Jeff Tostevin, Department of Physics Faculty of Engineering and Physical Sciences

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

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. 2N knockout at beam energies > 100 MeV/nucleon 9Be light nuclear target 1 2 [fast] spectator c 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

4. 1 2 A Sudden removal from the residue as a spectator 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. 2 1 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. z

6. Structure input – two nucleon overlaps

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

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

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

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

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

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

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

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

15. Correlated: 28Mg  26Ne(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. 2+ 0+ 4+ 2+ Knockout cross sections – correlated case 28Mg 26Ne(0+, 2+, 4+ , 22+) 82.3 MeV/u Sigma (mb) 1 2 J.A. Tostevin et al., PRC 70 (2004) 064602, PRC 74 064604 (2006

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. Weakly-bound 2n removal

19. 48Ca(-2n) to 46Ca(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. 48Ca(0+)  46Ca(0+), 2n, 100 MeV/nucleon

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 laboratory frame and Projectile rest frame and component equations

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

22. Sigma (mb) 2+ 0+ 4+ 2+ 1 2 28Mg→26Ne (all) – Full calcs, EC Simpson 28Mg (-2p) on 9Be at 82.3 MeV per nucleon D. Bazin, private communication

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

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

25. Status: 2N removal reactions reveal: 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.

26. Fin