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Isospin symmetry breaking corrections to the superallowed beta
decays from the angular momentum and isospin projected DFT:
brief overview focusing on sources of theoretical errors
and on limitations of the „static” MR DFT
Extension of the static approach:
 towards NO CORE shell model with basis cutoff
dictated by the self-consistent p-h configurations
 examples:
32Cl-32S,
38Ca-38K
62Zn-62Ga,
Summary & perspectives
adopted from J.Hardy’s, ENAM’08 presentation
10 cases measured with accuracy ft ~0.1%
3 cases measured with accuracy ft ~0.3%
 test of the CVC hypothesis
(Conserved Vector Current)
1.5%
0.3%
- 1.5%
~2.4%
Towner & Hardy
Phys. Rev. C77, 025501 (2008)
|Vud| = 0.97418 + 0.00026
 test of unitarity of the CKM matrix
weak
eigenstates
CKM
mass
Cabibbo-Kobayashi eigenstates
-Maskawa
|Vud|2+|Vus|2+|Vub|2=0.9997(6)
0.9490(4)
0.0507(4)
<0.0001
I=0+,T=1,Tz=-1
I=0+,T=1, Tz=0
ground state
in N-Z=+/-2 (e-e) nucleus
antialigned state
in N=Z (o-o) nucleus
Project on good isospin
(T=1) and angular
momentum (I=0)
Project on good isospin
(T=1) and angular
momentum (I=0)
rediagonalization)
rediagonalization)
(and perform Coulomb
(and perform Coulomb
2=2(1-d )
|
=0>
| <T~1,T
C
~ z=+/-1,I=0| T+/- |I=0,T~1,T
z
~
1.0025
0.975
|Vud|
0.974
0.973
1.0000
(a)
0.970
superallowed 0+0+
b-decay
mirror T=1/2
p-decay
nuclei
62
0.9950
superallowed 0+0+
b-decay
(a)
0.9975
n-decay
(b)
0.5
0.9925
p-decay
mirror T=1/2
nuclei
I.S. Towner and J. C. Hardy,
Phys. Rev. C 77, 025501(2008).
Ft=3071.4(8)+0.85(85); Vud=0.97418(26)
Liang, N. V. Giai, and J. Meng,
(b) H.Phys.
Rev. C 79,064316 (2009).
(c,d) W. Satuła, J. Dobaczewski,
W. Nazarewicz,
M. Rafalski, Phys. Rev. Lett. 106, 132502 (2011);
Phys. Rev. C 86, 054314(2012).
0
-0.5
(c)(d)
n-decay
10
dC(SV)- d(HT)
[%]
C
(a)
(d)
(b)
0.972
0.971
(c)
|Vud|2+|Vus|2+|Vub|2
0.976
38
10 20 30 40 50 60 70 A
Ft=3070.4(9); Vud=0.97444(23) PRL
Ft=3073.6(12); Vud=0.97397(27) PRC
O. Naviliat-Cuncic and N. Severijns,
Eur. Phys. J. A 42, 327 (2009);
Phys. Rev. Lett. 102, 142302 (2009).
Basis-size dependence:
~10%
Configuration dependence:
jp
Functional dependence:
l
i
SV: Ft=3073.6(12)
Vud=0.97397(27)
=0.99935(67)
SHZ2: Ft=3075.0(12)
Vud=0.97374(27)
asym=42.2MeV!!!
DE [MeV]
=0.99890(67)
l
l
s
i
jn
y
x
A=34
SV
34Ar
i
x
s
jn
 34Cl
1.0
34Cl
0.5
|Vud|2+|Vus|2+|Vub|2=
jp
y
jp
1.5
dC [%]
|Vud|2+|Vus|2+|Vub|2=
x
s
jn
 34S
DEI=0,T=1
0
-0.1
-0.2
-0.3
DEHF
DEIV
(TO)
Relative orientation of shape and current
y
j1 j2 j3
…………
{|I>(1)}k1 {|I>(2)}k2 {|I>(3)}k3
Ei |Ii>
jn
…………..
{|I>(n)}kn
DE (MeV)
6
theory
exp
32Cl
5
4
3
(2+)
(2+)
2
(2+)
1
0
(0+)
I=0+
I=1+
I=2+
(2+)
I=3+
W.Satula, J.Dobaczewski, M.Konieczka, W.Nazarewicz, Acta Phys. Polonica B45, 167 (2014)
1000
0
(keV)
4000
T
3000
2000
32Cl
4622, 4636
(keV)
4000
I=1+
I=1+
T
1
1
3000
1
1
0
2000
1
0
1
1000
1
0
1
theory
7002keV
experiment
theory
0keV
experiment
Experiment: δC ≈ 5.3(9)%
SM+WS calculations: δC ≈ 4.6(5)%.
D. Melconian et al., Phys. Rev. Lett. 107, 182301 (2011).
W.Satula, J.Dobaczewski, M.Konieczka, W.Nazarewicz, Acta Phys. Polonica B45, 167 (2014)
32S
Excitation energy of 0+ states [MeV]
62Zn,
5
EXP
(old)
I=0+ states below 5MeV
SM
SM
(GXPF1) (MSDI3)
EXP
(new)
SVmix
2pph
(6 Slaters)
2nph
4
1pp2p2h
1nph
3
2
K.G. Leach et al.
PRC88, 031306 (2013)
1
0
1pph
HF
0+ ground state
I=0+
before
mixing
-522
g.s. + p1
+
n1
+
n2
+
p2
+
pp1
EXP
-523
-524
-525
dC [%]
-526
6
5
4
3
2
1
0
~200keV
normalized
-510
EHF (MeV)
Energy (MeV)
Stability of configuration – interaction calculations
n1
p1
-511
-512
Z
X~Y
Static approach gives: dC=8.9%
3.0
EXP
dC=1.5%
DE [MeV]
2.5
2.0
1.5
I=0+, T=1
1.0
0.5
dC=1.7%
0.0
mixing:
38Ca
4 Slaters
38K
3 Slaters
Isospin symmetry breaking corrections from the
„static” double-projected DFT are in very good
agreement with the Hardy–Towner results.
We have to go BEYOND STATIC MR-EDF in order
to address high-quality spectroscopic data available
today.
First attempts are very encouraging at least
concerning energy spectra!!!
mixing the X,Y,Z orientations in light nuclei
Tz=-1  Tz=0
1.5
averages
dC [%]
mixing
1.0
0.5
0
T&H
10
14
18
22
A
26
30
34
W.Satula, J.Dobaczewski, M.Konieczka, W.Nazarewicz, Acta Phys. Polonica B45, 167 (2014)
DE (MeV)
0.6
0.4
0.2
0
SV
SHZ2
42Sc
nK
pK
Excitation energy [MeV]
3/2
5/2
7/2 K
1/2
Mixing of states projected from the antialigned configurations:
3.0
( )
42Sc
T=1
2.5
2.0
1.5
1.0
0.5
T=0
0
0
1
2 3
4 5
6
angular momentum
7
I=0+,T=1
Tz=-/+1
(N-Z=-/+2)
|<T+/->|2=2(1-dC)
I=0+,T=1
n
n
p
p
n
n
CORE
CORE
aligned configurations
n p or n p
n p
T=0
Mean-field can differentiate between
n p and n p
only through time-odd polarizations!
Tz=0 (N-Z=0)
p
p
anti-aligned configurations
n p or n p
n p
T=1
T=0
T=1 states
are not representable in a
„separable” mean-field!
n
n
E-E CORE
p
p
anti-aligned configurations
n p or n p
n p
T=1
T=0
T=1 states
are not representable in a
„separable” mean-field!!!