Post on 06-Feb-2016
description
INTC meeting, CERNINTC meeting, CERN 11
Exploring the X(5) characteristic in the Exploring the X(5) characteristic in the mass A ~ 80 region : Coulomb excitation mass A ~ 80 region : Coulomb excitation
of of 7878Sr nucleusSr nucleus
Dipa BandyopadhyayDipa Bandyopadhyay
University of YorkUniversity of York
INTC meeting, CERNINTC meeting, CERN 22
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.
Microscopic picture in the region A ~80
40 Ref: Nazarewiczet al., NPA 435, (1985) 397
INTC meeting, CERNINTC meeting, CERN 33
Ref: Nazarewicz et al., NPA 435 (1985) 397
Prolate : 78Sr
Prolate + Oblate
: 74,76Sr, 80Sr
Prolate-Spherical
-Oblate : 80Sr
Prolate-Spherical: 82Sr
Spherical : 84Sr
Energy surfaces obtained with Woods-Saxon potential :
shape change with change in neutron number
Competition between different shapes may create transitional region.
INTC meeting, CERNINTC meeting, CERN 44
P factor estimation : A measure of deformation driving quadrupole quadrupole force vs spherical driving pairing force.
28 50 82 126
82
50
28
N
Z
76,78Sr
78,80Zr
p-drip line
N-drip line
N=90
For X(5),
[ E. A. McCutchan et al, PRC 70, 011304 ]
Np, N n ~ number of valence protons
and neutrons.
INTC meeting, CERNINTC meeting, CERN 55
Critical points in Symmetry (Casten) Triangle[F Iachello PRL 85, 3580(2000); PRL 87 052502(2001)]
U(5)
O(6) SU(3)
E(5) X(5)
V=V(),> 0, = 0
V=V(),> 0,
independent
Spherical harmonic vibrator
Axially deformed rotor unstable deformed rotor
=0
> 0, =0 > 0, unstable
INTC meeting, CERNINTC meeting, CERN 66
Examples of X(5) symmetry ~ N=90 isotones (152Sm)
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.
Casten & ZamfirPRL 87,
052503(2001)
INTC meeting, CERNINTC meeting, CERN 77
Candidate for X(5) symmetry; 78Sr
D. S. Brenner et al, AIP Conference Proceedings 638, 223 (2002)
INTC meeting, CERNINTC meeting, CERN 88
Systematic of Sr nuclei (Z=38) : R4/2 ~ E(41
+)/E(21
+)
3.33
2.0
2.9076,78Sr
INTC meeting, CERNINTC meeting, CERN 99
N
Z
30
32
34
36
38
40
42
30 32 34 36 38 40 42 484644
2.18 2.362.322.29 2.24 2.02
2.072.072.232.272.28
2.28
2.642.542.502.46
2.382.151.902.16
2.221.86
2.652.372.45
2.11
2.22
2.81 2.54 2.32 2.23
2.16 2.11 2.31
2.11
2.02
2.07
2.38
2.34 2.23
2.56 2.34
2.85
2.86
E(41+)/E(21
+) systematic; A~80 : expected value for X(5) ~ 2.90
INTC meeting, CERNINTC meeting, CERN 1010
R4/2 systematic and the P factor estimations
are necessary but not sufficient conditions to characterize a nucleus as X(5).
INTC meeting, CERNINTC meeting, CERN 1111
Many nuclei which follow the expected X(5) trend closely!!!!Clark et al PRC 68, 037301(2003)
INTC meeting, CERNINTC meeting, CERN 1212
…Fail to follow their X(5) characteristics except : 126Ba, 130Ce &N=90 isotones from Nd (Z=60) to Er (Z=68).
Clark et al PRC 68, 037301(2003)
INTC meeting, CERNINTC meeting, CERN 1313
We must measure the transition strengths between thelevels of the yrast and non yrast bands along with thelevel energies to confirm the X(5) assignment to 78Sr.
INTC meeting, CERNINTC meeting, CERN 1414
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
+)].
INTC meeting, CERNINTC meeting, CERN 1515
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 4+ 2+ 0+ transition
INTC meeting, CERNINTC meeting, CERN 1616
Fusion-evaporation approach: 40Ca(40Ca,2p)78Sr , 118 and 121 MeV, Jurogam + RITUNuclear physics group, University of York
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: 501.9 (2), I ~ 100% ], [ 78Rb: 278.3 (2), I ~ 100% and 503.2 (4), I ~ 80%
keV ] compared to that of 78Sr [ 278.5(4), I ~ 100% & 503.7(4), I ~ 100% keV ].
Hence gating is also not very effective.
1200
278 keV gated -ray spectra
INTC meeting, CERNINTC meeting, CERN 1717
Requirement
Pure intense radioactive beam of 78Sr.
Problem78Rb will be produced with several magnitude higher
(~109) compared to 78Sr (~106)
SolutionElectron 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.
INTC meeting, CERNINTC meeting, CERN 1818
3.0 MeV/A 78Sr on 1 mg/cm2 58Ni target;MINIBALL efficiency : 10%; CD detector angle – 150 – 500 in laboratory frame.
Coulomb excitation of 78Sr : Target selection
Higher Z gives higher yield but looses in kinematic focusing!!!
58Ni
INTC meeting, CERNINTC meeting, CERN 1919
3.0 MeV/A 5x104 ions/sec 78Sr on 1 mg/cm2 58Ni target; MINIBALLefficiency : 10%; CD detector angle – 150 – 500 in laboratory frame.
Coulomb excitation of 78Sr : yield estimate
1E+0
1E+1
1E+2
1E+3
1E+4
1E+5
1E+6
Yie
ld/1
0 d
ays
Aim : E(02
+), E(22
+) and E(42
+) , B(E2; 81
+ 61
+),
B(E2; 61
+ 41
+), B(E2; 02
+ 21
+), [B(E2; 22
+ 02
+)]
21+ 41
+ 61+ 02
+ 81+22
+ 42+
Yie
ld /
10
day
s
102
103
104
105
106
100
101
INTC meeting, CERNINTC meeting, CERN 2020
Requesting Beam : 78Sr [ T
½ ~ 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
Coulomb excitation of 78Sr
INTC meeting, CERNINTC meeting, CERN 2121
CollaborationD. 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.
INTC meeting, CERNINTC meeting, CERN 2222
ADDENDUM
INTC meeting, CERNINTC meeting, CERN 2323
The CD detector at 150 – 500 detects most of the scattered particles
INTC meeting, CERNINTC meeting, CERN 2424
0 30 60 90 120 150 1801E-04
1E-03
1E-02
1E-01
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
Yield in 2 degree bins in the CM frame
CM angle (degrees)
Yie
ld p
er 2
deg
rees
in T
het
a
Rutherford X-section estimate
CD detector angle
INTC meeting, CERNINTC meeting, CERN 2525
70 80 90 100 110 120 130 140 150 160 1701E-09
1E-08
1E-07
1E-06
1E-05
1E-04
1E-03
1E-02
1E-01
78Sr yield : 40Ca+40Ca (ALICE predictions)
Elab (MeV)
Yie
ld (
mb
)
INTC meeting, CERNINTC meeting, CERN 2626
78Y 77Y 78Sr 77Sr 76Sr 75Sr 74Sr 77Rb 76Rb 75Rb 74Rb 76Kr 75kr 74Kr 73Kr 72kr 71Kr 75Br 73Br 71Br 70Se 68Se 69As 67As1E-5
1E-4
1E-3
1E-2
1E-1
1E+0
1E+1
1E+2
1E+3
Yield of diff isotopes : 40Ca + 40Ca 118 MeV(Alice)
Yie
ld (
mb)
INTC meeting, CERNINTC meeting, CERN 2727
Systematic of N=40 nuclei : R4/2 ~ E(41
+)/E(21
+)
3.33
2.0
2.90
78Sr 80Zr
INTC meeting, CERNINTC meeting, CERN 2828
Systematic of N=40 nuclei : B(E2; 21
+ 01
+)
78Sr
INTC meeting, CERNINTC meeting, CERN 2929
H= - ħ2/2B[(1/4)(4/)/1/(2sin3)
(sin3//–Q2k/sin2V]
k
Bohr Hamiltonian :
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.
INTC meeting, CERNINTC meeting, CERN 3030
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 (Q1
2+Q22+Q3
2)+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.
INTC meeting, CERNINTC meeting, CERN 3131
5.653.03Second excitation :
R = (E02 – E01
)/
(E21 – E01
)
3.332.502.002.902.20Initial excitations
R = (E41 – E01
)/
(E21 – E01
)
SU(3)O(6)U(5)X(5)E(5)Property
Importance of E02+ state in case of transitional nuclei:
INTC meeting, CERNINTC meeting, CERN 3232
Systematic of Sr isotopes (Z=38) : B(E2; 21
+ 01
+)Collective
78Sr 98Sr
Sharp change in observable : signature of shape transition
INTC meeting, CERNINTC meeting, CERN 3333
INTC meeting, CERNINTC meeting, CERN 3434
Isotope chart
2.2 x106
2.4 x109