Deformation of the N=Z nucleus 72 Krvia beta decayJosé Antonio Briz Monago1,212

Instituto de Estructura de la Materia, CSIC,

Subatech Laboratory, CNRS/IN2P3, University of Nantes, Ecole des Mines de Nantes

for the IS370 collaboration”Advances in Radioactive Isotope Science Conference 2014”
ITO International Research Center, Tokyo, Japan
1-6 June 2014

Motivation

Total Absorption Spectroscopy study

Results

Conclusions

Motivation: Why 72
36 Kr36 ?
Predictions of shape coexistence in 72 Kr:“the poster child of nuclear shape isomers”

60

Only 70 Br and 72 Kr predicted oblate deformedin the N=Z line from A=40 up to A=100.

72
36t ry40

me5Asym3γKr36

Scale 0.20 (MeV)alA xi

4204550.00

P. Möller et al., At. Data and Nucl. Data Tables 59, 185(1995)

Deformation of the N=Z nucleus

72

Kr via beta decayJosé Antonio Briz Monago

0.10
0.200.30
Spheroidal Deformation ε20.400P. Möller et al., Phys. Rev. Lett. 103, 212501 (2009)

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Motivation

Total Absorption Spectroscopy study

Results

Conclusions

Motivation: Why 72
36 Kr36 ?
2113

P726+High spin states interpreted as a prolate band [DeA97]

EATLRO1322

First excited 0+ state: shape isomer head of the prolate band [Bou03].
Mixing λ=0.1 with the 0+ oblate gs (two-level calculation).

4++2
4B(E2;0+1 → 21 ) = 4997(647) e fm [Gad05] → |β 2 |=0.330(21).
&24+B(E2;2+1 → 01 ) = 999(129) e fm

2720 e2fm4
710

02+ PROLATE?
671
0+810 e2fm4OBLATE?
72

Kr ground state predicted oblate deformed [Naz85,Mol95].

0+KrIS478 experiment (spokeperson B.S. Nara Singh, Univ. York) at ISOLDE(CERN) of 72 Kr Coulex whose preliminary results indicate 2+1 state isprolate deformed.
Recent results already shown today in H. Iwasaki talk [Iwa14]:+2
4+B(E2, 4+1 → 21 ) = 2720(550) e fm → 21 Prolate;+2
4++B(E2, 2+1 → 01 ) = 810(150) e fm → Small overlap between 0 and 2 w.f.
B(E2;4+→2+)
1
1=3.4; 1.43 (rotor) and 2.0 (vibrator).
B(E2;2+ →0+ )11However, no evidence on the sign of the ground state deformation (prolate or oblate).
[Naz85] W. Nazarewicz et al., Nucl. Phys. A435, 397 (1985)[Mol95] P. Möller et al., At. Data Nucl. Data Tables 59, 185 (1995)[DeA97] G. de Angelis et al., Phys. Lett. B 415, 217 (1997)
Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz Monago[Bou03] E. Bouchez et al., Phys. Rev. Lett. 90, 082502 (2003)[Gad05] A. Gade et al., Phys. Rev. Lett. 95, 022502 (2005)[Iwa14] H. Iwasaki et al., Phys. Rev. Lett. 112, 142502 (2014)ARIS 2014 Conference, Tokyo (Japan) June 2014

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Motivation

Total Absorption Spectroscopy study

ResultsConclusions

Determination of nuclear shape via B(GT) distributions
GT strength distributions found to depend sensitively on the nuclear shape (quadrupoledeformation) for 80 Zr, 76 Sr and 72 Kr [Ham95].
Mean field calculations [Sar99] and [Sar01] predict different B(GT) distributions for different
deformations of the ground state of the parent nucleus.

Sr (next N=Z even-even nucleus)

Qβ

ΣB(GT) (gA2/4π)

76543Oblate

21

ProlateQEC0[Ham95] I. Hamamoto et al., Z. Phys. A353, 145 (1995)

1234567Energy (MeV)[Nac04] E. Nácher et al., PRL 92 232501 (2004)[Sarr99] P. Sarriguren et al., Nucl. Phys. A658, 13 (1999)[Sarr01] P. Sarriguren et al., Nucl. Phys. A691 631 (2001)
Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz Monago

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Motivation

Total Absorption Spectroscopy study

ResultsConclusions

Determination of the beta feeding distribution

High density of levels for highexcitation energies causing very
fragmented feeding distribution andde-excitation pattern
Low photopeak efficiency for highenergy gammas with HPGe detectors
C.L. Duke et al., Nuclear Physics A151, 609 (1970)
B. Rubio et al., J. Phys. G 31, S1477 (2005)

Apparent strength is located at lower
energies
As a result: overestimated strength atlow excitation energies andunderestimated for high excitationenergies

Pandemonium effect

J.C. Hardy et al., Phys. Lett. 71B, 307 (1977)

Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz MonagoARIS 2014 Conference, Tokyo (Japan) June 2014

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Motivation

Total Absorption Spectroscopy study

ResultsConclusions

Determination of the beta feeding distribution

High density of levels for highexcitation energies causing very
fragmented feeding distribution andde-excitation pattern
Low photopeak efficiency for highenergy gammas with HPGe detectors
C.L. Duke et al., Nuclear Physics A151, 609 (1970)
B. Rubio et al., J. Phys. G 31, S1477 (2005)

Apparent strength is located at lower
energies
As a result: overestimated strength atlow excitation energies andunderestimated for high excitationenergies

Pandemonium effect

J.C. Hardy et al., Phys. Lett. 71B, 307 (1977)

Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz Monago

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Motivation

Total Absorption Spectroscopy study

Results

Conclusions

Determination of the beta feeding distribution

High density of levels for highexcitation energies causing very
fragmented feeding distribution andde-excitation pattern
Low photopeak efficiency for highenergy gammas with HPGe detectors
Apparent strength is located at lowerenergies
As a result: overestimated strength atlow excitation energies andunderestimated for high excitationenergies

C.L. Duke et al., Nuclear Physics A151, 609 (1970)
B. Rubio et al., J. Phys. G 31, S1477 (2005)
Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz Monago

Pandemonium effect

J.C. Hardy et al., Phys. Lett. 71B, 307 (1977)

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Motivation

Total Absorption Spectroscopy study

Results

Conclusions

TAS experimental setup

Reduced statistics in β -gated spectrum due to:72

Kr17.1 s72
QEC=5129 keV

Geometric efficiency of beta detector:

Br≈ 16 %

78.6 s72
QEC=8799 keVSeRoom background suppressed byshielding components and coincidence
condition.

8.4 d

72
QEC=361 keV

As

26 hQEC=4356 keV

72

Gestable

Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz Monago

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Motivation

Total Absorption Spectroscopy study

Results

Conclusions

TAS data analysis
Experimental data (d) is the result of the convolution of Response function (R) of TAS
detector and the feeding at a certain level (f):
Xd (i ) =R (i , j ) ⊗ f (j ) + contam.
jSolve the Inverse problem with the Expectation-Maximization Algorithm [Dem77]:sf (j ) = P

1i R (i , j )R (i , j )f s−1 (j )d (i )XP
ij R (i , j )fs−1 (j ) + contam.

f0 is chosen as an uniform feeding distribution.
The application of this algorithm to the TAS problem is explained in detail in [Tai07]
Relative gamma transition intensities measured with the HPGe detector are included ind(i).
Through this methodology we try to reproduce both:the TAS experimental spectrum andthe relative gamma transition intensities.
[Dem77] A. P. Dempster et al. J. R. Statist. Soc. B 39 (1977) 1[Tai07] J. L. Taı́n, D. Cano-Ott Nucl. Inst. and Meth. A 571, (2007) 719 and 728

RESPONSE MATRIX (R) is obtained from Monte Carlo simulations (GEANT4) and decay
scheme information (High Resolution information available+Statistical Models).
Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz Monago

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ResultsConclusions

Beta gated analysis: Check of goodness
Check of results:
Reproduction of experimental TAS spectrum:
Xd(i) =R (i , j ) ⊗ f (j ) + contam.

Reproduction of gamma transition intensities
measured with HPGe detector (10 mostintense lines reaching the ground state).

jGamma transition intensities following 72Kr decay

Experimental
Calculated

3

1018
Experimental (HPGe)

Counts16
Calculated (TAS)

102

1412Iγ (%)

10Relative deviation (%)

1100 0

1000

2000

3000

4000

5000

6000

7000

8000

10850

604-50-100021000

2000

3000

4000

5000

6000

7000

Energy (keV)

Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz Monago

8000

0γ

8,0γ

3,0γ

4,0γ

5,0γ

10,0γ

11,0γ

15,0ARIS 2014 Conference, Tokyo (Japan) June 2014

γ19,0γ23,0γ

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Motivation

Total Absorption Spectroscopy study

Results

Conclusions

Result from first set of dataA

B(GT) (g2 /4 π)Preliminary B(GT) distribution for 72Kr beta decay
10.90.8Σ B(GT) (TAS from this work)
Σ B(GT) (High-Res. from [Piq])

0.70.60.5
0.4
0.3
0.20.100500

1000

1500

20002500
Eexc (keV)

Result from the analysis of only a set of data, not full statistics.
Evidence of “Pandemonium effect”[Piq] I. Piqueras et al., Eur. Phys. J. A 16, 313-329 (2003)
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Motivation

Total Absorption Spectroscopy study

ResultsConclusions

1.6

Σ B(GT) for 72Kr decay measured with TAS
Predictions for OblateAΣ B(GT) (g2 /4 π)Comparison with theoretical predictions (QRPA)

1.4Predictions for Prolate

1.2
10.8
0.6
0.4
0.2
00500

1000

1500

2000

2500
Eexc in 72Br (keV)

QRPA approach using the SLy4 Skyrme-type force for the oblate and prolate minima in the72
Kr potential energy surface. An standard quenching factor of 0.77 is used [Sar09].

[Sar09] P. Sarriguren, Phys. Rev. C 79, 044315 (2009)
Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz Monago

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Total Absorption Spectroscopy study

Results

Conclusions

1.6AΣ B(GT) (g2 /4 π)Comparison with theoretical predictions (QRPA)

1.4

Σ B(GT) for 72Kr decay measured with TAS
Predictions for Oblate
Predictions for Prolate
TAS (exp)

1.2

YR
INA

10.8

M
I
L
E

0.6

PR

0.4
0.2
00500

1000

1500

2000

2500
Eexc in 72Br (keV)

QRPA approach using the SLy4 Skyrme-type force for the oblate and prolate minima in the72
Kr potential energy surface. An standard quenching factor of 0.77 is used [Sar09].

[Sar09] P. Sarriguren, Phys. Rev. C 79, 044315 (2009)
Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz Monago

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Motivation

Total Absorption Spectroscopy study

ResultsConclusions

1.6AΣ B(GT) (g2 /4 π)Comparison with theoretical predictions (QRPA)

1.4

Σ B(GT) for 72Kr decay measured with TAS
Predictions for Oblate
Predictions for Prolate
TAS (exp)

1.2

RYA
IN

10.8

MIL
E

0.6

PR

0.4
0.2
00500

1000

1500

2000

2500
Eexc in 72Br (keV)

QRPA approach using the SLy4 Skyrme-type force for the oblate and prolate minima in the72
Kr potential energy surface. An standard quenching factor of 0.77 is used [Sar09].
Preliminary results suggest:

First experimental evidence of the negative sign of quadrupole moment of 72 Kr gs → β2 < 0.
First time an oblate deformed gs has been inferred from the B(GT) distribution of its β decay.

Oblate minimum corresponds to β2 ≈ −0.176 (th.)[Sar09] P. Sarriguren, Phys. Rev. C 79, 044315 (2009)
Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz MonagoARIS 2014 Conference, Tokyo (Japan) June 2014

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Motivation

Total Absorption Spectroscopy study

ResultsConclusions

1.6AΣ B(GT) (g2 /4 π)Comparison with theoretical predictions (QRPA)

1.4

Σ B(GT) for 72Kr decay measured with TAS
Predictions for Oblate
Predictions for Prolate
Predictions for λ =0.1
TAS (exp)

1.2

YR
INA

10.8

MILE0.6

PR

0.4
0.2
00500

1000

1500

2000

2500
Eexc in 72Br (keV)

Preliminary results are compatible with 10 % mixing1 [Bou03] with the prolate 0+ excitedstate but no improvement is observed.
[Sar09] P. Sarriguren, Phys. Rev. C 79, 044315 (2009)[Bou03] E. Bouchez et al., Phys. Rev. Lett. 90, 082502 (2003)
1The distribution for 10 % mixing ratio is a rough estimation to guide the eye (0.1 times the value of B(GT) for prolate minimum plus 0.9
times the value for the oblate minimum) and not strictly an appropriate calculation.
Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz Monago

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Total Absorption Spectroscopy studyResults

Conclusions

Conclusions

1

The preliminary results from our study suggest a dominantly oblate deformation of
the 72 Kr in the ground state.

2Preliminary, we conclude that it is the first time an oblate deformed gs has beeninferred from the B(GT) distribution of its β decay. First experimental evidence ofthe sign of the deformation (and the intrinsic quadrupole moment) of the 72 Kr groundstate.

3

The preliminary experimental B(GT) distribution does not exclude a certain prolate
mixing for the dominantly oblate ground state but it does not improve theexperiment-theory agreement.

Deformation of the N=Z nucleus

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Kr via beta decayJosé Antonio Briz Monago

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Motivation

Total Absorption Spectroscopy study

ResultsConclusions

Acknowledgements

Thanks to the IS370 collaboration:
J. A. Briz1 , M. J. G. Borge1 , O. Tengblad1 ,A. Algora2 , E. Nácher1,2 , B. Rubio2 , J.L. Taı́n2
S.Courtin3 , Ph. Dessagne3 , F. Maréchal3 , Ch. Miehé3 ,E. Poirier3 , L.M. Fraile4 , W. Gelletly5 and the ISOLDE (CERN) team61
Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain
Instituto de Fisica Corpuscular, CSIC-Univ. Valencia, E-46071 Valencia, Spain
3
Institut de Recherches Subatomiques, IN2P3-CNRS, F-67037 Strasbourg CEDEX 2, France
4
Universidad Complutense, E-28040 Madrid, Spain
5
University of Surrey, Guildford, GU2 7XH, Surrey, UK
6ISOLDE, CERN, CH-1211 Geneva 23, Switzerland.
2Deformation of the N=Z nucleus

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