Microscopic nucleon-nucleus optical potentials for -rich systems

Jeremy W. Holt Department of University of Washington

INT workshop: Reactions and structure of exotic nuclei, 03/05/2015 OUTLINE

Physics motivations

Neutron-capture rates in r-process

Neutron star structure (inner crust)

Charged-current weak reactions in newly formed neutron stars

Nucleon self in homogeneous

Improvements in theory: perturbative chiral nuclear that reproduce saturation

Benchmark to phenomenological potentials close to

Corrections to the Lane parametrizaton of the asymmetry dependence

Microscopic opcal potenal 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 opcal potenal for neutron-rich systems J. W. Holt, University of Washington INPUTS FROM

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 opcal potenal for neutron-rich systems J. W. Holt, University of Washington CHALLENGE 2: EQUILIBRIUM STATE OF INNER CRUSTS

Outer crust is a lattice of nuclei with gas of

Inner crust contains lattice of neutron-rich nuclei together with “dripped”

Neutron drip density:

Dripped neutrons

Bound neutrons

Outer Crust Inner Crust

Microscopic opcal potenal for neutron-rich systems J. W. Holt, University of Washington GLOBAL OPTICAL POTENTIALS (PHENOMENOLOGICAL)

Koning & Delaroche, NPA (2003)

Energy dependence

Microscopic opcal potenal 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 opcal potenal 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 opcal potenal for neutron-rich systems J. W. Holt, University of Washington MICROSCOPIC FROM “NEXT-TO-FIRST PRINCIPLES”

Quark/ (high energy) dynamics

Approximate chiral symmetry (left- and right- handed transform independently)

n Nucleon/ (low energy) dynamics

Compatible with explicit and spontaneous chiral p symmetry breaking

Microscopic opcal potenal 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 Heavy (ρ, ω) Λ

0 π (q/Λ) N Systematic expansion Nucleon momenta Pion q (q/Λ)2

QCD chiral symmetry

quarks (q/Λ)3

(q/Λ)4 Pions weakly-coupled at low momenta!

Microscopic opcal potenal 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 opcal potenal 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 opcal potenal 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 (q/Λ)2 and lifetime

QCD chiral symmetry

quarks (q/Λ)3

(q/Λ)4 Pions weakly-coupled at low momenta!

Microscopic opcal potenal 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 opcal potenal 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 opcal potenal 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 opcal potenal for neutron-rich systems J. W. Holt, University of Washington SATURATION OF SYMMETRIC

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 opcal potenal 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 opcal potenal 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 opcal potenal 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 opcal potenal 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 opcal potenal 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 opcal potenal for neutron-rich systems J. W. Holt, University of Washington REAL AND IMAGINARY /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 opcal potenal 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 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 opcal potenal 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 opcal potenal for neutron-rich systems J. W. Holt, University of Washington THE -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- in the neutrinosphere

Microscopic opcal potenal for neutron-rich systems J. W. Holt, University of Washington WHERE DO (ANTI-) 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 opcal potenal for neutron-rich systems J. W. Holt, University of Washington NUCLEON HARTREE-FOCK SELF-ENERGIES

Supernova simulations treat protons and neutrons as 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 opcal potenal for neutron-rich systems J. W. Holt, University of Washington PHASE SPACE ANALYSIS

Charged-current reactions ( ) with

nucleon kinematic regions

phase space

Mean-field effects

Microscopic opcal potenal 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 opcal potenal 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 -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 opcal potenal for neutron-rich systems J. W. Holt, University of Washington