0 νββ nuclear matrix elements within QRPA and its variants
21
0νββ nuclear matrix elements within QRPA and its variants W. A. Kamiński 1 , A. Bobyk 1 A. Faessler 2 F. Šimkovic 2,3 , P. Beneš 4 1 Dept. of Theor. Phys., Maria Curie-Skłodowska University, Lublin, Poland 2 Inst. of Theor. Phys., University of Tuebingen, Germany 3 Dept. of Nucl. Phys., Comenius University, Bratislava, Slovakia 4 IEAP, Czech Technical University, Prague, Czech Republic
description
0 νββ nuclear matrix elements within QRPA and its variants. W. A. Kamiński 1 , A. Bobyk 1 A. Faessler 2 F. Š imkovic 2,3 , P. Bene š 4. 1 Dept. of Theor. Phys., Maria Curie-Skłodowska University, Lublin, Poland 2 Inst. of Theor. Phys., University of Tuebingen, Germany - PowerPoint PPT Presentation
Transcript of 0 νββ nuclear matrix elements within QRPA and its variants
0νββ nuclear matrix elements within QRPA
and its variants
W. A. Kamiński1, A. Bobyk1 A. Faessler2
F. Šimkovic2,3, P. Beneš4
1Dept. of Theor. Phys., Maria Curie-Skłodowska University, Lublin, Poland2Inst. of Theor. Phys., University of Tuebingen, Germany3Dept. of Nucl. Phys., Comenius University, Bratislava, Slovakia4IEAP, Czech Technical University, Prague, Czech Republic
Motivation
Upper bound on the neutrino mass:
010
21 GTM
mm
ee
e
ee
m
Experiment gives upper bound on must come from the theory
eemM
021T
m
m iOmmOfMee
QRPA drawbacks
BCS state is not a QRPA ground state:
0QRPA jma
do not fulfil the bosonic commutation relations
MJnpMJpn
aaA
)(
The operators:
QRPA drawbacks (cont.)
QRPA ground state has a non-vanishing quasiparticle content:
0QRPA~QRPAˆ00
1 jjj aajn
The QRPA built naively on the BCS would be a pure TDA:
BCS~BCS)()()()(
pnMJpn
m
JpnMJpn
m
JpnMJAYAXQ
What should we learn?
The description of the ground state should be made consistent with that of the excited states
One should go beyond QBA and not neglect the scattering terms
Formalism – RQRPA
MJMJpnM(pn)Jjj AAjaa π )(
1
00ˆ~
The mapping:
The renormalized operators and amplitudes:
MJpnnpM(pn)JAnnπ )(
2/1)1(A
MJpnnpM(pn)JYnnπ )(
2/1)1( Y
Formalism – RQRPA (cont.)
The linear equations for q.p. densities:
npnn
npnp
npnp nnj YYYˆ
ppnp
ppnn
ppnn nnj YYYˆ
mJ
m
Jpnpn J
2
)(
2ˆ YYwith
Solve the RQRPA iteratively, i.e. na(out)=na(in).
Formalism – SQRRPA
The modified BCS tensors:
aaaaa nvuv 222
aaaa nvu 21 Computational procedure: iterate
between BCS and RQRPA untill the convergence is achieved, i.e. na(out)=na(in).
76Ge → 76Se: dependence on the s.p. basis
10 13 16 20 26-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
M2
GT
[M
eV-1
]
SRQRPARQRPAQRPA
13 16 19 23
SRQRPARQRPAQRPA
number of levels
no core16O core
100Mo → 100Ru: dependence on the s.p. basis
13 16 19-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
M2 G
T [
MeV
-1]
QRPARQRPASRQRPA
13 16 19 23
SRQRPARQRPAQRPA
number of levels
no core16O core
116Cd → 116Sn
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0gpp
-0.1
0.0
0.1
0.2
M 2
GT [
MeV
-1]
gph=1.0 QRPAgph=1.0 RQRPAgph=1.0 SRQRPAgph=0.8 QRPAgph=0.8 RQRPAgph=0.8 SRQRPA
128Te → 128Xe
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6gpp
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
M 2
GT [
MeV
-1]
gph =1.0 QRPAgph =1.0 RQRPAgph =1.0 SRQRPAgph =0.8 QRPAgph =0.8 RQRPAgph =0.8 SRQRPA
130Te → 130Xe
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8gpp
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
M 2
GT [
MeV
-1]
gph=1.0 QRPAgph=1.0 RQRPAgph=1.0 SRQRPAgph=0.8 QRPAgph=0.8 RQRPAgph=0.8 SRQRPA
136Xe → 136Ba
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6gpp
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
M 2
GT [
MeV
-1]
gph =1.0 QRPAgph =1.0 RQRPAgph =1.0 SRQRPAgph =0.8 QRPAgph =0.8 RQRPAgph =0.8 SRQRPA
146Nd → 146Sm
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4gpp
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
M 2
GT [
MeV
-1]
gph =1.0 QRPAgph =1.0 RQRPAgph =1.0 SRQRPAgph =0.8 QRPAgph =0.8 RQRPAgph =0.8 SRQRPA
150Nd → 150Sm
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4gpp
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
M 2
GT [M
eV-1
]
gph=1.0 QRPAgph=1.0 RQRPAgph=1.0 SRQRPAgph=0.8 QRPAgph=0.8 RQRPAgph=0.8 SRQRPA
Summary
Conclusions
The RQRPA and the SRQRPA are more stable with growing dimension of the single-particle model space
The RQRPA reproduces the experimental data for higher values of the particle-particle force
The SRQRPA behaves like QRPA, but the collapse is pushed forward towards higher gpp values
Conclusions (cont.)
0νββ nuclear matrix elements can be accurately reproduced within QRPA, RQRPA and SQRPA by fixing the gpp value using 2νββ experimental data
For the closed and partially closed shell nuclei (48Ca, 116Sn, 136Xe) a further improvement in the description of pairing interaction is necessary
References
S. M. Bilenky, A. Faessler, F. Šimkovic, Phys. Rev. D 70, 033003 (2004)
V. A. Rodin, A. Faessler, F. Šimkovic, P. Vogel, Phys. Rev. C 68, 044302 (2003)
A. Bobyk, W. A. Kamiński, F. Šimkovic, Phys. Rev. C 63, 051301(R) (2001)
Thank you for attention!
W. A. Kamiński, A. Bobyk A. FaesslerF. Šimkovic, P. Beneš
