1 TCP06 Parksville 8/5/06 Electron capture branching ratios for the nuclear matrix elements in...

1TCP06 Parksville 8/5/06

Electron capture branching ratios for the nuclear matrix elements in double-beta decay

using TITAN

◆ Nuclear matrix elements in double-beta decay.◆ Present uncertainties◆ Measurement of electron-capture branching ratios.◆ A new method using TITAN

D. Frekers, J. Dilling, I. Tanihata

and TITANEC collaboration


Double Beta Decay

◆ Two-neutrino decay (2) This decay is allowed by the standard model and has been observe

d. Calculations of the nuclear matrix elements are the main issues to

understanding the decay rates.◆ Zero-neutrino decay (0)

This mode of decay is forbidden by the standard model. Requires the neutrino to be a Majorana particle with a mass. Recent observations of the neutrino oscillation suggest the non-zero

mass of the neutrino and thus this decay mode may exist. New generation experiments for detecting this mode of decay are in

progress. Majorana neutrino mass would be determined if this mode of decay

is observed and reliable estimation of the nuclear matrix elements are available.


Rate of a 2 decay

€

A Z →A (Z + 2)+ 2e− + 2ν e

€

Γ2ν = G2ν (Q,Z ) M DGT2ν 2

where G2ν (Q,Z ) = CGF

2cosΘc

⎡ ⎣ ⎢

⎤ ⎦ ⎥

4

F−2 f (Q)

Q: decay Q value

GF: Fermi coupling constant

Qc: Cabibbo angle

F-: Coulomb factor for - decay

f(Q): phase space factor

C: Relativistic correction

€

M DGT2ν 2

: Nuclear matrix element

[Allowed by the standard model]


Nuclear matrix element for 2 decays

€

M DGT2ν =

0gsf σ kτ k

−k∑ 1m

+ 1m+ σ kτ k

−k∑ 0gs

i

12Q + E(1m

+ ) − E0m∑

=M m (GT +)M m (GT − )

Emm∑

Gamow-Teller transitions to all available states.

Fermi-type transitions are negligible due to the isospin conservation.

AZ

A(Z+1)

A(Z+2)

.

.

....

2

1+1+

1+1+

0+ i

0+ f


Rate of 0 decay (Neutrinoless decay)

€

A Z →A (Z + 2)+ 2e−[Forbidden by the standard model]

€

Γ

€

Γ0ν = G0ν (Q,Z ) M DGT0ν −

gV

gAM DF

0ν2

mν e

Both Gamow-Teller and Fermi transitions are involved.

€

mν e is the effective Majorane neutrino mass

= Uei2 mi

i∑

Uei: mixing matrixmi: mass eigenvalues of neutrinos


Matrix elements of 0 decay

€

M DGT0ν = f σ lσ kτ l

−τ k−HGT (rlk ,Ea ) i

lk∑

M DF0ν = f τ l

−τ k−HF (rlk ,Ea ) i

lk∑

Rlk: proton neutron distance in the nucleus

Ea: energy parameter related to the excitation energy


Theoretical approaches to the matrix elements

◆ Weak-coupling shell model based on G-matrix nucleon-nucleon interactions W.C Haxton and G.J. Stephenson, Jr., Part. Nucl. Phys 12 (1984)

409. E. Caurier et al., Phys. Rev. Lett. 77 (1996) 1954. But not available for all double beta-decay candidates.

◆ Quasiparticle Random phase approximation (QRPA) J. A. Halbleib and R. A. Solensen, Nucl. Phys. A 98 (1967) 542. J. Suhonen, Phys. Lett. B 607 (2006) 87.


◆ One can test the precession of calculations by comparing calculations to measured two-neutrino decay rate. The operator involved in the 2 decay mode is the Gamow-Teller operator that connects the initial and final states via virtual transitions to J=1+ states in the intermediate nucleus, only.

◆ The neutrinoless mode, on the other hand connect to all states in the intermediate nucleus.

◆ For this reason, comparison in 2 is not a direct test of the precision of the 0 rate calculation, but can be taken as a necessary condition for the reliability of the calculation.

M. Bhattacharya et al., Phys. Rev. C 58 (1998) 1247.


Theoretical situation (QRPA)

◆ Both decay modes can be described with ONE parameter, gpp, that is the particle-particle coupling part of the proton-neutron two-body interaction.

◆ gpp is fixed by the experimental 2 decay half life (gpp~1)

◆ 0 decay is insensitive to gpp.

◆ So just trust us!!

gpp = 0.89 gpp = 0.96gpp = 1.00 gpp = 1.05

1+ 2+3+ 4+ 5+6+7+ 8+ 1- 2- 3- 4- 5- 6- 7-0-

40.0

30.0

20.0

10.0

0.0

-10.0

Decomposition of MGT

Only 1+ is sensitive to gpp

However…


The case of A=116

J. Suhonen, Phys. Lett. B 607 (2005) 87.

116Cd

Single state dominance

One can obtain the transition strength of MEC and M separately.

Exp. -

Exp. EC (direct mea.)

Exp. EC (3He,t)

M. Bhattacharya et al. Phys. Rev. C 58 (1998) 1247.

H. Akimune et al., Phys. Lett. B 394 (1997) 23.


Experimental data also show inconsistency

◆ Direct measurement of Electron capture (MEC=0.69) Extremely small branching compared with - decay. (~0.023%)

◆ Nucleon transfer reactions (MEC=0.18) Uncertainty between the proportionality of between B(GT) and the

(3He,t) charge exchange cross section.


Difficulty in electron capture branching ratio

◆ Measurement should be made by detecting Kx-rays after capture of electrons under the back ground of x-rays and rays associated with - decays.

◆ Neutron activation method,… Reaction with accelerated beam and tape transport system. Kx-rays after shake off by electrons. Bremsstrahlung from electrons. Beta delayed gamma emission. Impurity of decay sample.


A New Method at TITAN

◆ Observation of x-ray from decays of trapped ions. No material around the decaying nuclei. All electrons are swept away by the magnetic field. No impurity


ISAC Facility at TRIUMF

M. Bhattacharya et al., PRC 58 (1998)1247.

TITAN


TITAN Mass measurement mode

1

2

3

4

TITAN EC measurement mode

2

1

3


EBIT (Electron Beam Ion Trap)

◆ Use it without the electron gun.

(Penning trap mode)◆ 7 ports for X-ray detection

port for X-raydetector

trap center

E-gun(can be retracted)

distance from trap center [mm]-600 -400 -200 0 200 400

B[T]2

4

6

0


100Tc case as an example

◆ Optimization High detection effici

ency of 17.5 keV X-rays

Low efficiency for rays.

High rejection of e-

■ Detector thickness■ Be window thicknes

s■ Magnetic field stren

gth

0.01% branch

beta: 10000gamma: 44 500 700

For 1 EC

T1/2=15.8 s


Simulated spectra (100Tc)X-ray spectrum by a Si detector (2mm thick)

8x108 decays @0.002% branching ratio with -ray anticoincidence with 90% rejection rate.

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Detected energy [keV]

B Counts/0.5keV

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B Counts

Additional background for 1.5x108 decays.


Simulated spectra (100Tc)

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B Counts/0.5keV

X-ray spectrum by a Si detector (2mm thick)

8x107 decays @0.1% branching ratio and no -ray anti-coincidence rejection, or

8x108 decays @0.01% branching ratio with -ray anticoincidence with 90% rejection rate.


Summary

◆ Radioactive beam facilities and ion traps provides a new possibility for a precise determination of an extremely small branching ratio of electron capture.

◆ It will give the best test ground for nuclear models of double beta decay. It thus provides information on the matrix elements of 0 decays.

◆ Please refer to the paper by D. Frekers, J. Dilling, and I. Tanihata submitted to publication for detailed discussion of other cases of double beta decays.

Thank you

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