#### Transcript The sensitivity of probes to DDSP - uni

### The sensitivity of probes to DDSP

*at high densities*

Qingfeng Li * DDSP: Density dependent symmetry potential

### Outline

Brief introduction to the DDSP.

Predicted sensitive probes to DDSP at high densities.

However , too many (huge)

**uncertainties**

other potentials, from collision term, from from models and from experiments, etc are awaiting us to solve.

Several examples.

No conclusions, only remarks.

2020/4/26 ASY-EOS Workshop 2008,Catania

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### SP is relatively small

= Binding energy from Liquid-drop mass formula: Isospin-dependent EoS (energy density as a function of and ):

*E*

*E*

( ,0)

*E*

s ym ( ) 2

*O*

( 4 ), (

*n*

*p*

) / Initial 2 : Au: 0.0392

; Pb:0.0447

Zr96:0.0278;Ru96:0.0069

Sn132:0.0587; Sn124:0.0375

It would not be a big deal if the uncertainty in E sym was not big 2020/4/26 ASY-EOS Workshop 2008,Catania

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### The origin of the DDSP ---From the RBUU point of view.

*L*

~

*X*

1 2

*L F*

*HF*

*X*

,

*H L I L F L*

int

*p*

,

*t*

*p*

*i*

2 1 2 1 4

*L*

*g*

*p*

Re

*F*

*X*

,

*p*

,

*t*

*p*

*M N*

*L*

*g*

*p*

,

*t*

*X*

*U*

*M p*

* Re

*x*

*U*

*x*

1 2 1 2

*g*

*U*

1 4

*U*

*F*

*F*

*g*

*X*

Re

*F*

*X*

,

*d*

2

*W el*

*p*

2 ,

*in*

*p*

*d p*

3 2 ,

*p*

2 ,

*d p*

2

*p*

3 , 4 3

*p*

4

*d*

3

*p*

2

*v d*

*el*

,

*in d*

*s*

, 4

*F el*

2 ,

*in d*

*p*

*F el*

1 ,

*in*

*p*

2

*p*

*p*

3 Re

*F*

*X*

,

*p*

,

*t*

*X*

*

*E M*

*

*f*

*p*

*p*

4

*E*

2 3 4 2020/4/26 ASY-EOS Workshop 2008,Catania

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### The isospin effects in RBUU

*E Sym*

1 6

*pp*

,

*nn*

,

*np K f*

2

*E f*

1 2 {

*g*

2 4

*m*

2

*g*

2

*m*

2

*d*

*d*

*pp*

,

*nn*

,

*np d*

(

*E F*

2 [ 1

*g*

2

*m*

2

*M*

* 2

*A*

(

*K f*

,

*M*

* )] )}

*B*

2 1 1

*d*

cos Hartree Term

*A*

(

*K f*

,

*M*

* )

*d*

*pp*

,

*nn*

,

*np d*

4 ( 2 ) 3

*F i*

*d*

3

*k*

*k*

2 (

*k*

2

*M*

* 2 ) 3 / 2 2

*i*

2

*i*

*t*

2020/4/26 Interaction Direct Term ASY-EOS Workshop 2008,Catania Exchange Term

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### Density dependence of symmetry potential at low and high densities

Phenomenological Skyrme parameter sets 18 sets From B. Alex Brown, PRL 85, 5296 (2000) Uncertainty comes mainly from

**high density region**

2020/4/26 ASY-EOS Workshop 2008,Catania

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### Is the DDSP at high densities mainly important to neutron star?

It might impact on nuclear physics when one investigates the HICs induced by radioactive beam at intermediate energies.

Now, the community tries to find the effect of DDSP on observables from HICs at intermediate energies (~0.25 2.0A GeV) 2020/4/26 ASY-EOS Workshop 2008,Catania

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### Predicted probes of DDSP at high densities from the HICs

The (double)

**ratio**

of multiplicities of charged nucleons, s, s, pions, kaons and hard photons as functions of E b , b, N/Z; p t , y, E kin , etc.

The (double)

**flow**

, flow difference, differential flow of nucleons, pions as functions of E b ,b,N/Z,p t , y, E kin , etc.

2020/4/26 ASY-EOS Workshop 2008,Catania

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### Difficulties and Uncertainties

① ② ③ 2020/4/26 With the increase of beam energy (to ~A GeV): the compression stage is shorter The effect of nucelar MF on dynamics is weaker The isospin asymmetry during dynamic evolution is reduced The dynamics is dominated by CT rather than the nuclear MF.

In addition to and more complicated , other resonances and mesons produce which makes the situation much Large medium modification on the collision term The relativistic effects in kinetic or dynamic transports ……(from experimental sides?)

**Not easy to achieve our goal**

ASY-EOS Workshop 2008,Catania

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Meson multiplicity ratio and double ratio

*New “puzzles”*

E b =1.528A GeV INM Au+Au (N/Z=1.494) HIC 132 Sn+ 124 Sn From W. Reisdorf etal, NPA781,459(2007) 2020/4/26 From X. Lopez etal PRC75, 011901(R) (2007) ASY-EOS Workshop 2008,Catania

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### The update of UrQMD for heavy ion reactions at E

b

### ~0.1-2A GeV

SP for all baryons. (for some non-nucleonic particles, C-G coefficients of isospin coupling are employed.

MD for all baryons. (isospin independent) Coulomb Baryon.

interaction between two mesons or Meson More EoS parameter sets. (H, S, HM, SM), which describe the ground state properties of finite nuclei equally well (K NM ranges from 200 to 400 MeV). The medium modified N-N elastic cross section (optional). Relativistic effect on relative distances in phase space of two particles (Lorentz transformation). See, e.g., JPG32,151(2006) and PLB659,525(2008) 2020/4/26 ASY-EOS Workshop 2008,Catania

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Example I uncertainty from Afterburner program 1.

2.

To construct clusters of nucleons, one Afterburner analyzing program is usually used to couple to the transport model.

But, usually, it is paid less attention. There exist two types: In QMD-like models, the phase-space coalescence model is employed. In BUU-like models, a density cut (in coordinate space) is often used to find out free nucleons.

Due to the smallness of DDSP effect, one should check the effect from the difference of the two types.

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2020/4/26 ASY-EOS Workshop 2008,Catania

### Cluster freeze-out

2020/4/26 “Coalescence Model” ASY-EOS Workshop 2008,Catania “Density-cut”

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### p

t

### dependence of the N/Z ratio

c = 0 /10 Sensitive to SP at both low and high densities n/p (double) ratios at small pt are influenced by the freeze-out criteria The ratios at large pt are not influenced by the freeze-out criteria.

**Argument: one needs to investigate the isospin dependent momentum dependent term**

2020/4/26 ASY-EOS Workshop 2008,Catania

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### Example II: contamination in

### reconstruction

at freeze-out “contaminated reconstruction” mode 2020/4/26 “clean reconstruction” mode ASY-EOS Workshop 2008,Catania

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### p

t

### dependence of

0

### /

++

### ratio

“contamination” effect is huge at small E kin due to the rescattering of nucleons.

**Two modes give two different ratios (L) and scaled ratios (R) vs E kin in both low and high regions.**

2020/4/26

**The reconstruction should be analyzed with care.**

ASY-EOS Workshop 2008,Catania

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Example III: Mesonic Coulomb Potential and reduction of N channel on Pion flows (v 1 and v 2 ) 0.05

1.5A GeV FOPI data, from W.Reisdorf etal, NPA781,459(2007) v1 + 0

*=*

+ 0.04

-v 2 0

*=<(p x 2 -p y 2 )/p t 2 >*

2020/4/26 b 0 :0.25-0.45

ASY-EOS Workshop 2008,Catania

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### Several remarks

The isospin-independent terms are also needed to check carefully when investigating the symmetry potential at high densities.

Nucleon-related quantities should be paid much more attention.

Higher beam energy HIC is not always better. HICs at beam energies ~100-800A MeV are recommended at this time.

Better Afterburner program is needed

**Detailed comparison between transport models is urgently needed.**

**I call for closer cooperation between theoretical and experimental physicists.**

2020/4/26 ASY-EOS Workshop 2008,Catania

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### As were done before

2020/4/26 We will be the next, yes?

ASY-EOS Workshop 2008,Catania

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2020/4/26

### Thanks

**Contact me? **

ASY-EOS Workshop 2008,Catania

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