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Register a new userQuark Cluster Model Equations for $betabeta$ Decay
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In a separate paper we have discussed the possibility that six quark clusters can affect the rate of double-beta decay. In this article we develop the formalism needed in the evaluation of the energy of all six-quark cluster configurations, which can arise in a harmonic oscillator basis up to $2 hbar omega$ excitations. The symmetries that were found useful for this purpose were the combined spin color symmetry $SU_{cs}(6)$, the orbital symmetry $SU_{o}(6)$ and the isospin symmetry $SU_I(2)$.
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We study double gamma ($gammagamma$) decay nuclear matrix elements (NMEs) for a wide range of nuclei from titanium to xenon, and explore their relation to neutrinoless double-beta ($0 ubetabeta$) NMEs. To favor the comparison, we focus on double-magnetic dipole transitions in the final $betabeta$ nuclei, in particular the $gammagamma$ decay of the double isobaric analog of the initial $betabeta$ state into the ground state. For the most probable decay with equal-energy photons, our large-scale nuclear shell model results show a good linear correlation between the $gammagamma$ and $0 ubetabeta$ NMEs. Our analysis reveals that the correlation holds for $gammagamma$ transitions driven by the spin or orbital angular momentum due to the dominance of zero-coupled nucleon pairs, a feature common to $0 ubetabeta$ decay. Our findings point out the potential of future $gammagamma$ decay measurements to constrain $0 ubetabeta$ NMEs, which are key to answer fundamental physics questions based on $0 ubetabeta$ experiments.
To describe the double-charge-exchange (DCE) processes, we have designed recently the $(pn,2p2n)$-QTDA model which fully includes the pairing correlations and four quasiparticle excitations. It has been applied in $2 u$ double beta decays (DBDs), and the double charge-exchange resonances (DCERs). Here we extend it to $ 0 u $ DBD and discuss the relationship between the nuclear matrix elements (NMEs), and the DCE reaction matrix elements (RMEs) with the same spin-isospin structure. We do it for all final $0^+$ states, even in the region of DCERs, where the DBD is energetically forbidden. As an example, we evaluate the DBD $^{76}$Ge $rightarrow ^{76}$Se, both for $2 u$ and $0 u$ modes, as well as the associated DCE sum rules, excitation energies within the $Q$-value window for DBD, and the $Q$-value itself. We find that the $0 u$ NMEs are correlated with the RMEs, both at low energy, and in the DCER region where most of the transition strength is concentrated. These findings occur in other nuclei as well and suggest that measurements of $0^+$ DCERs could provide useful information regarding the $ 0 u $ DBD. An analogous comparison and conclusion cannot be made for the $2^+$ states, since the $0 u$ NMEs and RMEs transition operators are not similar to each other in this case.
The precision of double-beta ($betabeta$) decay experimental half-lives and their uncertainties is reevaluated. A complementary analysis of the decay uncertainties indicates deficiencies due to small size of statistical samples, and incomplete collection of experimental information. Further experimental and theoretical efforts would lead toward more precise values of $betabeta$-decay half-lives and nuclear matrix elements.
Precise measurement of $gamma$-rays following ordinary (non-radiative) capture of negative muons by natural Se, Kr, Cd and Sm, as well as isotopically enriched $^{48}$Ti, $^{76}$Se, $^{82}$Kr, $^{106}$Cd and $^{150}$Sm targets was performed by means of HPGe detectors. Energy and time distributions were investigated and total life time of negative muon in different isotopes was deduced. Detailed analysis of $gamma$-lines intensity allows to extract relative yield of several daughter nuclei and partial rates of ($mu$,$ u$) capture to numerous excited levels of the $^{48}$Sc, $^{76}$As, $^{82}$Br, $^{106}$Ag and $^{150}$Tc isotopes which are considered to be virtual states of an intermediate odd-odd nucleus in 2$beta$-decay of $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{106}$Cd and $^{150}$Nd, respectively. These rates are important as an experimental input for the theoretical calculation of the nuclear matrix elements of 2$beta$-decay.
By using the finite temperature quantum field theory, we calculate the finite temperature effective potential and extend the improved quark mass density-dependent model to finite temperature. It is shown that this model can not only describe the saturation properties of nuclear matter, but also explain the quark deconfinement phase transition successfully. The critical temperature is given and the effect of $omega$- meson is addressed.
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