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Jeff Tostevin, Department of PhysicsFaculty of Engineering and Physical SciencesUniversity of Surrey, United Kingdom

Sensitivity of two-nucleon knockout to two-body correlations

Probing pair correlations: Experimental tools and associated models, CEA/SPhN Saclay, 13th -15th October 2008

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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

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

9Be

iJ1

21j

2j

TI ,

J [fast]spectatorc

light nuclear target

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Sudden removal from the residue as a spectator

12

11 ][ js

A

TS ,

J

iJIJ ][

Ijj ][ 21

22 ][ js

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

(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.

(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.

z

J2

1

6

Structure input – two nucleon overlaps

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Sampling the two-nucleon wave function

Interaction with the targetprobes wave functions at surface and beyond

TC RRb 28Mg 26Ne(2+)28Mg 26Ne(2+)

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Strongly-bound: (like) 2N removal

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Two-proton knockout: 38Si 36Mg

+2.80(64)

39.24

37Al20.64

+4.38

36Mg

38Si

+5.29

2p

1p

1p

+18.60

1n KO

indirect2p KO

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Removal probes single-nucleon wave functions

Interaction with the target probes wave functions at surface

ziJ

38Sin

p

targetTP RRb

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Target drills out a cylindrical volume at the surface

z

J2

1

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Antisymmetrized 28Mg 26Ne removal of

0+

2+

4+

uncorrelated

J.A. Tostevin, Journal of Physics: Conference Series 49 (2006) 21–26

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J.A. Tostevin, et al., PRC 70 064602 (2004).

Spin-structure - correlations in wave functions

28Mg(0+) 26Ne(0+), 2p, ~100 MeV/nucleon28Mg(0+) 26Ne(0+), 2p, ~100 MeV/nucleon

Stripping (mb)

0.573 0.286 S=0

0.061 0.143 S=1

All mechanisms (mb)

0.634 0.426 Stripping

0.466 0.301 Diffraction

… … S=0+1

1.150 0.750 (-2p) x 2 (S=0)

x 1.52

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Coherence of shell model correlations

28Mg (Z=12, N =16) 26Ne(0+)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) 012501J. A. Tostevin, EPJ Special Topics 150, 67 (2007) [RNB7 Proceedings]

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-0.2

0

0.2

0.4

0.6

0.8

Knockout cross sections – correlated caseS

igm

a (

mb)

0+ 2+ 2+4+1 2

28Mg 26Ne(0+, 2+, 4+ , 22+) 82.3 MeV/u 28Mg 26Ne(0+, 2+, 4+ , 22

+) 82.3 MeV/u

J.A. Tostevin et al., PRC 70 (2004) 064602, PRC 74 064604 (2006

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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’ (Hjorth-Jensen) 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.

48Ca(0+) 46Ca(0+),

2n, 100 MeV/nucleon

48Ca(0+) 46Ca(0+),

2n, 100 MeV/nucleon

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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

Projectile rest frame

laboratory frame and

and component equations

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Look at momentum content of sampled volume

ziJ

2

1

Probability of a residue with parallel momentum A

J. A. Tostevin, EPJ Special Topics 150, 67 (2007) [RNB7 Proceedings]

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28Mg→26Ne (all) – Full calcs, EC Simpson

D. Bazin, private communication

28Mg (-2p) on 9Be at 82.3 MeV per nucleon

-0.2

0

0.2

0.4

0.6

0.8

Sig

ma

(m

b)

0+ 2+ 2+4+1 2

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Two proton knockout from 38Si 36Mg(0+,2+)

38Si (2p) 83 A MeV

Re

sid

ue

mo

me

ntu

m d

istr

ibu

tion

0+

2+

A. Gade, JAT et al.,

to be published

Theory Expt.

0+ 56% 58(7)%

2+ 44% 42(7)%

dp/p=1.66%

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Two neutron knockout from 22Mg 20Mg(0+,2+)

22Mg (2n) 75.1 A MeV

Re

sid

ue

mo

me

ntu

m d

istr

ibu

tion

0+

2+

A. Gade, JAT et al.,

to be published

Expt.

0+ 84%

2+ ~16%

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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.

Status: 2N removal reactions reveal:

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Fin