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

Spectrum of the Gorkov Equation:

Extended HFB Theory: Pairing Self-Energies Energy Shifts and Widths Spectral Functions for particles and holes

7 Pairing in Infinite Nuclear Matter

Free Space SE (S=0,T=1) Interaction: (Bonn-B Potential) Pairing is a LOW DENSITY Phenomenon Pairing in Infinite Nuclear Matter

Pairing Gap  Anomal Density  Pairing Correlations in Nuclear Matter Pairing Gap  and Anomal Density  in Symmetric Nuclear Matter

Pairing-Field in a Nucleus RARA RARA

Neutron Spectrum : 11 Li : Continuum HFB Spectral Functions  Dissolution of Shell Structures!

g.s. Densities g.s. Densities  r 2 : 11 Li : Continuum HFB g.s. Densities

Neutron Spectral Functions in 9 Li(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 9 Li+n 10 Li S. Orrigo, H.L., PLB 677 (2009) & ISOLDE newsletter Spring 2010, p.5 15

Continuum Spectroscopy at REX-ISOLDE: 10 Li= 9 Li+n d( 9 Li, 10 Data: H. Jeppesen et al., REX-ISOLDE Collaboration, NPA 738 (2004) 511 & NPA 748 (2005) 374. S. Orrigo, H.L., PLB 677 (2009) & ISOLDE newsletter Spring 2010, p.5 16

17 New experimental results (Dec. 2013): 10 Li continuum spectroscopy at TRIUMF S. Orrigo, M. Cavallo, F. Capppuzzello et al.

Spectral Structures by Dynamical Polarization 18

Beyond the Mean-Field: Short-range Correlations in Nuclear Matter PLB483 (2000) 324 NPA723 (2003) 544 NPA (2005)in print Momentum Distribution n(p) = N(k F )  a(  p) d 

20 Nuclear Dynamics…

E th [MeV]E exp [MeV] (9.270) QRPA Response in 10 Be

DCP Neutron Spectral Distributions in 11 Be [0 + × 1/2+]: 0.79 [2 + × 5/2+]: 0.18 [0 + × 1/2-]: 0.58 [2 + × 3/2-]: 0.28

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:

Longitudinal Momentum Distributions: 17,19 C → 16,18 C + n Carbon Target, E l ab  900 AMeV Binding: Correlation Dynamics 17 C(5/2+,g.s.) S n (the.)=715keV C 2 S(g.s.) = 0.41  (the.): 132 MeV/c  (exp.): 143 ± 5 MeV/c  (-1n,the.): 124 mb  (-1n,exp.): 129± 22 mb Binding: Correlation Dynamics 19 C(1/2+,g.s.) S n (the.)=263keV C 2 S(g.s.) = 0.40  (the.): 69 MeV/c  (exp.): 68 ± 3 MeV/c  (-1n,the.): 192 mb  (-1n,exp.): 233± 51 mb 17 C 19 C

Hole Spectrum Particle Spectrum DCP Calculations (HFB+QRPA Core excitations) DCP Calculations (HFB+QRPA Core excitations) DCP Calculations (HFB+QRPA Core excitations) DCP Calculations (HFB+QRPA Core excitations) Dynamical Core Polarization: HFB g.s.: „3-body renormalized“ G- Matrix ph-Interactions: Fermi Liquid Theory 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),  ‘‘(3770)… Baryons: Confined qqq-configurations embedded into the continuum of meson-nucleon scattering states, e.g.  (1232), N*(1440),  (1405)… 29

Visualizing Quantum Interference in Microscopic Systems: Asymmetric Fano-Line Shapes of Resonances 30

Historically: The famous Silverman-Lassettre data He(e,e‘)He*( 1 500eV Note: q must be negative – q=

Fano-Resonances in Nuclei 32

Hamiltonian and Wave function The coupled equations (core nucleus integrated out): Multi-channel Fano wave function: 33

34 Extension to Several Open Channels n=2 open channels n=2 energetically degenerate solutions with outgoing flux

35 Solution 1: fully mixed Solution 2: continuum mixed  Resonance superimposed on a smoothly varying background! „Dark States“

36 Multi-channel Coupling

Resonance Scenarios in Nuclear Physics 37 The Fano-Wave Function:

Reaction Matrix Elements and Formation Cross Section The (single channel) Fano-Formula: 38

Correlation Dynamics in an Open Quantum System: d-wave Fano-Resonances in 15 C  ~60…140keV Sonja Orrigo, H.L., Phys.Lett. B633 (2006) 39

Xu Cao, H. L., PRL, submitted DD-Dynamics at Threshold Channel Coupling and the Line Shape of  (3770) X(3900) ?? q=-2.1 ±0.6

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