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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-21 20:52 |
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Conference: Bucharest University Faculty of Physics 2008 Meeting
Section: Theoretical Physics and Applied Mathematics Seminar
Title:
Double beta decay to the first 2^+$
Authors:
A. A. Raduta(a) and C. M. Raduta(b)
Affiliation:
(a) Department of Theoretical Physics and Mathematics, Bucharest UNiversity, BOBox MG11, Romania
(b) Institute of Physics and Nuclear Engineering,
Bucharest, POBox MG6, Romania
E-mail
raduta@ifin.nipne.ro
Keywords:
beta decay, quasiparticle random phase approximation, half life, the Gamow-Teller transition operator, nuclear deformation, the Gammow-Teller giant resonance, boson expansion, many body theory
Abstract:
One of the most exciting subject of nuclear physics is that of double beta decay.
The interest is generated by the fact that in order to describe quantitatively the decay rate one has to treat consistently the neutrino properties as well as the nuclear structure features.
The process may take place in two distinct ways:
a) by a $2\nu\beta\beta$ decay where the initial nuclear system, the mother nucleus, is transformed in the final stable nuclear system, usually called the daughter nucleus, two electrons and two anti-neutrinos;
b) by the $0\nu\beta\beta$ process where the final state does not involve any neutrino. The latter decay mode is
especially interesting since one hopes that its discovery might provide a definite answer to the question whether the neutrino is a Majorana or a Dirac particle. Unfortunately, there is no reliable test for the nuclear matrix elements and consequently only upper limits for the neutrino mass and the strength of right handed electroweak interaction can be obtained. On the other hand, for the $2v\beta\beta$ process plenty of data are available. Since similar nuclear matrix elements are used for describing both processes, it has been proposed to use, in the $0\nu\beta\beta$ calculations, those matrix elements which provide a realistic description of the $2\nu\beta\beta$ process. Due to this feature many theoretical efforts have been focused on the treatment of the $2\nu\beta\beta$ decay. The formalism which yields results for the ground to ground $2\nu\beta\beta$ transition which are closest to the corresponding data is the pnQRPA approach. Within this formalism the transition which leaves the daughter nucleus in an excited state is forbidden. Here, we consider the case when the endpoint of a Gamow-Teller (GT) transition is the first excited state $2^+$. In order to make this transition possible, a higher pnQRPA treatment of the Gamow-Teller transition operator is used \cite{Rad0}.
This is written as a polynomial in the dipole proton-neutron and quadrupole charge conserving QRPA boson operators, using the prescription of the boson expansion formalism \cite{Rad7}.
With the obtained anharmonic structure of the transition operator, the $2\nu\beta\beta$ process ending on the first $2^+$ state in the daughter nucleus undergoes through one, two and three boson states describing the odd-odd intermediate nucleus. The approach uses a single particle basis which is obtained by projecting out the good angular
momentum from an orthogonal set of deformed functions \cite{Rad4}. The basis for mother and daughter nuclei have different deformations. Due to the specific properties of the single particle basis, the formalism is quite flexible allowing a unified description of the double beta decay to excited collective states in spherical and deformed nuclei.
The GT transition amplitude as well as the half lives were calculated for eleven transitions. Results are compared with the available data as well as with some predictions obtained with other methods \cite{Suh1}. The agreement with experimental data is reasonable. The transition matrix elements obtained in our formalism are smaller than those obtained in Ref.\cite{Suh1} with a spherical basis, which
agrees some previous considerations pointing to the conclusion that the nuclear deformation decreases the transition matrix elements\cite{Zami}. We remark the good agreement between our prediction for $^{100}$Mo and that of Ref.\cite{Hir} obtained with a deformed SU(3) single particle basis.
The process half-life is influenced by both the Q-value and the nuclear deformation. Comparing the involved matrix elements with those characterizing the ground to ground transition one concludes that the present ones are by
one to two orders of magnitude smaller.
It is worth mentioning that the double beta transitions to excited states have been considered by several authors in the past, but the calculations emphasized the role of the transition operator and some specific selection rules. Many of calculations regarded the neutrinoless process. Thus, in Ref.\cite{Verg2} it was shown that the neutrinoless transition to the excited $0^+$ for medium heavy nuclei might be characterized by matrix elements which are larger than that of ground to ground transition and that happens since in the first transition, the change of the $K$ quantum number is less.
Here we show that the transition $0^+\to 2^+$ in a $2\nu\beta\beta$ process is allowed by renormalizing the GT transition operator with some higher RPA corrections.
\end{abstract}
\maketitle
\begin{thebibliography}{99}
\bibitem{Rad0}A. A. Raduta, C. M. Raduta, Phys. Lett. B 647 (2007) 265.
\bibitem{Rad7}A.A.Raduta, A.Faessler and S.Stoica, Nucl. Phys. {\bf A534}
(1991) 149.
\bibitem{Rad4}A. A. Raduta, D. S. Delion and N. Lo Iudice, Nucl. Phys.
{\bf A 564} (1993) 185.
\bibitem{Suh1} J. Toivanen, J. Suhonen, Phys. Rev. C {\bf 55} (1997) 2314.
\bibitem{Zami} L. Zamick and N. Auerbach, Nucl. Phys. {\bf A 658} (1999) 285.
\bibitem{Hir} J. G. Hirsch {\it et al.,} Phys. Rev. {\bf 51} (1995) 2252.
\bibitem{Verg2}J. D. Vergados, Phys. Lett. {\bf 109 B} (1982),96; {\bf 113 B} (1982) 513.
\end{thebibliography}
\end{document}
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