Probing correlations by use of two-nucleon removal

1. Probing correlations by use of two-nucleon removal Methods of many-body systems: mean field theories and beyond - March 20 - 22, 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), 042501

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

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

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

7. 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 D. Bazin et al., PRL 91 (2003) 012501 K. Yoneda et al., PRC submitted; three cases. 26Si (Z=14, N =12)  24Si 28Mg (Z=12, N =16)  26Ne   and also 30S and 34Ar

9. Spectroscopic strengths – independent particles

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

11. Radial localisation: 28Mg  26Ne as 2 1

12. Antisymmetrized: 28Mg  26Ne as

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

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

15. 2+ 0+ 4+ 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) summed 2+

16. 2+ 0+ 4+ 2+ Knockout cross sections – correlated SM case 28Mg 26Ne(0+, 2+, 4+ , 22+) 82.3 MeV/u Sigma (mb) 1 2

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

18. Importance of diffractive terms 28Mg 26Ne(0+, 2+, 4+ ,22+) 82.3 MeV/u

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