1. Probing correlations by use of two-nucleon removal
Methods of many-body systems: mean field theories and beyond - March , 2006, RIKEN, Saitama, Japan.
Jeff Tostevin
Department of Physics
School of Electronics and Physical Sciences
University of Surrey, UK

2. Question that arose at RIBF meeting was …..
Can one observe experimentally the correlations of pairs of nucleons in exotic nuclei – by using suitable nuclear reactions (with fast secondary beams - RIBF) ?
I will consider the direct 2N knockout reaction mechanism – will show specific test cases and some first applications – and that results show sensitivity to pair correlations.
Quenching of calculated strength is a common feature in comparisons of structure calculations (e.g. the shell model) with experiment. What are the expectations for 2N removal?

3. Asymmetric nuclei – two Fermi surfaces
22O  21O
32Ar  31Ar
Z=8
N=14
Sn=6.8 MeV
Sp=23 MeV
Z=18
N=14
Sn=22 MeV
Sp=2.4 MeV
A.Gade et al., Phys. Rev. Lett. 93 (2004),

4. Two nucleon knockout – restricted reaction setZ
32Ar
34Ar
54Ti
44S
2p from
neutron rich
28S
30S
52Ca
42Si
26P
28P
34Si
24Si
26Si
32Al
34Al
2n from neutron deficient
28Mg
30Mg
32Mg
28Na
30Na
32Na
26Ne
28Ne
30Ne N

5. 9Be 1 2 Two-nucleon removal – at 80 - 100 MeV/u [fast] spectator c
Experiments are inclusive (with respect to the target final states). Core final state measured – using coincident gamma rays.

6. Structure – need nucleon overlaps
Spectroscopic
factor/strength 1 2
In two-nucleon case there are (in general) several coherent 2N configurations – the two-nucleon motions are correlated

7. z Reaction drills out a cylindrical volume at surface
Cross section will be sensitive to the spatial localisations of pairs of nucleons near the surface
No spin selection rule (for S=0 versus S=1 pairs) from the reaction mechanism
What can we learn of the 2N wave function and 2-body correlations from this sampled volume? z

8.   Good sd-shell test cases and also 30S and 34Ar
D. Bazin et al., PRL 91 (2003)
K. Yoneda et al., PRC submitted; three cases.
28Mg (Z=12, N =16)  26Ne
26Si (Z=14, N =12)  24Si  
and also 30S and 34Ar

9. Spectroscopic strengths – independent particles

10. Uncorrelated: 28Mg  26Ne(0+,2+,4+), 82.3 MeV/u
uncorrelated [d5/2]2
Sigma (mb) 0+ 2+ 4+
summed 2+

11. Radial localisation: 28Mg  26Ne as1

12. Antisymmetrized: 28Mg  26Ne as

13. Antisymm’d: 28Mg  26Ne(0+,2+,4+), 82.3 MeV/u
antisymmetrized [d5/2]2 0+ 2+ 4+
summed 2+

14. Correlations in the shell model wave function
28Mg (Z=12, N =16)  26Ne(0+)

15. Role of correlations 28Mg 26Ne(0+, 2+, 4+ ) 82.3 MeV/u
uncorrelated [d5/2]2
antisymm’d [d5/2]2
correlated (SM)
Sigma (mb) 0+ 2+ 4+
summed 2+

16. Knockout cross sections – correlated SM case
28Mg 26Ne(0+, 2+, 4+ , 22+) MeV/u
Sigma (mb) 0+ 2+ 4+ 1 2

17. Two-neutron removal – g.s. branching fractions
correlated
uncorrelated
Sigma (0+) / Sigma(inclusive)
26Si
30S
34Ar
K. Yoneda et al., Phys Rev C, submitted

18. Importance of diffractive terms
28Mg 26Ne(0+, 2+, 4+ ,22+) MeV/u

19. Two-nucleon removal – suppression - Rs(2N)
Preliminary
28Mg
-2p
30S
26Si
-2n (Yoneda et al.)
34Ar
54Ti(gs)
-2p

20. Summary
At fragmentation energies (>50 MeV/u) reaction theory is rather accurate, allowing one to extract quantitative structure information and test structure model predictions.
Limited two neutron/proton knockout data - but these reveal sensitivity to correlations in the 2N wave functions – (in both S=0 and S=1 configurations) – and effects of pairing in active 2N configurations.
Direct 2N knockout reaction mechanism can be very clean and selective – need for more test cases and applications.
Data sets (5 cases) are consistent with a suppression of 2N strength relative to the shell model ~0.50(5). This compares with a typical 1N removal suppression of order 0.6 – 0.7 for well-bound nucleons.