates increase with temperature and the electron densities. - In high electron densities, it increases more slowly. similar trend of temperature dependence as shell model - better agreement in 54 Fe than 56 Fe - ρy e = 10 9 g/cm 3 : λ e 5 MeV, close to threshold energy sensitive to detailed GT distribution larger discrepancy Y. F. Niu, N. Paar, D. Vretenar, N. Paar, Phys. Rev. C 83, 045807 (2011) T 9
Summary & Perspectives Summary: The fully self-consistent RRPA model with density-dependent meson-nucleon couplings, for non-charge and charge exchange modes, is extended to finite temperature. Low-lying dipole excitations in nuclei at finite temperature the modification of temperature to pygmy structure in 132 Sn. the prediction of the new low-lying excitation modes at finite temperature. The electron capture cross sections and rates in stellar environment, including multipole excitations, are calculated based on self-consistent finite temperature RRPA. Perspectives: More effects: pairing, particle vibration coupling,... Large scale calculation of electron capture rates for astrophysics input.
Acknowledgements Collaborators: Jie Meng: School of Physics, Peking University, China Nils Paar: Physics Department, University of Zagreb, Croatia Dario Vretenar: Physics Department, University of Zagreb, Croatia