Symmetry Energy. in Structure and in Central and Direct Reactions

: in Structure and in Central and Direct Reactions Pawel Natl Superconducting Cyclotron Lab, US The 12 th International Conference on Nucleus-Nucleus Collisions June 21-26, 2015, Catania, Italy

Bulk Properties of Strongly-Interacting Matter Nuclei Isospin DensityNeutron Stars

Equation of State Nuclei Isospin DensityNeutron Stars Reactions - coarse. Structure - detailed, but competition of macroscopic & microscopic effects

Energy in Uniform Matter E (ρ n, ρ p ) = E ( 0 (ρ) + S(ρ) ρn ρ ) p 2 + O(... 4 ) ρ symmetric matter (a)symmetry energy ρ = ρ n + ρ p E 0 (ρ) = a V + K ( ρ ρ0 ) 2 +... S(ρ) = a V 18 ρ a + L ρ ρ 0 +... 0 3 ρ 0 Known: a a 16 MeV K 235 MeV Unknown: aa V? L?

ρ in Nuclear Mass Formula Textbook Bethe-Weizsäcker formula: E = a V + a S 2/3 Z 2 + a C 1/3 + a (N Z ) 2 a + E mic Symmetry energy: charge n p symmetry of interactions nalogy with capacitor: E a = a a (N Z ) 2 (N Z )2 a a?volume Capacitance? E a = independent capacitors r E = Q2 2C (N Z )2 a a (N Z )2 a V a + 2/3 a S a Thomas-Fermi (local density) approximation: C ρ dr a a () = = S(ρ) aa V, for S(ρ) aa V TF breaks in nuclear surface at ρ < ρ 0 /4 PD&Lee NP818(2009)36

Mass Formula & Isospin Symmetry Symmetry-energy details in a mass-formula are intertwined with details of other terms: Coulomb, Wigner & pairing + even those asymmetry-independent, due to (N Z )/ - correlations along stability line (PD)! Best would be to study the symmetry energy in isolation from the rest of mass-formula! bsurd?! Charge invariance to rescue: lowest nuclear states characterized by different isospin values (T,T z ), T z = (Z N)/2. Nuclear energy scalar in isospin space: sym energy E a = a a () (N Z )2 = 4 a a () T 2 z E a = 4 a a () T 2 = 4 a a() T (T + 1)

Isobaric Chains and Symmetry Coefficients Energy Levels of =16 Isobaric Chain Curvature < > symmetry coefficient T=2 T=1 Isobaric nalog States

Symmetry Coefficient Nucleus-by-Nucleus Mass formula generalized to the lowest state of a given T : T (T + 1) E(, T, T z ) = E 0 () + 4a a () + E mic + E Coul In the ground state T takes on the lowest possible value T = T z = N Z /2. Through +1 most of the Wigner term absorbed.?lowest state of a given T : isobaric analogue state (IS) of some neighboring nucleus ground-state. T z =-1 T z =0 T z =1 Study of changes in the symmetry term possible nucleus by nucleus T=1 T=0 EIS = E = a [ T (T + 1) ] a + E mic

From a a () to S(ρ) Strong a a () dependence [PD & Lee NP922(14)1]: lower more surface lower ρ lower S a a () from IS give rise to constraints on S(ρ) in Skyrme-Hartree-Fock calculations

uxiliary Info: Skins Results f/different Skyrme ints in half- matter. Isoscalar (ρ=ρ n +ρ p ; blue) & isovector (ρ n -ρ p ; green) densities displaced relative to each other. s S(ρ) changes, so does displacement.

Jefferson Lab Direct: p Interference: n Strategies for n and p Densities PD elastic: p + n charge exchange: n p ρ n +ρ p p σ p ρ n ρ p IS p π + n

Why Isovector Rather than Neutron Skins Isovector skin: in no-curvature, no-shell-effect, no-coulomb limit, the same for every nucleus! Not suppressed by low (N Z )/! Nucleon optical potential in isospin space: U = U 0 + 4τT U 1 isoscalar potential U 0 ρ, isovector potential U 1 (ρ n ρ p ) In elastic scattering U = U 0 ± N Z U 1 In quasielastic charge-exchange (p,n) to IS: U = 4τ T + U 1 Elastic scattering dominated by U 0 Quasielastic governed by U 1 Geometry usually assumed the same for U 0 and U 1 e.g. Koning & Delaroche NP713(03)231?Isovector skin R from comparison of elastic and quasielastic (p,n)-to-is scattering?

Quasielastic (p,n) Reaction to IS: Skin or No-Skin? Data: Patterson et al. NP263(76)261 Calculations: PD & Singh (preliminary) with and without change R in radius of U 1 compared to elastic Before n-skin: Stephen Schery

Size of Isovector Skin Large 0.5 fm skins!

Constraints on Symmetry-Energy Parameters

Constraints on S(ρ)

Pions Probe System at High-ρ! Elementary processes: N + N N +, N + π Song&Ko PRC91(15)014901 PD PRC51(95)716 π test the maximal densities reached and collective motion then

Pions as Probe of High-ρ B- Li: S(ρ > ρ 0 ) n/p ρ>ρ0 π /π + E sym (MeV) 80 60 40 20 0 E a sym E b sym Pions originate from high ρ ρ/ρ 0 1 2 3 (n/p) ρ/ρ0 >1 1.6 1.5 1.4 132 Sn+ 124 Sn, b=1 fm E/=200 MeV 2.3 2.1 (π /π ) like + 1.9-1.3 1.7 1.2 1.5 0 10 20 30 0 10 20 3 0 t (fm/c)

Dedicated Experimental Efforts SMURI-TPC Collaboration (8 countries and 43 researchers): comparisons of near-threshold π and π + and also n-p spectra and flows at RIKEN, Japan. NSCL/MSU, Texas &M U Western Michigan U, U of Notre Dame GSI, Daresbury Lab, INFN/LNS U of Budapest, SUBTECH, GNIL China IE, Brazil, RIKEN, Rikkyo U Tohoku U, Kyoto U T-TPC Collaboration (US & France)

FOPI: π /π + at 400 MeV/nucl and above Hong & PD, PRC90(14)024605: measured ratios reproduced in transport irrespectively of S int (ρ) = S 0 (ρ/ρ 0 ) γ : π /π + 5.5 5 4.5 4 3.5 3 2.5 FOPI 2 u+u 400 MeV 1.5 200 MeV 1 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 γ

Original Idea Still Correct for High-E π s π - /π + 10 u+u overall pion ratio γ=0.5 γ=0.75 γ=1.0 γ=1.5 γ=2.0 1 0 20 40 60 80 100 120 140 KE c.m. (MeV) S int (ρ) = S 0 (ρ/ρ 0 ) γ charge-exchange reactions blur signal

Conclusions Symmetry-energy term weakens as nuclear mass number decreases: from a a 23 Mev to a a 9 MeV for 8. Weakening of the symmetry term can be tied to the weakening of S(ρ) in uniform matter, with the fall of ρ. IS energies insufficiently constrain L skin info needed! Isovector skins - large and relatively weakly dependent on nucleus! Large R 0.5 fm L 70 fm Comprehensive analysis of elastic/quasielastic scattering data needed! In the region of ρ ρ 0, S(ρ) is quite uncertain. One promising observable is high-en charged-pion yield-ratio around NN threshold. PD&Lee NP922(14)1; Hong&PD PRC90(14)024605; PD&Singh US NSF PHY-1068571 & PHY-1403906 + Indo-US Grant