1. FB-18, Santos, Brazil 1 Experimental State of n-n Correlation Function for Borromean halo Nuclei Investigation Presented by: M. Petrascu HH-NIPNE, Bucharest E-mail: petrascu@tandem.nipne.ro

2. FB-18, Santos, Brazil 2 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

3. FB-18, Santos, Brazil 3 Overview Short introduction The C nn Correlation Function Examples of measured C nn Conclusions concerning C nn for 11 Li, based on the measurements and investigations performed up to now A new theory of C nn Conclusions concerning the posibilities to test experimentaly the new theory

4. FB-18, Santos, Brazil 4 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)

5. FB-18, Santos, Brazil 5 Pre-emission of halo neutrons in a fusion process It was predicted M.Petrascu, et al.Balkan Physics Letters 3(4), 214. (1995) that, due to the very large dimension of 11 Li, one may expect that in a fusion process on a light target, the valence neutrons may not be absorbed together with the 9 Li core, but may be emitted in the early stage of the reaction. Indeed, the experimental investigations of neutron pre-emission in the fusion of 11 Li halo nuclei with Si targets have confirmed this view. (M. Petrascu et al., Phys. Lett. B 405, 224 (1997))

6. FB-18, Santos, Brazil 6 The C nn Correlation Function

7. FB-18, Santos, Brazil7

8. 8 The C nn Correlation Function C nn (q) is given by: In Eq. N c (q) represents the yield of coincidence events and N nc (q) represents the yield of uncorrelated events. The normalization constant k is obtained from the condition that C nn (q) = 1 at large relative momenta. The relative momentum q is given by q=1/2|p 1 -p 2 |, p 1, p 2 being the momenta of the two coincident neutrons.

9. FB-18, Santos, Brazil 9 Examples of C nn Correlation Function The first measured C nn for 11 Li Ieki et al Phys. Rev. Lett. 70, 730 (1993) r 0 =5.5 fm r rms =13.7 fm

10. FB-18, Santos, Brazil 10 The second measured of C nn for 11 Li Marques et al Phys. Lett.B476 219 (2000) Marques has obtained a lower value of r 0 =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 r 0 to 2.7 fm. But at that time the theory of C nn was based on a many particle model which could be not be valid for 11 Li. We will consider this problem later.

11. FB-18, Santos, Brazil 11 The third measured of C nn for 11 Li M. Petrascu et al Phys.Rev.C 69 011602 (2004) By using denominator A, built from single detected neutrons we obtained a correlation function corresponding to the red line of the figure (r 0 =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. (r 0 =4.2 fm). The blue curve represents the correlation function in agreement with COSMA 1 model. Our results favor COSMA 1. The value of r rms predicted by COSMA 2 is too far to be accounted by the small anomalies seen in denominator B.(interesting discussion concerning denominator B, later)

12. FB-18, Santos, Brazil 12 Conclusions concerning C nn for 11 Li, based on the measurements and investigations performed up to now The measured C nn 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 11 Li and 11 Be 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 C nn 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)

13. FB-18, Santos, Brazil 13 A New Theory of C nn 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 C nn, 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

14. FB-18, Santos, Brazil 14 A New Theory of C nn This 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 C nn around p nn = 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)

15. FB-18, Santos, Brazil 15 A comparison between the correlation function of the insert of previous fig. with the results of Ieki et al.

16. FB-18, Santos, Brazil 16 Illustation of the large screening effect in the case of Si in comparison with C (Central, l=0 coll.) From M. Petrascu et al., Phys. Rev. C 73,057601 (2006

17. FB-18, Santos, Brazil 17 Collisions at l cr

18. FB-18, Santos, Brazil 18 Results of the sharp cut-off calculations Target R HALO (fm) ζ exp % ζ % P [1] % P [2] % Pa [2] % ∑P[i] % 12 C 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

19. FB-18, Santos, Brazil 19 Possibility to test experimentally of the new theory From M.Petrascu et al. Phys. Atomic Nuclei 69, 1261, (2006).

20. FB-18, Santos, Brazil 20 Experimental indication for existence of a sink in the C nn data 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 de- nominator 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 ?

21. FB-18, Santos, Brazil 21 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 11 Li 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 11 Li and 11 Li beams.

22. FB-18, Santos, Brazil 22 Acknowledgement The authors of this report are grateful to Lauro Tomio for sending them the theoretical results prior to publication.