1. Dipa Bandyopadhyay University of York
Exploring the X(5) characteristic in the mass A ~ 80 region : Coulomb excitation of 78Sr nucleus
Dipa Bandyopadhyay
University of York
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2. Microscopic picture in the region A ~80
Ref: Nazarewicz
et al., NPA 435,
(1985) 397 40
At prolate shape (2~0.35) the largest gap appears for particle
number 38 which corresponds to Z of Sr isotopes.
At oblate shape (2 ~-0.3) the major shell gap occurs at particle
number 36, which corresponds to N of 74Sr.
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3. Competition between different shapes may create transitional region.
Energy surfaces obtained with Woods-Saxon potential :
shape change with change in neutron number
Prolate : 78Sr
Prolate + Oblate
: 74,76Sr, 80Sr
Prolate-Spherical
-Oblate : 80Sr
Prolate-Spherical:
82Sr
Spherical : 84Sr
Ref: Nazarewicz et al., NPA 435 (1985) 397
Competition between different shapes may create transitional region.
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4. Np, N n ~ number of valence protons and neutrons. For X(5),
P factor estimation : A measure of deformation driving quadrupole quadrupole force vs spherical driving pairing force.
Np, N n ~ number of valence protons
and neutrons.
For X(5),
[ E. A. McCutchan et al, PRC 70, ]
N=90 82
p-drip line Z 50
78,80Zr
76,78Sr 28 28 50 82
126 N
N-drip line
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5. Critical points in Symmetry (Casten) Triangle
[F Iachello PRL 85, 3580(2000); PRL (2001)]
U(5)
=0
Spherical harmonic vibrator
V=V(),
> 0,
 independent
V=V(),
> 0,  = 0
X(5)
E(5)
SU(3)
O(6)
 > 0, =0
 > 0, unstable
Axially deformed rotor
 unstable deformed rotor
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6. Examples of X(5) symmetry ~ N=90 isotones (152Sm)
Casten & Zamfir
PRL 87,
052503(2001)
R 4/2 = E(41+)/E(21+) = 2.90; E(02+)/E(21+) = 5.65;
Larger energy spacing in the excited band;
B(E2)s of yrast transitions are in between that of vibrator and rotor;
B(E2)s of non yrast transitions are smaller compared to that of yrast transitions.
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7. Candidate for X(5) symmetry; 78Sr
D. S. Brenner et al, AIP Conference Proceedings 638, 223 (2002)
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8. 76,78Sr Systematic of Sr nuclei (Z=38) : R4/2 ~ E(41+)/E(21+) 3.33
2.90
2.0
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9. E(41+)/E(21+) systematic; A~80 : expected value for X(5) ~ 2.9042
2.34
2.23
2.11 40
2.86
2.56
2.34
2.22
2.02 38
2.81
2.54
2.23
2.85
2.32
2.07 Z 36
2.38
1.86
2.22
2.11
2.16
2.11
2.31 34
2.28
2.16
1.90
2.15
2.38
2.45
2.37
2.65
2.28
2.27
2.23
2.07
2.07
2.46
2.50
2.54
2.64 32 30
2.18
2.29
2.32
2.36
2.24
2.02 30 32 34 36 38 40 42 44 46 48 N
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10. R4/2 systematic and the P factor estimations
are necessary but not sufficient conditions to
characterize a nucleus as X(5).
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11. Many nuclei which follow the expected X(5) trend closely!!!!
Clark et al PRC 68, (2003)
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12. …Fail to follow their X(5) characteristics except : 126Ba, 130Ce &
Clark et al PRC 68, (2003)
…Fail to follow their X(5) characteristics except : 126Ba, 130Ce &
N=90 isotones from Nd (Z=60) to Er (Z=68).
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13. We must measure the transition strengths between the
levels of the yrast and non yrast bands along with the
level energies to confirm the X(5) assignment to 78Sr.
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14. Yrast band energies upto 26ħ. B(E2)s of first 2 yrast transitions.
Known:
Yrast band energies upto 26ħ.
B(E2)s of first 2 yrast transitions.
Negative parity non yrast band.
Tentative positive parity band.
We will measure:
The second 0+ band.
B(E2)s of yrast states upto 8ħ.
B(E2; 02+  21+).
[B(E2; 22+  02+)].
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15. X(5) prediction demands it to be 4+ 2+ 0+ transition
Fusion-evaporation approach: 58Ni(28Si,2)78Sr Gammasphere + microball
D. Rudolph et al, Phys. Rev C56,(1997)98
???
X(5) prediction demands it to be transition
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16. Fusion-evaporation approach: 40Ca(40Ca,2p)78Sr ,
118 and 121 MeV, Jurogam + RITU
Nuclear physics group, University of York
278 keV gated -ray spectra
1200
77Rb has very similar half life and  endpoint energies compared to 78Sr.
So -tagging is not very effective in this case. 77,78Rb has very similar energies
[ 77Rb: (2), Ig ~ 100% ], [ 78Rb: (2), Ig ~ 100% and (4), Ig ~ 80%
keV ] compared to that of 78Sr [ 278.5(4), Ig ~ 100% & 503.7(4), Ig ~ 100% keV ].
Hence  gating is also not very effective.
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17. Pure intense radioactive beam of 78Sr.
Requirement
Pure intense radioactive beam of 78Sr.
Problem
78Rb will be produced with several magnitude higher
(~109) compared to 78Sr (~106)
Solution
Electron beam ion source (EBIS)
Successfully used to produce light Sr nuclei at CERN-ISOLDE
Nucl. Phys. 763A, 45 (2005)
Procedure
CF4 gas is introduced in the ion source to form SrF+.
No high-rate contaminants not specially RbF+ is expected.
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18. 3.0 MeV/A 78Sr on 1 mg/cm2 58Ni target;
Coulomb excitation of 78Sr : Target selection
3.0 MeV/A 78Sr on 1 mg/cm2 58Ni target;
MINIBALL efficiency : 10%; CD detector angle – 150 – 500 in laboratory frame.
58Ni
Higher Z gives higher yield but looses in kinematic focusing!!!
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19. Coulomb excitation of 78Sr : yield estimate
3.0 MeV/A 5x104 ions/sec 78Sr on 1 mg/cm2 58Ni target; MINIBALL
efficiency : 10%; CD detector angle – 150 – 500 in laboratory frame.
106
105
104
103
Yield / 10 days
102
101
100
21+
41+
61+
02+
22+
81+
42+
Aim : E(02+), E(22+) and E(42+) , B(E2; 81+  61+),
B(E2; 61+  41+), B(E2; 02+  21+), [B(E2; 22+  02+)]
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20. Coulomb excitation of 78Sr
Requesting
Beam : 78Sr [ T½ ~ 2.5 min ]
Energy : 3.0 MeV/A
Beam time : 10 days [Considering the challenges related to
maintain a stable high intensity beam, we agree to accept
10 days beam time separated in different time slots]
Ion source : EBIS with CF4 gas [ Beam with Rb
contamination is not acceptable]
Beam intensity : > 5 x 104 s-1
(Assumed 3 out of 12 pulses from the PSB to
ISOLDE and total 2% transmission efficiency)
Primary target : Nb metal powder of thickness 50 gm/cm2
Secondary target : 58Ni of thickness 1 mg/cm2
Detectors : MINIBALL + CD
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21. Collaboration D. Bandyopadhyay University of York, UK Spokesperson
C. J. Barton University of York, UK
J. E. Butterworth University of York, UK
R. Wadsworth University of York, UK
B. S. Nara Singh University of York, UK
D. Jenkins University of York, UK
M. Bentley University of York, UK
S. Fox University of York, UK
P. E. Garrett University of Guelph, Canada
C. E. Svensson University of Guelph, Canada
E. Clement CEA-Saclay, France Contactperson
N. Pietralla Technische Universitaet Darmstadt, Germany
L. M. Fraile CERN, Switzerland
P. Delahaye CERN, Switzerland
F. Wenander CERN, Switzerland
N. Warr University of Koln,Germany
J. Cederkall Lund University, Sweden
A. Ekstrom Lund University, Sweden
R. Krucken TU Munich, Germany
T. Kroll TU Munich, Germany
R. Gernhauser TU Munich, Germany
The MINIBALL and REX-ISOLDE collaboration.
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22. ADDENDUM
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23. The CD detector at 150 – 500 detects most of the scattered particles
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24. Rutherford X-section estimate
CD detector angle
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25. INTC meeting, CERN
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26. INTC meeting, CERN
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27. 78Sr 80Zr Systematic of N=40 nuclei : R4/2 ~ E(41+)/E(21+) 3.33 2.90
2.0
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28. 78Sr Systematic of N=40 nuclei : B(E2; 21+ 01+) INTC meeting, CERN
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29. H= - ħ2/2B[(1/4)(4/)/1/(2sin3)
Bohr Hamiltonian :
H= - ħ2/2B[(1/4)(4/)/1/(2sin3)
(sin3//–Q2k/sin2V] k
This Hamiltonian lives in 5-dimensional space with two intrinsic
variables ,  and three Euler angles  i(i=1,2,3)
If potential depends only on , V(,) = U(),
one can write separating the variables,
H = (,  i) + Eƒ(  )
The second part of the Hamiltonian is exactly solvable in a five-
dimensional infinite potential well corresponding to E(5) symmetry,
U() = 0,    w , u() = ,  >  w.
>> phase transitions in coordinate.
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30. Q2k/sin2=4/3 (Q12+Q22+Q32)+Q32 [(1/ sin2
X(5) symmetry : connecting U(5) and SU(3)
Situation is much more complex compared to E(5).
Bohr Hamiltonian does not support any other exact solution like E(5).
However, there is an approximate solution to Bohr Hamiltonian,
which describes many of the properties of the X(5).
Consider the potential at = 00
Q2k/sin2=4/3 (Q12+Q22+Q32)+Q32 [(1/ sin2

And look for solution like,
(,, i) = LK(,) DL M,K ( i)
Separate the potential (approximately) in  and with a square well
potential for  and harmonic oscillator potential for 
U(,) = u() + u()
The equation can be solved now and the corresponding symmetry
is known as X(5) symmetry.
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31. SU(3) O(6) U(5) X(5) E(5) Property
Importance of E02+ state in case of transitional nuclei:
5.65
3.03
Second excitation :
R = (E02 – E01)/
(E21 – E01)
3.33
2.50
2.00
2.90
2.20
Initial excitations
R = (E41 – E01)/
SU(3)
O(6)
U(5)
X(5)
E(5)
Property
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32. 78Sr 98Sr Systematic of Sr isotopes (Z=38) : B(E2; 21+ 01+) Collective
Sharp change in observable : signature of shape transition
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33. INTC meeting, CERN
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34. Isotope chart 2.2 x106 2.4 x109 INTC meeting, CERN
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