nucleon-nucleon momentum correlation functions induced by the radioactive beams yu-gang ma

Yu-Gang Ma 18th Few Body Conference, 2006, Santos, Brazil

Nucleon-Nucleon momentum correlation functionNucleon-Nucleon momentum correlation functions induced by the radioactive beamss induced by the radioactive beams

Yu-Gang MaYu-Gang MaShanghai Institute of Applied Physics (SINAP, CAS)Shanghai Institute of Applied Physics (SINAP, CAS)

• Introduction• Our results: nn, np, pp vs Ebind, Esep? Halo nuclei?

• conclusions


weak correlation function11Li (+ 208Pb) -> 9Li + n + n (+208Pb)Ieki et al., PRL70, 730 (1993)

Our work will focus on the systematic studies on nucleon-nucleon correlation function for light nuclei!


Two-Proton correlation functions

q (MeV/c)1+

R(q

) p-p correlationfunction

212

1ppq

R(q) sensitive to the space-time properties of emitting sources

Emitting Source Target

Proj

Detector Arrays 22112112 )(1, pYpYqRppY

1p

2p

Final State Interaction (Coulomb + Nuclear: s-wave peak) + Pauli


Intensity interferometry: from large scales ...

Star

R

d << R

Static systems: exploring the geometry (size, R)

HBT: R. Hanbury Brown, R.Q. Twiss, Phil. Mag., Ser. 7 45 (1954) 663

… to subatomic physic scales (, K-K, , p-p, n-n, IMF-IMF, …)

Fast evolving systems: 10-23-10-15 sec: geometry changing in time

DetectorsNuclear reaction

d >> RR+V

G. Goldhaber et al., PR 120 (1960) 300


Theoretical Calculation formula of two particles correlation

In particular, the geometry of a collision is not a scale model of imaging a star. But for HBT……


Source-sizes from angle-averaged correlations

20

23

0

2/exp2

1)( rr

rrS

extracted from C(20 MeV/c)2/12rrrms

Gaussian sources extensively used

One-parameter approach (r0)


HI collisions at intermediate energies

Need probes of the space-time properties of the emission

• Transport theory is a tool to treat space-time evolution of nucleonic system, it is a good method to exlore the nucleon-nucleon correlation function.

• Use transport theory to relate dynamics to EOS, NN, …

NN collisions,compression, pre-equilibrium

Breakup, expansion

Secondary decays

Short time scales Long time scales


S. Pratt, Physical Review Letters. 53 (1984) 1219


Our results

stability check Fits to the data (n-n correl. function)

Cp-n vs Ebinding Cp-h vs Esep

Cp-p vs proton halo? EOS, Sigma_nn etc

Y.B. Wei, YGM et al., Phys Lett B 586, 225 (2004)Y.B. Wei, YGM et al., J Phys G 30, 2019 (2004)

YGM et al., Phys. Rev. C 73, 014604 (2006)


QMD

Isospin-dependent Quantum Molecular Dynamics Model: N-body transportation theory model Including the most important parts for nuclear reaction at intermediate energy

Nuclear mean field:

.Fragment Recognition, a naive coalescence modelΔR3.5fm; ΔP300MeV/c

Nucleon-nucleon collision and Pauli blocking etc are considered


Check of stability of IQMD


Firstly we reproduce the experimental results of two halo neutrons for 14Be +12C @ 35MeV/n:

The reaction channel:

14Be(+12C)-> 12Be + n + n (+12C)

It is obviously that the cal. results reproduce the exp. data very well.

Y.B. Wei, YGM et al.,

Phys. Lett. B 586, 225 (2004)

Data: Marques et al., PLB 476, 219 (2000)


11Li (+ 208Pb) -> 9Li + n + n (+208Pb) @ 28MeV/u

The obvious different results were obtained between 2 halo neutrons (solid line) and 2 core neutrons (dash line).

Large space extension low C(q)

Data: Ieki et al., PRL70, 730 (1993)


Systematical study: n-p correlation Ebinding

11-14B (N,C,Li) + C xn + xp + … @ 800MeV/u


Just like that of binding energy per nucleon, the relationship between the HBT strength Cph and the separation energy still exits monotonic character.

How about the separation energy ?

In model, we can also explore the correltaion between proton and the most outside neutron (Cph), see what happens? This correlation should reveal the extent of single-neutron separation.


A new criterion of halo nuclei?A new criterion of halo nuclei?

Z. Ren et al., PRC (96)Z. Ren et al., PRC (96)


0 2 4 6 81E-4

1E-3

0.01

0.1

1

Den

sity

(fm

-3)

Radius (fm)

Mass density SHF

normal 27S

halo 27S

0 2 4 6 8

1E-4

1E-3

0.01

0.1

1

Radius (fm)

Den

sity

(fm

-3)

Proton density SHF

halo 27S

normal 27S

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

27S halo

28S

29S

30S

27S normal

CP

P (

q)

q (MeV/c)

Mixed p-p phasespace @ the last coll.

Density distribution and pp HBTDensity distribution and pp HBT


6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.41.4

1.5

1.6

1.7

CP

P (

q=

20M

eV/c

)

Ebinding

(MeV/n)

Ebinding

(MeV/n)27S 6.95928S 7.47929S 7.74830S 8.122

S-isotopes

0 1 2 3 4 5 6 7 81.40

1.45

1.50

1.55

1.60

1.65

1.70s

2p(MeV/n):

27S 0.928S 3.3629S 5.3530S 7.148

Cpp

s2p

(MeV)

The similar behavior is expected for double-neutron halo nuclei.

A new criterion of halo nuclei?A new criterion of halo nuclei?

If two-proton halo structure is assumed

no halo nuclei

no halo nuclei


Conclusions

Experimental two halo neutrons correlation function (11Li, 14 Be) can be well fitted by the transport model: QMD

n-p correlation function depends on the binding energy of the system. More close binding system, the stronger np correlation.

P-halo n correlation function depends on the single neutron separation energy. However, difficult accessible in the experiment.

p-p correlation function is useful to search for proton-halo nuclei. Weak correlation is expected for 2p halo nuclei.

Systematic experiment should be done in near future.


The influences of nuclear transport property on HBT

total pair momentum nuclear EOS

in-medium n-n cross sectionimpact parameterincident energy emission time

YGM et al., Phys. Rev. C 73, 014604 (2005)


Total pair momentum dependence


In-medium cross section dependence


Impact parameter dependence


Emission time & evolution time

•in low Ptot, neutron and proton has a similar emission rate;• in higher Ptot, neutron has earlier emission time;•Higher Ptot. Earlier Temission

nucleon-nucleon correlation function is stronger in earlier evolution time


Conclusions

Experimental two halo neutrons correlation function (11Li, 14 Be) can be well fitted by the transport model: QMD

n-p correlation function depends on the binding energy of the system. More close binding system, the stronger np correlation.

P-halo n correlation function depends on the single neutron separation energy. However, difficult accessible in the experiment.

p-p correlation function is useful to search for proton-halo nuclei. Weak correlation is expected for 2p halo nuclei.

Systematic experiment should be done in near future.


Thanks for your attention!


Systems with different binding character leads to different HBT strength and shape.


Sensitivity to space-time extent

Final State Interactions (Coulomb+Nuclear) + Pauli

Directional information:Shape, Lifetime

•Pauli exclusion principle

xqx

yqy

zqz

r

eqq

2

min

• Coulomb:

Dip at q ~ 0

1+R

(q)

q (MeV/c)0 50 100

Large source

Small source

q (MeV/c)

• Nuclear:

Peak at cMeVq /20

VcMeVR

1)/20(

Size

(S wave)

),,( zyxr


In the QMD model, we can choose the random initialization or a fixed Stable Initialization. What is the difference on the HBT results?

nucleon-nucleon momentum correlation functions induced by the radioactive beams yu-gang ma

Documents

li n n

data nn

np correlation ebinding11

new criterion of halo

doubleneutron halo nuclei

halo neutrons solid

subatomic physic scales

li c xn xp