Isospin flows from the past to the future: Recent progress and open questions of isospin physics Bao-An Li1 & Sherry J. Yennello2 1Arkansas State University 2 Texas A&M University The goal of isospin physics Determine the role of isospin degree of freedom in nuclear dynamics Extract the symmetry energy from isospin-sensitive observables Predictions for RIA and GSI Discussions

The Goal (A consensus ??) Among the major questions: Understand the isospin dependence of in-medium nuclear effective interactions, extract the isospin dependence of thermal, mechanical and transport properties of asymmetric nuclear matter playing important roles in nuclei, neutron stars and supernove. (A consensus ??) Among the major questions: 1. EOS of neutron-rich matter, especially the density dependence of symmetry energy Esym(ρ) 2. Momentum-dependence of the symmetry potential and the neutron-proton effective mass splitting mn*-mp* in neutron-rich matter 3. Isospin-dependence of the in-medium nucleon-nucleon cross sections in neutron-rich matter 4. Nature of liquid-gas phase transition in isospin asymmetric nuclear matter Approaches to reach the goal: Determine the role of isospin degree of freedom in nuclear dynamics Identify isospin-sensitive observables constraining/answering the above questions Develop advanced dynamical and statistical models, incorporating more information about the masses, binding energies and the isospin-dependence of level density parameter of exotic nuclei from nuclear structure studies, perform large scale simulations and compare with data Current status: Some experimental constraints on the Esym(ρ) at subnormal densities have been obtained. Several proposals to extract the Esym(ρ) at higher densities were put forward. Many interesting isospin effects were observed in heavy-ion collisions at intermediate energies. However, it remains unclear what new physics can be extracted from these effects. More work are needed on question 2, 3 and 4 which are equally important as the question 1.

Esym (ρ) predicted by microscopic many-body theories EOS of Isospin Asymmetric Nuclear Matter : Esym (ρ) predicted by microscopic many-body theories Symmetry energy (MeV) DBHF Effective field theory RMF BHF Green function Variational Density A.E. L. Dieperink et al., Phys. Rev. C68 (2003) 064307

Esym(ρ) from phenomenological approaches B. Cochet, K. Bennaceur, P. Bonche, T. Duguet and J. Meyer, nucl-th/0309012 J. Stone, J.C. Miller, R. Koncewicz, P.D. Stevenson and M.R. Strayer, PRC 68, 034324 (2003). New Skyrme interactions Easym 87 effective interactions Ebsym

The multifaceted influence of symmetry energy in astrophysics and nuclear physics J.M. Lattimer and M. Prakash, Science Vol. 304 (2004) 536-542. A.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. (2005) in press, nucl-th/0410066 isotransport n/p, π-/π+ Isospin Physics isocorrelation t/3He K+/K0 isoscaling isodiffusion isofractionation

from energy-momentum conservation on the proton Fermi surface The proton fraction x at ß-equilibrium in proto-neutron stars is determined by The critical proton fraction for direct URCA process to happen is Xc=1/9 from energy-momentum conservation on the proton Fermi surface Slow cooling: modified URCA: Critical points of direct URCA process Consequence: long surface thermal emission up to a few million years APR Akmal et al. Faster cooling by 4 to 5 orders of magnitude: direct URCA PSR J0205+6449 in 3C58 was suggested as a candidate A.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. (2005) in press.

Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list !)

The n/p ratio of pre-equilibrium nucleons as a probe of Esym(ρ) Symmetry energy Symmetry potential soft Statistically one expects: Dynamical simulations B.A. Li, C.M. Ko and. Z. Ren, PRL 78 (1997) 1644 B.A. Li, PRL 85 (2000) 4221 soft (N/Z)free/(N/Z)bound at 100 fm/c stiff

The n/p ratio of pre-equilibrium nucleons is one of the most sensitive observables to the Esym(ρ) as expected from the statistical consideration and predicted by several dynamical models (as also mentioned by M. Di Toro) Experimental situation: (several examples) Unusually high n/p ratio of pre-equilibrium nucleons beyond the Coulomb effect was observed by Dieter Hilscher et al. using the Berlin neutron-ball in both heavy-ion and pion induced reactions around 1987 Similar phenomenon was observed in heavy-ion experiments at MSU using the Rochester neutron-ball by Udo Schröder et al. around 1997 More recent experiments dedicated to the study of n/p ratio of pre- equilibrium nucleons are being analyzed by the MSU-UW collaboration Generally, a high n/p ratio of pre-equilibrium nucleons emitted from subnormal densities requires a soft symmetry energy. However, no model comparison has been made, thus no indication on the Esym(ρ) has been obtained yet.

Isospin transport (including those known as isospin-equilibrium, stopping, translucency, migration, transfer, diffusion, flow, distillation, fractionation, you name it) Isospin equilibrium can be achieved below the Fermi energy at a rate faster than the thermal equilibration Above the Fermi energy, however, isospin equilibrium is never achieved before the system breaks apart even in the most central reactions. Transport model calculations indicate that the isospin relaxation/diffusion rate is slower than that for thermal equilibration The degree of isospin translucency/stopping/diffusion is sensitive to the Esym(ρ). The isospin diffusion data from MSU indicates Esym(ρ)=32(ρ/ρ0)1.1 for ρ<1.2ρ0, and the asymmetric part of the isobaric incompressibility is found to be Kasy(ρ0)=-550 MeV Isospin dependence of collective flow and balance energy was observed. Indications of reduced in-medium nucleon-nucleon cross sections were found. Neutron enrichment in the neck region was observed. It is probably due to both isospin fractionation and formation of light symmetric clusters in the overlap region of two neutron-skins (Talks by M. Di Toro, Lee Sobotka et al.)

Transition from stopping to translucency around the Fermi Energy IBUU simulations by B.A. Li z S.J. Yennello et. al. NSCL/MSU-TAMU data Other isospin tracers, such as 9Be/7Be, 11B/10B and 13C/12C all lead to the same conclusion n and p originally from the target Ni n and p originally from the projectile Ar

Isospin translucency at relativistic energies X=p+d X=t/3He F. Rami et al. (FOPI/GSI) A measure of isospin transport in the reaction A+B using any isospin tracer X Only at midrapidity in most central collisions Rx=0 RBUU simulations by Hombach et al. (Giessen group)

The latest from NSCL/MSU on rapidity dependence of isospin transport Using X=7Li/7Be as the isospin tracer in mid-central 124Sn+112Sn at 50 MeV/A M.B. Tsang et al.

Ri at forward rapidities from simulations by Shi and Danielewicz Using X=d = (N-Z)/(N+Z) of the projectile-like fragment as the isospin tracer: Stiff Esym(ρ) Soft Esym(ρ) Ri is a stable signal Non-diffusion effects: cancelled out Ri ~ IEOS ->Diffusion effect Softer Esym(ρ) leads to higher isospin diffusion because the corresponding symmetry potential is larger at subnormal densities

Momentum-independent Influence of the momentum dependence of the symmetry potential on the dynamics of isospin diffusion, IBUU04 simulations by L.W. Chen, C.M. Ko and B.A. Li ρ ρ Momentum-dependent Momentum-independent Having the same Esym (ρ)=32 (ρ/ρ0)1.1

Comparing momentum-dependent IBUU predictions with data on isospin diffusion from MSU Experiments favors: Esym()=32 (/ρ0 )1.1 for ρ<1.2ρ0 Kasy(ρ0)~-550 MeV L.W. Chen, C.M. Ko and B.A. Li, PRL 94, 32701 (2005). M.B. Tsang et al. PRL 92, 062701 (2004) Isobaric incompressibility of asymmetric nuclear matter

Isospin fractionation and isoscaling Isospin fractionation: The free nucleons are more neutron-rich than the heavy-residue as predicted by both dynamical and thermal models due to the formation of symmetric light clusters (Koonin and Randrup) and/or the increasing symmetry energy with density (Muller and Serot, et. al.). Consistent with the n/p ratio of pre-equilibrium nucleons, the (n/p)residue ratio of the heavy-residue is also sensitive to the Esym(ρ). Isoscaling or t3 scaling (if α=-β) was observed in all kinds of reactions from fission, deep inelastic collisions to multifragmentation. The data are really beautiful. Explanations are very clear in both dynamical and statistical models. Searching for violations/conditions of the isoscaling is most interesting (Tsang et al, conditions for …)! Bao-An Li’s possibly biased observations and comments that you are more than welcome to disagree with: 1. Regardless how interesting the isoscaling phenomenon is, very little has been extracted so far about the Esym(ρ) from studying isoscaling R21 (N,Z) = Y2(N,Z) / Y1(N,Z) = C exp ( α N +β Z) 2. The scaling coefficient is α = 4 Csym/T ( (Z/A)12 – (Z/A)22 ) in the grand canonical statistical model and the EES model. Except in the EES model, the csym is the symmetry energy of normal nuclei. Several studies have placed a lot of efforts on extracting csym. Most of the extracted values of csym are about the same as the well-known symmetry energy at normal density extracted from nuclear masses as they should be. In my opinion, the interpretation of small csym vaules extracted involves too many assumptions that are not all well justified. 3. The isoscaling parameter α is sensitive to the Esym(ρ) NOT because of the csym, BUT due to the isospin asymmetries (Z/A)1 and (Z/A)2 of the two fragmenting residues. They are sensitive to the Esym(ρ) due to the dynamical isospin fractionation in the earlier stage of the reaction. 4. Why not just infer and study the Z/A of a single source in one reaction, instead of the (Z/A)12 – (Z/A)22 in two reactions through isoscaling? The former measures a first order effect of symmetry energy on Z/A while the latter measures a second order effect. Is not the isospin diffusion study or measuring directly the Z/A of the projectile-like or target-like residues the answer? Is not the latter much more efficient and easy to interpret? 5. Statistically, isoscaling appears for fragments from any two systems having the same T. Thus all systems reaching the plateau of the caloric curve should show isoscaling. Since the α depends on T and it is something so difficult to measure accurately, I personally do not expect to learn anything soon about the symmetry energy from statistical analysis of isosclaing before T is measured accurately. It is better to compares data directly with dynamical models, such as AMD and/or BNV, by varying the Esym(ρ) used in the models.

Isoscaling observed in many reactions Y2/ Y1 M.B. Tsang et al. PRL, 86, 5023 (2001)

Isoscaling data from residues of 64Ni (25MeV/nucleon) BigSol data R21 (N,Z) = Y2/Y1 R21 = C exp ( α N )

INDRA-ALADIN data

Predictions for RIA Besides more precise studies at low densities, it allows the determination of symmetry energy at high densities where it is most uncertain and most important for several questions in astrophysics. Three examples: Isospin fractionation Neutron-proton differential flow π - yields and π -/π + ratio

Symmetry energy and single nucleon potential used in an isospin- and momentum-dependent transport model stiff ρ soft density B.A. Li, C.B. Das, S. Das Gupta and C. Gale, PRC 69, 034614, NPA 735, 563 (2004).

Momentum dependence of the isoscalar potential Variational calculations by Wiringa

Momentum dependence of the symmetry potential Consistent with the Lane potential Lane potential extracted from n/p-nucleus scattering data indicates: for Ekin < 100 MeV

Neutron-proton effective mass splitting in neutron-rich matter

Isospin-dependent in-medium nucleon-nucleon cross sections NN cross sections in free-space in neutron-rich matter in symmetric matter

Formation of dense, asymmetric nuclear matter at RIA and GSI Soft Esym n/p ratio of the high density region Stiff Esym

Isospin fractionation (distillation): at isospin equilibrium EOS requirement: low (high) density region is more neutron-rich with stiff (soft) symmetry energy Symmetry enengy Isospin asymmetry of free nucleons stiff soft ρ0 density

Neutron-proton differential transverse flow:

Near-threshold pion production with radioactive beams at RIA and GSI ρ stiff soft density yields are more sensitive to the symmetry energy Esym(ρ) since they are mostly produced in the neutron-rich region However, pion yields are also sensitive to the symmetric part of the EOS

Pion ratio probe of symmetry energy

Time evolution of π-/π+ ratio in central reactions at RIA and GSI soft stiff

Differential ratios

Coulomb effects on π-/π+ ratio is well known

The Goal Among the major questions: Understand the isospin dependence of in-medium nuclear effective interactions, extract the isospin dependence of thermal, mechanical and transport properties of asymmetric nuclear matter playing important roles in nuclei, neutron stars and supernove. Among the major questions: 1. Equation of state of neutron-rich matter, especially the density dependence of symmetry energy Esym(ρ) 2. Momentum-dependence of the symmetry potential and the neutron-proton effective mass splitting in neutron-rich matter 3. Isospin-dependence of the in-medium nucleon-nucleon cross sections in neutron-rich matter 4. Nature of liquid-gas phase transition in isospin asymmetric nuclear matter Approaches to reach the goal: Determine the role of isospin degree of freedom in nuclear dynamics Identify isospin-sensitive observables constraining/answering the above questions Develop advanced dynamical and statistical models, incorporating more information about the masses, binding energies and the isospin-dependence of level density parameter of exotic nuclei from nuclear structure studies, perform large scale simulations and compare with data Current status: Some experimental constraints on the Esym(ρ) at subnormal densities have been obtained. Several proposals to extract the Esym(ρ) at higher densities were put forward. Many interesting isospin effects were observed in heavy-ion collisions at intermediate energies. However, it remains unclear what new physics can be extracted from these effects. More work are needed on question 2, 3 and 4 which are equally important as the question 1.

Discussions

Equation of State of Isospin Asymmetric Nuclear Matter K. Oyamatsu, I. Tanihata, Y. Sugahara, K. Sumiyoshi and H. Toki, NPA 634 (1998) 3.

Sensitivity of the Various Structure Measurements Iso Tanihata Radii Density Skin

Neutron-proton differential elliptical flow

Pion production at RIA from neutron-neutron scatterings are more sensitive to the symmetry energy !

Coulomb effects on π- and π+ spectra

Isospin fractionation at RIA Isospin asymmetry

Correlation of π-/ π+ and n/p ratios in high density region

Comparing momentum-independent BUU predictions with MSU data E(, d) = E(, 0)+Esym() d2, Esym()  ()  Data favors a stiff symmetry terms near Esym()  ()2 M.B. Tsang et al. PRL 92, 062701 (2004) MSU DATA 124Sn+112Sn

Strength of the symmetry potential with and without momentum dependence

Particle Flux: Isospin Flow: Isospin transport (diffusion) in heavy-ion collisions as a probe of Esym (ρ) at subnormal densities Particle Flux: Isospin Flow: Isospin diffusion coefficient DI depends on the symmetry potential L. Shi and P. Danielewicz, Phys. Rev. C68, 017601 (2003).

Summary Esym(ρ) is very important for both astrophysics and nuclear physics Isospin diffusion experiments favors: Esym()=32 (/ρ0 )1.1 for ρ<1.2ρ0 Kasy(ρ0)~-550 MeV Several sensitive probes for Esym() at high densities are found. Such as, the π-/ π+ ratio, in particular at low transverse momentum, is promising for determining the Esym() up to Need a powerful Time Projection Chamber (TPC) at RIA

symmetry energy Isospin- asymmetric nuclear matter with three Body Force symmetry energy Lombardo et al.

Lane Potential W.Zuo,U.Lombardo,Bao-An Li

Effects of symmetry energy on t/3He ratio

Effects of symmetry energy on n-p correlation function

Effects of the symmetry potential on nucleon-nucleon correlation functions

Isospin-dependence of flow G.D. Westfall et al.

Isospin-dependence of transverse flow

Isospin dependence of balance energy G.D. Westfall et al.