2rd June, 2014

ARIS 2014, Tokyo, Japan

Beyond the IMME
(Isobaric Multiplet Mass Equation)
Marion MacCormick
Institut de Physique Nucléaire
Orsay, FRANCE

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Experimental Isobaric Analogue States

2rd June, 2014

7 < A < 60

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Experimental Isobaric Analogue States (IAS)
Mass, M of each nuclear configuration is fully defined by

M space, spinparity, isospin

M A / ,J ,Isospin projection (good quantum number)T∑t ,Isospin
and TT

Evaluated experimental isobaric analogue states from T = 1/2 to T = 3 and associated IMME coefficients
M. MacCormick, G. Audi, Nuclear Physics A 925 (2014) 61–95
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ARIS 2014, Tokyo, JapanIsobaric Multiplet Mass Equation (IMME)IMME

M T, TaM

E–T TE

a1 E
isoscalar, E

theoreticalcbb

Δ

E

c

3E

isovector, E isotensor Coulomb energies
neutron ‐ 1H mass difference
Δ→ coefficients a, b, c extracted from quadratic fits to evaluated experimental data(AME2012, NUBASE2012, ENSDF)

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Evaluated IMME coefficients
M T, Taba"bulk" mass, 104 keV scaleb~ 103 keV scalec~ 102 keV scale

d1~ 10 keV scale

Marion MacCORMICKcd

Main focus
T=1 and T=3/2 datasets
Multiplets subdivided in4n groups

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E–T T

1 E

First evaluation linked
in to the AME

Most extended dataset A~60
New T=5/2 and T=3 data

Marion MacCORMICKglobal function→ mass predicitionsa coefficients

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ARIS 2014, Tokyo, JapanbΔEGeneral smooth function
Homogeneously charged
spherical nucleus
b720. A /Marion MacCORMICKcte keV

b coefficients

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Staggering
A < 40Progressive
attenuation
beyond A=40

T=1/2 and 3/2
out of phase

Marion MacCORMICKb coefficients

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4n groups
Spherical model
reference

Variations of +200 to‐100 keV dominate
the experimentalresolution

Marion MacCORMICKb coefficients

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Marion MacCORMICK

3Ec coefficients

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ARIS 2014, Tokyo, Japan+

A=44

0 0+ 0+

T=1 Key Measurements
0+ 0+44

Sc – 44Tii – 44V

0+ 0+ 0+ 0+ 0+ 0+ 0+ 0+

44

V g.s. is isomer
contaminated

1+0‐ 2+ 4+ 3+ 1+
No experimental data‐+2+ 4 2for52

Co, 56Cu and 60Ga+4+ 6 4+ 2+

ground states

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T=1Page 11

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ARIS 2014, Tokyo, Japan

Beyond the quadratic IMME

MassdTZ3a bTz cTZ21(68 %)error barsMarion MacCORMICKd coefficients

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3Mass

99.7%

a bTz cTZ2dTZ3A=8, 32, 52
A=9, 35, 53→A=33
Year 2000
d2.95

0.9 keV→→By 201233
Ar → +3 keV
33 i
Cl → +6 keV
d0.08 0.32 keV

Marion MacCORMICKd coefficients

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ARIS 2014, Tokyo, Japand-coefficients

Precision

For T=3/2, in theory:
d1
6M

M

3M

3M

d‐coefficients appear through basic symmetry
The precision is crucial to establishing non‐zero d‐coefficientsHow does the d‐coefficient react (δd) to small experimental mass shifts (δM)?
The d‐coefficient is 3 times more sensitive toMarion MacCORMICKmass shifts
d coefficients

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ARIS 2014, Tokyo, JapanHow do the c‐coefficients react to imposing d≅0?

24 datasets, 16 with all four IAS levels measured

Which high precision measurements would have the greatest impact?

Effect of single measurements on global datatset.

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T=3/2 Key Measurements
AE*Element(keV)Jπ

g.s.
4791

(7/2‐)
7/2‐

29

S

g.s.

(5/2+)

21 Mg
49 Mn
21 Na
53 Co
49 Feg.s.
4833
8975
4395
g.s.

5/2+(7/2‐)
5/2+
7/2‐
(7/2‐)

9B

14654.7

3/2‐

53
9Ni
C

g.sg.s.

(7/2‐)(3/2‐)

Marion MacCORMICK2012 Zhang
2007 Dossat
1973 MSU
32
S(3He,6He)29S
2014
2007 Dossat
1973 Sextro
2007 Dossat
2012 Zhang
1974 MSU
11
B(p,t)9Bi
2012 Zhang
1971

Mass Shiftfor d→0(keV)

(keV)

40
1239
135080161841824

26.1
30
8.780
120

2.5

13.5252.1240
40.5
T = 3/2

Accuracy

CrV

EvaluatedPrecision

Precision

4545

Most recent data

Sensitivity based priority

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T=3/2 Unidentified IAS(all areEstimated E*

Nearest in ENSDF(keV)(keV))A

Element

11

Ci

11952

101216040 (IAS)Γ = 270

15Oi

11173

1011151

7

100% p‐decay

39

Cai

6378 106450

1043Tii

4195 1047

Cri

4161

504169

12No51

Fei

4447

504456

13NoJπData stops @ 3220

observations
50 keVnone

Hypothesis: the other measured multiplet states are accurate.
Marion MacCORMICKT = 3/2Page 17

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Summary and Conclusions
 AME2012 and NUBASE2012 IAS highlights
o 107 new IAS states linked in to g.s. masses
o Most precise and complete set of IAS experimental datao New data sets for T=5/2 and T=3
 Fitted Isobaric Multiplet Mass Equation (IMME) coefficients
 Clear global trends observed in a-, b- and c-coefficients
 d-coefficients for 4-point datasets
 Key T=1 experimental measurements Key T=3/2 experimental measurements
 Unidentified T=3/2 IAS
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References and further reading
E.P. Wigner in the Proceedings of the Robert A. Welch Foundation Conference on Chemical Researchedited by W.0. Milligan, Welch Foundation, Houston, 1958, Vol. 1, p. 88.
Isobaric mass equation for A=1‐45 and systematics of Coulomb displacement energies.
M. S. Antony, J. Britz, J. B. Bueb, and A. Pape
Atomic Data and Nuclear Data Tables 33 (1985) 447;

and also
M.S. Antony, J. Britz and A. Pape, Atomic Data and Nuclear Data Tables 34 (1985) 279;
A. Pape and M.S. Antony, Atomic Data and Nuclear Data Tables 39 (1988) 201;
M.S. Antony, J. Britz and A. Pape, ,Atomic Data and Nuclear Data Tables 40 (1988) 9.
J.Britz, A.Pape, M.S.Anthony, At.Data Nucl.Data Tables 69, 125 (1998)
Evaluated experimental isobaric analogue states from T = 1/2 to T = 3 and associated IMME coefficients
M. MacCormick, G. Audi, Nuclear Physics A 925 (2014) 61–95

NUBASE 2012 and AME2012
The NUBASE2012 evaluation of nuclear properties
G. Audi, F.G.Kondev, M.Wang, B.Pfeiffer, X.Sun, J. Blachot, M. MacCormick
Chinese Physics C, vol. 36 December 2012 (pp. 1157 – 1286)
The AME2012 atomic mass evaluation (I) Evaluation of input data, adjustment procedures
G. Audi, M. Wang, A.H.Wapstra, F.G.Kondev, M.MacCormick, X.Xu, B. Pfeiffer
Chinese Physics C, vol. 36 December 2012 (pp. 1287 – 1602)

http://amdc.impcas.ac.cn/evaluation/data2012/nubase.html

http://amdc.impcas.ac.cn/evaluation/data2012/ame.html

The AME2012 atomic mass evaluation (II) Tables, graphs and references
M. Wang, G. Audi, A.H. Wapstra, F.G. Kondev, M. MacCormick, X. Xu, B. Pfeiffer
Chinese Physics C, vol. 36 December 2012 (pp. 1603‐2014)

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