1. 1 Jeff Tostevin, Department of Physics Faculty of Engineering and Physical Sciences University of Surrey, United Kingdom Sensitivity of two-nucleon knockout to two-body correlations Probing pair correlations: Experimental tools and associated models, CEA/SPhN Saclay, 13 th -15 th October 2008

2. 2 2N knockout spectroscopy: Which correlations? Interest: (i) assessing shell model wave functions and effective interactions, (ii) spectroscopy near shell gaps and role of 2N correlations  as may be revealed by inclusive and partial cross sections, and/or 2N removal fragment momentum distributions. Correlations: (i) nucleons bound in same mean field (ii) antisymmetry / angular momentum (iii) SR, LR and Tensor - strength outside shell model/mean field model spaces (iv) residual interaction/pair correlations

3. 3 2N knockout at beam energies > 100 MeV/nucleon Experiments are inclusive (with respect to the target final states). Residue final state measured – using gamma rays, whenever possible – and momenta (p // ) of the residues. Cross sections are large and they include both: Stripping (inelastic/absorptive) and diffractive (elastic) interactions of the removed nucleon(s) with the target 9 Be 1 2 [fast] spectator c light nuclear target

4. 4 Sudden removal from the residue as a spectator 1 2 A Core/residue state is assumed a spectator – so reaction probes the two nucleon overlap and (in general) there are several active 2N configurations – overlap determined by the two nucleon amplitudes (TNA) in shell model.

5. 5 Target drills out a cylindrical volume at the surface (i) Cross section will be sensitive to the spatial correlations of pairs of nucleons near surface (ii) No spin selection rule (for S=0 versus S=1 pairs) in the reaction mechanism (iii) We can gain first expectation of the extent to which we are sensitive to ‘correlations’ by looking at the 2N overlaps in the sampled volume – and effect on the cross sections (iv) No mismatch considerations. (i) Cross section will be sensitive to the spatial correlations of pairs of nucleons near surface (ii) No spin selection rule (for S=0 versus S=1 pairs) in the reaction mechanism (iii) We can gain first expectation of the extent to which we are sensitive to ‘correlations’ by looking at the 2N overlaps in the sampled volume – and effect on the cross sections (iv) No mismatch considerations. z 2 1

6. 6 Structure input – two nucleon overlaps

7. 7 Sampling the two-nucleon wave function Interaction with the target probes wave functions at surface and beyond 28 Mg  26 Ne(2 + )

8. 8 Strongly-bound: (like) 2N removal

9. 9 Two-proton knockout: 38 Si  36 Mg +2.80(64) 39.24 37 Al 20.64 + 4.38 36 Mg 38 Si +5.29  2p  1p  +18.60 1n KO indirect 2p KO

10. 10 Removal probes single-nucleon wave functions Interaction with the target probes wave functions at surface z 38 Si n p target

11. 11 Target drills out a cylindrical volume at the surface z 2 1

12. 12 Antisymmetrized 28 Mg  26 Ne removal of 0+0+ 2+2+ 4+4+ uncorrelated J.A. Tostevin, Journal of Physics: Conference Series 49 (2006) 21–26

13. 13 J.A. Tostevin, et al., PRC 70 064602 (2004). Spin-structure - correlations in wave functions 28 Mg(0 + )  26 Ne(0 + ), 2p, ~100 MeV/nucleon Stripping (mb) 0.573 0.286 S=0 0.061 0.143 S=1 All mechanisms (mb) 0.634 0.426 Stripping 0.466 0.301 Diffraction … … S=0+1 1.150 0.750 (-2p) x 2 (S=0) x 1.52

14. 14 Coherence of shell model correlations 28 Mg (Z=12, N =16)  26 Ne(0+)

15. 15 Correlated: 28 Mg  26 Ne(0 +,2 +,4 + ), 82.3 MeV/u Data: D. Bazin et al., PRL 91 (2003) 012501 J. A. Tostevin, EPJ Special Topics 150, 67 (2007) [RNB7 Proceedings]

16. 16 Knockout cross sections – correlated case Sigma (mb) 0+0+ 2+2+ 2+2+ 4+4+ 12 28 Mg  26 Ne(0 +, 2 +, 4 +, 2 2 + ) 82.3 MeV/u J.A. Tostevin et al., PRC 70 (2004) 064602, PRC 74 064604 (2006

17. 17 Ratio of measured to calculated cross sections J.A. Tostevin and B.A. Brown, PRC 74 064604 (2006), PRC 70 064602 (2004) Figure: A. Gade

18. 18 Weakly-bound 2n removal

19. 19 48 Ca(-2n) to 46 Ca(0 + ) – beyond the sdpf-space With Alex Brown, Ed Simpson: Perturbative calculation of two-neutron TNA when using a ‘realistic’ (Hjorth- Jensen) NN interaction, estimating the component amplitudes across several major oscillator shells  Cross section is enhanced by a factor of 2 compared to including only the [f7/2] 2 term (preliminary): cf.1.32 in pf the shell calculation. 48 Ca(0 + )  46 Ca(0 + ), 2n, 100 MeV/nucleon 48 Ca(0 + )  46 Ca(0 + ), 2n, 100 MeV/nucleon

20. 20 Sudden 2N removal from the mass A residue Sudden removal: residue momenta probe the summed momenta of pair in the projectile rest frame A Projectile rest frame laboratory frame and and component equations

21. 21 Look at momentum content of sampled volume z 2 1 Probability of a residue with parallel momentum  A J. A. Tostevin, EPJ Special Topics 150, 67 (2007) [RNB7 Proceedings]

22. 22 28 Mg→ 26 Ne (all) – Full calcs, EC Simpson D. Bazin, private communication 28 Mg (-2p) on 9 Be at 82.3 MeV per nucleon Sigma (mb) 0+0+ 2+2+ 2+2+ 4+4+ 12

23. 23 Two proton knockout from 38 Si  36 Mg(0 +,2 + ) 38 Si (  2p) 83 A MeV Residue momentum distribution 0+0+ 2+2+ A. Gade, JAT et al., to be published Theory Expt. 0 + 56% 58(7)% 2 + 44% 42(7)% dp/p=1.66%

24. 24 Two neutron knockout from 22 Mg  20 Mg(0 +,2 + ) 22 Mg (  2n) 75.1 A MeV Residue momentum distribution 0+0+ 2+2+ A. Gade, JAT et al., to be published Expt. 0 + 84% 2 + ~16%

25. 25  SR/LR/Tensor correlations: observe systematic suppression of 1N and 2N strength cf shell model – allows the identification of structure effects beyond these systematics  knockout mechanism is sensitive to details of 2N (shell model) wave functions and effective interactions – enhancement although no reaction mechanism spin selectivity  knockout of other than two well-bound nucleons is complicated by the (strong) indirect – 1N knockout + particle decay – 2N removal mechanism.  have identified spectroscopic value of momentum distributions of -2N reactions and have a more complete calculation available. Status: 2N removal reactions reveal:

26. 26 Fin