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Register a new userRealistic shell model calculation of $2 ubetabeta$ nuclear matrix elements and role of shell structure in intermediate states
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We discuss two conditions needed for correct computation of $2 u betabeta$ nuclear matrix-elements within the realistic shell-model framework. An algorithm in which intermediate states are treated based on Whiteheads moment method is inspected, by taking examples of the double GT$^+$ transitions $mbox{$^{36}$Ar}rightarrowmbox{$^{36}$S}$, $mbox{$^{54}$Fe}rightarrowmbox{$^{54}$Cr}$ and $mbox{$^{58}$Ni} rightarrowmbox{$^{58}$Fe}$. This algorithm yields rapid convergence on the $2 ubetabeta$ matrix-elements, even when neither relevant GT$^+$ nor GT$^-$ strength distribution is convergent. A significant role of the shell structure is pointed out, which makes the $2 ubeta beta$ matrix-elements highly dominated by the low-lying intermediate states. Experimental information of the low-lying GT$^pm$ strengths is strongly desired. Half-lives of $T^{2 u}_{1/2}({rm EC}/{rm EC}; mbox{$^{36}$Ar}rightarrowmbox{$^{36}$S})=1.7times 10^{29}mbox{yr}$, $T^{2 u}_{1/2}({rm EC}/{rm EC};mbox{$^{54}$Fe}rightarrow mbox{$^{54}$Cr})=1.5times 10^{27}mbox{yr}$,$T^{2 u}_{1/2}({rm EC} /{rm EC};mbox{$^{58}$Ni}rightarrowmbox{$^{58}$Fe})=6.1times 10^{24}mbox{yr}$and $T^{2 u}_{1/2}(beta^+/{rm EC};mbox{$^{58}$Ni} rightarrowmbox{$^{58}$Fe})=8.6times 10^{25}mbox{yr}$ are obtained from the present realistic shell-model calculation of the nuclear matrix-elements.
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The $lambda$ and $m_{betabeta}$ mechanisms of neutrinoless double beta decay ($0 ubetabeta$) occur with light neutrino exchange via $W_L-W_R$, and $W_L-W_L$ mediation, respectively. In the present study, we calculate the nuclear matrix elements (NMEs) for the $m_{betabeta}$ and $lambda$ mechanisms of $0 ubetabeta$, which has origin in the left-right symmetric model with right-handed gauge boson at TeV scale. The NMEs are calculated for one of the $0 ubetabeta$ decaying isotope $^{48}$Ca in the interacting nuclear shell-model using the GXPF1A effective interaction of $pf$-shell. The NMEs are calculated in both closure and nonclosure approaches using four different methods: closure, running closure, running nonclosure, and mixed methods. All the NMEs are calculated incorporating the effects of the finite size of nucleons and the revisited higher order terms such as isoscalar and weak magnetism terms of the nucleon currents. Inclusion of the short-range nature of nucleon-nucleon interaction in Miller-Spencer, CD-Bonn, and AV18 parametrizations is also taken care of. The comparative dependence of the running closure and running nonclosure NMEs with the spin-parity of the allowed states of intermediate nucleus $^{48}$Sc, the coupled spin-parity of the two initial decaying neutrons and the final two protons, the cutoff excitation energy of $^{48}$Sc, the cutoff number of states of $^{48}$Sc are also examined. Results show that there are about 2-20% enhancements in different types of total NMEs, calculated in the nonclosure approach as compared to the closure approach. The significant enhancements are found in the $M_{qGT}$ and $M_{qT}$ type NMEs for the inclusion of the higher-order terms of the nucleon currents.
The nuclear matrix elements of neutrinoless double-$beta$ decay for nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd are studied within the triaxial projected shell model, which incorporates simultaneously the triaxial deformation and quasiparticle configuration mixing. The low-lying spectra and the $B(E2:0^+rightarrow2^+)$ values are reproduced well. The effects of the quasiparticles configuration mixing, the triaxial deformation, and the closure approximation on the nuclear matrix elements are studied in detail. For nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd, the nuclear matrix elements are respectively reduced by the quasiparticle configuration mixing by 6%, 7%, 2%, 3%, and 4%, and enhanced by the odd-odd intermediate states by 7%, 4%, 11%, 20%, and 14%. Varying the triaxial deformation $gamma$ from $0^circ$ to $60^circ$ for the mother and daughter nuclei, the nuclear matrix elements change by 41%, 17%, 68%, 14%, and 511% respectively for $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd, which indicates the importance of treating the triaxial deformation consistently in calculating the nuclear matrix elements.
We approach the calculation of the nuclear matrix element of the neutrinoless double-beta decay process, considering the light-neutrino-exchange channel, by way of the realistic shell model. To this end, we start from a realistic nucleon-nucleon potential and then derive the effective shell-model Hamiltonian and neutrinoless double-beta decay operator within the many-body perturbation theory. We focus on investigating the perturbative properties of the effective shell-model operator of such a decay process, aiming to establish the degree of reliability of our predictions. The contributions of the so-called short-range correlations and of the correction of Pauli-principle violations to the effective shell-model operator, the latter introduced in many-valence nucleon systems, are also taken into account. The subjects of our study are a few candidates to the neutrinoless double-beta decay detection, in a mass interval ranging from A=48 up to A=136, whose spin- and spin-isospin-dependent decay properties we have studied in previous works. Our results will be finally compared with shell-model calculations for the same set of nuclei.
Neutrinoless double beta decay searches are currently among the major foci of experimental physics. The observation of such a decay will have important implications in our understanding of the intrinsic nature of neutrinos and shed light on the limitations of the Standard Model. The rate of this process depends on both the unknown neutrino effective mass and the nuclear matrix element associated with the given neutrinoless double-beta decay transition. The latter can only be provided by theoretical calculations, hence the need of accurate theoretical predictions of the nuclear matrix element for the success of the experimental programs. This need drives the theoretical nuclear physics community to provide the most reliable calculations of the nuclear matrix elements. Among the various computational models adopted to solve the many-body nuclear problem, the shell model is widely considered as the basic framework of the microscopic description of the nucleus. Here, we review the most recent and advanced shell-model calculations of the nuclear matrix elements considering the light-neutrino-exchange channel for nuclei of experimental interest. We report the sensitivity of the theoretical calculations with respect to variations in the model spaces and the shell-model nuclear Hamiltonians.
The nuclear matrix element (NME) of the neutrinoless double-$beta$ ($0 ubetabeta$) decay is an essential input for determining the neutrino effective mass, if the half-life of this decay is measured. The reliable calculation of this NME has been a long-standing problem because of the diversity of the predicted values of the NME depending on the calculation method. In this paper, we focus on the shell model and the QRPA. The shell model have a rich amount of the many-particle many-hole correlations, and the QRPA can obtain the convergence of the result of calculation with respect to the extension of the single-particle space. It is difficult for the shell model to obtain the convergence of the $0 ubetabeta$ NME with respect to the valence single-particle space. The many-body correlations of the QRPA are insufficient depending on nuclei. We propose a new method to modify phenomenologically the results of the shell model and the QRPA compensating the insufficient point of each method by using the information of other method complementarily. Extrapolations of the components of the $0 ubetabeta$ NME of the shell model are made toward a very large valence single-particle space. We introduce a modification factor to the components of the $0 ubetabeta$ NME of the QRPA. Our modification method gives similar values of the $0 ubetabeta$ NME of the two methods for $^{48}$Ca. The NME of the two-neutrino double-$beta$ decay is also modified in a similar but simpler manner, and the consistency of the two methods is improved.
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