Nuclear Structure Tools for Continuum Spectroscopy H. Lenske Institut für Theoretische Physik Justus-Liebig-Universität Giessen

Continuum Tools, H. Lenske, ECT* 2016 Agenda: Many-body theory in weakly bound nuclei Sampling the continuum „Pairing“ resonances in 10Li Bound states in the continuum (BiC) and Fano-dynamics Summary Continuum Tools, H. Lenske, ECT* 2016

Nuclear Many-Body Approaches Continuum Tools, H. Lenske, ECT* 2016

Strategies for Nuclear Spectroscopy Multi-configuration Shell Model Truncation to a few valence shells Complete np-nh treatment in the valence sector Multi-configuration Mean-Field Model Truncation in ph-number Limited, but unrestricted configuration space

Density Functional Theory and Multi-Phonon QRPA Theory Single Particle Self-Energy: Landau-Migdal Residual Interaction : Choice of wave function:

Binding Energies of Sn-Isotopes DFT and HFB: Binding Energies of Sn-Isotopes N. Tsoneva, H.L., PRC 2008…2016

Giessen DFT & QPM: „(D)QPM“ 1-,1+,2+… new Modes of Excitation PhysRevC.91.044318 (2015) PhysRevC.90.024304(2014)

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

Discretization of the Single Particle Continuum Continuum Dynamics: Discretization of the Single Particle Continuum

Frequently used discretization methods Expansion into a discrete basis {fnℓ}: eigenfunctions of the 3-D quantum Harmonic oscillator Spherical Bessel functions with infinite well boundary condition at R>>Rturn : jℓ (kR)=0 Binning of the continuum (Austern, CDCC…): Direct integration by e.g. Numerov method: Continuum Tools, H. Lenske, ECT* 2016

Discretization of the Single Particle Continuum Continuum Tools, H. Lenske, ECT* 2016

Numerical approach by expansion into a basis Expand uℓj into a (complete) basis {fnℓ} Choice of (orthonormal) basis: spherical Bessel functions {fnℓ =Anℓxnℓjℓ(xnℓ)} with xnℓ = qnℓr and fnℓ(R)=0 ↔ jℓ(qnℓR)=0 Obtain the knℓj values from the eigenvalue problem The scattering phase shifts are obtained by (c/o the famous Luescher formula of LQCD!) Continuum Tools, H. Lenske, ECT* 2016

½+ proton Scattering Phase Shifts on C Isotopes Continuum Tools, H. Lenske, ECT* 2016

½+ Proton Partial Wave Cross Section on C Isotopes Continuum Tools, H. Lenske, ECT* 2016

Density of States in the Continuum: the Speed Plot Continuum Tools, H. Lenske, ECT* 2016

½+ Proton Density of States in C isotopes Continuum Tools, H. Lenske, ECT* 2016

Sampling the 5/2+ resonance in p+12C Continuum Tools, H. Lenske, ECT* 2016

Evolution of Neutron Single Particle Continuum Strength Density of States in the Continuum  Speed plot Jp=5/2-

QRPA 1- and 2+ Multipole-Response 128Sn Microscopic DD-QRPA

Pairing across the Dripline Continuum Dynamics: Pairing across the Dripline

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

Pairing Theory as Coupled Channels Problem: The Gorkov-Equations

Pairing in the Continuum S. Orrigo, H.L., PLB 677 (2009)

Mapping to Single Particle Pairing Self-Energies Energy Shifts and Widths Spectral Functions for particles and holes

Spectrum of the Gorkov Equation:

Neutron Spectral Functions in 9Li(3/2-)

Neutron Spectral Functions in 9Li(3/2-): Continuum Admixtures into the g.s. Continuum Admixture!

Pairing Resonances in Dripline Nuclei: 9Li+n 10Li S. Orrigo, H.L., PLB 677 (2009) & ISOLDE newsletter Spring 2010

n+9Li Scattering Phase Shifts Jp=½+ Jp=½- n+9Li s-wave Mean-Field: as : -1.35 [fm] rs : 32.94 [fm] Pairing: as : 1.76[fm] rs : -2.18 [fm] Continuum Tools, H. Lenske, ECT* 2016

Effective Range Expansion and Pole Structure n+9Li s-wave virtual state: Mean-Field: as : -1.35 fm rs : 32.94 fm  E=-1.38 MeV Pairing: as : 1.76 fm rs : -2.18 fm  E=-3.63 MeV Continuum Tools, H. Lenske, ECT* 2016

 talk of Manuela Cavallaro Continuum Spectroscopy of 10Li=9Li+n via d(9Li,10Li)p@2.36AMeV Numerical challenge for „standard (d,p) stripping theory“: How to evaluate a 3-D integral with only oscillatory wave functions? New TRIUMF data and analysis:  talk of Manuela Cavallaro Data: H. Jeppesen et al., REX-ISOLDE Collaboration, NPA 738 (2004) 511,;NPA 748 (2005) 374.

Bound States in the Continuum Continuum Tools, H. Lenske, ECT* 2016

1/2+ Particle and Hole Strength Functions in 14C Particle strength function

Interference of Closed Channels (BiC) and Open Channels: Fano-Dynamics of Asymmetric Resonance Line Shapes Science 340,716 (2013): Stimulated Ionization of double-excited He

Reaction Amplitude and Formation Cross Section The Fano-Formula:

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

Sonja Orrigo, H.L., et al. Phys.Lett. B633 (2006) Correlation Dynamics in an Open Quantum System: 5/2+ Fano-Resonances in 15C by Core Polarization G~60…140keV Sonja Orrigo, H.L., et al. Phys.Lett. B633 (2006)

Bound States by Correlation Dynamics through Continuum Coupling The DCP picture: Binding by Virtual Continuum Coupling The s.p. shell model picture H.L.,J. Prog.Part.Nucl. 561 (2004)

Supported by DFG, BMBF, HIC for FAIR, and GSI Summary Discretization of the single particle continuum Sampling continuum observables Correlations across the particle threshold in Li-isotopes Bound States in the Continuum Interference of open and closed channels …with special ontributions by Sonja Orrigo and Nadia Tsoneva Supported by DFG, BMBF, HIC for FAIR, and GSI Continuum Tools, H. Lenske, ECT* 2016