Geiger-Nuttall Research Articles

Critical Examination of Gamow's Theory of Alpha Particle Decay

Gamow’s Theory of Alpha Particle Decay was initially formulated for a limited set of nuclei. In this study, the researchers extend the scope and assessed the applicability of the theory to a broader range of nuclides especially those with different proton and neutron compositions. Three objectives were formulated to undertake the research. The researcher utilized one-dimensional WKB approximation to calculate the probability of tunneling through the potential barrier, which is a simplification compared to other formulas. The Geiger-Nuttall law, which describes a dependence of the disintegration constant on the range of α-particles, was deduced using the Gamow theory describing the passage of the α-particles through the Coulomb barrier by the quantum mechanical tunneling effect. Ground-to-ground state α-transitions for α-active nuclides were analyzed based on their half-lives and their dependence on various factors. The study revealed that all α-active nuclides whose Z ranges between 70 to100 undergoes similar alpha decay processes.

Theoretical calculations of proton emission half-lives based on a deformed Gamow-like model* *Supported in part by the National Natural Science Foundation of China (12175100, 11975132), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of Hunan Province, China (21B0402, 18A237), the Natural Science Foundation of Hunan Province, China (2018JJ2321), the Innovation Group of

In this study, proton emission half-lives were investigated for deformed proton emitters with based on the presented deformed Gamow-like model, where the deformation effect was included in the Coulomb potential. The experimental half-lives of proton emitters can be reproduced within a factor of 3.45. For comparison, the results from the universal decay law and the new Geiger-Nuttall law are also presented. Furthermore, the relevance of the half-lives to the angular momentum l for 117La, 121Pr, 135Tb, and 141Ho were analyzed, and the corresponding possible values of l were proposed: l = 3, 3, 4, 4.

Nearly Symmetric, Asymmetric, Very Asymmetric, and Super Asymmetric Fission Half-Lives of Heavy and Superheavy Elements Using a Modified Geiger-Nuttall Law

Nearly Symmetric, Asymmetric, Very Asymmetric, and Super Asymmetric Fission Half-Lives of Heavy and Superheavy Elements Using a Modified Geiger-Nuttall Law

α decay half-lives of nuclei W, Re, Os, Ir and Pt in the range 157≤A≤193 using the modified generalised liquid drop model (MGLDM)

The α-decay half-lives for the isotopes of nuclei W, Re, Os, Ir and Pt in the range have been studied by using the Modified Generalised Liquid Drop Model (MGLDM). The half-lives predicted for some even–even nuclei by using the deformed Two Potential Approach (TPA) [Comm. Theo. Phys. 74, 055301 (2022)] are considered and included for the comparison. Additionally, we have analysed the α-decay half-lives using eight ℓ-dependent empirical formulae, and compared the results with the experimental data. The standard deviation and the average deviation for by using MGLDM is obtained as 0.6025 and 0.5403, respectively. Also, the results of MGLDM match well with predictions of TPA, with standard deviation of 0.47 and 0.44 respectively. A dip in the half-life curve or a peak in the decay energy curve at 82, a magic neutron number of the daughter nuclei of increases the viability of the calculations. Also, the linear nature of Geiger-Nuttall law, Universal law, the relation connecting and and the New Geiger-Nuttall law helps to calculate the half-lives of newly synthesized and unknown isotopes, making MGLDM more reliable.

An empirical formula for the two-proton decay half-lives in the ground and excited states

We proposed an empirical formula for the half-life of two proton emissions in the ground and excited states. The proposed empirical formula has a half-life dependence on the Q-value and the atomic number of the parent, similar to the Geiger-Nuttall law and the Viola and Seaborg formula. The half-lives of 6Be, 12O, 16Ne, 19Mg, 45Fe, 48Ni, 54Zn, and 67Kr nuclei are calculated using the present empirical formula. The empirical formula has the lowest standard deviation with experimental data (σ=1.39) compared to previously predicted formulas, indicating that the formula can reproduce the experimental half-lives well. The predictions of the half-lives are made for another 56 nuclei whose two-proton emission is energetically feasible (Q2P>0). These half-life values are compared with five theoretical models and two empirical formulas. The predicted half-lives are in good agreement with other theoretical predictions. The predicted half-lives of two-proton emission in the excited states of 14O⁎, 17,18Ne⁎, 22Mg⁎, 29S⁎, and 94Ag⁎ nuclei are compared with the experimental half-lives and also with different models' and formulas' predictions. The experimentally observed half-lives of the excited states are better reproduced using the proposed formula compared with previous theoretical predictions. Only the proposed formula can reproduce the experimental half-lives of 94Ag⁎ in excited states.

Half-lives for proton emission and α decay within the deformed Gamow-like model

In this work, α decay and proton emission half-lives are studied by the deformed Gamow-like model, which introduces the effects of nucleus deformation. The calculations show that it is necessary to consider the deformation in the calculation for nuclei far from the shell. Moreover, this model is used to predict the proton emission half-lives of the nuclei far from the shell more accurately. The calculations indicate that our deformed model follows the Geiger-Nuttall law. Furthermore, the deformed Gamow-like model is used to study the shell structure, and we find that the number of the next neutron shell is likely to be 152. This work may benefit future research on the search for superheavy nuclei and new proton radionuclides.

Quest for a universal cluster preformation formula: A new paradigm for estimating the cluster formation energy

This study presents a holistic picture of the preformation of nuclear clusters with credence to the kinematics of their emissions. Besides the fitting of the preformation formula to reproduce the experimental half-lives, we have investigated the interrelationship between the parameters involved in the cluster decay process for medium, heavy and superheavy nuclei. Based on the established conceptual findings, we propose a new cluster preformation probability (P 0) formula that incorporates all influential parameters of the cluster radioactivity and thus has an edge over the existing formulae in the literature. Further, we hypothesize that a fraction of the decay energy is needed for cluster formation within the parent nucleus. The proposed formula opens a new paradigm to separately estimate the energy contributed during the cluster formation from its emission and thus shows that the contribution of the Q-value splits into three major parts accounting for the energy contributed during the cluster preformation, its emission and recoil of the daughter nucleus. Moreover, the expression P 0 is adept at accommodating the theorized concept of heavy particle radioactivity (HPR). The result reveals that, like α-decay, a proper estimation of the P 0- and Q-value in the cluster studies is enriched with qualitative information about the nuclear structure. However, from the analysis, the Geiger-Nuttall law is not the best compromise in the clustering due to the non-linearity between log10 T 1/2 and , unlike in α-decay. We have demonstrated that with the inclusion of the proposed formula, the half-life predictions from both microscopic R3Y and phenomenological M3Y NN potentials closely agree with the available experimental data and that the slight variation can be traced to their peculiar barrier characteristics.

An empirical formula for the alpha decay half-lives

Using 377 available experimental data, we have obtained an empirical formula to calculate alpha decay half-lives based on Geiger–Nuttall law for even–even, even–odd, odd–even and odd–odd nuclei. The coefficients of Geiger–Nuttall law have been modified as a function of the atomic number of the parent nucleus and the orbital angular momentum. The obtained root mean square deviations from experimental half-lives for even–even, even–odd, odd–even and odd–odd nuclei are 0.3265, 0.5412, 0.4848 and 0.4353, respectively. For most nuclei, the obtained results from this formula are in good agreement with the experimental data. We compared our results with other formulas such as universal decay law, Royer, AKRA, MYQZR and Luo. Also, using this formula, we presented predictions for superheavy nuclei with [Formula: see text]–124 using the [Formula: see text]-values based on the finite range droplet model and Weizsäcker–Skyrme. It is found that the behavior of the half-life of alpha decay is sensitive to the used [Formula: see text]-values.

New Geiger-Nuttall law for cluster radioactivity half-lives* *Supported in part by the National Natural Science Foundation of China (12175100, 11975132), the construct program of the key discipline in hunan province, the Research Foundation of Education Bureau of Hunan Province, China (18A237), the Shandong Province Natural Science Foundation, China (ZR2022JQ04), the Opening Project of Cooperative Innovation Center for Nuclear Fuel Cycle

In this study, derived from Balasubramaniam's formula [Phys. Rev. C 70, 017301 (2004)] and further considering the effect of the parent nucleus mass, blocking effect, and effect of reduced mass on cluster radioactivity half-lives, we propose a new Geiger-Nuttall law that is model-independent to systematically evaluate the half-lives of this process for 16 even-even nuclei and 10 odd-A nuclei. For comparison, a single universal curve for cluster radioactivity and α decay proposed by Poenaru [Phys. Rev. C 83, 014601 (2011)], a scaling law proposed by Horoi [J. Phys. G: Nucl. Part. Phys. 30, 945 (2004)], an extension of the Viola-Seaborg formula from α decay to cluster radioactivity proposed by Ren et al. [Phys. Rev. C 70, 034304 (2004)], a new semi-empirical formula for exotic cluster decay proposed by Balasubramaniam et al. [Phys. Rev. C 70, 017301 (2004)], and a unified formula for the half-lives of α decay and cluster radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)] are also used. The calculated results of our new Geiger-Nuttall law are in good agreement with the experimental half-lives, with the least rms being 0.606, and are better than the compared values. Moreover, we extend this formula to predict the cluster radioactivity half-lives of 51 nuclei whose decay energies are energetically allowed or observed but not yet quantified in NUBASE2020.

Improved Geiger–Nuttall law for $$\alpha $$-decay half-lives of heavy and superheavy nuclei

Improved Geiger–Nuttall law for $$\alpha $$-decay half-lives of heavy and superheavy nuclei

Systematics of alpha-active nuclides and on the validity of the Geiger-Nuttall law

Geiger-Nuttall law, which describes a dependence of the disintegration constant on the range of α-particles, was deduced using the Gamow theory describing the passage of the α-particles through the Coulomb barrier by the quantum mechanical tunneling effect. Ground-to-ground state α-transitions for natural and artificial α-active nuclides were analyzed utilizing the Geiger-Nuttall rule. From rough analysis five group-like branches on the dependence of α-decay half-lives on α-particle energy was observed. Detailed analysis shows that precise linear dependence of the logarithm of α-decay half-lives on the reciprocal of square root ofthe α-particle energy for even-even isotopes of the U, Pu and Cm there are. However, for some even-even isotopes of the Po, Ra and Th regular behaviour of mass numbers was broken. This non-regularity of the mass numbers on the Geiger-Nuttall line is explained by the nuclear shell model.

Short History of Nuclear Decays Including Nuclear Fission

A short history of the different kinds of nuclear decay modes (α decay, β decay, γ decay, induced fission, spontaneous fission, ternary and multi-cluster fission, fissioning shape isomers, and cluster radioactivities) is presented below, showing how the important research activities at the end of 19th century and the beginning of the 20th one, lead to the discovery of atomic nucleus by Ernest Rutherford in 1911. We shall start with X-rays—a precursor of all these phenomena. The first observation of alpha-, beta-, and gamma radiations was made by Antoine Henri Becquerel in 1896, who observed that beta-rays are deviated by a magnetic field. Marie and Pierre Curie coined the name radioactivity after they produced two new elements: polonium and radium. Alpha particles were first described in the investigations of radioactivity by Ernest Rutherford in 1899, and by 1907 they were identified as He2+ ions. In 1928, George Gamow had solved the theory of alpha decay via tunneling through a potential barrier. The alpha particle is trapped in a potential well by the nucleus. According to the principles of quantum mechanics, it has a small probability of tunneling through the barrier and escape from the nucleus. Gamow solved a model potential for the nucleus and derived, from first principles, a relationship between the half-life of the decay, and the energy of the emission, which had been previously discovered empirically, and was known as the Geiger-Nuttall law.

Correlation between α-particle preformation factor and α decay energy

α-particle preformation factors, one of the most significant quantities in α decay, are systematically investigated, which are extracted from the ratios between theoretical α-decay half-lives calculated by the generalized liquid drop model and experimental data. The results indicate that both α-particle preformation factors Pα and α decay energy Qα are important observed quantities for revealing the nuclear shell structure information. And a nice linear relationship exists between log10⁡Pα and Qα−1/2, which means the famous Geiger-Nuttall law can not only describe α decay half-lives but deal with α-particle preformation factors, as well as the nuclear shell effects play key roles in α-particle preformation. Furthermore, the results indicate that Z=82 and N=126 closed shells play more important roles than Z=50 and N=82 shell closures in which the shell effect of N=126 is stronger than that of Z=82 in the α decay process. Besides, the unpaired nucleons will inhibit the preformation of α-particle. After considering the above significant physical effects, a global analytic formula with only twelve parameters for α-particle preformation factors is proposed based on the direct observation quantity of the nuclear shell effect i.e., α decay energy. The outstanding precision of this formula in describing the α-particle preformation factors indicates that it can be used to perform accurate calculations for α decay half-lives as well as provide some general guidance for microscopic study on α-particle preformation factors and nuclear structure.

Systematic study on $$\alpha $$-decay half-lives: a new dependency of effective sharp radius on $$\alpha $$-decay energy

Within the framework of the proximity formalism, we present a systematic study to analyze the effects of the $$\alpha $$ -decay energy through the effective sharp radius parameter on the $$\alpha $$ -decay half-lives of 227 nuclei in the range $$61 \le Z \le 99$$ . Wentzel-Kramers-Brillouin (WKB) calculations with the proximity potential Zhang 2013 are carried out to obtain the theoretical values of the $$\alpha $$ -decay half-lives. In this work, we introduce a new $$Q_{\alpha }$$ -dependent (QD) form of the effective sharp radius which significantly reduces the standard deviation of estimated half-lives using the Zhang 2013 model in comparison with the corresponding experimental data in our selected mass range. We evaluate the validity of this simple formula using the Geiger-Nuttall (G-N) plots and semi-empirical formulas. The modified form of the Zhang 2013 model is also found to work well in $$\alpha $$ -decay studies of superheavy nuclei (SHN) with $$Z=117-120$$ . Our results reveal that the calculated half-lives for the use of new proposed form of the effective sharp radius in the proximity potential can reproduce the closed-shell effects at neutron magic number $$N=126$$ and $$N=184$$ .

Limitations of the Geiger-Nuttall law in heavy cluster decay

Geiger-Nuttall law is the simplest relation in radioactive decay relating the half-life and the decay energy. Initially restricted to $\ensuremath{\alpha}$ decay of individual isotopes, generalizations unifying different isotopes and decay modes under a single set of constant coefficients were subsequently achieved. This motivates investigating to what extent such generalizations are possible. We also examine whether there exists a universal Geiger-Nuttall law that can simultaneously describe all decay modes and nuclei including heavy clusters. We show that the validity of Geiger-Nuttall law and its generalizations hinges on the assumption that half-life can be approximated linearly as a function of the square root of the ratio of the decay energy to the Coulomb barrier height. Systematic calculation of the ratio across the nuclear chart for 12 decay modes reveals that it varies over its whole range between 0 and 1. Consequently, no linear approximation can unify all the nuclei and decay modes under a single set of coefficients, and thus no universal Geiger-Nuttall law is possible in contrast to previous claims. In cluster decay, the ratio varies within 0.6--1 where nonlinearity becomes significant such that no generalized Geiger-Nuttall description of heavy clusters is possible. In the ongoing attempts of unification, it might be necessary to go beyond the Geiger-Nuttall law and incorporate additional terms proportional to the decay energy and/or its square root.

New Geiger-Nuttall law for two-proton radioactivity * *Supported in part by the National Natural Science Foundation of China (11205083, 11505100, 11705055), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of Hunan Province, China (15A159, 18A237), the Natural Science Foundation of Hunan Province, China (2015JJ3103, 2015JJ2121, 2018JJ2321), the Innovation Group of Nuclear and

In the present work, a two-parameter empirical formula is proposed, based on the Geiger-Nuttall law, to study two-proton ( ) radioactivity. Using this formula, the calculated radioactivity half-lives are in good agreement with the experimental data as well as with calculated results obtained by Goncalves et al. [Phys. Lett. B 774, 14 (2017)] using the effective liquid drop model (ELDM), Sreeja et al. [Eur. Phys. J. A 55, 33 (2019)] using a four-parameter empirical formula, and Cui et al. [Phys. Rev. C 101: 014301 (2020)] using a generalized liquid drop model (GLDM). In addition, this two-parameter empirical formula is extended to predict the half-lives of 22 possible radioactivity candidates with radioactivity released energy , obtained from the latest evaluated atomic mass table AME2016. The predicted results are highly consistent with those obtained using other theoretical models such as the ELDM, GLDM and four-parameter empirical formula.

New look at Geiger-Nuttall law and α clustering of heavy nuclei * *Supported by the National Natural Science Foundation of China (12075121, 11605089, 11975167, 11535004, 11761161001), the Natural Science Foundation of Jiangsu Province (BK20150762, BK20190067), the National Major State Basic Research and Development Program of China (2016YFE0129300)

The Geiger-Nuttall (GN) law of α decay is commonly explained in terms of the quantum tunneling phenomenon. In this study, we show that such an explanation is actually not enough regarding the α particle clustering. Such a conclusion is drawn after exploring the involved coefficients of the GN law based on the conventional description of α decay, namely the formation of an α cluster and its subsequent penetration. The specific roles of the two former processes, in the GN law, manifest themselves via the systematical analysis of the calculated and experimental α decay half-lives versus the decay energies across the and shell closures. The α-cluster preformation probability is then found to behave in a GN-like pattern. This previously ignored point is explicitly demonstrated as the product of an interplay between the mean-field and pairing effect, which in turn reveals the structural influence on the formation of the α cluster in a simple and clear manner. In addition to providing an effective method to evaluate the amount of surface α clustering in heavy nuclei, the present conjecture supports other theoretical treatments of the α preformation probability.

Systematical Analysis of Alpha-active Nuclides

The systematical analysis of alpha-active nuclides is useful for both the nuclear technology applications and understanding of nuclear structure study. Geiger-Nuttall law, which describes a dependence of the disintegration constant on the range of α-particles, was deduced from the Gamow theory explaining the passage of the α-particles through the Coulomb barrier by the quantum mechanical tunneling effect. Ground-to-ground state α-transitions for natural and artificial α-active nuclides were analyzed utilizing the Geiger-Nuttall rule. From rough analysis five group-like branches on the dependence of α-decay half- lives on α-particle energy were observed. Detailed analysis shows that precise linear dependences of the logarithm of α-decay half-lives on the reciprocal of square root of the α- particle energy for even-even isotopes of the U, Pu and Cm there are. However, for some even-even isotopes of the Po, Ra and Th regular behaviour of mass numbers was broken. This non-regularity of the mass numbers on the Geiger-Nuttall line is explained by the nuclear shell model.

Proton Radioactivity of Heavy Nuclei of Atomic Number Range 72 < Z < 88

We have studied proton radioactivity of heavy nuclei of atomic number range 72 < Z < 88. We have calculated the energy released during the proton decay (QP) and half-lives of proton decay. To study the competition between different decay modes, we have compared the proton decay half lives with that of the decay modes such as alpha decay, beta decay, cluster decay and spontaneous fission. To check the Geiger–Nuttall law for proton decay, we have plotted the logarithmic proton decay half-lives versus 1/sqrt(Q). We have also highlighted possible proton emitters with the corresponding energies and half-lives in the atomic number range 72 < Z < 88.

A new formalism for the study of the surface tension coefficient of α-nuclei systems using the density-dependent nucleon-nucleon interactions

This study investigates the nuclear surface tension coefficient, γ, of the proximity formalism by using the microscopic double-folding (DF) model with the realistic density-dependent (DD) nucleon-nucleon interaction of the effective M3Y forces type (including DDM3Y1, CDM3Y4 and BDM3Y1) for the ground-state to ground-state α transition of 230 parent nuclei with Z = 61-99. In fact, the present work can be considered as an expansion of the previous study which has been performed by Gharaei and Mohammadi using CDM3Y6 version in 2019. Within the propsed approach, we have tried to present a new approach for the calculation of the surface energy coefficient, γ, in alpha-decay by integrating the proximity and DF potential models. In addition, we present a new dependency of the surface energy coefficient, γ, on the asymmetry parameter, , of the considered α-nuclei systems by fitting all of the calculated values. The obtained results suggest a new formalism for the coefficient γ that is dependent directly on the selection of the interaction type. We also test the validity of the suggested formula. To this aim, by using the the obtained formula of the coefficient γ in the original version of the proximity potentials, we calculate the theoretical values of the alpha-decay half-lives for different nuclei in the framework of the WKB approximation. The calculated results are compared with the corresponding experimental data and those obtained from the original proximity potential 1977. It is shown that the modified forms of the proximity potential model, labeled as Prox. New (DDM3Y1), Prox. New (CDM3Y4) and Prox. New (BDM3Y1), provide better descriptions of the experimental α-decay half-lives than the proximity potential 1977 (Prox. 77). Further, the best results are obtained using the Prox. New (CDM3Y4) potential model for our selected mass range. Using the modified forms of the proximity potential, we examined the closed-shell effects in nuclei and the validity of the Geiger-Nuttall law. Additionally, the results of the Prox. New (CDM3Y4) potential model are compared with the various empirical formulas for alpha decay half-lives. Ultimately, the prediction of alpha decay half lives is made for superheavy nuclei with Z=117-120.