1. Probing the nuclear symmetry energy at sub-saturation densities with 3H/3He ratio
Good afternoon, everyone, my name is Yongjia wang, I come from Huzhou University, Huzhou is located at latitude thirty degree and one hundred and twenty degree, very close to Shanghai. The title of my presentation is probing the nuclear symmetry energy at sub-normal densities with triton/helium-three yield ratio.
Yongjia Wang (王永佳)1, Chenchen Guo (郭琛琛)2, and Qingfeng Li (李庆峰)1
1. Huzhou University (湖州师范学院), Huzhou, China
2. Beijing Normal University (北京师范大学), Beijing, China
NuSYM15 Krakow Jun 29, 2015

2. Probing the nuclear symmetry energy at sub-saturation densities with 3H/3He ratio
east longitude
120°
north latitude
30°
Good afternoon, everyone, my name is Yongjia wang, I come from Huzhou University, Huzhou is located at latitude thirty degree and one hundred and twenty degree, very close to Shanghai. From Shanghai may take two hours by car to Huzhou. The title of my presentation is probing the nuclear symmetry energy at sub-normal densities with triton/helium-three yield ratio.
Yongjia Wang (王永佳)1, Chenchen Guo (郭琛琛)2, and Qingfeng Li (李庆峰)1
1. Huzhou University (湖州师范学院), Huzhou, China
2. Beijing Normal University (北京师范大学), Beijing, China
NuSYM15 Krakow Jun 29, 2015

3. Probing the nuclear symmetry energy at sub-saturation densities with 3H/3He ratio
Outline
Motivation
experimental side and transport model side
UrQMD model description
recent updates and the main distinguishing feature
Results and Summary
I’m going to divide this talk into three parts. The first part is motivation, I will give the reason why we concentrate on triton/helium-three ratio again, from both transport model and experimental side. Second, I would like to give a introduction about the UrQMD transport model and some recent updates and its the main distinguishing feature. In the last part, I will give some results from the updated UrQMD model and a summary.
NuSYM15 Krakow Jun 29, 2015

4. Method: experimental data + model simulation
Motivation
Symmetry energy:
Method: experimental data + model simulation
esym (MeV)
Probes:
Nuclear structure:
mass, neutron skin thickness,
IAS,PDR, GDR …
Nuclear reaction:
isospin diffusion, isoscaling, π-/π+,
double n/p, transverse flow,3H/3He,
elliptic flow, balance energy…
Neutron star: mass and radii …
As already talked by previous speakers, symmetry energy is very important, that’s a reason why we are all here. Many attempts have been made and Many probes have been proposed, while the magnitude of symmetry energy and its density dependence are currently uncertain.
NuSYM15 Krakow Jun 29, 2015

5. Motivation: from transport model side
Stiff symmetry energy
gives much more 3H.
Soft symmetry energy
BUU-type model
Lie-Wen Chen, et al., PRC (2003)
QMD-type model
Why we concentrate on triton/helium-three ratio again? Actually, the triton/helium-three has been suggested as a sensitive probe of symmetry energy before within both BUU-type and QMD type model. Both Those two studies showed that the ratio calculated with soft symmetry energy is larger than that with stiff one. But in BUU calculation, a stiff symmetry energy gives much more tritons, while in QMD calculations, a soft symmetry energy gives much more tritons.
stiff
soft
Qingfeng Li, et al., PRC (2005);
Yingxun Zhang, et al., PRC (2005)
NuSYM15 Krakow Jun 29, 2015

6. Motivation: from transport model side
Stiff symmetry energy
gives much more 3H.
BUU-type model
IBUU04 + phase-space
coalescence afterburner
G.-C. Yong, et al. PRC (2009).
The 3H/3He yield ratio is not sensitive to symmetry energy.
Lie-Wen Chen, et al., PRC (2003)
QMD model
moreover, recently, using the IBUU model plus a phase-space coalescence afterburner, showed that the triton/helium-three ratio is not sensitive to symmetry energy anymore. Thus, those different result from transport models certainly deserve further studies.
Soft symmetry energy
gives much more 3H.
stiff
soft
Qingfeng Li, et al., PRC (2005);
Yingxun Zhang, et al., PRC (2005)
NuSYM15 Krakow Jun 29, 2015

7. Motivation: from experimental side
Recently published experimental data about 3H and 3He:
System: 40Ca+ 40Ca, 96Zr+ 96Zr, 96Ru+ 96Ru,197Au+197Au
Energy: 120A MeV~1000A MeV
Impact parameter: b0<0.15, b0=b/bmax, with bmax=1.15(At1/3+Ap1/3)
FOPI Collaboration, NPA (2010)，NPA (2012).
This data set offers new opportunities for studying the 3H/3He ratio over wide ranges of both, beam energy and system size.
J. Brzychczyk’s talk on
NuSYM14
The energy spectra of 3H and 3He were measured in Lanzhou.
See Z. G. Xiao’s talk
Let’s see the motivation from experimental side. First and foremost, we all know that 3H and 3He can be more easily detected because they are charged particles. Recently, FOPI collaboration published a large amount yield data for light charged clusters. This data set offers new opportunities for studying the 3H/3He ratio over wide ranges of both, beam energy and system size. In addition, very recently, experimentalists in Krakow created KRATTA, it can be used to measure 3H/3He data. 3h and 3he were also measured in Lanzhou, prof zhigang xiao will talk about this later on.
NuSYM15 Krakow Jun 29, 2015

8. Motivation: from experimental side
T. X Liu, W. G. Lynch, et al. PRC
Michael David Youngs
PhD thesis, MSU, 2013.
pBUU, ImQMD
Large discrepancy!
Akira Ono’s AMD model works better.
Moreover, the energy spectra of 3H and 3He were measured at MSU a few years ago. And found that this is a large discrepancy between model calculation and the data. As already talked by ono yesterday, AMD model works better on this direction. But I think more calculation with other transport model are still necessary. Thus, in view of these experimental progress and model dependent when study the ratio, the sensitivity of 3h/3he ratio to the nuclear symmetry energy is a subject of continuing interest.
NuSYM15 Krakow Jun 29, 2015

9. Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model
S.A. Bass, et al., Prog. Part. Nucl. Phys.41: (1998);
M. Bleicher, et al.,JPG (1999).
Lorentz-covariant dynamics
Relativistic-QMD
UrQMD
Collision term
Mean field term
QMD
improve and extand collision term
Main update:
Skyrme interaction are introduced to the UrQMD model.
Similar to ImQMD
Yingxun Zhang, et al.
PRC
Yongjia Wang, et al.
PRC
Next, I would like to give a brief introduction about UrQMD model and its recent updates. The UrQMD model inherited the mean-field potential part from QMD model and the two-body collision term from Relativistic-QMD, thus is can be used to describe heavy-ion collisions in wide energy range. Recently, the Skyrme energy density functional is introducted into UrQMD model in order to better reproduce the experimental data at SIS energies and understand the density dependent nuclear symmetry energy. In the present code, those parameters can be directly calculated using Skyrme parameters. There are two main advantages for introducing Skyrme interaction, first, more than 240 Skyrme interactions exist in literature and they describe well the ground state properties of nuclei. Second, they predict very different properties away from saturated density. Thus, it is very convenient for us to consider different EOS in transport model.
α, β, η, gsur, gsur,iso, A, B, C, gρτ are parameters which can be directly calculated
using Skyrme parameters (x0~x3,t0~t3).
The advantage of Skyrme interaction:
1. more than 240 parameter sets and describe well the ground state properties of nuclei
2. different properties away from saturated density
NuSYM15 Krakow Jun 29, 2015

10. Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model
S.A. Bass, et al., Prog. Part. Nucl. Phys.41: (1998);
M. Bleicher, et al.,JPG (1999).
Lorentz-covariant dynamics
Relativistic-QMD
UrQMD
Collision term
Mean field term
QMD
improve and extand collision term
Main update:
Skyrme interaction are introduced to the UrQMD model.
Similar to ImQMD
Yingxun Zhang, et al.
PRC
Yongjia Wang, et al.
PRC
Besides, the mean-field part, collision term and cluster recognition are also very important. In this work the treatment of those two parts are the same as our previous work. And those parameter sets are suitable for describing heavy ion collisions at intermediate energies which will be seen later.
Two neutrons could be formed in the same fragment with a larger relative distance compare to two protons, due to the Coulomb forces between the latter.
α, β, η, gsur, gsur,iso, A, B, C, gρτ are parameters which can be directly calculated
using Skyrme parameters (x0~x3,t0~t3).
Medium modified NN cross section, see Yongjia Wang, et al. PRC
iso-MST: proton-neutron or neutron-neutron R0=3.8 fm, proton-proton: R0=2.8 fm; P0=0.25 GeV/c. Yingxun Zhang, et al. PRC
NuSYM15 Krakow Jun 29, 2015

11. Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model
Main difference between UrQMD and other QMD models
Collision term
t=timestep
… … …
t=timestep+1
t=tcoll. (n)
t=tcoll. (1)
propagation
in mean field
(r(0),p(n))
Procedure:
1. calculate 'collision' times, find the minimum tcoll(1)
2. update all particles r(1)=r(0)+p(0)/m*tcoll(1), cascade mode
3. check whether this collision is allowed or not , if the collision is allowed, the momenta p(0) will be changed,if not, p(1)=p(0)
redo 1,2 and 3, unitl tcoll(n) great than timestep
Clearly, collision happens one after another, and each one has its own collision time.
Next, I would like to introduce the distinguishing feature of UrQMD model. As mentioned before, the collision term of UrQMD model inherited from rQMD model, thus compare to ordinary QMD model, main difference exist in collision term. The procedure of collision term is quite different from others. Since time is limit, I don’t want to talk in detail, just give the summary, two body collision happens one after another, and each collision has its own collision time. If you wrote code, you will understand this difference.
NuSYM15 Krakow Jun 29, 2015
IWND'14 - Aug 15-19, 2014

12. Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model
Next show some results from the updated UrQMD model, this is charge distribution for gold-gold collision at 150\250\400, calculations with different model assumptions are all close to the FOPI data.
Model calculations reproduce well the charge distribution.
NuSYM15 Krakow Jun 29, 2015
IWND'14 - Aug 15-19, 2014

13. Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model
Au+Au
b=0~7 fm
150~400A MeV
The collective flow can also be reproduced well. for instance, this is rapidity dependent directed flow, this is rapidity dependent elliptic flow, this is transverse momentum dependent flow. Clearly, those experimental data can be reproduced fairly well.
Successfully reproduce recent FOPI experimental data.
Yongjia Wang, et al.,PRC
NuSYM15 Krakow Jun 29, 2015

14. Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model
L=89±45 MeV
Consistent with Tϋbingen QMD and UrQMD model calculations.
Cozma, et al., PRC (2013)
P. Russotto, et al. PLB (2011)
And the updated version was also used to study the neutron and proton elliptic flow data, simulation with several Skyrme interactions which give similar values of iso-scalar incompressibility but very different density dependences of the symmetry energy, the slope parameter is extracted to be 89+/- 45MeV, the result is consistent with Tϋbingen QMD model and previous UrQMD calculations in which the same FOPI/LAND data was used.
Yongjia Wang, et al.,PRC
NuSYM15 Krakow Jun 29, 2015

15. Results Selected Skyrme forces in this work:
In order to study the ratio, we chosen the following thirteen Skyrme interactions, they give almost the same K0,but very different density dependent symmetry energy. The L value spread from about six to one hundred and sixty mev. In addition, symmetry energy predicted by those four interactions track each other closely at low densities, but L values spread from 60 to 100 mev.
Yongjia Wang, et al., EPJA51:37(2015)
NuSYM15 Krakow Jun 29, 2015

16. Results
Underestimate both 3H and 3He. (As well as 4He, overestimate free protons and neutrons).
Sources of 3H and 3He
Sequential decay process
(emit from pre-fragments)
B. Dynamic process
(random collection of nucleons)
This figure shows the time evolution of tritons, helium-three and their ratio. First, it can be seen that, the UrQMD model calculations underestimate the yields of both $^3$H and $^3$He. this underestimation can not be resolved solely by considering uncertainties in the stiffness of the equation of state or in the medium modification of the two-body collision term. There are two sources of forming 3h and 3he, first is sequential decay process, second is dynamics process, our calculation miss the first source because the sequential decay code is not included, we assuming the degree of this underestimate is quantitatively the same for 3H and 3He.
Second, Most of the 3H and 3He are produced with 30 fm/c to 60 fm/c, in this time span, density drops from normal to sub-normal. At 30 fm/c the ratio reflect the high-density behavior of symmetry energy, since they composed of early emitted neutron and protons, As the reaction proceeds, at final the ratio reflects the low density behavior of symmetry energy.
Third, Skz4 (soft) gives much more 3H, because at sub-normal density, Skz4 gives a more repulsive symmetry potential, leading to a larger phase-space distribution for neutrons. Hence, more neutrons and neutron-rich light clusters such as $^3$H are produced. The yield of Helium-three does not exhibit sensitive to symmetry energy, due to the $^3$He yield is also affected by the Coulomb potential between two protons which reduces the sensitivity to the symmetry energy.
Assuming the degree of underestimation is quantitatively the same for 3H and 3He.
Skz4 (L= 5.75 MeV)
SkO’ (L= MeV)
SkI1 (L= MeV)
NuSYM15 Krakow Jun 29, 2015

17. Results
High density: 5~30 fm/c
Low density: 30 fm/c ~ end
2. Most of the 3H and 3He are produced within 30 fm/c to 60 fm/c.
3. Early emitted 3H and 3He reflect the high-density behavior of symmetry energy.
This figure shows the time evolution of tritons, helium-three and their ratio. First, it can be seen that, the UrQMD model calculations underestimate the yields of both $^3$H and $^3$He. Due to the lack of some quantum features in the QMD-like models, this underestimation can not be resolved solely by considering uncertainties in the stiffness of the equation of state or in the medium modification of the two-body collision term. Second, Most of the 3H and 3He are produced with 30 fm/c to 60 fm/c, in this time span, density drops from normal to sub-normal. At 30 fm/c the ratio reflect the high-density behavior of symmetry energy, since they composed of early emitted neutron and protons, As the reaction proceeds, at final the ratio reflects the low density behavior of symmetry energy.
Third, Skz4 (soft) gives much more 3H, because at sub-normal density, Skz4 gives a more repulsive symmetry potential, leading to a larger phase-space distribution for neutrons. Hence, more neutrons and neutron-rich light clusters such as $^3$H are produced. The yield of Helium-three does not exhibit sensitive to symmetry energy, due to the $^3$He yield is also affected by the Coulomb potential between two protons which reduces the sensitivity to the symmetry energy.
Skz4 (L= 5.75 MeV)
SkO’ (L= MeV)
SkI1 (L= MeV)
NuSYM15 Krakow Jun 29, 2015

18. Results High density low density NuSYM15 Krakow Jun 29, 2015
This is the transverse momentum distributions of 3H and 3He as well as the ratio at reaction times t=30 fm/c and 150 fm/c. it can be seen that, at t=30 fm/c 3H and 3He with high energy are more abundant than that with low energy, these clusters mainly reflect the behavior of symmetry energy at high densitiesat t=150 fm/c, more and more low- energy 3H and 3He clusters were emitted from low density environment, and finally the ratio reflects the behavior of symmetry energy at sub-saturation densities.
High density
low density
NuSYM15 Krakow Jun 29, 2015
IWND'14 - Aug 15-19, 2014

19. Results 1.The linearity increases with decreasing density.
2.Calculations with those
four forces centered in
the shaded band.
3. Large Exp. uncertainty
prevents us from getting a tighter constraint. L
Esym(0.03)
MSL0 60
8.92
SkO’ 69
8.97
SV-sym34 81
8.50
Ska35s25 99
8.78
This figure shows the $^3$H/$^3$He ratios calculated with the 13 selected Skyrme parametrizations as a function of the symmetry energy at three sub-normal density points. It can be seen that the linearity between the $^3$H/$^3$He ratio and the symmetry energy increases with decreasing density, which indicates a strong correlation between them at low densities. The $^3$H/$^3$He ratios calculated with those four interactions are close to each other and centered in the shaded band. Obviously, the large uncertainty of the experimental data prevents us from getting a tighter constraint.
Red circle: MSL0, SkO', SV-sym34, Ska35s25
NuSYM15 Krakow Jun 29, 2015

20. Results Energy dependence: Isospin dependence:
They are beam energy dependence and isospin dependence triton/helium ratio, it can be seen that, At low beam energies, the ratio is quite sensitive to the symmetry energy, however, the experimental data cannot be well reproduced. It is imply that the method for constructing clusters is not fully valid at low beam energies. At high energies, the ratio is still sensitive to the symmetry energy, but the sensitivity decreases with increasing beam energy due to the increase of both, the nucleon density and the number of nucleon-nucleon collisions. Furthermore, the calculations with MSL0 and Ska35s25, for which the difference in $L$ is as large as $\sim$39 MeV, are very close to each other, indicating the sensitivity of the $^3$H/$^3$He ratio to the stiffness of the symmetry energy is more obvious at low densities.
At low beam energies, the data cannot be well reproduced.
Calculations with MSL0 and SKa35s25
are very close to each other.
L (MeV)
Esym(0.03) MeV
MSL0 60
8.92
Ska35s25
98.89
8.78
NuSYM15 Krakow Jun 29, 2015

21. Thanks for your attention!
Summary
3H/3He total yield ratio is sensitivity to the nuclear symmetry at sub-saturation densities.
Calculations with MSL0, SkO’, SV-sym34, and Ska35s25 are all in good semi-quantitative agreement with FOPI data. This result is consistent with our previous results based on the elliptic flow of free nucleons.
Additional calculations with other clustering algorithms and model assumptions will be certainly required to confirm the sensitivity of the 3H/3He ratio to the stiffness of the symmetry energy and the constraint obtained from this observable.
3H/3He yield ratio is sensitivity to the nuclear symmetry at sub-saturation densities.
Calculations with MSL0, SkO’, SV-sym34, and Ska35s25 are all in good semi-quantitative agreement with FOPI data. This result is consistent with our previous results based on the elliptic flow of free nucleons.
Additional calculations with other clustering algorithms and model assumptions will be certainly required to confirm the sensitivity of the 3H/3He ratio to the stiffness of the symmetry energy and the constraint obtained from this observable.
Thanks for your attention!
NuSYM15 Krakow Jun 29, 2015

22. Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model
Yongjia Wang, et al.,PRC
IWND Lanzhou Aug 15-19, 2014

24. Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model
Main difference between UrQMD and other QMD models
2. In-medium differential cross section
The scattering angles between the outgoing partners is determined by the collision term of the RBUU equation.
G. Mao, et al., Phys. Rev. C53, 2933; Phys. Rev. C 57, 1938.
IBUU: isotropic
ImQMD: Cugnon's parameterization
J. J. Cugnon, et al., Nucl. Instrum. Methods B111, 215 (1996).
The second difference is the in-medium differential cross section. In UrQMD, the scattering angles between the outgoing partners is determined by the collision term of the RBUU equation. While, as far as I know, in IBUU model, the differential cross section is isotropic, and the Cugnon parametrization is used in the ImQMD model. Why do I mention the differential cross section, because it determined the scattering angle, and the measured experimental data always relative to angle covered by detectors. Thus, attention should be paid to differential cross section.
NuSYM15 Krakow Jun 29, 2015
IWND'14 - Aug 15-19, 2014