fb-18, santos, brazil 1 experimental state of n-n correlation function for borromean halo nuclei...

FB-18, Santos, Brazil 1

Experimental State of n-n Correlation Function for Borromean halo Nuclei

Investigation

Presented by: M. Petrascu HH-NIPNE, BucharestE-mail: [email protected]


Authors

• M. Petrascu HH-NIPNE, Romania• A. Constantinescu Univ. Bucharest, Romania• I. Cruceru HH-NIPNE, Romania• M. Giurgiu Tech. Univ. Buch., Romania• A. Isbasescu HH-NIPNE, Romania• H. Petrascu HH-NIPNE, Romania• S. Serban HH-NIPNE, Romania• V. Stoica HH-NIPNE, Romania• I. Tanihata TRIUMF, Canada• W. G. Lynch NSCL, Michigan Univ. USA• M. A, Famiano W. Michigan Univ. USA• K. Ieki Rikkyo Univ., Tkyo, Japan


Overview

• Short introduction

• The Cnn Correlation Function

• Examples of measured Cnn

• Conclusions concerning Cnn for 11Li, based on the measurements and investigations performed up to now

• A new theory of Cnn

• Conclusions concerning the posibilities to test experimentaly the new theory


Short Introduction

The neutron halo nuclei were discovered by Tanihata, et al., Phys .Lett. 160 B 380 (1985)The designation of “halo” for the low density matter around the core was first introduced by: P. G. Hansen, B. Jonson, Europhys. Lett. 4 409 (1987)Pre-Emission : Short cut for Pre-Equilibrium Emission.First Pre-Emission paper: M. Petrascu et al. Phys. Lett. B 405, 224 (1997)


Pre-emission of halo neutrons in a fusion process

Li-11core

SiLi-11core

Sinn

A B

Li-11core

Si

n

n

C

n

n

It was predicted M.Petrascu, et al.Balkan Physics Letters 3(4), 214. (1995) that, due to the very large dimension of 11Li, one may expect that in a fusion process on a light target, the valence neutrons may not be absorbed together with the 9Li core, but may be emitted in the early stage of the reaction. Indeed, the experimental investigations of neutron pre-emission in the fusion of 11Li halo nuclei with Si targets have confirmed this view. (M. Petrascu et al., Phys. Lett. B 405, 224 (1997))


The Cnn Correlation Function

Veto2

0.2mm

Veto1

1mm(1PM)

Li beam 11

Degrader Scint

0.5mm 0.5mm

Window

M U S I C

Si-Det. 0.15mm

A1, A2,.........,A10

Neutron ArrayDetector

81Modules

ScintC

Be beam 11

D1 D2


The Cnn Correlation Function

• Cnn(q) is given by:

• In Eq. Nc(q) represents the yield of coincidence events

and Nnc(q) represents the yield of uncorrelated events. The normalization constant k is obtained from the condition that Cnn(q) = 1 at large relative momenta. The relative momentum q is given by q=1/2|p1-p2|, p1, p2

being the momenta of the two coincident neutrons.

)(

)()(

qN

qNkqC

nc

cnn

)(

)()(

qN

qNkqC

nc

cnn

)(

)()(

qN

qNkqC

nc

cnn


Examples of Cnn Correlation Function

• The first measured Cnn for 11Li

Ieki et al Phys. Rev. Lett. 70, 730 (1993)

r0=5.5 fmrrms=13.7 fm


The second measured of Cnn for 11Li

Marques et al Phys. Lett.B476 219 (2000)

Marques has obtained a lower value of r0=4.2 fm. He assumed the existence of residual correlation for the single detected neutrons. In view of elimination of this effect he applied an iterative calculation lowering by this the value of r0 to 2.7 fm. But at that time the theory of Cnn was based on a many particle model which could be not be valid for 11Li. We will consider this problem later.


The third measured of Cnn for 11Li

M. Petrascu et al Phys.Rev.C 69 011602 (2004)

0 5 10 15 20 25 30 35 400

1

2

3

4

5

6

7

8

9

10

A13.3 fm

Exp. points (B)

(rrms

=10.2 fm)

(rrms

= 8.3 fm)COSMAI

C(q

)

q (MeV/c)

By using denominator A, built from single detected neutrons we obtained a correlation function corresponding to the red line of the figure (r0=5 fm, in agreement with Ieki.) By using denominator B, built by event mixing, we obtained a correlation function represented by the experimental points with error bars. (r0=4.2 fm). The blue curve represents the correlation function in agreement with COSMA1 model. Our results favor COSMA1. The value of rrms predicted by COSMA2 is too far to be accounted by the small anomalies seen in denominator B.(interesting discussion concerning denominator B, later)


Conclusions concerning Cnn for 11Li, based on the measurements and investigations performed

up to now• The measured Cnn correlation strengths appear to be rather

low.• The residual correlation is assumed but not demonstrated. • The demonstration of residual correlation can be obtained by

performing a combined experiment with 11Li and 11Be• The experiments performed up to now, were using either

coulomb dissociation or pre-emission of neutrons on a Si target. In both cases the statistics of events are rather poor.

• A considerable increase of statistics of neutron pairs can be obtained by exploiting the target screening effect ( M. Petrascu et al., Phys. Rev. C 73,057601 (2006), M.Petrascu et al. Phys. Atomic Nuclei 69, 1261, (2006).

• An important event occurred in 2005, The publication of a new theory of Cnn correlation function, based on a three body model of the Borromean halo nuclei, M. T. Yamashita, T. Frederico, L. Tomio, Phys.Rev.C 72, 011601R (2005) (18 July 2005)


A New Theory of Cnn

• The 3-body wave function describing the core and the 2 weakly bound neutrons is obtained by solving the Faddeev equations. In order to obtain Cnn, the final state interaction is taken into account. The model is parametrized by minimal number of physical inputs which are directly related to known observables S(2n), the n-n s-scattering length


A New Theory of CnnThis figure is taken from the quoted in slide #12 paper. The most interesting is the insert in which one can see the interference minimum of Cnn around pnn= 50 MeV/c. The authors are normalizing to 1 the function of the insert in order to compare with experimental points. The open circles are from: M. Petrascu et al. Nucl. Phys A738, 503 (2004). The solid circles are from: F. M. Marques et al., Phys. Lett. B476, 219 (2000)


A comparison between the correlation function of the insert

of previous fig. with the results of Ieki et al.

0 10 20 30 40 500.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Cn-

n

q(MeV/c)


Illustation of the large screening effect in the case of Si in comparison with C (Central, l=0 coll.)

2.6 fm

4.1 fm

l=0

4.8 fm

Si

9Li

Halo

core

11Li

2.6 fm

l=0

4.8

fm

2.3 fmC

11Li Halo

9Li core

From M. Petrascu et al., Phys. Rev. C 73,057601 (2006


Collisions at lcr

2.6 fm

4.8 fm

b=28 fml=14

4.1 fm

LiSi

4.8

fm

b=2.3 fml=9

Li-9

C

2.3 fm

2.6 fm


Results of the sharp cut-off calculations

Target RHALO

(fm)

ζexp

%

ζ %

P[1]

% P[2]

% Pa[2]

% ∑P[i] %

12C 4.8 70.1 41.8 49.2 8.9 ~100

4.2 61 47.5 37.2 15.1 ~100

3.6 46.9 49.8 22.0 28.1 ~100

Si 4.8 36+4 37.9 47.1 14.4 38.4 ~100

4.2 28.6 40.8 8.1 50.9 ~100

3.6 20.5 32.7 4.2 63.0 ~100


Possibility to test experimentally of the new theory

0 5 10 15 20 25 30 35 400123456789

10C(q

)

q (MeV/c)

0 5 10 15 20 25 30 35 400123456789

10

From M.Petrascu et al. Phys. Atomic Nuclei 69, 1261, (2006).


Experimental indication for existence of a sink in the Cnn data

2 4 6 8 10 12 1405

10152025303540

543

21

( iii )

N /

(0

.5 M

eV

/c)

N /

(2

Me

V/c

)N

/ (

0.5

Me

V/c

)

2 4 6 8 10 12 14

02468

101214

x100

x100

( ii )

q (MeV/c)

2 4 6 8 10 12 14

05

10152025303540

x1000

( i )

Fig.5 from:M.Petrascu et al. P.R.C 69,011602 (2004)

This discussion refers to Fig (ii). By solid squares is denoted the denominator built from single detected neutrons. (A). By open circles is denoted the denominator built by event mixing (B) Denominator type B is criticized in published work: “In the event mixing the denominator is generated by randomly mixing the neutrons from the coincidence sample. This method has the advantage that the uncorrelated distribution corresponds to the same class of collisions as in the case of the numerator, but has the disadvantage that it may distort the correlation one wants to measure because it may not succeed to decorrelate completely the events. In the single product tchnoque the denominator is constructed by the product of single neutron distribution (R. Ghetti et al. Nucl. Phys. A660 ,20 (1999). For us was a puzzle why the denominator B is lower then denominator A ?


Conclusions concerning the posibilities to test experimentaly

the new theory• The last performed investigations on the target

screening effect are shown the possibility to reach much higher statistics for detected neutron pairs by using a C target instead a Si target

• The simulation performed on the expected error bars is showing for 11Li the possibility to solve the theoretical predicted minimum in the correlation function.

• In order to avoid possible correlation effects one has to use in the future experiment 11Li and 11Li beams.


Acknowledgement

• The authors of this report are grateful to Lauro Tomio for sending them the theoretical results prior to publication.

fb-18, santos, brazil 1 experimental state of n-n correlation function for borromean halo nuclei...

Documents

petrascu hhnipne

cnn correlation function

petrascu et

li halo nuclei

preemission of halo

cruceru hhnipne

isbasescu hhnipne

serban hhnipne