Spectroscopic factors from direct Spectroscopic factors from direct reactions reactions A unique information to study nuclear shell structure ESNT, february 2008 A. Obertelli, CEA-IRFU/SPhN ich extend can we ‘determine’ the absolute shell occupancy of nucleo Extraction of Spectroscopic Factors - direct reactions - first-importance information for nuclear spectroscopy - ‘model dependent’ SF = ϕ A f a nlj ϕ A +1 i
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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 - PowerPoint PPT Presentation
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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
€
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).
€
σ pp (E,ρ ) =σ ppfree (E) ×
1+ 0.17 × E1.51ρ 2
1+ 9.7 × ρ1.2
€
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.’