Jeff Tostevin Department of Physics School of Electronics and Physical Sciences

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RISING Workshop, Surrey, 29th-30th March 2004

Jeff TostevinDepartment of PhysicsSchool of Electronics and Physical SciencesUniversity of Surrey, UK

Reactions using nucleon knockout

RISING WorkshopSurrey, 29th-30th March 2004

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One- and two-nucleon knockout reactions

Peripheral collisions (E 50A MeV; MSU, RIKEN, GSI)

heavy mass A residue is detected,with coincident-ray detection

Events contributing will be both break-up and stripping both of which leave a mass A residue in the final state

T+xN

A+xN

light targetT=9Be,12C

Sudden removal of nucleons

P0

A

P||

Target T left ing.s. or excited state

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One- and two nucleon knockout – to date

One-nucleon knockout predominantly – proof of purpose and of accuracy

Light nucleus sector – p and sd-shell (Ni looked at but not optimum detection/resolution)

Small number of final states and gamma-rays

Semi-classical (eikonal) reaction theory seems to work quantitatively.

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Orientation for magnitudes - extreme sp model

Single neutron removal from 23O [1d5/2]6 [2s1/2]

2s1/2 Sn=2.7 MeV

1d5/2 Sn=5.5 MeV

RIKEN (PRL 88 (‘02) 142502)72 MeV/u + 12C target;

sp(2s1/2)=64 mb

sp(1d5/2)=23 mb

-n = 6 sp(1d5/2)+ sp(2s1/2)

= (138 + 64) = 202 mb

-n = 6 sp(1d5/2)+ sp(2s1/2)

= (138 + 64) = 202 mb

n

-n = 233(37)mb-n = 233(37)mb

typical cross sections 20 – 30 mb

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Single-neutron knockout from 17C

=0,2admixture

=0,2admixture

=2pure

V. Maddalena et al. PRC 63

(2001) 024613

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Structure – we probe single particle overlaps

Nucleon removal from A+1 will leave mass A residue inthe ground or an excited state - amplitude for finding nucleon with sp quantum numbers ,j, about core state c in A+1 is

c

1A rj,

c1AN1Acc EES ,|,)(F rrj

)S(C|)(F | d 22c jj rrSpectroscopicfactor - occupancyof the stateUsual to write

1| )( | d ; )( )S(C)(F 200

2c rrrr jj

I || 1c1 jIjI AA

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0 0 .2 0 .4 0 .6 0 .8 1S th eo /(2 j+ 1 )

0

0 .2

0 .4

0 .6

0 .8

1

1 .2

S exp

/(2j

+1)

l = 0

l = 1l = 2

l = 3

Experimental v shell model spectroscopic factors

P.G. Hansen and J.A.Tostevin, ARNPS 53 (2003), 219

More bound systems

Can define reduction factor

th Shell model structure plus eikonal reaction

1 th

texp

sR

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Rs factors – deviations from the shell model

0 5 10 15 20 25N ucleon Separation Energy [M eV ]

0

0.2

0.4

0.6

0.8

1

Red

uctio

n F

acto

r R

s

-n-pe,e 'p

22O

32Ar

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Two nucleon knockout – go south, or west

2p from neutron rich

1T

32Mg

34Al

34Si

32Na30Na

32Al

30Mg

30Ne

28Mg

26Ne 28Ne

28Na

30S

26Si

28P

28S

26P

24Si

2n from neutron deficient

Z

N

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2p knockout – production or detailed spectroscopy?

D. Bazin et al., PRL 91 (2003) 012501.

32Mg 30Ne

2p knockout(~1mb)

productionrate R

productionrate R/1000

e.g.Coulex

30Ne

could gainx100 rate

reaction mechanism is?

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Two nucleon knockout – reaction mechanism

D. Bazin et al., PRL 91 (2003) 012501

40

0

20

2p removal

2s1/2

1d5/2

1p1/2

1p3/2

23O 21O23O 21O

n + 21On + 21O

0+2+

1

-1n

28Mg 26Ne28Mg 26Ne

22O22O

-1n

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Direct two nucleon knockout – uncorrelated

02

22

12

c0N2strip | )|S| )(1|S| (1|S| | d b

Estimate assuming removal of a pairof uncorrelated nucleons -

)()((A))(A, 21c210 1rrrr

2 ,

)( 21stripstrip )( 21stripstrip

1

2

c

12

A

p particles

q particles

contribution from direct 2N removal 2N

)( pq

)(2

1)q(q)(

2

1)p(p

strip

stripstrip2N

)( pq

)(2

1)q(q)(

2

1)p(p

strip

stripstrip2N

D. Bazin et al., PRL 91 (2003) 012501

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Uncorrelated two proton removal

12

c

12

A mb 1.50(1) :Expt

mb 1.8)22(2

1)4(4

then)(1d Assuming

strip2N

45/2

mb 1.50(1) :Expt

mb 1.8)22(2

1)4(4

then)(1d Assuming

strip2N

45/2

D. Bazin et al., PRL 91 (2003) 01250128Mg 26Ne(inclusive)28Mg 26Ne(inclusive)

mb 0.35)00(

mb 0.322)0(

mb 0.29)22(

strip

strip

strip

with weights 0+: 1.33 to the 26Ne 2+: 1.67final states 4+: 3.00

with weights 0+: 1.33 to the 26Ne 2+: 1.67final states 4+: 3.00

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Correlated two proton removal

),( ,])]2()1([[ 2211

)(

2211 jjC JMcIjj

I

JIccJM

1

2

c

11j22j

A

There is now no SF factorisation

There is now no SF factorisation

J.A. Tostevin et al., RNB6 proceedings, in press

||

||

2121 jjIjj

IJIIJ c

Spin states populated

amplitudes of nucleon-

pair wave functions about

core configurations c.

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Shell model (sd-shell) 2N amplitudes

28Mg 26Ne(0+)28Mg 26Ne(0+)

C(2s1/2)2 = – 0.305

C(1d3/2)2 = – 0.301C(1d5/2)2 = – 1.05

C(1d3/2)2 = – 0.050

C(d5/2,d3/2)= + 0.374

C(1d5/2)2 = – 0.637

C(s1/2,d5/2)= – 0.061

C(s1/2,d3/2)= – 0.139

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

28Mg 26Ne(4+)28Mg 26Ne(4+)

C(d5/2,d3/2) = 0.331

C(1d5/2)2 = 1.596B.A. Brown, private communication

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Cross sections – correlated and uncorrelated

28Mg 26Ne(0+, 2+, 4+) S = (in mb) / 0.2928Mg 26Ne(0+, 2+, 4+) S = (in mb) / 0.29

1.43Inclusive cross section (in mb) 1.50(10)

Sth Sexp Sth exp th

unc. corr. (mb) (mb)

0+ 1.33 2.4(5) 1.83 0.70(15) 0.53

2+ 1.67 0.3(5) 0.55 0.09(15) 0.16

4+ 3.00 2.0(3) 1.79 0.58(9) 0.52

2+ - 0.5(3) 0.76 0.15(9) 0.22

J.A. Tostevin, G. Podolyák, et al., RNB6 proceedings, in press, and in preparation

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Nature of the two-nucleon correlations

P0Removed nucleon pair are spatially correlated but no restriction on pair spin S or relative orbital angular momentum in formalism. All contributing pair wave functions are included.

Unlike.e.g. (p,t) reaction – where angular momentum selection on the p | t vertex selects nn pair in S=0, T=1, relative s-state configuration.

Can assess by projecting [ T=1, S=0, =0 ] relative motion component from the pair wave functions Sth(rel)

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Cross sections – relative s-state correlations

28Mg 26Ne(0+, 2+, 4+ ,2+)28Mg 26Ne(0+, 2+, 4+ ,2+)

Sth Sexp Sth

rel corr.

0+ 1.60 2.4(5) 1.83

2+ 0.14 0.3(5) 0.55

4+ 2.00 2.0(3) 1.79

2+ 0.46 0.5(3) 0.76

J.A. Tostevin, G. Podolyák, et al., RNB6 proceedings, in press, and in preparation

D. Bazin et al., PRL 91 (2003) 012501

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Test case - earlier data from Berkeley (~10%)

Kidd et al., Phys Rev C 37 (1988) 26132N removal from 12C

B.A. Brown, 2N amplitudes

2N removal from 12CB.A. Brown, 2N amplitudes

12C10Be (2p) 5.82 mb

S(2p)=27.18 MeV 5.88

5.33 mb

5.30(30)

5.15 mb

5.81(29)

12C10C (2n) 4.26 mb

S(2n)=31.84 MeV 5.33(81)

3.91 mb

4.44(24)

3.84 mb

4.11(22)

1.05 GeV 2.10 GeV 250 MeVEnergy/nucleon

J.A. Tostevin et al., RNB6 proceedings, in press and in preparation

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Surface localisation of knockout reactions

12Be+9Be 11Be(gs)+X, 80A MeV12Be+9Be 11Be(gs)+X, 80A MeV

TC RRb

Eikonal theory:localisation provided by core survival requirement

9Be

c

12Bebv

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Skyrme Hartree-Fock radii and densities (1)

W.A. Richter and B.A. Brown, Phys. Rev. C67 (2003) 034317

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Skyrme Hartree-Fock radii and densities (2)

B.A. Brown, S. Typel, and W.A. Richter,Phys. Rev. C65 (2002) 014612

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Weakly bound states – with good statistics

• neutron proton


Red

ucti

on F

acto

r R

s

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More strongly bound states – deep hole states

• neutron proton


inclusive

Red

ucti

on F

acto

r R

s

Jeff Tostevin Department of Physics School of Electronics and Physical Sciences

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