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Sensitivity of two-nucleon knockout to
two-body correlations
Probing pair correlations: Experimental tools
and associated models, CEA/SPhN Saclay,
13th -15th October 2008
Jeff Tostevin, Department of Physics
Faculty of Engineering and Physical Sciences
University of Surrey, United Kingdom
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2N knockout spectroscopy: Which correlations?
Interest: (i) assessing shell model wave functions and
effective interactions, (ii) spectroscopy near shell gaps
and role of 2N correlations  as may be revealed by
inclusive and partial cross sections, and/or 2N removal
fragment momentum distributions.
Correlations: (i) nucleons bound in same mean field
(ii) antisymmetry / angular momentum
(iii) SR, LR and Tensor - strength outside
shell model/mean field model spaces
(iv) residual interaction/pair correlations
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2N knockout at beam energies > 100 MeV/nucleon
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Ji
9Be
I ,T
j1
2
j2
J
c
light
nuclear
target
[fast]
spectator
Experiments are inclusive (with respect to the target final
states). Residue final state measured – using gamma rays,
whenever possible – and momenta (p//) of the residues.
Cross sections are large and they include both:
Stripping (inelastic/absorptive) and diffractive (elastic)
interactions of the removed nucleon(s) with the target
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Sudden removal from the residue as a spectator
S, T
[ j1 j2 ]I
1
[1s] j1
A
2
[ 2 s] j2
J
[ IJ ]J i
Core/residue state is
assumed a spectator –
so reaction probes the
two nucleon overlap and
(in general) there are
several active 2N
configurations – overlap
determined by the two
nucleon amplitudes
(TNA) in shell model.
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Target drills out a cylindrical volume at the surface
z
2
J
1
(i) Cross section will be sensitive to
the spatial correlations of pairs of
nucleons near surface
(ii) No spin selection rule (for S=0
versus S=1 pairs) in the reaction
mechanism
(iii) We can gain first expectation of
the extent to which we are sensitive
to ‘correlations’ by looking at the 2N
overlaps in the sampled volume –
and effect on the cross sections
(iv) No mismatch considerations.
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Structure input – two nucleon overlaps
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Sampling the two-nucleon wave function
b  RC  RT
28Mg with
26Ne(2
+)
Interaction
the target
probes wave functions at
surface and beyond
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Strongly-bound: (like) 2N removal
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Two-proton knockout: 38Si  36Mg
indirect
2p KO

1p
+2.80(64)
+18.60
36Mg
1n KO

20.64

+4.38
1p
2p
37Al
+5.29
38Si

39.24
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Removal probes single-nucleon wave functions
38Si
n
p
Interaction with the
target probes wave
functions at surface
Ji
b  RP  RT
target
z
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Target drills out a cylindrical volume at the surface
2
J
1
z
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Antisymmetrized 28Mg  26Ne removal of
1.1-1.2
uncorrelated
1-1.1
0.9-1
0.8-0.9
0.7-0.8
4+
0.6-0.7
0.5-0.6
0.4-0.5
2+
0+
0.3-0.4
0.2-0.3
0.1-0.2
0-0.1
J.A. Tostevin, Journal of Physics: Conference Series 49 (2006) 21–26
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Spin-structure - correlations in wave functions
28Mg(0+)
 26Ne(0+), 2p, ~100 MeV/nucleon
Stripping (mb)
All mechanisms (mb)
0.634
0.426
Stripping
0.466
0.301
Diffraction
…
…
S=0+1
1.150
0.750
(-2p)
x 1.52
0.573
0.286 S=0
0.061
0.143 S=1
x 2 (S=0)
J.A. Tostevin, et al., PRC 70 064602 (2004).
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Coherence of shell model correlations
28Mg
(Z=12, N =16)  26Ne(0+)
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Correlated: 28Mg  26Ne(0+,2+,4+), 82.3 MeV/u
Data: D. Bazin et al., PRL 91 (2003) 012501
J. A. Tostevin, EPJ Special Topics 150, 67 (2007) [RNB7 Proceedings]
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Knockout cross sections – correlated case
28Mg
26Ne(0+, 2+, 4+ , 22+) 82.3 MeV/u
Sigma (mb)
0.8
0.6
0.4
0.2
0
-0.2
0+
2+
1
4+
J.A. Tostevin et al., PRC 70 (2004) 064602, PRC 74 064604 (2006
2+
2
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Ratio of measured to calculated cross sections
J.A. Tostevin and B.A. Brown, PRC 74 064604 (2006), PRC 70 064602 (2004)
Figure: A. Gade
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Weakly-bound 2n removal
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48Ca(-2n)
to 46Ca(0+) – beyond the sdpf-space
With Alex Brown, Ed Simpson:
Perturbative calculation of
two-neutron TNA when
using a ‘realistic’ (HjorthJensen) NN interaction,
estimating the component
amplitudes across several
major oscillator shells 
Cross section is enhanced
by a factor of 2 compared
to including only the [f7/2]2
term (preliminary): cf.1.32
in pf the shell calculation.
 46Ca(0+),
2n, 100 MeV/nucleon
48Ca(0+)
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Sudden 2N removal from the mass A residue
Sudden removal: residue momenta probe the
summed momenta of pair in
the projectile rest frame
A
laboratory frame
and
Projectile rest
frame
and component equations
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Look at momentum content of sampled volume
2
1
Ji
z
Probability of a residue with parallel momentum A
J. A. Tostevin, EPJ Special Topics 150, 67 (2007) [RNB7 Proceedings]
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(all) – Full calcs, EC Simpson
28Mg
(-2p) on 9Be at
82.3 MeV per nucleon
Sigma (mb)
28Mg→26Ne
0.8
0.6
0.4
0.2
0
-0.2
0+
21+
4+
D. Bazin, private communication
22+
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Residue momentum distribution
Two proton knockout from 38Si  36Mg(0+,2+)
38Si
0+
2+
(2p) 83 A MeV
Theory
Expt.
0+
56%
58(7)%
2+
44%
42(7)%
dp/p=1.66%
A. Gade, JAT et al.,
to be published
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Residue momentum distribution
Two neutron knockout from 22Mg  20Mg(0+,2+)
0+
22Mg
(2n)
75.1 A MeV
Expt.
0+
84%
2+ ~16%
A. Gade, JAT et al.,
2+
to be published
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Status: 2N removal reactions reveal:
 SR/LR/Tensor correlations: observe systematic
suppression of 1N and 2N strength cf shell model – allows
the identification of structure effects beyond these
systematics
 knockout mechanism is sensitive to details of 2N (shell
model) wave functions and effective interactions –
enhancement although no reaction mechanism spin
selectivity
 knockout of other than two well-bound nucleons is
complicated by the (strong) indirect – 1N knockout + particle
decay – 2N removal mechanism.
 have identified spectroscopic value of momentum
distributions of -2N reactions and have a more complete
calculation available.
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Fin