A U.S. Department of EnergyOffice of Science LaboratoryOperated by The University of Chicago
Argonne National Laboratory
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Probing Shell Structure in Neutron-Rich Nuclei above 48Ca:Using the Tools at Hand
Day 2
Michael P. Carpenter
RIA Summer School SeminarJuly 2006
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Outline of Lectures
Day 1• Nuclear Structure – a brief perspective • Changing Shell Structure in the Neutron Rich world.• -decay studies and deep inelastic reactions to
study excited states in 54Ti and 56Ti – looking for evidence of shell gaps at N=32 and N=34.
Day 2• Coulomb Excitation of 52,54,56Ti• 2-proton knockout and -decay into 52Ca• 56,58,60Cr using Gammasphere and the FMA• Future plans.
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N = 32 Gap: YES N = 34 Gap: NO
00+
15542+
1554
26754+
1121
31996+
524
61357+
2936
65398+
3340
404
6769(9+ )
230
7570(10 + )
8790(11+
)
50Ti
00+
17562+
27044+
33886+
58977+
64008+ 66299+
751610 +
879011+
GXPF1
00 +
10502+
1050
23184 +
1268
30296 +
711
4288(8 + )
1259
6693(10 + )
2405
8857
2164
9088
2395
231
52Ti
00 +
12132 +
24184 +
31036 +
45398+ 4750
7 +
61818 +
679010+
75109 +
953811+
1067212+
GXPF1
00 +
1495(2 +)
1495
2497(4 +)
1002
2936(6 +)
439
5111
2175
(7 + )
5459(8 + )
2523
348
5904(8 + )
2967
6187(9 + )
728284
6432(10+ )
245
54Ti
00 +
15092 +
26334+
31526 +
53847+
57708+
62088+
65639 + 679310
+
907511+
1048712+
GXPF1
00 +
1128(2 + )
1128
2289(4 + )
1161
2979(6 + )
690
((8 + ))
1230
56Ti
00+
15162+
25294+
30446+
8 + 53529
+ 5387
693710 +
GXPF1
3228 34
R.V.F. Janssens et al., PLB 546, 22 (2002) B. Fornal et al., PRC 70, 064304 (2004)
1129
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Beyond 2+ Energies
E(2+) values are a strong indicator of shell structure, but..
Additional evidence for the presence or absence of shell effects is most welcome and very desirable!
Measure B(E2; 0+ 2+) values
At present, this can only be done with Ti nuclei from fragmentation
Intermediate Energy Coulomb Excitation!
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Coulex of 132,134Sn at HRIBF
• rays measured with BaF array for 132,134Sn
• Surprise B(E2) increases for 132Sn.
R. Varner et al., Eur. Phys. J. A25, s01 (2005) 391.
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Beyond 2+ Energies: B(E2; 0+ 2+) valuesAu
bmin
Smaxbmin = a0 cot (max/2) /
a0 =ZS ZAu e2
m0c2 2
Zero degree detector
Ti
ETi ≈ 80 MeV/nucl.
≈ 0.4, ≈ 1.1bmin ≈ 20 fm
“touching spheres”1.2(ATi
1/3+AAu1/3) ≈ 11 fm
TOF +
SeGA array
Primary Beam: 130 MeV/u 76Ge Yields: 24000 s-1 52Ti; 2400 s-1 54Ti; 75 s-1 56Ti
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SEGA Array @ NSCL
The 75% Ge Crystal has its outer electrode divided into 8 segments along the crystal axis and 4 segments perpendicular to the axis, resulting in 32 fold segmentation
SEGA with 16 Ge
W. Mueller et al., NIMA 466, 492 (2001)
beam
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GRETINA (Segmented Ge-Shell)
• Tapered hexagon shape.• Highly segmented 6x6=36• 7 modules with 4 crystals each –
cover ≈ 1π solid angle (cover 4π will take 30 modules).
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SEGA and GRETINA
Gamma-ray energy (2keV/channel)
30Na from 32Al Beam
30Na from 30Mg Beam
340
370410250
175
190
150
140
340
370410
250
175
770430 (3+--2+)
Simulation SeGA Simulation GRETINA
30Mg (pn) → 30Na (100 MeV/u) v/c=0.43charge exchange reactionGamma-gamma coincidence
NSCL data SeGA (E. Rodriguez-Vieitez et al.)
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Particle Identification at the S800
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76Ge and 197Au: the Test CasesLab Frame
Projectile Frame
Primary beam: 76Ge @ 140 MeV/nucl.Secondary beam: 76Ge @ 81 MeV/nucl.
= 0.392197Au target thickness: 257.67 mg/cm2
max = 3.06° (CM)Number of 76Ge particles detected: 26.1E6
76Ge•E= 562.6(6)keV(<max) = 394(47) mb•B(E2, ) = 2923(346) e2fm4
•Adopted values:•E= 562.93(3)keV•B(E2, ) = 2780(30) e2fm4
197Au•E= 547.03(24) keV(<max) = 94(20) mb•B(E2, ) = 4223(898) e2fm4
•Adopted values:•E= 547.5(3) keV•B(E2, ) = 4494(409) e2fm4
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197Au check: Do we know what we are doing?
D.-C. Dinca et al., PRC 71, 041302(R) (2005)
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An accurate technique that allows for absolute B(E2) measurements
-50
-25
0
25
50
75
100
125
150
175
200
225
250
40Ar 36Ar 24Mg 30S 78 Kr 58Ni 76Ge 26Mg
Intermediate-energyCoulomb excitationAdopted value
Adopted and measured B(E2) values for stable nuclei
Adopted valueCoulomb excitationResonance fluorescenceDoppler shift attenuationRecoil distributionElectron scatteringIntermediate-energyCoulomb excitation
Mg26
B(E2) values fromdifferent methods for 26Mg
J. Cook et al., (NSCL/MSU)
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B(E2; 0+ 2+) values
52Ti, 2+ 0+ (g.s.) 54Ti, 2+ 0+ (g.s.) 56Ti, 2+ 0+ (g.s.)
56TiE= 1129(7) keV(<max) = 155(51) mbB(E2, ) = 599(197) e2fm4
54TiE= 1497(4) keV(<max) = 83(15) mbB(E2, ) = 357(63) e2fm4
52TiE= 1050(2) keV(<max) = 119(16) mbB(E2, ) = 593(81) e2fm4
D.-C. Dinca et al., PRC 71, 041302(R) (2005)
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Shell Effects in Ti isotopes: What do we know?
48Ti 50Ti 52Ti 54Ti 56Ti200
400
600
800
B(E
2, )
(e2 f
m4 )
26 28 30 32 34 N
48Ti 50Ti 52Ti 54Ti 56Ti
600
800
1000
1200
1400
1600
1800
2000 26
E(2
+) E
nerg
y (k
eV)
28 30 32 34
From an experimentalist’s point of view: N = 28 and N=32 gaps are quite visiblein BOTH the E(2+) energies and in the B(E2;0+ 2+) values
and there is no experimental evidence for a N=34 gap
D.-C. Dinca et al., PRC 71, 041302(R) (2005)
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Comparison with GXPF1
48Ti 50Ti 52Ti 54Ti 56Ti200
400
600
800
B(E
2, )
(e2 f
m4 )
26 28 30 32 34 N
GXPF1
The Shell Model with the GXPF1 interaction has problems with(a)N=34 and with (b) the B(E2) values for ALL Ti
48Ti 50Ti 52Ti 54Ti 56Ti0
500
1000
1500
2000
E(2+) GXPF1
26
E(2
+ ) Ene
rgy
(keV
)
28 30 32 34N
ep = 1.5, en = 0.5
D.-C. Dinca et al., PRC 71, 041302(R) (2005)
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Possible Interpretation
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FPD6 and GXPF1
The data may be telling us that the gap between p3/2 and p1/2 is at least as large as GXPF1 says, but that p1/2 and f5/2 are at leastas close together as FPD6 indicates
FPD6
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32 34
(6+)
(4+)
Recent Theory Development: GXPF1AGXPF1A vs GXPF1:T=1 matrix elementsinvolving p1/2 and f5/2
modified p1/2 - f5/2) gap
reduced by ~0.5 MeV
M. Honma et al., Proc. ENAM (2004)
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31 33
exp
Recent Theory Development: GXPF1A
B. Fornal et al., PRC in press
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Comparison with GXPF1A
48Ti 50Ti 52Ti 54Ti 56Ti200
400
600
800
B(E
2, )
(e2 f
m4 )
26 28 30 32 34 N
GXPF1
48Ti 50Ti 52Ti 54Ti 56Ti0
500
1000
1500
2000
E(2+) GXPF1
26
E(2
+ ) Ene
rgy
(keV
)
28 30 32 34N
GXPF1AGXPF1A
M. Honma et al., Proc. ENAM (2004)
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Value of effective charges?
B(E2) = (Apep + Anen)2
A Ap An 48 8.8 15.450 10.7 9.552 9.0 14.454 10.7 10.656 10.3 11.4
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Value of effective charges?
B(E2) = (Apep + Anen)2
A Ap An
48 8.8 15.450 10.7 9.552 9.0 14.454 10.7 10.656 10.3 11.4
With ep= 1.15 en= 0.8 according to R. du Rietz et al., PRL 93, 222501 (2004)
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Experimental Evidence for N=32 Gap: 52Ca
J.I. Prisciandaro et al., PLB 501, 17 (2001)
E(2+) in 52Ca comes from a1983 ISOLDE -decay study (A.Huck et al., PRC 31, 2226 (1985))where the separation between decay and n-delayed decay wasa problem
At NSCL 52Ca intensity is too small for aCoulex experiment 2p knockout!!
(?)— Exp.
○ FPD6
GXPF1
28 34
32
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2p knockout into 52Ca
Direct processKnock-out of 2 f7/2 protons from 54Ti
Cross section is small (~ 0.32 mb) 52Ca is magic
No direct feeding of 2+ state: Consistent with a Neutron excitation
A. Gade et al., PRC in press.
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2p knockout into 52Ca
2p knockout provides a way to study proton cross-shell excitations in n-rich nuclei
3- is (d3/2 or s1/2)-1 (f7/2)) excitation
A. Gade et al., PRC in press.
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2p-knockout “by-products”
First Transitions in 55Ti from 2p-knockout with 57Cr
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Pushing towards n-rich Cr: 59,60Cr
•59Cr from 48Ca(13C,2p)59Cr at 130 MeV•60Cr from 48Ca(14C,2p)60Cr at 130 MeV
s(2p) < 1 mb s(3n/4n) ~ 100 mb
S.J. Freeman et al., PR C 69, 064301 (2004)
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14C(48Ca,2p)60Cr @ 130 MeVE
E
ET2
M/Q
Pushing towards n-rich Cr: 60Cr
Ni
FeMnC
r
Ca scattered beam
Ti
60/17
57/16
56/16
60/17
57/16
56/16
Ni
FeMnC
r
Ca scattered beam
Ti
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Fe
Mn
Cr
824438339
1291
569250129
1007 1070643
ray energy (keV)
643
810815
986 1033607
60Cr
M=60 dataM=60 data
M=60 Z=24 M=60 Z=24 datadatawith subtractionswith subtractions
Pushing towards n-rich Cr: 60Cr
S. Zhu et al., to be published
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Gate on 644 keV
Gate on 810-815 keV
Gate on 985 keV 815
815 985
985643
643
ray energy (keV)
Cou
nts
per c
hann
el
M=60M=60Z=24 Z=24 datadata
0+
2+
643 keV
Cr60
985 keV
815 keV
1033 keV
Pushing towards n-rich Cr: 60Cr (N=36)
S. Zhu et al., to be published
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Pushing towards n-rich Cr: 57Cr (N=33)
A. N. Deacon et al., PLB 622, 151 (2005) .
A=57
A=57Z=24
14C(48Ca,n)57Cr @ 130 MeV
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57Cr: signs of collectivity
A. N. Deacon et al., PLB 622, 151 (2005) .
g9/2 prolate structure also seen in 55Cr
Good agreement with GXPF1
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Fed in 59V β decay, most likely in νf5/2 → πf7/2, expect at least 5/2− to have νf5/2 parentage
9/2+ @ only 503 keVOblate deformation?Weak coupling?
Honma, Otsuka, Brown and Mizusaki: full fp basis, GXPF1
interaction
Interpretation: 59Cr (N=35) and the Shell Model
0+
2+880
Cr58
S.J. Freeman et al., PR C 69, 064301 (2004)
13C(48Ca,2p)59Cr @ 130 MeV
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Deformation Forms Shell Gaps Too!
N=341/23/2 [301]9/2 [404]
5/2 [303]
1/2
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1.6 MeV
Prolate band,terminating
503 keV & isomer
Oblate structure
57,59Cr: Shape Driving by the g9/2 orbital
S. Freeman et al. PRC 69, 064301 (2004)A. Deacon et al. PLB 622, 151 (2005)
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More from the Deep Inelastic
56Cr32
58Cr34
60Cr36
•E(2+0+) decreases with A• Level sequence not regular just yet!? Small oblate deformation ?
48Ca + 238U and 48Ca + 208Pb
Zhu et al., to be published
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Conclusions & Outlook
• Neutron-rich nuclei continue to surprise us! - there is a N=32 shell gap just above 48Ca in Ti (and Cr) confirmed by level structure and B(E2; ) - first indications for the onset of oblate(?) deformation (and the shape driving influence of the g9/2 orbital) seen
in 59,60Cr - 54Ca is an important measurement (N=34 gap)
• Theory needs work - the GXPF1 interaction is not the complete answer - the location of the p1/2 and f5/2 orbitals in n-rich nuclei
above 48Ca needs further study - the g9/2 intruder needs to be included
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Approach: -decay spectroscopy of fragments with (A,Z) selections NSCL, ISAC prompt -ray spectroscopy following deep inelastic reactions (thick & thin targets) ATLAS Coulomb excitation NSCL, (HRIBF) fusion-evap. reactions @ radioactive targets ATLAS knockout reactions from fast fragments NSCL
Data obtained with each of these techniques and facilities complement each other!
Where did we go and what did we do
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Don’t Forget your Collaborators!
• ANL: R.V.F. Janssens, S Zhu, M.P. Carpenter F.G. Kondev et al.,
• NSCL: P. Mantica, S. Liddick, et al., A. Gade, D.-C. Dinca, D. Bazin, et al.,
• Cracow: B. Fornal, R. Broda et al.• Manchester: S. Freeman, A. Deacon, et al.• Lowell: P. Chowdury• FSU: S. Tabor et al.• TRIUMF: G. Hackman, C. Morton et al.
• Theory: M. Honma, T. Otsuka, B.A. Brown, T. Mizusaki