Isospin effects in neutron and proton flows
by Qingfeng Li @ FIAS, (AvH fellow, Host: Horst Stöcker)
Thanks: Marcus Bleicher, Sven Soff, Zhuxia Li
19.04.23 Qingfeng Li for GSI 2006
Outline
Our purpose -and- many observables The isospin effect on nucleons The flows and the differential flows The importance of precise measurement
on neutrons Good future, laborious work.
19.04.23 Qingfeng Li for GSI 2006
The purpose
The uncertainty in symmetry term, especially in the density dependence of symmetry energy
Obviously, it is closely related to Astrophysics and neutron-rich structure and reaction physics (with large neutron access).
19.04.23 Qingfeng Li for GSI 2006
Normal Observables Particle species: emitted neutrons and protons,
resonances (), Sigmas, light and heavy fragments, mesons (pions, kaons,etc)
Single-particle observables: excitation function of particle multiplicities, (transverse)momentum-/energy-/rapidity- distribution, momentum quadrupole (Qzz), radial-/direct-/elliptic- flows,…
Two-particle correlations: HBT (coordinate-momentum corr.), angular correlation, …
19.04.23 Qingfeng Li for GSI 2006
“New” observables Single-/double- negatively/positively charged p
article (nucleons, pions, kaons, etc) ratios from Ru/Zr+Zr/Ru (mass symmetric but isospin asymmetric) reactions (FOPI), or from Sn-isotope reactions (Michigan).
Vartl, (FOPI), or Rt/l=dN/dYx/dN/dYz
flow difference/differential flow (Fn-p,v2pm) of neg
atively-positively charged particles
19.04.23 Qingfeng Li for GSI 2006
To study the isospin effects Nucleons are still one of the most sensitive
candidates, which should be preferentially considered
Now, experimentally, it is able to measure neutrons with much more higher precision. Hmmm, right?
Other particles? Of course important, but raise more uncertainties. As the first step, I suggest to measure neutrons and protons.
19.04.23 Qingfeng Li for GSI 2006
Many efforts At quite low densities (/
0=0.01-0.05) Nucl-ex/0602023
At subnormal densities (compared with BUU):
At supranormal densities:
05.10 )/(6.31 symE + free
69.00 )/(6.31 symE
*+
?
~ 0.3
19.04.23 Qingfeng Li for GSI 2006
Symmetry energy effects on nucleons
2005-PhysRevC_72_034613
S-IS-II
0 30 60 90 120 1500
1
2
u|r
|<2
fm
t (fm/c)
48Ca+52Ca, Eb100A MeV, <11%
1
2
3
um
ax
0.5
1.0
1.5
dN
/dt
15
30
45
N
1.71.81.92.02.12.22.3
n/p
=0.3
19.04.23 Qingfeng Li for GSI 2006
Flows and differential transverse flow
To explore the medium at early stage when the central density is high.
The differential transverse flow suggested by Bao-An:
The multiplicities of nucleons should be firstly nicely reproduced by model.
px
nx pp If
19.04.23 Qingfeng Li for GSI 2006
Pion elliptic flow difference
2006-JPG_32_151
ZPA352,171(1995): by Bass, Hartnack, etal(neutron squeeze-out)PLB 562, 215(2003): by Greco, Baran, etal(neutron-proton v2 difference)
IE @ supranormal densities!
Eb=800A GeVb=7-9 fm
At pt~0.2-0.5 GeV/c,v_2^pm reflects explicitlythe density dependence ofsym.ene. at u>1.
19.04.23 Qingfeng Li for GSI 2006
Nucleon double ratio from Ru/Zr+Zr/Ru
2006-PhysRevC_73_051601(R)
Others: Bao-An Li et al.: (using Sn isotoptes)Double N/P ratio: Phys.Lett.B634:378-382,2006 Double pi-/pi+ ratios:Phys.Rev.C73:034603,2006 Double N-P differential flow :nucl-th/0606003
Advantage: to show simultaneously the dependence on symmetry energyand the degree of isospinequilibrium
The symmetry energy effect On FD is enhanced whenEb~400A MeV, b/b0~0.5
19.04.23 Qingfeng Li for GSI 2006
Isopin dependent medium effects on N-N elastic cross sections
2006-JPG_32_407
MF and C come from the same Lagrangian. They are both isospin dependent
19.04.23 Qingfeng Li for GSI 2006
At Eb~400A MeV When comparing with those at Eb< 100A MeV: more IMF, excitataion energies of IMF are also lar
ge. They will decay (statistically/promptly/sequentially?) afterwards.
The isospin-asymmetric and high-excited IMF play important role in final results.
The treatment of isospin effects on the late stage (in some after-burner program) should be paid more attention. (When to terminate the transport computation?)
19.04.23 Qingfeng Li for GSI 2006
My suggestions Experimentally:Experimentally:1. Multi-systems and Multi-observables. such as: Zr+Ru/Ru+Zr and Sn132+Sn124/Sn112+Sn112 For nucleons: multiplicities, (hence, the transverse momdnetu
m of n/p ratio), transverse and elliptic flows (hence, the flow diff./diff.flow) are required to measure.
2. Higher precision. (at least, errors should be well <10%) Theoretically:1. A completely self-consistent and relativisitic transport model
(at least, in the N-- system)+ a good after-burner program are indispensable, since the isospin effects are small.