Theoretical analysis of the possible ultra-low-Q-value decay branch of Cs

We have investigated the feasibility of observing an ultra-low-Q-value beta-decay branch of ¹³⁵Cs by applying the microscopic quasiparticle-phonon model with a realistic two-body nuclear interaction. This work was motivated by an earlier combined experimental and theoretical work on decays of ¹¹⁵In. The inaccuracy of the ground-state-to-ground-state Q value limits our ability to draw definite conclusions, and therefore modern precision measurements for it are called for. We present the computed partial half-lives of each channel for the most likely ranges of Q values.     

Systematic calculations of cluster radioactivity half-lives in trans-lead nuclei

In the present work, based on the Wentzel-Kramers-Brillouin (WKB) theory, considering the cluster preformation probability (\begin{document}$ P_{c} $\end{document}), we systematically investigate the cluster radioactivity half-lives of 22 trans-lead nuclei ranging from ²²¹Fr to ²⁴²Cm. When the mass number of the emitted cluster \begin{document}$ A_{c} $\end{document} \begin{document}$ < $\end{document} 28, \begin{document}$P_{c} $\end{document} is obtained by the exponential relationship of \begin{document}$ P_{c} $\end{document} to the α decay preformation probability (\begin{document}$ P_{\alpha} $\end{document}) proposed by R. Blendowskeis \begin{document}$ et $\end{document} \begin{document}$ al. $\end{document} [Phys. Rev. Lett. 61, 1930 (1988)], while \begin{document}$ P_{\alpha} $\end{document} is calculated through the cluster-formation model (CFM). When \begin{document}$ A_{c} $\end{document} \begin{document}$ \ge $\end{document} 28, \begin{document}$ P_{c} $\end{document} is calculated through the charge-number dependence of \begin{document}$ P_{c} $\end{document} on the decay products proposed by Ren \begin{document}$ et $\end{document} \begin{document}$ al. $\end{document} [Phys. Rev. C 70, 034304 (2004)]. The half-lives of cluster radioactivity have been calculated by the density-dependent cluster model [Phys. Rev. C 70, 034304 (2004)] and by the unified formula of half-lives for alpha decay and cluster radioactivity [Phys. Rev. C 78, 044310 (2008)]. For comparison, a universal decay law (UDL) proposed by Qi \begin{document}$ et $\end{document} \begin{document}$ al. $\end{document} [Phys. Rev. C 80, 044326 (2009)], a semi-empirical model for both α decay and cluster radioactivity proposed by Santhosh [J. Phys. G: Nucl. Part. Phys. 35, 085102 (2008)], and a unified formula of half-lives for alpha decay and cluster radioactivity [Phys. Rev. C 78, 044310 (2008)] are also used. The calculated results of our work, Ni's formula , and the UDL can well reproduce the experimental data and are better than those of Santhosh's model. In addition, we extend this model to predict the half-lives for 51 nuclei, whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020.     

Benford＇s Law and β-Decay Half-Lives

The experimental values of 2059 β-decay half-lives are systematically analyzed and investigated. We have found that they are in satisfactory agreement with Benford＇s law, which states that the frequency of occurrence of each figure, 1-9, as the first significant digit in a surprisingly large number of different data sets follows a logarithmic distribution favoring the smaller ones. Benford＇s logarithmic distribution of β-deeay half-lives can be explained in terms of Neweomb＇s justification of Benford＇s law and empirical exponential law of β-decay half-lives. Moreover, we test the calculated values of 6721 β-decay half-lives with the aid of Benford＇s law. This indicates that Benford＇s law is useful for theoretical physicists to test their methods for calculating β-decay half-lives.     

Average and recommended half-life values for two-neutrino double-beta decay: Upgrade ’05

All existing “positive” results on two-neutrino double-beta decay in different nuclei were analyzed. Using the procedure recommended by the Particle Data Group, weighted average values for half-lives of ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ⁹⁶Zr, ¹⁰⁰Mo, ¹⁰⁰Mo−¹⁰⁰Ru(0 ₁ ⁺ ), ¹¹⁶Cd, ¹⁵⁰Nd, ¹⁵⁰Nd− ¹⁵⁰Sm(0 ₁ ⁺ ) and ²³⁸U were obtained. Existing geochemical data were analyzed and recommended values for half-lives of ¹²⁸Te, ¹³⁰Te, and ¹³⁰Ba are proposed. We recommend the use of these results as presently the most precise and reliable values for half-lives. Presented by A.S. Barabash at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

β~--Decay Half-Lives for Waiting Point Nuclei Around N=126

We have systematically analyzed the experimental β--decay half-lives of waiting point heavy nuclei around neutron number N = 126. A new set of parameters for the exponential formula of β~--decay half-lives is proposed. The forbidden transition effects are included in the new set of parameters self-consistently. Theoretical β~--decay half-lives of nuclei around N = 126 are compared with recent theoretical results and experimental data. It is found that the new theoretical results are in better agreement with experimental data. The unknown β~--decay half-lives of some nuclei in this region are predicted for studies on nuclear structure far from stability and the nucleosynthesis in stars.     

α-decay half-lives of superheavy nuclei and general predictions

The generalized liquid drop model (GLDM) and the cluster model have been employed to calculate the α-decay half-lives of superheavy nuclei (SHN) using the experimental α-decay Q values. The results of the cluster model are slightly poorer than those from the GLDM if experimental Q values are used. The prediction powers of these two models with theoretical Q values from Audi et al. (Qaudi) and Muntian et al. (QM) have been tested to find that the cluster model with Qaudi and QM could provide reliable results for Z>112 but the GLDM with Qaudi for Z≤112. The half-lives of some still unknown nuclei are predicted by these two models and these results may be useful for future experimental assignment and identification.     

A plunger set-up for measuring picosecond nuclear half-lives

A plunger set-up has been designed and constructed to measure picosecond nuclear half-lives using recoil distance method (RDM). The system has been used to measure the half-lives of nuclear states in³⁵Cl,^37,38Ar and⁴⁰K. The shortest half-life measured with the system isT _1/2=0.36(14) ps for the 4366 keV (8⁺) state and the longest half-life isT _1/2=1.10(7) ns for the 2543 keV (7⁺) state in⁴⁰K.     

Applicability of the Group Method for Analyzing Decay Curves

A formerly proposed method for analyzing experimental decay curves was tested to estimate its applicability depending on the following conditions: ratio of half-lives, time elapsing from measuring the first point to measuring the last one, number of points measured, portions of individual activities, and way of performing preliminary analysis for chosing the groups of experimental points.     

Surface geometry and shadow of a Schwarzschild black hole with a halo

We studied the surface geometry and shadows of a Schwarzschild black hole with a halo containing quadrupolar and octopolar terms. It was found that the quadrupole term causes a Schwarzschild black hole to be prolate at the quadrupole strength \begin{document}$ {\cal{Q}}<0 $\end{document} and oblate at \begin{document}$ {\cal{Q}}>0 $\end{document}, and the octopole term causes to the shadow stretch upward at the octopolar strength ngth \begin{document}$ {\cal{O}}<0 $\end{document} and downward at \begin{document}$ {\cal{O}}>0 $\end{document}. The shadow of a Schwarzschild black hole with a halo stretches and squeezes along the horizontal direction at \begin{document}$ {\cal{Q}}<0 $\end{document} and \begin{document}$ {\cal{Q}}>0 $\end{document}, respectively. Meanwhile, the black hole shadow shifts upward at \begin{document}$ {\cal{O}}<0 $\end{document} and downward at \begin{document}$ {\cal{O}}>0 $\end{document}. We present the light rays that form the shadow boundary to explain the emergence of the extraordinary patterns of the black hole shadow with quadrupole and octopole terms. From the observable width W, height H, oblateness K, and distortion parameter \begin{document}$ \delta_{c} $\end{document} of the black hole shadow, we can determine the quadrupole and octopolar strengths of a Schwarzschild black hole with a halo. Our results show that the quadrupolar and octopolar terms yield a series of interesting patterns for the shadow of a Schwarzschild black hole with a halo.