Spectroscopic factors from direct reactions

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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
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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 _at_ low incident-energy
GANIL DWBA, CDCC (sp X sections) shell-model (SF)
Nucleon-removal reactions _at_ intermediate-energy
NSCL persectives at GSI S-matrix theory HF wave
functions shell-model
NSCL J. Tostevin (Surrey)
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Shell occupancy from (e,ep) 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)
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Removal of deeply-bound nucleons
A. Gade at al., Phys. Rev. Lett. 93, 042501 (2004)
The recent result from 2004 2007
?S (MeV)
Trend not (yet) understood
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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
shell at MSU (accepted) 2- dedicated transfer
reactions at GANIL (accepted) 3- developments
in S-matrix / theory 4- Proton-induced nucleon
removal (perspective)
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1- Confirm the observed trend Strongly-bound-nucle
on removal from the sp shell
NSCL-MSU experiment (2009)
A
A-1
16C(9Be,X)15B _at_ 100 MeV/u ?S 17.8 MeV ?-removal
on a ?-rich nucleus
14O(9Be,X)13O _at_ 100 MeV/u ?S 18.6 MeV expected
to be closed shell (addendum to be proposed)
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2-Independent from the reaction
mechanism? 14O(d,t) and 14O(d,3He) in inverse
kinematics _at_ 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
?S18.6 MeV
?S
Transfer reactions consistent with (e,ep)
analyses BUT small ?S available
?S (MeV)
J. Lee et al., Phys. Rev. C 73, 044608 (2006) J.
Lee et al., Phys. Rev. C 75, 064320 (2007)
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Experimental setup
Exclusive measurements with MUST2 VAMOS
coincidences at GANIL
BTD1
BTD2
Dipole
Q1
Q2
DC12
IC
Plast.
SPIRAL beam 14O _at_ 19 MeV/nucleon Intensity 5.104
pps
MUST2 silicon detectors Light-particle detection
VAMOS magnetic spectrometer beam-like-residue
detection
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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,ep) experiment
R0.62(20) using radii from one-body HF wave
function Matter rms constrained by elastic
scattering
N. Keeley (2007)
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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)
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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)?
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4- Should we probe other parts of the
WF? Hydrogen-induced knockout reactions (p,2p)
and (p,pn)
Stable nuclei / (e,ep) 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,ep) at high missing momentum
• (p,2p) and (p,pn) at high energy (gt100
  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)
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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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