jeff tostevin department of physics school of electronics and physical sciences
DESCRIPTION
Reactions using nucleon knockout RISING Workshop Surrey, 29 th -30 th March 2004. Jeff Tostevin Department of Physics School of Electronics and Physical Sciences University of Surrey, UK. A. P 0. P ||. One- and two-nucleon knockout reactions. - PowerPoint PPT PresentationTRANSCRIPT
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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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
Single-neutron knockout from 17C
=0,2admixture
=0,2admixture
=2pure
V. Maddalena et al. PRC 63
(2001) 024613
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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
Skyrme Hartree-Fock radii and densities (1)
W.A. Richter and B.A. Brown, Phys. Rev. C67 (2003) 034317
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RISING Workshop, Surrey, 29th-30th March 2004
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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RISING Workshop, Surrey, 29th-30th March 2004
Weakly bound states – with good statistics
• neutron proton
P.G. Hansen and J.A.Tostevin, ARNPS 53 (2003), 219
Red
ucti
on F
acto
r R
s
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RISING Workshop, Surrey, 29th-30th March 2004
More strongly bound states – deep hole states
• neutron proton
P.G. Hansen and J.A.Tostevin, ARNPS 53 (2003), 219
inclusive
Red
ucti
on F
acto
r R
s