Spectroscopy at the Particle Threshold H. Lenske 1 Agenda: • Pairing in the continuum • Nuclear Polarizability and Spectral Functions • Continuum spectroscopy and Fano-Resonances • Summary 2 Pairing in the Continuum: Quasiparticle Resonances 3 Extended HFB Theory as Coupled Channels Problem: The Gorkov-Equations H E ( H ) ~ u(jq) (r) | (s) jm ; ~ v(jq) (r) | (s) jm Mean-Field Hamiltonian (q p,n): Pairing- Field & Density (q p, n) : 2 q 1 VSE q H 2 U() 2m 2 j 1 (q) q (r) | v n j (r) |2 4 n j 2 2 j 1 (q) ( q )* q (r ) u n j ( r ) v n j ( r ) 4 n j Spectrum of the Gorkov Equation: Extended HFB Theory: Pairing Self-Energies • Energy Shifts and Widths • Spectral Functions for particles and holes Pairing in Infinite Nuclear Matter (k F ) d 3q 2 0 V ( k , q ) u(q; k ) v(q; k ) ~ N(k ) V (k F , k F ) ( k F ) I k F , SE F F F F SE 3 G (k F ) N(k F )VSE0 (k F , k F ) I k F , (k F ) ~ e F (k F ) e 1 G (k F ) 3(1G ( k F )) G ( kF ) 7 Pairing in Infinite Nuclear Matter Free Space SE (S=0,T=1) Interaction: (Bonn-B Potential) Pairing is a LOW DENSITY Phenomenon Pairing Gap and Anomal Density Pairing Correlations in Nuclear Matter in Symmetric Nuclear Matter Pairing Gap Anomal Density Pairing-Field in a Nucleus RA RA 11Li : Continuum HFB Spectral Functions Neutron Spectrum : Dissolution of Shell Structures! 11Li : Continuum HFB g.s. Densities g.s. Densities g.s. Densities r2 : for q p, n : (q) v(jq) (r) | (s) jm q (r ) j q 2 j 1 (q) 2 de | v ( e , r ) | j 4 Neutron Spectral Functions in 9Li(3/2-): Continuum Admixtures into the g.s. Continuum Admixtures! Pairing in the Continuum S. Orrigo, H.L., PLB 677 (2009) 14 Pairing Resonances in Dripline Nuclei 9Li+n 10Li S. Orrigo, H.L., PLB 677 (2009) & ISOLDE newsletter Spring 2010, p.5 15 Continuum Spectroscopy at REX-ISOLDE: d(9Li,10Li)p@2.36AMeV 10Li=9Li+n S. Orrigo, H.L., PLB 677 (2009) & ISOLDE newsletter Spring 2010, p.5 Data: H. Jeppesen et al., REX-ISOLDE Collaboration, NPA 738 (2004) 511 & NPA 748 (2005) 374. 16 New experimental results (Dec. 2013): 10Li continuum spectroscopy at TRIUMF 1 3 3 5 , 2 2 2 2 S. Orrigo, M. Cavallo, F. Capppuzzello et al. 17 Spectral Structures by Dynamical Polarization 18 Beyond the Mean-Field: Short-range Correlations in Nuclear Matter Momentum Distribution n(p) = N(kF) a(w, p) dw PLB483 (2000) 324 NPA723 (2003) 544 NPA (2005)in print Nuclear Dynamics… 20 QRPA Response in 10Be Eth [MeV] Eexp [MeV] 2+ 3.220 3.368 1- 6.423 5.960 0+ 6.513 6.179 2- 6.446 6.263 3- 7.372 7.371 J c 4- (9.270) 1+ 7.122 3+ 7.159 0- 7.374 DCP Neutron Spectral Distributions in [0+ × 1/2+]: 0.79 [2+ × 5/2+]: 0.18 [0+ × 1/2-]: 0.58 [2+ × 3/2-]: 0.28 11Be Spectral Distributions in Carbon Isotopes …normalized to sum rule E1 Dipole E2 Quadrupole Polarizability of C-Isotopes: HFB+QRPA results Multipole polarizabilties coefficients by sum rules: S n ( ) E n a 2 a T 0 S 1 ( ) P S 0 ( ) Longitudinal Momentum Distributions: 17,19C → 16,18C + n Carbon Target, Elab 900 AMeV •Binding: Correlation Dynamics 17C •17C(5/2+,g.s.) • Sn(the.)=715keV • C2S(g.s.) = 0.41 G(the.): 132 MeV/c G(exp.): 143 ± 5 MeV/c s(-1n,the.): 124 mb s(-1n,exp.): 129± 22 mb •Binding: Correlation Dynamics •19C(1/2+,g.s.) 19C • Sn(the.)=263keV • C2S(g.s.) = 0.40 G(the.): 69 MeV/c G(exp.): 68 ± 3 MeV/c s(-1n,the.): 192 mb s(-1n,exp.): 233± 51 mb Dynamical Core Polarization: •HFB g.s.: „3-body renormalized“ GMatrix • ph-Interactions: Fermi Liquid Theory Hole Spectrum Particle Spectrum Fano Resonances Interactions of Closed and Open Channels: Fano Resonances 27 The Spectral Situation encountered in Atoms, Molecules, Nuclei, and Hadrons • A closed channel E* is embedded into a continuum of open channels • E* interacts via V(r) with open channels given by scattering states • E* Interacts via V(r) with closed channels, e.g. of (simple) bound states Bound State Embedded into the Continuum - BSEC 28 Examples: • Atoms: self-ionizing states of multi-electron configuration • Nuclei: Multi-particle-hole states above threshold • Mesons: Confined qq-configurations embedded into the continuum of meson-meson scattering states, e.g. (1232), (770), Y‘‘(3770)… • Baryons: Confined qqq-configurations embedded into the continuum of meson-nucleon scattering states, e.g. (1232), N*(1440), L(1405)… 29 Visualizing Quantum Interference in Microscopic Systems: Asymmetric Fano-Line Shapes of Resonances Y E aii( d ) d bk k(c) i k 30 Historically: The famous Silverman-Lassettre data He(e,e‘)He*(1P) @ 500eV Note: q must be negative – q=-1.84 31 Fano-Resonances in Nuclei 32 Hamiltonian and Wave function H11b H 0 V31 0 H 22s V32 V13 V23 H 33x The coupled equations (core nucleus integrated out): b n zn nJ V13 j ' c z j ' c 0 c s.p. motion w.r.t. the g.s. s j z nJ V23 j ' c z j 'c 0 c j' ( E JC ) z j ' c j ' c V31 n zn d ' j ' c V32 ' z ' 0 n Multi-channel Fano wave function: 33 Extension to Several Open Channels • n=2 open channels • n=2 energetically degenerate solutions with outgoing flux G1 VE 2 ; G 2 WE G G i 2 i arctan G(E ) P G( E ) E E G ( E ) dE ' G( E ') E ' E 34 Solution 1: fully mixed 1 P z( E , E ') sin ( E E ') cos EE' G1 G2 sin a1 ; b1E ' z ( E , E ') ; c1E ' z ( E , E ') G G G Solution 2: continuum mixed a2 0 ; b2 E ' G1 G2 ( E E ') ; c 2 E ' ( E E ') G G „Dark States“ Resonance superimposed on a smoothly varying background! 35 Multi-channel Coupling 36 Resonance Scenarios in Nuclear Physics The Fano-Wave Function: 37 Reaction Matrix Elements and Formation Cross Section M Y E , | T | 1 | T | | T | sin cot * E , VE | T | E , The (single channel) Fano-Formula: | q cot | s =s ~ M 2 1 cot | T | q= E , | T | 2 s 1 s ~ | T | * E , VE 2 2 s 38 Correlation Dynamics in an Open Quantum System: d-wave Fano-Resonances in 15C G~60…140keV Sonja Orrigo, H.L., Phys.Lett. B633 (2006) 39 DD-Dynamics at Threshold Channel Coupling and the Line Shape of Y(3770) D D threshold 3739.2 MeV D0 D0 threshold 3729.7 MeV q=-2.1±0.6 X(3900) ?? 3.65 (2s / 3686) Xu Cao, H. L., PRL, submitted 40 Summary • Dynamics at the particle threshold • Pairing at the dripline/in the continuum • Nuclear polarizabilities • Fano resonances in atomic nuclei • Tools for continuum spectroscopy • Universality of quantum interference …with contributions by Sonja Orrigo (Valencia) and Xu Cao (Giessen/Lanzhou) 41