Beta-decay studies in N~Z nuclei using no-coreconfiguration-interaction model

Wojciech Satułain collaboration with: J. Dobaczewski, W. Nazarewicz, M. Rafalski & M.

Konieczka

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:

Summary & perspectives

examples: 32Cl-32S, 62Zn-62Ga, 38Ca-38K

towards NO CORE shell model with basis cutoff dictated by the self-consistent p-h configurations

Superallowed I=0+ T=1 I=0+ T=1 Fermi beta decays(testing the Standard Model of elementary particles)

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 & HardyPhys. Rev. C77, 025501 (2008)

weak eigenstates

mass eigenstates

CKMCabibbo-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-

adopte

d f

rom

J.H

ard

y’s

, EN

AM

’08

pre

senta

tion

~ ~|

Skyrme-Hartree-FockDF

ground statein N-Z=+/-2 (e-e) nucleus

antialigned statein N=Z (o-o) nucleus

Project on good isospin (T=1) and angular momentum (I=0)

(and perform Coulomb rediagonalization)

<T~1,Tz=+/-1,I=0| |I=0,T~1,Tz=0>T+/-

Project on good isospin (T=1) and angular momentum (I=0)

(and perform Coulomb rediagonalization)

|2=2(1-dC)

I=0+,T=1,Tz=-1

I=0+,T=1, Tz=0BRQb

t1/2

How to calculate the superallowed Fermi beta

decay ME using the double-projected DFT

framework?

superallowed 0+0+

b-decay

|Vu

d| (a)

p-decaymirror T=1/2

nuclei

n-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

|Vu

d | 2+|V

us | 2+

|Vu

b | 2superallowed 0+0+

b-decayp-decay

n-decay

mirror T=1/2nuclei

(a)

(b)

(c)(d)

|Vud| & unitarity of the CKM – a survey

-0.5

0

0.5

10 20 30 40 50 60 70 A

dC

- d

C

[%

](S

V)

(HT

)

W. Satuła, J. Dobaczewski, W. Nazarewicz, M. Rafalski, Phys. Rev. Lett. 106, 132502 (2011); 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).

Vud=0.97418(26)Ft=3071.4(8)+0.85(85);

Ft=3070.4(9); Vud=0.97444(23) PRLFt=3073.6(12);Vud=0.97397(27) PRC

H. Liang, N. V. Giai, and J. Meng, Phys. Rev. C 79,064316 (2009).

6210

38

jp

0.5

1.0

1.5

jn

jn

jn

jp

jp

ls

i

ll

iss

-0.3

-0.2

-0.1

0

Relative orientation of shape and current

DE

[M

eV]

dC [

%]

i

A=34SV

A=34SV 34Ar 34Cl

34Cl 34S

DEI=0,T=1

DEHF DEIV

(TO)

x xx

y y y

Vud=0.97397(27)Ft=3073.6(12)

|Vud|2+|Vus|2+|Vub|2==0.99935(67)

Functional dependence:

SV:

Vud=0.97374(27)Ft=3075.0(12)

|Vud|2+|Vus|2+|Vub|2==0.99890(67)

SHZ2:

asym=42.2MeV!!!

Basis-size dependence:~10%

Configuration dependence:

SOURCES OF THEORETICAL ERRORS

MEAN-FIELDcompute „n” self-consistent Slater determinants

corresponding to low-lying p-h excitations

j1 j2 j3 jn…………

PROJECTIONnon-orthogonal set of K- and T-mixed states

{|I>(1)}k1{|I>(2)}k2

{|I>(3)}k3{|I>(n)}kn

…………..

Ei |Ii>

STATE MIXING Hill-Wheeler equation : Hu=ENu

32Cl

I=1+I=0+ I=2+

(2+)

(2+)

(2+)

(2+)(0+)

0

1

2

3

4

5

6D

E (

MeV

)

I=3+

No-core shell model with basis cutoff dictated by the self-consistent p-h DFT states

theoryexp

W.Satula, J.Dobaczewski, M.Konieczka, W.Nazarewicz, Acta Phys. Polonica B45, 167 (2014)

our: δC ≈ 6(2)%

0

1000

2000

3000

4000

(keV)

1

1

1

T

1

1

32Cl I=1+

theory

0

1000

2000

3000

4000

(keV)

theory experiment

T

0

0

1

1

1

4622, 4636

32S I=1+

experiment7002keV

W.S

atu

la, J.D

obacz

ew

ski, M

.Kon

iecz

ka, W

.Naza

rew

icz,

Act

a P

hys.

Polo

nic

a B

45

, 1

67

(2

01

4)

0keV

D. Melconian et al., Phys. Rev. Lett. 107, 182301 (2011).

Experiment: δC ≈ 5.3(9)%SM+WS calculations: δC ≈ 4.6(5)%.

0

1

2

3

4

5

0+ ground state

EXP(old)

SM(MSDI3)

SM(GXPF1)

62Zn, I=0+ states below 5MeVExcit

ati

on

en

erg

y o

f 0

+ s

tate

s [

MeV

]

SVmix

(6 Slaters)

HF

1pph

1nph

2nph

1pp2p2h

2pph

I=0+ before mixing

EXP(new)

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

-526

-525

-524

-523

-522EXPp1 n1 n2 p2 pp1+ + + +

Stability of configuration – interaction calculations

g.s.+En

erg

y (

MeV

)

normalized

0123456

dC [

%]

-512

-511

-510

EH

F (M

eV

) p1

n1

Z

X~Y

~200keV

Static approach gives: dC=8.9%

I=0+, T=1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

38Ca 38K

EXP dC=1.5%

dC=1.7%

DE [

MeV

]

A case of A=38 (38Ca38K)

mixing: 4 Slaters 3 Slaters

Summary & perspectives

We have to go BEYOND STATIC MR-EDF in orderto address high-quality spectroscopic data availabletoday.

First attempts are very encouraging at least concerning energy spectra!!!

Isospin symmetry breaking corrections from the „static” double-projected DFT are in very good agreement with the Hardy–Towner results.

0

0.5

1.0

1.5

10 14 18 22 26 30 34

Tz=-1 Tz=0

mixing the X,Y,Z orientations in light nuclei

A

dC [

%]

averages

mixing

T&H

W.Satula, J.Dobaczewski, M.Konieczka, W.Nazarewicz, Acta Phys. Polonica B45, 167 (2014)

0

0.5

1.0

1.5

2.0

2.5

3.0

0 2 4 61 3 5 7

Exc

itati

on

en

erg

y [

MeV

]

angular momentum

T=1

T=0

Mixing of states projected from the antialigned configurations:

nK pK 0

0.20.40.6

1/2 3/2 5/2 7/2

SVSHZ2

DE

(M

eV)

K

42Sc

42Sc ( )

T=1 statesare not representable in a

„separable” mean-field!

T=0n pT=0

T=1n p

Mean-field can differentiate between

n p and n ponly through time-odd polarizations!

aligned configurationsn p

nn p p

n panti-aligned configurations

or n por n p

nn p pCORE CORE

Tz=-/+1 I=0+,T=1

I=0+,T=1BR

(N-Z=-/+2)

(N-Z=0)Tz=0

Qb

t1/2

ISOSPIN PROJECTION

MEAN FIELD

How to calculate the superallowed Fermi beta

decay using the projected DFT framework?|<T+/->|2=2(1-dC)

n panti-aligned configurations

or n p

nn p pE-E CORE

MEAN FIELD

T=1 statesare not representable in a „separable” mean-field!!!

T=0

T=1n p