Spectroscopic factors from direct reactions A unique information to study nuclear shell structure ESNT, february 2008 A. Obertelli, CEA-IRFU/SPhN To which extend can we ‘determine’ the absolute shell occupancy of nucleons? Extraction of Spectroscopic Factors - direct reactions - first-importance information for nuclear spectroscopy - ‘model dependent’

Transfer low incident-energy Nucleon-removal intermediate-energy Our probes to extract SF for radioactive nuclei measuredcalculated extracted 2 main experimental tools for radioactive nuclei Needs a good understanding of: - reaction mechanism - single-part. structure (WF modeling) IPN Orsay GANIL N. Keeley (Warsaw) NSCL J. Tostevin (Surrey) GANIL DWBA, CDCC (sp X sections) shell-model (SF) NSCL + persectives at GSI S-matrix theory HF wave functions shell-model Collaborations

Shell occupancy from (e,e’p) measurements W. Dickhoff and C. Barbieri, Progress in Part. and Nucl. Phys. 52, 377 (2004) Reduction of experimental SF Q1: is our “standard” description of shells correct? No.

Removal of deeply-bound nucleons A. Gade at al., Phys. Rev. Lett. 93, (2004) ΔS (MeV)  The ‘recent’ result from 2004 & 2007 Trend not (yet) understood

Program 1- Complementary ‘knockout’ experiment in the sp shell at MSU (accepted) 2- dedicated transfer reactions at GANIL (accepted) 3- developments in S-matrix / theory 4- Proton-induced nucleon removal (perspective) 2 experiments to come developments in Glauber theory to be done perspectives for high-energy nucleon-removal studies

1- Confirm the observed trend Strongly-bound-nucleon removal from the sp shell 16 C( 9 Be,X) MeV/u  S= 17.8 MeV  -removal on a -rich nucleus P // 9 Be A A-1 NSCL-MSU experiment (2009) 14 O( 9 Be,X) MeV/u  S= 18.6 MeV expected to be closed shell (addendum to be proposed)

2-Independent from the reaction mechanism? 14 O(d,t) and 14 O(d, 3 He) in inverse 20 MeV/u A. Gade at al., Phys. Rev. Lett. 93, (2004) ΔS (MeV) 14 O(d,t) 13 O 14 O(d, 3 He) 13 N ΔS=18.6 MeV 14 O Experiment at GANIL, SPIRAL (L. Nalpas et al., accepted in dec 07) Transfer reactions consistent with (e,e’p) analyses BUT small ΔS available J. Lee et al., Phys. Rev. C 73, (2006) J. Lee et al., Phys. Rev. C 75, (2007) ΔSΔS

Experimental setup Exclusive measurements with MUST2 & VAMOS coincidences at GANIL BTD1 Q1Q1 Q2Q2 Dipole DC1&2 IC Plast. MUST2 silicon detectors Light-particle detection VAMOS magnetic spectrometer beam-like-residue detection SPIRAL beam MeV/nucleon Intensity: pps BTD2

Validation of the SF extraction method for transfer SF consistent with (e,e’p) experiment R~0.62(20) using radii from one-body HF wave function Matter rms constrained by elastic scattering N. Keeley (2007) Analysis: CDCC (Continuum-Discretized Coupled Channel) + finite-range Benchmark: 16 O(d,t) and 16 O(d, 3 He) in direct kinematics Comparison with available data at 14 & 26 MeV/u

3- Is it a sign of some missed dependence in the NN interaction? S-matrix theory and cross-section calculations ‘local’ code  being able to make our own predictions  independent check of existing code(s)  make our own assumptions and (maybe) improvements Inputs: Hartree-Fock densities (HFBrad code by Bennaceur & Dobascewski)  calculates S-matrices (for core & removed nucleon) and X sections  S (MeV) 46 Ar 32 Ar 24 Si 28 S  -removal -removal December 07

One-nucleon-removal calculations Investigation of the density dependence G.Q. Li and R. Machleidt, Phys. Rev. C 48, 1702 (1993); Phys. Rev. C 49, 566 (1994). Density-dependence in  NN may introduce strong differences for deeply bound nucleons vs ‘peripheral’ nucleons Perspective Test with deeply-bound nucleon removal at different energies MeV/nucleon (GSI)? 38 Si n p

4- Should we probe other parts of the WF? Hydrogen-induced knockout reactions (p,2p) and (p,pn) Stable nuclei / (e,e’p) sensitive to the inner part of the WF SRC affect the inner part of the WF sensitivity of (e,e’p) at high missing momentum (p,2p) and (p,pn) at high energy (>100 MeV/nucleon) sensitive to the inner part  optimal hadronic probe to get shell occupancies  r  =G(r)  (r) MF SRC LRC Perspective (2) Proton-induced removal of deeply-bound nucleons in radioactive nuclei Ex. 14 O(p,pn), 16 C(p,2p)

Are occupation numbers observable ? R. J. Furnstahl and H.-W. Hammer, Phys. Lett. B 531, 203 (2002) ‘It is not only that the momentum distribution is difficult to extract but that it cannot be isolated in principle within a calculational framework based on low-energy degrees of freedom.’ ‘We conclude that occupation numbers (or even momentum distributions) cannot be uniquely defined in general.’