The non-parametric bootstrap method is used to evaluate the uncertainties of two $α$ decay formulas, the universal decay law (UDL) and the new Geiger-Nuttall law (NGNL). Such a method can simultaneously obtain the uncertainty of each parameter, the correlation between each pair of parameters, and the total, statistical, and systematic uncertainties of each formula. Both even-even (ee) nuclei and odd-A (oA) nuclei are used in the analysis. The collected data are separated into three parts: ee nuclei, oA nuclei without spin or parity change (oA\_nc), and oA nuclei with spin and/or parity change (oA\_c). Based on the residues between observed data and corresponding calculations, the statistical and systematic uncertainties are decomposed from the total uncertainty, from which one can clarify the effects from the shell structure, pairing, and angular momentum change on describing $α$ decay half-life. If $N > 126$ and $N \leqslant 126$ nuclei are considered together, the systematic uncertainty of residues between observed and predicted half-lives are larger than if those groups are considered separately. Without shell correction term, a much larger systematic uncertainty is found if parameters obtained for $N \leqslant 126$ nuclei are used to describe the half-lives of $N > 126$ nuclei. A global hindrance on the $α$ decay process is found in oA\_nc (oA\_c) nuclei comparing with ee (oA\_nc) nuclei. If parameters obtained from ee (oA\_nc) nuclei are used, the half-lives of oA\_nc (oA\_c) nuclei are generally underestimated with large systematic uncertainties, which can be related to the contribution of pairing effect and angular momentum. The recently observed superallowed decay from $^{104}$Te to $^{100}$Sn is also discussed based on uncertainty analysis. (Abstract is not fully presented because of length limitation)
We apply the shell-model wave-functions of $^{76}Ge$ to calculate the nuclear matrix elements and the half-life of the $2νββ$ decay in $^{76}Ge$. Our result is comparable to the recent observed $2νββ$-decay half-life of $^{76}Ge$. Furthemore it provides the upper limit of the effective neutrino mass is about 0.4 eV from the recent experimental data of the $0νββ$-decay half-life.
Recommended 2 $β$ (2 $ν$) half-life values and their systematics were analyzed in the frame- work of a simple empirical approach. T$^{2 ν}$$_{1/2}$ ~ 1/E$^{8}$ trend has been observed for $^{128,130}$Te recommended values. This trend was used to predict T$^{2 ν}$$_{1/2}$ for all isotopes of interest. Current results were compared with other theoretical and experimental works.
We have developed a Mathematica program which uses three-dimensional, isotropic harmonic oscillator wavefunctions for the solutions interior to the nucleus, and Coulomb wavefunctions for the exterior. The algorithm enables us to calculate the half life for alpha decay for alpha decay for varying depths of the nuclear potential well.
A complete calculation of phase space factors (PSF) for Majoron emitting $0νβ^-β^-$ decay modes is presented. The calculation makes use of exact Dirac wave functions with finite nuclear size and electron screening and includes life-times, single electron spectra, summed electron spectra, and angular electron correlations. Combining these results with recent interacting boson nuclear matrix elements (NME) we make half-life predictions for the the ordinary Majoron decay (spectral index $n$=1). Furthermore, comparing theoretical predictions with the obtained experimental lower bounds for this dec…
Nuclear radial distance is a prerequisite for generating any alpha-decay half-life formula by taking a suitable effective potential. We study the emission process of alpha particles from an isolated quasi-bound state generated by an effective potential to a scattering state. The effective potential is expressed in terms of Frahn form of potential which is exactly solvable and an analytical expression for half-life is obtained in terms of Coulomb function, wave function and the potential. We then derive a closed form expression for the decay half-life in terms of the parameters of the potential…
An investigation of the calculated $α$ decay half-lives of super heavy nuclei (SHN) reveals that the diffuseness parameter is a great bottleneck for achieving accurate results and predictions. In particular, when universal proximity function is adopted for nuclear potential, half-life is found to vary significantly and nonlinearly as a function of diffuseness parameter. To overcome this limiting hurdle, a new semiempirical formula for diffuseness that is dependent on charge and neutron numbers is proposed in this work. With the model at hand, half-lives of 218 SHN are computed, for 68 of which…
Spontaneous fission and alpha decay are the main decay modes for superheavy nuclei. The superheavy nuclei which have small alpha decay half-life compared to spontaneous fission half-life will survive fission and can be detected in the laboratory through alpha decay. We have studied the alpha decay half-life and spontaneous half-life of some superheavy elements in the atomic range Z = 100-130. Spontaneous fission half-lives of superheavy nuclei have been calculated using the phenomenological formula and the alpha decay half-lives using Viola-Seaborg-Sobiczewski formula (Sobiczewski et al. 1989)…
Some time ago the possibility of classical (without Gamow tunneling) universal description of radioactive nuclei decay was demonstrated. Such possibility is basis on the classical interpretation of Bohmian Psi-field reality in Bohmian-Chetaev mechanics and the hypothesis for the presence of dissipative forces, generated from the Gryzinski translational precession of the charged particles spin, in Langevin- Kramers diffusion mechanism. In this paper is present an unified model of proton, alpha decay, cluster radioactivity and spontaneous fission half-life as explicit function which depends on t…
The results by A.S. Barabash [Phys. Rev. {\bf C 81}, 035501 (2010)] are shown to be incomplete. Tellurium data sets were reanalyzed using the best practices of ENSDF evaluations. Present analysis indicates much higher value for the 2$ν$-mode half-life time in $^{128}$Te and the corresponding ratio of $^{128,130}$Te half-lives. These values imply the $T^{2 ν}_{1/2}$ $\sim$ $\frac{1}{E^{8}}$ $ββ$-decay transition energy trend that is consistent with the two-nucleon mechanism of $ββ$(2$ν$)-decay.
In this work, we expand upon our previous study, the effect of surface vibrations (low-lying vibrational states) on the calculation of penetration probability in alpha decay of spherical isotopes [Phys.Rev.C91,034611(2015)]. To this aim, the Coulomb and proximity potential model, taking in to account the ground state deformations of the involved nuclei along with the surface vibrations in the daughter nucleus, is used to evaluate the alpha decay probability. The results are compared with those obtained by spherical potential barrier, which shows the dramatic effect of employing the ground stat…
We develop a versatile and analytically solvable potential which fairly reproduces the combined potential of an $α+$nucleus system resulting from both the attractive nuclear and repulsive electrostatic potentials. The potential is expressed in terms of the radial position, mass and proton number of the $α$-particle and the daughter nucleus and certain parameters governing the depth, height and steepness of the barrier. The potential generated is typically a pocket near the origin and a barrier adjacent to it. The Schrödinger equation with the above mentioned potential is then solved for the wa…
A search for excited state transitions of double beta decay in Pd110 and double electron capture in Pd102 has been performed in the HADES underground laboratory with two low background HPGe detectors in sandwich configuration. After an exposure of 35.92 kg*d, no signal was found. The frequentist spectral analysis resulted in lower half-life limits of 1.98e20 yr and 1.72e20 yr (95% CL) for the first 0+ and 2+ excited state in Pd110 respectively. This is an improvement by more than a factor of 3 with respect to previous measurements. In Pd102, the lower half-life limit could be improved to 5.95e…
Using the finite temperature quasi-particle random phase approximation (FTQRPA) on the basis of finite temperature Skyrme-Hartree-Fock + BCS method, we study $β^-$-decay half-lives for even-even neutron magic nuclei with N=82 in a finite temperature environment. We find that the $β^-$-decay half-life first decreases as the temperature increases for all the nuclei we study, although the thermal effect is found to be small at temperatures relevant to r-process nucleosynthesis. Our calculations indicate that the half-life begins to increase at high temperatures for open shell nuclei. We discuss t…
In the present work, we systematically study the proton radioactivity half-lives of 33 spherical nuclei based on the relationship between the Skyrme parameters and the macroscopic quantities of nuclear matter. Using the two-potential approach with the spherical Skyrme-Hartree-Fock model, the correlation between proton radioactivity half-life and macroscopic quantities was analyzed. Moreover, we obtained a new Skyrme parameter set by fitting the two most weighted macroscopic quantities. Compared with Skyrme parameters MSL0 and the theoretical model of proton radioactivity UDLP, the theoretical …
Half-life number sequences collected from nuclear data charts are found to obey the Newcomb-Benford law. Based on this fact, it has been suggested recently, that this law should be used to test the quality of nuclear decay models. In this paper we briefly recall how, when and why the Newcomb-Benford law can be observed in a set of numbers with a given probability distribution. We investigate the special case of nuclear half-lives, and show that the law provides no additional clue in understanding decay half-lives. Thus, it can play no significant role in testing nuclear decay theories.
A sensitive search of the 4-fold forbidden non-unique beta decay of V-50 has been performed. A total exposure of 185.8 kg x d has been accumulated. A reliable half-life value with the highest precision so far of $(2.29 \pm 0.25) \cdot 10^{17}$ years of the electron capture decay of V-50 into the first excited state of Ti-50 could be obtained. A photon emission line following the 4-fold forbidden beta decay into the first excited state of Cr-50 could not be observed, resulting in a lower limit on the half-life of the beta decay branch of $1.7 \cdot 10^{18}$ years. This is barely in agreement wi…
Experimental $α$-decay half-life, spin, and parity of 398 nuclei in the range 50$\leq$Z$\leq$118 are utilized to propose a new formula (QF) with only 4 coefficients as well as to modify the Tagepera-Nurmia formula with just 3 coefficients (MTNF) by employing nonlinear regressions. These formulas, based on reduced mass ($μ$) and angular momentum taken away by the $α$-particle, are ascertained very effective for both favoured and unfavoured $α$-decay in addition to their excellent match with all (Z, N) combinations of experimental $α$-decay half-lives. After comparing with similar other empirica…
We present a formalism to describe proton emission from odd-odd nuclei based on a scattering like approach. Special emphasis is given to the case of transitions between states with different deformations. As an example we estimate the proton half-life of the odd-odd nucleus $^{58}$Cu. Our calculations show that the change of deformation in the decay process has a significant influence on the half-life. In addition, the angular momentum coupling of proton and neutron orbitals can result in an important $K$-hindrance of the decay. To fully account for the observed half-life in $^{58}$Cu, one has…
The Oklo data constrain the depth of the nuclear potential well to a small margin of error, determined by various unknowns, such as the reactor temperature. However, we show that even these small variations could allow the U-238 half-life to vary by more than one order of magnitude.
The lifetimes of $α$ decays of the recently produced isotopes of the elements 112, 114, 116 and the element $^{294}118$ and of some decay products have been calculated theoretically within the WKB approximation using microscopic $α$-nucleus interaction potentials. These nuclear potentials have been obtained by folding the densities of the $α$ and the daughter nuclei with the M3Y effective interaction, supplemented by a zero-range pseudo-potential for exchange along with the density dependence. Spherical charge distributions have been used for calculating the Coulomb interaction potentials. The…
Half life values for $α$-decay in the mass region $A=150-200$ have been calculated in the Microscopic Super Asymmetric Fission Model. The interaction between the $α$-particle and the daughter nucleus has been obtained in the double folding model with the microscopic interaction DDM3Y1. Theoretical densities for the nuclei involved have been calculated in Relativistic Mean Field approach with the Lagrangian density FSU Gold. Spectroscopic factors for $α$-decay, calculated as the ratios of the theoretically calculated and experimentally measured half life values, show a simple dependence on the …
We analyze the $^{134}_{55}$Cs$\rightarrow^{134}_{56}$Ba and $^{135}_{55}$Cs$\rightarrow^{135}_{56}$Ba $β^-$ decays, which are crucial production channels for Ba isotopes in Asymptotic Giant Branch (AGB) stars. We reckon, from relativistic quantum mechanis, the effects of multichannel scattering onto weak decays, including nuclear and electronic excited states (ES) populated above $\simeq$ 10 keV, for both parent and daughter nuclei. We find increases in the half-lives for $T>10^8$ K (by more than a factor 3 for $^{134}$Cs) as compared to previous works based on systematics. We also discuss ou…
Half-life of $^{136}$Xe for neutrinoless double-$β$ decay calculated with effective axial-vector current coupling unified for two-neurtino and neutrinoless double-$β$ decay modes
Neutrinoless double-beta decay represents the most promising approach for revealing some of the most important, yet-unknown, properties of neutrinos related to their absolute masses and their nature. This transition involves beyond standard model theories that predict the violation of the lepton number conservation by two units. There is no experimental confirmation yet for this decay, but new experiments have set lower-limits for the associated half-lives in the case of several isotopes. Using an effective field theory that describes this transition, we calculate half-life ratios for five exp…
The results of experimental studies of the low-energy isomeric state in the $^{229}$Th nucleus are presented. The work is consisted of several stages. During the first stage $^{229}$Th nuclei were excited with the inverse internal conversion to the low-lying isomeric level in plasma that was formed by laser pulse at the $^{229}$Th-containing target surface. Then thorium ions having excited nuclei were extracted from the plasma by an external electrical field and implanted into thin SiO$_2$ film grown on a silicon substrate (that is a dielectric material with about 9 eV band-gap). Gamma decay o…
