Double beta-decay workshop May 11-13 (11), 2016

TRIUMF, Vancouver

Takaharu Otsuka University of Tokyo / MSU / KU Leuven

Nucleon pairs in double-beta decay

SupportedbyMEXTandJICFuSasapriorityissue(Elucida;onofthefundamentallawsandevolu;onoftheuniverse)tobetackledbyusingPost‘K’Computer

N.Shimizua,J.Menendezb,Y.Iwataa,Y.Utsunoa,c,M.Honmad,T.AbebaCenterforNuclearStudy,UniversityofTokyobDepartmentofPhysics,UniversityofTokyocJapanAtomicEnergyAgencydUniversityofAizu

Outline 1.  Neutrinoless double beta decay 48Ca -> 48Ti

2.  Decay from neutron closed-shell nuclei

3.  Decay from spherical open-shell nuclei

4.  Open question on rotational nuclei

A large-scale shell model calculation on 48Ca -> 48Ti neutorinoless double beta decay

Y. Iwata et al., PRL 116, 112502 (2016)

Amongmanyearlierstudies,wecarriedoutsomewhatlargershell-modelcalcula;onsinthesd+pfshell.

SM(pf)

MBPT

QRPA

IBM

EDF

NME can be decomposed into individual contributions with spin/parity (Jπ) of two decaying neutrons :

What can be physical implications ? What can be foreseen ?

Outline 1.  Neutrinoless double beta decay 48Ca -> 48Ti

2.  Decay from neutron closed-shell nuclei

3.  Decay from spherical open-shell nuclei

4.  Open question on rotational nuclei

The model space is truncated to the f 7/2 only, for the purpose of schematic studies of certain basic features.

48Ca ground state => f 7/2 closed shell This is also the condensate of J=0+ pair (4 pairs).

We can take f7/2 part of the dbd operator.

i, j, k, l =f7/2

because Dn (S+n)4 |0> ~ - D+

n (S+n)2 |0>

f7/2 single orbit model

Neutrinoless double beta decay operator x0 S+p Sn + x2 D+

p Dn + …

Quadrupole-quadrupole proton-neutron interaction gives 48Ti ground state as (c0 S+

p S+n + c2 D+

p D+n) (S+

n)2 |0> with c0 and c2 both positive

Thus, there is always cancellation between S+p Sn and D+

p Dn contributions.

S+n (p)

: J=0 pair of neutrons (protons)

(S+)4 |0>48Ca ground state : closed shell

D+n (p)

: J=2 pair of neutrons (protons)

D+p Dn (S+

n)4 |0> ~ - D+p D+

n (S+n)2 |0>

S+p Sn (S+

n)4 |0> ~ + S+p (S+

n)3 |0>

opposite sign

x0=-3.32, x2=-2.37 same sign

We can verify some properties, by tuning the strength of the quadrupole pairing (Q-pairing) interaction VQ.

Monopole Pairing interaction VM , T=1 J=0 part of the interaction.

VQ = - G2 (½) ([a+j a+

j ](2) [a~j a~j ](2) ) = - G2 (D+

D ~)

where G2 = - <j2; J=2 | V | j2; J=2 > usually G2 > 0 (0.94 for GXPF1B)

Quadrupole Pairing interaction VQ , T=1 J=2 part of the interaction.

VM = - G0 (½) ([a+j a+

j ](0) [a~j a~j ](0) ) = - G0 (S+

S ~)

where G0 = - <j2; J=0 | V | j2; J=0 > usually G0 > 0 (2.24 for GXPF1B)

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

NME(J=0),f7/2single-j

GT Fermi tensor total

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5

protonpair48Ti:f7/2only

Jp=0

Jp=2

The ground state of 48Ti ={(c0 S+

p S+n + c2 D+

p D+n) (S+

n)2 +…} |0>

# of the proton pair =

0.952

0.75

this probability

change of NME by J=0 and 2

ScalingofQ-pairing

0.82

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

NME(J=2),f7/2single-j

GT Fermi tensor total

original

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1 1.5 2 2.5

protonpair48Ti:pfshell

Jp=0

Jp=2

Jp=4

This feature can be seen in the full pf shell calculation

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

NME(J=2),fullpf-shell

GT Fermi tensor totalScalingofQ-pairing

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

NME(J=0),fullpf-shell

GT Fermi tensor total

The J=2 T=1 TBME’s are scaled.

S pair = Σ i αi S i

D pair = Σ i<i βij D ij coherentsum

-2.5

-2

-1.5

-1

-0.5

0-4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

X,J=0DBDOP.

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

X,J=2DBDOP.

Correlation between TBME’s of Interaction and double-beta decay

V,Interac;on

(MeV

)

J=0

J=2

V,Interac;on

(MeV

)

f7/2

Two categories (a) correlations (b) small values for dbd Signs are basically the same

< i j ; J |V or X | k l ; J >

Outline 1.  Neutrinoless double beta decay 48Ca -> 48Ti

2.  Decay from neutron closed-shell nuclei

3.  Decay from spherical open-shell nuclei

4.  Open question on rotational nuclei

Sphericalgroundstateinopenshell

(S+)k |0>ground state : condensation of J=0 pairs

Quadrupole-pairing neutron-neutron interaction mixes as c1 (S+

n)k – c2 (D+n D+

n) (S+n)k-2 |0>

with c1 and c2 both positive. Ground state correlation (backward scattering) amplitude.

D D amplitudes with opposite sign between neutron-neutron Q-pairing interaction and neutron-neutron quadrupole-quadrupole interaction (which is much weaker)

This is a robust property determined by the double commutator.

Double-beta decay from this state tends to lead to x1’ S+

p (S+n)k-1 – x2’ (D+

p D+n) (S+

n)k-2 |0> with x1’ and x2’ both positive

Quadrupole-quadrupole proton-neutron interaction mixes as (c0 S+

p S+n + c2 D+

p D+n) (S+

n)2 |0> with c0 and c2 both positive

Another source of cancellation

Quadrupole-pairing neutron-neutron interaction mixes as c1 (S+

n)k – c2 (D+n D+

n) (S+n)k-2 |0>

with c1 and c2 both positive.

assuming Q-pairing J=2 pair ~ [ Q, S + ] ~ J=2 dbd pair M-pairing J =0 pair ~ J=0 dbd pair

Contributions to NME increase in magnitude :

singlef7/2model

Outline 1.  Neutrinoless double beta decay 48Ca -> 48Ti

2.  Decay from neutron closed-shell nuclei

3.  Decay from spherical open-shell nuclei

4.  Open question on rotational nuclei

Rotational nuclei

Intrinsic state of the ground-state rotational band

(Λ+p ) Kp (Λ+

n)Kn |0>

Particle-number projected HFB state

(Λ+p ) Kp+1 (Λ+

n)Kn-1 |0>

Double beta decay ?

deformed pair : Λ+p,n = ξ0 S+

p,n + ξ2 D+p,n + ξ4 G+

p,n + …

Higher order terms may contribute, but HFB with N and Jp projections will include all effects. Possibility of a larger NME … good for establishing 0νν dbd

48Ca、76Ge、82Se、96Zr、100Mo、116Cd、128Te、130Te、150Nd、238U

Candidates 150Nd, 238U

From the standard list

150Nd 238U

E N D