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): Perturba ve 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 es mate 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 Theore cal 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. -15 0 0.1 0.2 0.3 0.4 np
Microscopic op cal poten al for neutron-rich systems J. W. Holt, University of Washington CORRECTIONS TO LANE PARAMETRIZATION
8
-3 6 n = 0.13 fm , E = 10 MeV linear fit
4 n 2 quadratic fit WI = 18.5 np - 14.4 np 2 neutrons
0 (MeV) I W -2 protons p W = -16.1 - 0.05 2 -4 I np np quadratic fit
-6 linear fit Holt, Kaiser & Miller, in prep. -8 0 0.1 0.2 0.3 0.4 np
Microscopic op cal poten al for neutron-rich systems J. W. Holt, University of Washington THE NEUTRINO-DRIVEN WINDS AND THE R-PROCESS
R-process from SNe requires large number of neutrons per seed nucleus
Proton fraction of outflow set by competing charged-current reactions
Robust r-process nucleosynthesis:
H.-T. Janka et al, Phys Rept 2007
(Anti-)neutrino decoupling region sensitive to nuclear physics inputs: especially nucleon single-particle energies in the neutrinosphere
Microscopic op cal poten al for neutron-rich systems J. W. Holt, University of Washington WHERE DO (ANTI-)NEUTRINOS DECOUPLE?
Neutrino reactions Anti-neutrino reactions Neutrino opacity
Charged-current
Martinez-Pinedo et al, Anti-neutrino opacity J Phys G (2014)
Neutral-current
Charged-current
Microscopic op cal poten al for neutron-rich systems J. W. Holt, University of Washington NUCLEON HARTREE-FOCK SELF-ENERGIES
Supernova simulations treat protons and neutrons as quasiparticles in the mean-field approximation
Nuclear interactions attractive at low momenta and
Mean field effects further widen the neutrons energy gap between protons and neutrons protons Q-value for (anti-)neutrino absorption changes significantly
Microscopic op cal poten al for neutron-rich systems J. W. Holt, University of Washington PHASE SPACE ANALYSIS
Charged-current reactions ( ) with
lepton nucleon kinematic regions
phase space
Mean-field effects
Microscopic op cal poten al for neutron-rich systems J. W. Holt, University of Washington WEAK REACTION RATES INCLUDING MATTER EFFECTS
(1) Chiral NN potential at mean-field level
(2) Pseudo-potential (reproduces exact energy shift when used at the mean field level)
Fumi (1955), Fukuda & Newton (1956)
Nucleon energies: Rrapaj, Holt, Bartl, Reddy & Schwenk, arXiv:1408.3368
Microscopic op cal poten al for neutron-rich systems J. W. Holt, University of Washington FUTURE WORK
Nuclear equation of state for astrophysical simulations
Clustering at low densities, match to virial EoS
Extrapolate to high-density, high-temperature regime
Optical potentials for neutron-rich nuclei Derive spin-orbit terms
Fold with theoretical/empirical density distributions
Neutrino reactions in proto-neutron stars
Develop consistent equation of state
Merge with numerical simulations of core-collapse supernovae
Microscopic op cal poten al for neutron-rich systems J. W. Holt, University of Washington