Microscopic nucleon-nucleus optical potentials for neutron-rich systems Jeremy W. Holt Department of Physics University of Washington INT workshop: Reactions and structure of exotic nuclei, 03/05/2015 OUTLINE Physics motivations Neutron-capture rates in r-process nucleosynthesis Neutron star structure (inner crust) Charged-current weak reactions in newly formed neutron stars Nucleon self energy in homogeneous matter Improvements in theory: perturbative chiral nuclear forces that reproduce saturation Benchmark to phenomenological potentials close to valley of stability Corrections to the Lane parametrizaton of the isospin asymmetry dependence Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington CHALLENGE 1: R-PROCESS NUCLEOSYNTHESIS Astrophysical Core-collapse Neutron-star site? supernovae mergers http://www.csm.ornl.gov http://numrel.aei.mpg.de Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington INPUTS FROM NUCLEAR STRUCTURE Masses of neutron-rich nuclei Determine elemental abundance patterns along isotopic chains during equilibrium Beta-decay lifetimes Set timescale for formation of heavy elements from seed nuclei Partly responsible for peaks at A = 130 and A = 195 Neutron-capture rates Relevant during late-time freeze-out phase of the r-process Sensitivity studies vary capture rates over 1–2 orders of magnitude Surman et al., PRC (2009) Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington CHALLENGE 2: EQUILIBRIUM STATE OF NEUTRON STAR INNER CRUSTS Outer crust is a lattice of nuclei with gas of electrons Inner crust contains lattice of neutron-rich nuclei together with “dripped” neutrons Neutron drip density: Dripped neutrons Bound neutrons Outer Crust Inner Crust Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington GLOBAL OPTICAL POTENTIALS (PHENOMENOLOGICAL) Koning & Delaroche, NPA (2003) Energy dependence Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington LANE PARAMETRIZATION Isovector part of optical potential linear in the isospin asymmetry 80 Model predictions 60 40 (MeV) I U 20 Empirical DBHF Gogny RMF 0 Skyrme SkLya BHF -20 0 0.5 1 1.5 2 2.5 -1 k (fm ) Much less is known/predicted about isovector imaginary part Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington MICROSCOPIC OPTICAL POTENTIALS (HOMOGENEOUS MATTER) Identified with the on-shell nucleon self-energy [Bell and Squires, PRL (1959)] Hartree-Fock contribution (real, energy-independent): Second-order perturbative contibutions (complex, energy-dependent): Benchmarks: Depth and energy dependence of phenomenological volume parts (including isospin dependence) Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington MICROSCOPIC NUCLEAR PHYSICS FROM “NEXT-TO-FIRST PRINCIPLES” Quark/gluon (high energy) dynamics Approximate chiral symmetry (left- and right- handed quarks transform independently) n Nucleon/pion (low energy) dynamics Compatible with explicit and spontaneous chiral p symmetry breaking Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington NUCLEAR FORCES IN CHIRAL EFFECTIVE FIELD THEORY SEPARATION OF SCALES + SYMMETRIES CHIRAL EFFECTIVE FIELD THEORY Energy Low-energy theory of nucleons and pions Heavy mesons (ρ, ω) Λ 0 π (q/Λ) N Systematic expansion Nucleon momenta Pion mass q (q/Λ)2 QCD chiral symmetry quarks (q/Λ)3 (q/Λ)4 Pions weakly-coupled at low momenta! Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington NUCLEAR FORCES IN CHIRAL EFFECTIVE FIELD THEORY SEPARATION OF SCALES + SYMMETRIES CHIRAL EFFECTIVE FIELD THEORY Energy Low-energy theory of nucleons and pions Heavy mesons (ρ, ω) Λ 0 π (q/Λ) N Systematic expansion Nucleon momenta q Pion mass Fit to NN scattering (q/Λ)2 (future: lattice QCD?) QCD chiral symmetry quarks (q/Λ)3 (q/Λ)4 Pions weakly-coupled at low momenta! Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington NUCLEAR FORCES IN CHIRAL EFFECTIVE FIELD THEORY SEPARATION OF SCALES + SYMMETRIES CHIRAL EFFECTIVE FIELD THEORY Energy Low-energy theory of nucleons and pions Heavy mesons (ρ, ω) Λ 0 π (q/Λ) N Systematic expansion Nucleon momenta q Pion mass Consistent vertices in 2N (q/Λ)2 & 3N forces (also πN) QCD chiral symmetry quarks (q/Λ)3 (q/Λ)4 Pions weakly-coupled at low momenta! Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington NUCLEAR FORCES IN CHIRAL EFFECTIVE FIELD THEORY SEPARATION OF SCALES + SYMMETRIES CHIRAL EFFECTIVE FIELD THEORY Energy Low-energy theory of nucleons and pions Heavy mesons (ρ, ω) Λ 0 π (q/Λ) N Systematic expansion Nucleon momenta q Pion mass Fit to 3H binding energy (q/Λ)2 and lifetime QCD chiral symmetry quarks (q/Λ)3 (q/Λ)4 Pions weakly-coupled at low momenta! Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington NUCLEAR FORCES IN CHIRAL EFFECTIVE FIELD THEORY SEPARATION OF SCALES + SYMMETRIES CHIRAL EFFECTIVE FIELD THEORY Energy Low-energy theory of nucleons and pions Heavy mesons (ρ, ω) Λ 0 π (q/Λ) N Systematic expansion Nucleon momenta q Pion mass Frontier in nuclear structure (q/Λ)2 QCD chiral symmetry quarks (q/Λ)3 (q/Λ)4 Pions weakly-coupled at low momenta! Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington STARTING POINT: MICROSCOPIC CHIRAL NUCLEAR FORCES Regulating function sets resolution scale Variations in regulator Estimate of theoretical uncertainty Coraggio, Holt, Itaco, Machleidt & Sammarruca, PRC (2013) Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington NEUTRON MATTER EoS (T=0): Perturbave Features Coraggio, Holt, Itaco, Machleidt & Sammarruca, PRC (2013) 40 N3LO 2NF + N2LO 3NF [500 MeV] N3LO 2NF + N2LO 3NF [414 MeV] 36 E1 1st order 1st 32 2nd order 3rd order 28 Pade’ [2|1] 2nd E3 E 24 3rd [2|1] E2 20 E/A [MeV] 16 12 8 4 0 0.00 0.05 0.10 0.15 0.20 0.25 –3-3 -3 n ρ (fm [fm ]) n (fm ) Low-momentum potentials: improved perturbative properties Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington SATURATION OF SYMMETRIC NUCLEAR MATTER Coraggio, Holt, Itaco, Machleidt, Marcucci & Sammarruca, PRC (2013) & (2014) Uncertainty esmate Empirical Fit to triton lifetime cD Saturation energy: Saturation density: Nontrivial without Asymmetry energy: extra tuning Compressibility: Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington LIQUID-GAS PHASE TRANSITION and THE CRITICAL POINT (CP) Wellenhofer, Holt, Kaiser & Weise, PRC (2014) Predicted critical endpoint * Empirical CP Critical temperature: gas Theorecal CP liquid Critical density: liquid-gas Critical pressure: Experiment (compound nucleus & multifragmentation) [J. B. Elliott et al., PRC (2013) Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington 1ST- AND 2ND-ORDER VOLUME CONTRIBUTIONS 3NF 2NF (1st) ReΣ 2NF (2nd) ImΣ 2NF (2nd) Holt, Kaiser, Miller & Weise, PRC (2013) Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington MOMENTUM DEPENDENCE OF 3NF TERMS Holt, Kaiser, Miller & Weise, PRC (2013) Nearly all momentum dependence comes from the two-pion-exchange 3NF Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington BENCHMARK: PHENOMENOLOGICAL OPTICAL POTENTIALS Holt, Kaiser, Miller & Weise, PRC (2013) Re Σ Self consistency: 56 Typical phenomenological potential: Fe n3lo500 Im Σ Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington INDIVIDUAL CONTRIBUTIONS IN ASYMMETRIC MATTER q (MeV) q (MeV) 0 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 20 20 = 0.0 0 np np = 0.1 0 -20 n (2) -20 p U2N+3N n MeV (1) MeV -40 p U3N -40 n U (1) -60 p 2N -60 = 0 -80 -80 20 20 0 np = 0.2 np = 0.4 0 -20 -20 MeV -40 -40 MeV -60 -60 -80 -80 0 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 q (MeV) q (MeV) Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington REAL AND IMAGINARY PROTON/NEUTRON POTENTIALS E (MeV) E (MeV) E (MeV) E (MeV) 0 20 40 60 80 100 20 40 60 80 100 0 20 40 60 80 100 20 40 60 80 100 -10 -10 = 0.6 0 = 0.2 0 0 0 Un = 0.6 0 W -20 -20 n = 0.2 0 -5 U U W (MeV) p n W n -30 -30 (MeV) (MeV) (MeV) p = 0.0 -10 -10 np = 0.0 U(E) np U(E) -40 = 0.2 -40 W(E) W(E) np = 0.2 -15 np W = 0.4 Up = 0.4 p -50 np -50 np 0 0 -20 -20 0 = 0.8 = 0 -10 = 0.8 -10 0 0 0 = 0 -20 -20 W W U U n n -30 n n -30 -10 -10 (MeV) (MeV) (MeV) -40 -40 (MeV) U(E) U(E) -50 -50 W(E) W(E) W W U U p p -60 p p -60 -20 -20 -70 -70 0 20 40 60 80 100 20 40 60 80 100 0 20 40 60 80 100 20 40 60 80 100 E (MeV) E (MeV) E (MeV) E (MeV) Microscopic op)cal poten)al for neutron-rich systems J. W. Holt, University of Washington CORRECTIONS TO LANE PARAMETRIZATION 15 -3 n = 0.13 fm , E = 10 MeV quadratic fit 10 n linear fit U = 25.1 + 13.3 2 5 I np np neutrons 0 (MeV) I U protons quadratic fit -5 p 2 UI = -21.0 np + 13.8 np -10 linear fit Holt, Kaiser & Miller, in prep.