Spectroscopic factors from direct reactionsSpectroscopic factors from direct reactionsA unique information to study nuclear shell structure

ESNT, february 2008A. 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’

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SF = ϕ A f anlj ϕA +1

i

Transfer reactions @ low incident-energy

Nucleon-removal reactions@ intermediate-energy

Our probes to extract SF for radioactive nucleiOur probes to extract SF for radioactive nuclei

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σ =SF ×σ spmeasured calculated

extracted

2 main experimental tools for radioactive nuclei

Needs a good understanding of:- reaction mechanism- single-part. structure (WF modeling)

IPN OrsayGANILN. Keeley (Warsaw)

NSCL J. Tostevin (Surrey)

GANILDWBA, CDCC (sp X sections)shell-model (SF)

NSCL + persectives at GSIS-matrix theoryHF wave functionsshell-model

Collaborations

Shell occupancy from (e,e’p) measurementsShell 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 nucleonsRemoval of deeply-bound nucleons

A. Gade at al., Phys. Rev. Lett. 93, 042501 (2004)

ΔS (MeV)

The ‘recent’ resultfrom 2004 & 2007

Trend not (yet) understood

ProgramProgram

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 trend1- Confirm the observed trendStrongly-bound-nucleon removal from the sp shellStrongly-bound-nucleon removal from the sp shell

16C(9Be,X)15B @ 100 MeV/u S= 17.8 MeV-removal on a -rich nucleus

P//

9Be

A A-1

NSCL-MSU experiment (2009)

14O(9Be,X)13O @ 100 MeV/uS= 18.6 MeVexpected to be closed shell(addendum to be proposed)

2-Independent from the reaction mechanism?2-Independent from the reaction mechanism?1414O(d,t) and O(d,t) and 1414O(d,O(d,33He) in inverse kinematics @ 20 MeV/uHe) in inverse kinematics @ 20 MeV/u

A. Gade at al., Phys. Rev. Lett. 93, 042501 (2004)

ΔS (MeV)

14O(d,t)13O14O(d,3He)13N

ΔS=18.6 MeV

14O

Experiment at GANIL, SPIRAL (L. Nalpas et al., accepted in dec 07)

Transfer reactions consistent with (e,e’p) analysesBUT small ΔS available J. Lee et al., Phys. Rev. C 73, 044608 (2006)

J. Lee et al., Phys. Rev. C 75, 064320 (2007)

ΔS

Experimental setupExperimental setup

Exclusive measurements with MUST2 & VAMOS coincidences at GANIL

BTD1

Q1 Q2Dipole DC1&2 IC

Plast.

MUST2silicon detectors

Light-particle detection

VAMOSmagnetic spectrometer

beam-like-residue detection

SPIRAL beam14O @ 19 MeV/nucleon

Intensity: 5.104 pps

BTD2

Validation of the SF extraction method for transferValidation 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: 16O(d,t) and 16O(d,3He) 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?3- Is it a sign of some missed dependence in the NN interaction?S-matrix theory and cross-section calculationsS-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)

46Ar

32Ar

24Si

24Si

28S

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RS =σ exp

σ th

-removal-removal

December 07

One-nucleon-removal calculationsOne-nucleon-removal calculationsInvestigation of the density dependenceInvestigation of the density dependence

G.Q. Li and R. Machleidt, Phys. Rev. C 48, 1702 (1993); Phys. Rev. C 49, 566 (1994).

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σ pp (E,ρ ) =σ ppfree (E) ×

1+ 0.17 × E1.51ρ 2

1+ 9.7 × ρ1.2

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σ np (E,ρ ) =σ npfree (E) ×

1+ 0.003 × E1.51ρ 2

1+ 21.6 × ρ1.34

Density-dependence in σNN may introduce strong differences for deeply bound nucleons vs ‘peripheral’ nucleons

PerspectiveTest with deeply-bound nucleon removal at different energies 100-500 MeV/nucleon (GSI)?

38Sin

p

4- Should we probe other parts of the WF?4- Should we probe other parts of the WF?Hydrogen-induced knockout reactions (p,2p) and (p,pn)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 partoptimal hadronic probe to get shell occupancies

r=G(r) (r)MF

SRCLRC

Perspective (2)Proton-induced removal of deeply-bound nucleons in radioactive nucleiEx. 14O(p,pn), 16C(p,2p)

Are occupation numbers observable ?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.’