1. 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

2. 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:
EOS of neutron-rich matter, especially the density dependence of symmetry energy Esym(ρ)
Momentum-dependence of the symmetry potential and the neutron-proton effective mass splitting mn*-mp* in neutron-rich matter
Isospin-dependence of the in-medium nucleon-nucleon cross sections in neutron-rich matter
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.

3. 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)

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

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

6. 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 J in 3C58
was suggested as a candidate
A.W. Steiner, M. Prakash, J.M. Lattimer and P.J. Ellis, Phys. Rep. (2005) in press.

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

8. 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

9. 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.

10. 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.)

11. 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

12. 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)

13. 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.

14. 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

15. 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

16. 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, (2005).
M.B. Tsang et al.
PRL 92, (2004)
Isobaric incompressibility of asymmetric nuclear matter

17. 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.

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

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

20. INDRA-ALADIN data

21. 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

22. 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, , NPA 735, 563 (2004).

23. Momentum dependence of the isoscalar potential
Variational calculations by Wiringa

24. 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

25. Neutron-proton effective mass splitting in neutron-rich matter

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

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

28. 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

29. Neutron-proton differential transverse flow:

30. Near-threshold pion production with radioactive beams at RIA and GSIρ
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

31. Pion ratio probe of symmetry energy

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

33. Differential ratios

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

35. 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:
Equation of state of neutron-rich matter, especially the density dependence of symmetry energy Esym(ρ)
Momentum-dependence of the symmetry potential and the neutron-proton effective mass splitting in neutron-rich matter
Isospin-dependence of the in-medium nucleon-nucleon cross sections in neutron-rich matter
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.

36. Discussions

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

38. Sensitivity of the Various Structure Measurements
Iso Tanihata
Radii
Density
Skin

39. Neutron-proton differential elliptical flow

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

41. Coulomb effects on π- and π+ spectra

42. Isospin fractionation at RIA
Isospin asymmetry

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

44. 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, (2004)
MSU DATA 124Sn+112Sn

45. Strength of the symmetry potential with and without momentum dependence

46. 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, (2003).

47. 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

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

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

51. Effects of symmetry energy on t/3He ratio

52. Effects of symmetry energy on n-p correlation function

53. Effects of the symmetry potential on nucleon-nucleon correlation functions

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

55. Isospin-dependence of transverse flow

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