John Daoutidis October 5 th 2009 Technical University Munich Title Continuum Relativistic Random Phase Approximation in Spherical Nuclei.

Contents of the talk 1.Density Functional Theory in relativistic static phenomena, 1.Method to describe nuclear collective phenomena (RPA), 1.Exact treatment of the coupling to the continuum, 1.Results in spherical nuclei and comparison with experiment, 1.Conclusions. Contents

Density functional theory density matrix Mean field:Eigenfunctions:Interaction: Density functional theory exact!

Point-coupling model RELATIVISTIC POINT-COUPLING INTERACTIONS + gradients (finite range) σ ω ρ J=0, T=0 J=1, T=0 J=1, T=1 Covariant DFT Dirac s.p. equation + density dependent couplings

Contents Static properties (binding energies, nuclear radii, deformations, etc). Collective excitations (surface oscillations, rotations, etc.) Static DFT How can we explain reactions that lead to collective phenomena, from individual motion?

TD-DFT Random Phase Approximation small ampl. limit RPA : ground state density Photoabsorbtion cross section Strength function Time Dependent DFT:

Exact Coupling to Continuum How do we solve RPA ? Linear Response Formalism Configuration Space Formalism

Method #1: Configuration space formalism RPA matrix equation: Dimension determined by the size of the 1p-1h configuration. AB matrix Interaction:

Limitations of conf. space formalism 1) The p-h configuration space can be very large in the case of medium or heavy nuclei 2) Relativistic RPA requires also transitions to Dirac sea (antiparticles) Large dimension of RRPA matrix (>7000), Large numerical effort discrete spectrum Artificial width: Lorentzian with smearing parameter 2Δ ω [MeV] S( ω ) 0 3) Approximate treatment of the continuum ( put the nucleus in a box) 4)

Method #2: Linear Response Formalsim Linearized Bethe-Salpeter equation: Simple matrix equation or rank 350 (7 meson channels, 50 r-mesh points) Can have a continuous spectrum (resonance width) if R 0 cc’ is exact. Respons e ____ sum of separable terms:

Full Response function: Free Response function J. Daoutidis and P. Ring PRC 80 (2009) co nti nu um 1.Full continuum and Dirac sea are included (no truncation), 2.Escape width is automatically reproduced, 3.One order of magnitude faster numerical calculations. -u(r) and w(r) are the exact scattering wave functions solutions of Dirac equation for arbitrary energies. Free Response function: neglect υ ph

Overview Density Functional Theory in relativistic static phenomena,Density Functional Theory in relativistic static phenomena, Method to describe nuclear collective phenomena (RPA),Method to describe nuclear collective phenomena (RPA), Exact treatment of the coupling to the continuum,Exact treatment of the coupling to the continuum, Results in spherical nuclei and comparison with experiment,Results in spherical nuclei and comparison with experiment, Conclusions.Conclusions. Contents

Isoscalar Giant Monopole Resonance (breathing mode) Results ISGMR Continuum RRPA with PC-F1 force: J. Daoutidis, P. Ring, Discrerte RRPA with PC-F1 force: Niksic et. al. PRC 72 (2005) Continuum RRPA with PC-F1 force: J. Daoutidis, P. Ring, PRC 80 (2009) Discrerte RRPA with PC-F1 force: Niksic et. al. PRC 72 (2005)

Isovector Giant Dipole Resonance Giant isovector dipole oscillations -> neutrons oscillate against protons. t CRPA =1/20 t DRPA !

Isovector Giant Pygmy: IV-GPR Depends on the coupling to the continuum!

Quasiparticle CRPA Pairing correlations play a crucial role for open shell nuclei. RMF+BCS : - Simple - Successful in nuclei when  F not close to the continuum (drip lines)

Quasiparticle CRPA Applications: Isovector Giant Dipole Resonances QcRP A 1-

We have formulated the continuum QRPA based on the Point Coupling Relativistic mean field theory (PC-F1). We applied the continuum QRPA to multipole giant resonances in double magic nuclei as well as spherical open shell Tin isotopes. There are quantitative improvements, compared to the discrete RPA (escape widths, minimizing numerical effort, etc.) Summary and outlook Extend the model to meson exchange forces for better qualitative comparison. Include Relativistic Hartree Bogoliubov (RHB) theory in the static problem in order to treat pairing correlations at the cases where BCS fails (drip lines, halo nuclei). Extend to include deformed nuclei. SUMMARY