1. Isospin symmetry breaking effects in atomic nuclei
within extended Density Functional Theory
Wojciech Satuła
In colaboration with: Jacek Dobaczewski, Paweł Bączyk, Maciek Konieczka,
Koichi Sato, Takashi Nakatsukasa
Frontiers in nuclear structure theory:
golden decade of ab initio methods
spectacular developments in (SR) DFT, TD-DFT and
MR-DFT-rooted approaches
new developments: DFT-rooted NCCI
pn-mixed SR functionals
charge-dependent functionals
physics highlights: nuclear structure
beta decays
strong isospin symmetry breaking
effects (TED/MED)
Final remarks and perspectives

2. Resolution Effective (field) theories
Hot and dense quark-gluon matter
Hadron structure
DFT
collective
and
algebraic models CI
ab initio
LQCD
quark
models
Resolution
Hadron-Nuclear interface
Nuclear structure &
reactions
Effective (field) theories
Third Law of Progress in Theoretical Physics by Weinberg:
“You may use any degrees of freedom you like to describe a physical system, but if you use the wrong ones, you’ll be sorry!”

3. emergence of 3NF due to finite resolution
Effective or low-energy (low-resolution) theory explores separation of scales. Its formulation requires:
in coordinate space:
define R to separate short- and long-distance physics
or, in momentum space:
define L (1/R) to separate low and high momenta
replace (complicated and, in nuclear physics, unknown) short distance (or high momentum) physics by a LCP (local correcting potential)
(there is a lot of freedom how this is done concerning both the scale and form but physics is (should be!) independent on the scheme!!!)
from Hammer et al. RMP 85, 197 (2013)
emergence of 3NF due to finite resolution

4. Nuclear effective theory for EDF (nuclear DFT)
is based on the same simple and very intuitive assumption that low-energy nuclear theory is independent on high-energy dynamics
ultraviolet
cut-off L
regularization
Fourier
Coulomb
Long-range part of the NN interaction
(must be treated exactly!!!)
hierarchy of scales:
2roA1/3 ~
2A1/3 ro
correcting
potential
local ~ 10
There exist an „infinite” number
of equivalent realizations
of effective theories
where
denotes an arbitrary Dirac-delta model
Gaussian regulator
J. Dobaczewski, K. Bennaceur,
F. Raimondi,
J. Phys. G 39, (2012)

5. Proof of principle of the regularization range (scale) independence
for the gaussian-regularized density-independent EDFs
J. Dobaczewski, K. Bennaceur, F. Raimondi,
J. Phys. G 39, (2012)

6. Having defined the generator, the nuclear EDF is built using
mean-field (HF or Kohn-Sham) methodology
direct term
exchange term
lim da
a 0
Skyrme interaction - specific (local) realization of the
nuclear effective interaction:
spin-orbit
density dependence
10(11)
parameters
relative momenta
spin exchange LO
NLO

7. Look very similar except of „three-body” contributions!
Fractional powers of the density lead to singularities in extensions
involving restoration of broken symmetries:
 rotational (spherical) symmetry
 isospin symmetry (approximate)
 particle number…
and subsequent configuration mixing.
NCCI
SR-DFT
MR-DFT

8. (density independent) (density independent)
Our NCCI scheme:
Skyrme SV
(density independent)
is used at this stage
W.Satuła, P.Bączyk, J.Dobaczewski & M.Konieczka, Phys. Rev. C94, (2016)
Skyrme SV
(density independent)
is used at this stage

9. mixing of states projected from three-four p-h configurations
For details see: W.Satuła, P.Bączyk, J.Dobaczewski & M.Konieczka, Phys. Rev. C94, (2016)
-60
-55
-50
-45
-40
-35
-30
-25
-20
6Li TH 2+ 0+ 3+ 1+ TH
8Li 1+
Energy [MeV] 3+ 1+ 2+

10. Excitation energy of 0+ states [MeV]
No-core configuration-interaction formalism based on the isospin and angular momentum projected DFT
62Zn, I=0+ states below 5MeV HF p1 n1 n2
pp1 p2
I=0+
before
mixing
p|312 5/2>-1
p|312 3/2>
p|312 5/2>-2
p|312 3/2>2
p|310 1/2>
n|312 3/2>-1
n|310 1/2>
n|321 1/2>
EXP
(old) SM
(MSDI3)
(GXPF1)
EXP
(new)
K.G. Leach et al.
PRC88, (2013)
SVmix
(6 Slaters) 1 2 3 4 5
W.Satuła, J.Dobaczewski & M.Konieczka, arXiv: ;
JPS Conf. Proc. 6, (2015)
Excitation energy of 0+ states [MeV]
W.S., J. Dobaczewski,
M. Konieczka
arXiv: (2014)
JPS Conf. Proc. 6, (2015)
0+ ground state

11. Testing the fundamental symmetries of nature
Temporal dependence
of the fine structure
constant studies in 229Th
126
Weak interaction
studies in N=Z nuclei
superallowed b-decay 82
EDM search
in radium
bb0n searches 50
protons 82 28
Specific nuclei offer new opportunities for precision tests of:
CP and P violation
Unitarity of the CKM matrix
Possible temporal dependence
of the fine structure constant in 229Th 20 50 8 28
neutrons 2 20 2 8
neutron EDM

12. Superallowed 0+>0+ Fermi beta decays (testing the Standard Model)
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, (2008)
adopted from J.Hardy’s, ENAM’08 presentation
 test of unitarity of the CKM matrix
0.9490(4)
0.0507(4)
<0.0001
|Vud|2+|Vus|2+|Vub|2=0.9997(6)
|Vud| = -
mass
eigenstates
CKM
Cabibbo-Kobayashi
-Maskawa
weak
eigenstates

13. |Vud| & unitarity - world survey
-0.5
0.5 10 20 30 40 50 60 70 A
dC - dC [%]
(SV)
(HT)
H. Liang, N. V. Giai, and J. Meng,
Phys. Rev. C 79, (2009).
W. Satuła, J. Dobaczewski,
W. Nazarewicz, M. Rafalski
Phys. Rev. C 86, (2012)
I.S. Towner and J. C. Hardy,
Phys. Rev. C 77, (2008).
(a)
(b)
(c,d)
NCCI:
M. Konieczka, P. Bączyk, W. Satuła,
Phys. Rev. C 93, (R) (2016).
O. Naviliat-Cuncic and N. Severijns,
Eur. Phys. J. A 42, 327 (2009);
Phys. Rev. Lett. 102, (2009).
|Vud| & unitarity - world survey
superallowed 0+0+
b-decay
|Vud|
(a)
p-decay
mirror T=1/2
nuclei
n-decay
0.970
0.971
0.972
0.973
0.974
0.975
0.976
(b)
(c)
(d)
superallowed 0+0+
b-decay
p-decay
n-decay
mirror T=1/2
nuclei
(a)
(b)
(c)
(d)
0.9925
0.9950
0.9975
1.0000
1.0025
|Vud|2+|Vus|2+|Vub|2

14. |MGT| 6He(0+) 6Li(1+) Proof-of-principle calculation: 2.5 2.0
Gamow-Teller and Fermi matrix elements in T=1/2 sd- and ft- mirrors.
The NCCI study
M.Konieczka, P.Bączyk, W.Satuła, Phys. Rev. C93, (R) (2016); arXiv:
Proof-of-principle calculation:
6He(0+) Li(1+)
2.5
|MGT|
Knecht et al. PRL108,
(2012)
2.0
NCCI in 6Li
6He is fixed
NCCI in 6He
6Li is fixed
T=1/2 mirrors:
-1.5
-1.0
-0.5
0.5
1.0
1.5 20 30 40 50
(EEXP-ETH)/EEXP (%) A
Tz= 1/2
Tz=-1/2
masses:

15. |gAMGT| A |gAMGT| |MGT | 1 2 3 4 5 SM NCCI 20 30 40 50 SM NCCI1 2 3 4 5 SM
NCCI
|gAMGT| 20 30 40 50 A
(TH)
|MGT |
(EXP) SM
NCCI
Shell-model:
B. A. Brown and B. H. Wildenthal,
Atomic Data and Nuclear
Data Tables 33, 347 (1985).
G. Martinez-Pinedo et al.,
Phys. Rev. C 53, R2602 (1996).
T. Sekine et al.,
Nucl. Phys. A 467, (1987).
quenching
q~25%!!!
NCCI vs shell-model:
The NCCI takes into account
a core and its polarization
Completely different model
spaces
Different treatment of
correlations
Different interactions

16. Renormalization of axial-vector coupling constant by 2B-currents
ci from N and NN:
cD, cE fit to 3H, 4He properties
Menendez et al. PRL107, (2011)
β− decays of 14C and 22;24O
Ekstrom et al. PRL 113, (2014)
q2~ (from Ikeda sum rule)
See also:
Klos et al. PRC89, (2013)
q~0.9
Engel et al. PRC89, (2013)

17. M.Konieczka, M.Kortelainen, W.S., in preparation
24Al;4+ g.s. beta Decay
|p202 5/2>
GT strength
M.Konieczka, M.Kortelainen, W.S., in preparation

18. doubly magic nucleus 100Sn”
100In
NCCI
LSSM*) 1 2 3 4 5 6 7 8
exp
NCCI ~ ~
BGT = 10.2 for qgA=0.6
BGT = 9.1
EXP
+2.6
-3.0
NCCI 0+ 1+
ENERGY (MeV) 1+ 2+ 3+ 4+ 5+ 2+ 7+ 3+ 4+ 5+
6+ GROUND STATE
*) C.B. Hinke et al. Nature 486, 341, (2012) „Superallowed GT decay of the
doubly magic nucleus 100Sn”

19. T=1,I=0+ isobaric analogue states
from self-consistent 3D-isocranked HF: hl=h-lT
K. Sato, J. Dobaczewski, T. Nakatsukasa, and W. Satuła, Phys. Rev. C88 (2013),
hl=h-lT lx lz
normalized:
theory (red curve)
shifted
by 3.2MeV
separable
solution
p-n mixed
|n> |p> + -

20. CD local (strong) corrections to the Skyrme force
(class II (CIB) and III (CSB) Henley-Miller forces)
Class III corrects for MDE
Class II corrects for TDE

21. Mirror displacement energies with class II and III local
corrections to the Skyrme force
P.Bączyk, J.Dobaczewski, M.Konieczka, W.Satuła,
T.Nakatsukasa, K. Sato, arXiv:

22. Triplet Displacement Energies (TDE) with class II and III
local corrections to the Skyrme force

23. Challenges for Low-Energy Nuclear Theory
Perform proof-of-principle lattice QCD calculation for the lightest nuclei
Develop first-principles framework for light, medium-mass nuclei, and nuclear matter from 0.1 to twice the saturation density
Derive predictive nuclear energy density functional rooted in first-principles theory
Carry out predictive and quantified calculations of nuclear matrix elements for fundamental symmetry tests.
Unify the fields of nuclear structure and reactions.
Develop predictive microscopic model of fusion and fission that will provide the missing data for astrophysics and nuclear energy research.
Develop and utilize tools for quantification of theoretical uncertainties.
Provide the microscopic explanation for observed, and new, (partial-) dynamical symmetries and simple patterns

24. Isobaric Multiplet Mass Equation (IMME)
2.0
2.5
3.0
3.5
aA,T,I (MeV)
(1)
0.1
0.2
0.3
(2)
8,1,2
10,1,0
A,T,I
12,1,1
14,1,0
SVT CD
GFMC
EXP
P.Bączyk, J.Dobaczewski,
M.Konieczka, W.Satuła,
in preparation

25. Staggering in a(2) is due to TIME-ODD part of CIB
(type II) short-range functional
|K|=1
|K|=2
-0.1
0.1
0.2
daA,T,I (MeV)
(2)
time-even
time-odd
CIB
CSB
[CSB=0]
8,1,2
10,1,0
A,T,I
12,1,I
14,1,0