In colaboration with: Jacek Dobaczewski, Pawe Bczyk, Maciek - - PowerPoint PPT Presentation

• new developments:

DFT-rooted NCCI involving angular-momentum and isospin projections pn-mixed SR functionals charge-dependent functionals

• physics highlights

nuclear structure and beta decays strong-force isospin symmetry breaking effects (TDE/MDE) Isospin symmetry studies using SR-DFT and MR-DFT-rooted approaches: In colaboration with: Jacek Dobaczewski, Paweł Bączyk, Maciek Konieczka, Koichi Sato, Takashi Nakatsukasa

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!”

Effective or low-energy (low-resolution) theory explores separation

• f scales. Its formulation requires:

in coordinate space: define R to separate short- and long-distance physics

• r, in momentum space:

define Λ (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

Fourier

local correcting potential

hierarchy of scales: 2roA1/3 ro ~ 2A1/3

is based on the same simple and very intuitive assumption that low-energy nuclear theory is independent on high-energy dynamics

~ 10

Nuclear effective theory for EDF (nuclear DFT)

Long-range part of the NN interaction

(must be treated exactly!!!)

where

regularization

Coulomb

ultraviolet cut-off Λ denotes an arbitrary Dirac-delta model There exist an „infinite” number

• f equivalent realizations
• f effective theories

Gaussian regulator

• J. Dobaczewski, K. Bennaceur,
• F. Raimondi,
• J. Phys. G 39, 125103 (2012)

• J. Dobaczewski, K. Bennaceur, F. Raimondi,
• J. Phys. G 39, 125103 (2012)

lim δa

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 direct term exchange term

Skyrme (hadronic) interaction conserves such symmetries like:

• particle numer, parity…

LS LS LS

advantages: builts in correlations into single Slater determinant disadvantages: symmetry must be restored to compare theory to data

NCCI SR-DFT MR-DFT

There are two sources of the isospin symmetry breaking:

• , caused solely by the HF approximation
• , caused mostly by Coulomb interaction

(also, but to much lesser extent, by the strong force isospin non-invariance)

Find self-consistent HF solution (including Coulomb) deformed Slater determinant |HF>: in order to create good isospin „basis”: Apply the isospin projector:

Engelbrecht & Lemmer, PRL24, (1970) 607 See: Caurier, Poves & Zucker, PL 96B, (1980) 11; 15

Diagonalize total Hamiltonian in „good isospin basis” |α,T,Tz> takes physical isospin mixing

αC = 1 - |aT=Tz|2

AR

n=1

1 2 3 4 5 6 0.2 0.4 0.6 0.8 1.0 20 28 36 44 52 60 68 76 84 92

A

AR BR SLy4

αC [%]

E-EHF [MeV]

N=Z nuclei 100

This is not a single Slater determinat There are no constraints on mixing coefficients

~30%

∆αC

HF tries to reduce the isospin mixing by: in order to minimize the total energy Projection increases the ground state energy

(the Coulomb and symmetry

energies are repulsive)

Rediagonalization (GCM) lowers the ground state energy but only slightly below the HF

• E. Farnea et al.

PLB551, 56 (2003)

• A. Corsi et al. PRC84,

041304 (2011)

10 cases measured with accuracy ft ~0.1% 3 cases measured with accuracy ft ~0.3%

~2.4% 1.5% 0.3%

• 1.5%

test of the CVC hypothesis

(Conserved Vector Current)

Towner & Hardy

• Phys. Rev. C77, 025501 (2008)

weak eigenstates mass eigenstates

CKM

Cabibbo-Kobayashi

• Maskawa

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| = 0.97418 + 0.00026

• adopted from J.Hardy’s, ENAM’08 presentation

• 0.5

0.5 10 20 30 40 50 60 70 A

δC - δC [%]

(SV) (HT)

• H. Liang, N. V. Giai, and J. Meng,
• Phys. Rev. C 79,064316 (2009).
• W. Satuła, J. Dobaczewski,
• W. Nazarewicz, M. Rafalski
• Phys. Rev. C 86, 054314 (2012)

I.S. Towner and J. C. Hardy,

• Phys. Rev. C 77, 025501(2008).

(a) (b) (c,d)

• O. Naviliat-Cuncic and N. Severijns,
• Eur. Phys. J. A 42, 327 (2009);
• Phys. Rev. Lett. 102, 142302 (2009).

superallowed 0+0+ β-decay

|Vud|

(a)

π-decay mirror T=1/2 nuclei ν-decay

0.970 0.971 0.972 0.973 0.974 0.975 0.976

(b) (c) (d)

0.9925 0.9950 0.9975 1.0000 1.0025

|Vud|2+|Vus|2+|Vub|2

superallowed 0+0+ β-decay

π-decay ν-decay mirror T=1/2 nuclei

(a)

(b) (c)(d)

For the NCCI study see: W.Satuła, P.Bączyk, J.Dobaczewski & M.Konieczka, Phys. Rev. C94, 024306 (2016)

0.5 1.0 1.5 10 15 20 25 30 35 40 45 50 A

δC [%]

pDFT SM+WS

SM+WS results from:

• N. Severijns, M. Tandecki,
• T. Phalet, and I. S. Towner,
• Phys. Rev. C 78, 055501 (2008).
• W. Satuła, J. Dobaczewski, W. Nazarewicz, M. Rafalski
• Phys. Rev. C 86, 054314(2012).
• M. Konieczka, P. Bączyk, W. Satuła,
• Phys. Rev. C 93, 042501(R) (2016).

See also the NCCI study:

W.Satuła, P.Bączyk, J.Dobaczewski & M.Konieczka, Phys. Rev. C94, 024306 (2016)

3+

• 60
• 55
• 50
• 45
• 40
• 35
• 30
• 25
• 20

1+ 1+ 2+ 0+ 1+ 3+ 2+

Energy [MeV]

For details see: W.Satuła, P.Bączyk, J.Dobaczewski & M.Konieczka, Phys. Rev. C94, 024306 (2016)

1 2 3 4 5

0+ ground state EXP

(old)

SM

(MSDI3)

SM

(GXPF1)

62Zn, I=0+ states below 5MeV

Excitation energy of 0+ states [MeV] SVmix

(6 Slaters)

EXP

(new)

K.G. Leach et al. PRC88, 031306 (2013)

No-core configuration-interaction formalism based on the isospin and angular momentum projected DFT

W.S., J. Dobaczewski,

• M. Konieczka

arXiv:1408.4982 (2014) JPS Conf. Proc. 6, 020015 (2015)

W.Satuła, J.Dobaczewski & M.Konieczka, arXiv:1408.4982; JPS Conf. Proc. 6, 020015 (2015)

HF

π1 ν1 ν2 ππ1 π2

I=0+ before mixing

π|312 5/2>-1 π|312 3/2> π|312 5/2>-2 π|312 3/2>2 π|312 5/2>-1 π|310 1/2> ν|312 3/2>-1 ν|310 1/2> ν|312 3/2>-1 ν|321 1/2>

Gamow-Teller and Fermi matrix elements in T=1/2 sd- and ft- mirrors. The NCCI study

2.0 2.5

|MGT|

NCCI in 6Li

6He is fixed

NCCI in 6He

6Li is fixed

6He(0+) 6Li(1+)

Knecht et al. PRL108, 122502 (2012)

Proof-of-principle calculation: 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

• G. Martinez-Pinedo et al.,
• Phys. Rev. C 53, R2602 (1996).
• B. A. Brown and B. H. Wildenthal,

Atomic Data and Nuclear Data Tables 33, 347 (1985).

• T. Sekine et al.,
• Nucl. Phys. A 467, (1987).

1 2 3 4 5 1 2 3 4 5 SM NCCI

|gAMGT|

1 2 3 4 20 30 40 50

A |gAMGT|

(TH) (TH)

|MGT |

(EXP)

The NCCI takes into account a core and its polarization Completely different model spaces Different treatment of correlations

SM NCCI

Different interactions quenching q~25%!!!

q2~0.84-0.92 (from Ikeda sum rule) Ekstrom et al. PRL 113, 262504 (2014) β− decays of 14C and 22;24O

Menendez et al. PRL107, 062501 (2011)

q~0.9 See also:

Klos et al. PRC89, 029901 (2013) Engel et al. PRC89, 064308 (2013)

• K. Sato, J. Dobaczewski, T. Nakatsukasa, and W. Satuła, Phys. Rev. C88 (2013), 061301

separable solution p-n mixed solution |n> |p> +

• separable

solution

normalized: theory (red curve) shifted by 3.2MeV

λx λz

Class III corrects for MDE Class II corrects for TDE

8,1,2 10,1,0

A,T,I

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

aA,T,I (MeV)

(2)

12,1,1

EXP SVT GFMC

CD

SkMCD SLy4CD

0.5 1.0 1.5 2.0 2.5 3.0

aA,T,I (MeV)

(1)

8,1,2 10,1,0

A,T,I

SVT

12,1,2

GFMC

CD

VCD

Beta decay to 20Ne; 6 SD in NCCI Gamow-Teller matrix elements for 20Na 20Ne VERY PRELIMINARY RESULTS !!! Isospin symmetry breaking effects in GT decays of T=1 nuclei

NSM fom Brown, Wildenthal, Atomic and Nuclear Data Tables 33 (1985)

(from Maciek Konieczka) 0+ 2+ 2+ 2+ 2+