Exploring the X(5) characteristic in the mass A ~ 80 region : Coulomb excitation of 78 Sr nucleus

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


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


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.


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.


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


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)


Candidate for X(5) symmetry; 78Sr

D. S. Brenner et al, AIP Conference Proceedings 638, 223 (2002)


Systematic of Sr nuclei (Z=38) : R4/2 ~ E(41

+)/E(21

+)

3.33

2.0

2.9076,78Sr


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


R4/2 systematic and the P factor estimations

are necessary but not sufficient conditions to characterize a nucleus as X(5).


Many nuclei which follow the expected X(5) trend closely!!!!Clark et al PRC 68, 037301(2003)


…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)


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.


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

+)].


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


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


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.


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


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


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


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.


ADDENDUM


The CD detector at 150 – 500 detects most of the scattered particles


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


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

)


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)


Systematic of N=40 nuclei : R4/2 ~ E(41

+)/E(21

+)

3.33

2.0

2.90

78Sr 80Zr


Systematic of N=40 nuclei : B(E2; 21

+ 01

+)

78Sr


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.


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.


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:


Systematic of Sr isotopes (Z=38) : B(E2; 21

+ 01

+)Collective

78Sr 98Sr

Sharp change in observable : signature of shape transition



Isotope chart

2.2 x106

2.4 x109

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Exploring the X(5) characteristic in the mass A ~ 80 region : Coulomb excitation of 78 Sr nucleus

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