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Spectroscopic factors from direct reactions A unique information to study nuclear shell structure

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

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Spectroscopic factors from direct reactions A unique information to study nuclear shell structure

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  1. 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’

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

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

  4.    Removal of deeply-bound nucleons A. Gade at al., Phys. Rev. Lett. 93, 042501 (2004) The ‘recent’ result from 2004 & 2007 ΔS (MeV) Trend not (yet) understood

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

  6. P// 9Be 1- Confirm the observed trend Strongly-bound-nucleon removal from the sp shell NSCL-MSU experiment (2009) A A-1 16C(9Be,X)15B @ 100 MeV/u S= 17.8 MeV -removal on a -rich nucleus 14O(9Be,X)13O@ 100 MeV/u S= 18.6 MeV expected to be closed shell (addendum to be proposed)

  7. 14O(d,3He)13N 14O(d,t)13O 2-Independent from the reaction mechanism? 14O(d,t) and 14O(d,3He) in inverse kinematics @ 20 MeV/u Experiment at GANIL, SPIRAL (L. Nalpas et al., accepted in dec 07) A. Gade at al., Phys. Rev. Lett. 93, 042501 (2004) 14O ΔS=18.6 MeV ΔS Transfer reactions consistent with (e,e’p) analyses BUT small ΔS available ΔS (MeV) J. Lee et al., Phys. Rev. C 73, 044608 (2006) J. Lee et al., Phys. Rev. C 75, 064320 (2007)

  8. Experimental setup Exclusive measurements with MUST2 & VAMOS coincidences at GANIL BTD1 BTD2 Dipole IC Q1 Q2 DC1&2 Plast. SPIRAL beam 14O @ 19 MeV/nucleon Intensity: 5.104 pps MUST2 silicon detectors Light-particle detection VAMOS magnetic spectrometer beam-like-residue detection

  9. Validation of the SF extraction method for transfer Analysis: CDCC (Continuum-Discretized Coupled Channel) + finite-range Benchmark: 16O(d,t) and 16O(d,3He) in direct kinematics Comparison with available data at 14 & 26 MeV/u 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)

  10. 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 December 07 -removal 46Ar -removal 24Si 28S 24Si 32Ar S (MeV)

  11. 38Si One-nucleon-removal calculations Investigation of the density dependence n Density-dependence in NN may introduce strong differences for deeply bound nucleons vs ‘peripheral’ nucleons p G.Q. Li and R. Machleidt, Phys. Rev. C 48, 1702 (1993); Phys. Rev. C 49, 566 (1994). Perspective Test with deeply-bound nucleon removal at different energies 100-500 MeV/nucleon (GSI)?

  12. 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 MF r=G(r) (r) SRC LRC • 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 Perspective (2) Proton-induced removal of deeply-bound nucleons in radioactive nuclei Ex. 14O(p,pn), 16C(p,2p)

  13. Are occupation numbers observable ? R. J. Furnstahl and H.-W. Hammer, Phys. Lett. B 531, 203 (2002) ‘We conclude that occupation numbers (or even momentum distributions) cannot be uniquely defined in general.’ ‘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.’

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