Proton Radioactivity Half-lives Research Articles

Exploring the competition between α-decay and proton radioactivity: A comparative study of proximity potential formalisms

We have conducted a comprehensive and systematic study of the proton radioactivity and α-decay half-lives of neutron-deficient nuclei. This investigation involved the utilization of various Proximity potentials and also considered the incorporation of thermal effects. For the half-life calculations, we employed both temperature-independent and temperature-dependent interaction potentials. We observed that proton radioactivity serves as the dominant mode of decay for nuclides situated very close to the proton drip-line. We explored a universal curve that examines the correlation between the decimal logarithm of experimental half-lives and the negative decimal logarithm of the penetrability for both proton radioactivity and α-decay.

Description of temperature effects on proton radioactivity

Role of thermal effects of hot parent nuclei in the characteristics of proton emission process has been studied for the first time by analyzing the surface energy coefficient γ entering in the calculation of proximity potential for 15 experimentally detected proton emitters (67≤Z≤83) in the isomeric states. In the present work, the proton-nucleus interaction potentials are obtained by using one of the latest versions of proximity potential formalism proposed by Zhang et al. in 2013. In addition, the quantum mechanical tunneling probability and consequently the proton radioactivity half-lives are calculated within the framework of the semiclassical WKB method. We present a new temperature-dependent (TD) form of the coefficient γ based on thermal properties of hot proton emitters in the framework of the finite-temperature generalized liquid-drop model. By integrating temperature dependence into the surface energy coefficient of proximity potential Zhang 2013, a reasonable description of the experimental half-lives of proton radioactivity is achieved. We extend the modified form of the Zhang 2013 model to predict the proton radioactivity half-lives of 6 proton emitters in the isomeric states, whose proton radioactivity is energetically allowed or observed, but has not been quantified yet. The obtained results reveal that the predictions by our model are in good agreement with the other theoretical methods, namely UDLP proposed by Qi et al. (2012) [19] and NGNL proposed by Chen et al. (2019) [49]. In this work, we also attempt to introduce an empirical formula for estimating the half-lives of one-proton emission process from the excited states by taking into account both the thermal effects of all the available 15 hot proton emitters and the contribution of centrifugal potential. Our results indicate that the calculated proton radioactivity half-lives by the current formula are in good agreement with experimental data. This means that the correlation between the half-lives of proton decay processes and the nuclear temperature T of proton emitters can be suitable to deal with the proton radioactivity one-proton transition from isomeric states.

A systematic analysis for one proton radioactivity of ground state nuclei

We systematically studied proton radioactivity half-lives in the atomic number range 53≤Z≤83 using macroscopic models such as Coulomb and Proximity potential model, effective liquid drop model (ELDM), Generalized liquid drop model (GLDM), Universal decay law for proton emission (UDLP), Gammow-like model (GLM) and Unified fission model (UFM). The proton decay half-lives produced by the macroscopic models are compared with those of semi-microscopic approach such as DDM3Y and using effective interaction potentials such as JLM, M3Y+EX, R3Y+EX, SLy4, SRG, SKC and SKD. After detail analysis, it is found that among macroscopic models ELDM and semi-empirical formula UDLP produce proton decay half-lives close to experiments. Furthermore, among semi-microscopic approach, DDM3Y produces proton decay half-lives close to the experiments. Thus, Both ELDM and DDM3Y model can be effectively used in the prediction of half-lives of unexplored proton emitters.

Favored one proton radioactivity within a one-parameter model* *Supported by National Natural Science Foundation of China (Grant No.12175100 and No. 11705055), the construct program of the key discipline in Hunan province, the Research Foundation of Education Bureau of Hunan Province, China (Grant No. 18A237), the Innovation Group of Nuclear and Particle Physics in USC, the Shandong Province Natural Science Foundation, China (Grant No. ZR2019YQ01), and the Hunan Provincial Innovation Foundation For Postgraduate (Grant No. CX20210942).

In the present work, a phenomenological one-parameter model (OPM) based on the Wentzel-Kramers-Brillouin (WKB) theory is applied to study the favored one proton radioactivity (the orbital angular momentum l taken away by the emitted proton is equal to zero) half-lives. The calculated results can reproduce the experimental data well within a factor of ∼3. In addition, we extend the OPM to predict the half-lives of possible favored one proton radioactivity nuclei whose decay is energetically allowed or observed but not quantified in NUBASE2020. For comparison, a universal decay law of one proton radioactivity (UDLP) is also used. It is obviously found that our predicted results are close to the ones using UDLP. The predictions are helpful for searching for the new nuclides with favored one proton radioactivity.

Systematic study of proton radioactivity half-lives based on the relationship between Skyrme-Hartree-Fock and the macroscopic quantities of nuclear matter* *Supported in part by the National Natural Science Foundation of China (12175100), the construct program of the key discipline in Hunan province, the Research Foundation of Education Bureau of Hunan Province, China (18A237), the Natural Science Foundation of Hunan Province, China (2015JJ3103, 2015JJ2123), the Innovation Group of Nuclear and Particle Physics in USC

In this study, we systematically investigate the proton radioactivity half-lives of 33 spherical nuclei based on the relationship between 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 the macroscopic quantities is analyzed. Moreover, we obtain a new Skyrme parameter set by fitting the two most weighted macroscopic quantities. Compared with the Skyrme parameters MSL0 and the theoretical model of proton radioactivity UDLP, the theoretical proton radioactivity half-life calculated using the new Skyrme parameter set can better reproduce the experimental data.

Calculations on the proton decay with modified preformation probability

In this paper, the investigations have been conducted on the half-lives of proton radioactivity of 32 nuclei. The main goal of the paper is to improve the formation probability (Sp) that proposed by Chen et al. [Eur. Phys. J. A  57 (2021) 1]. The obtained results in mentioned paper have been reproduced with uncertainties for all parameters by fitting the experimental data of proton emitters. To carry out the further investigations, we have proposed a new Sp which has a different type of shape from linear. The replacement of the linear form with an exponential, one of the formation probabilities, has affected the rms result positively. The new form of Sp, which has been presented in this study, depends on the mass number of daughter nucleus like the previous one but in exponential form. The obtained findings here may be important for studies while making new predictions.

Proton radioactivity and α-decay of neutron-deficient nuclei

Proton radioactivity and α-decay half-lives of neutron-deficient nuclei have been systematically studied. The proton-nucleus interaction potential is developed by single folding the density distribution of the daughter nuclei with the effective M3Y-Paris nucleon-nucleon (NN) interaction. The penetrability is calculated with the Wentzel-Kramers-Brillouin approximation. The applicability of the universal decay law on the proton decay half-lives has been examined and a new set of parameters has been identified. The competition between α-decay and proton radioactivity of neutron-deficient nuclei has been investigated. The proton radioactivity is found to be the dominant mode of decay for nuclides located very close to the proton drip-line. The effect of using different microscopic proton and neutron density distributions on the half-lives for these two decay modes is studied. It is found that the calculated half-lives with the microscopic densities that obtained from the self-consistent Hartree–Fock-Bogoliubov method successfully reproduce the experimental data. The impact of nuclear deformation on the half-lives is investigated for these two decay modes. The influence of nonlocality through the finite-range exchange part of the NN interaction on the α-decay process is elucidated. Our theoretical calculations have been confirmed experimentally and satisfactory agreement has been achieved.

Proton radioactivity within the generalized liquid drop model with various versions of proximity potentials

In the present work, we systematically investigate the proton radioactivity half-lives of spherical proton emitters adopting a generalized liquid drop model (GLDM) with 16 different proximity potentials, of which the proximity potential Prox.77-13 gives the closest results to the experimental data. Combined with the previous conclusion that the GLDM with proximity potential Prox.77-13 can also best describe α decay half-lives, which makes the model more uniform and consistent. Further, we use the proximity potential Prox.77-13 in GLDM to predict the proton radioactivity half-lives of 14 spherical proton emitters that are allowed energetically but not yet observed experimentally or specifically quantified. Finally, we research the Geiger−Nuttall law for proton radioactivity. The results reveal that the Geiger−Nuttall law can also be well used to study the proton radioactivity half-lives of isotopes with the same orbital angular momentum l.

Systematic study of proton radioactivity of spherical proton emitters with Skyrme interactions

Proton radioactivity is an important and common process of the natural radioactivity of proton-rich nuclei. In our previous work [J. H. Cheng et al., Nucl. Rhys. A 997, 121717 (2020)], we systematically studied the proton radioactivity half-lives of 53< Z <83 nuclei within the two-potential approach with Skyrme-Hartree-Fock. The calculations can well reproduce the experimental data of spherical nuclei. The present work is an extension of the previous work. We systematically study 32 proton radioactivity half-lives of spherical nuclei with the two-potential approach with Skyrme-Hartree-Fock (TPA-SHF) within 115 different versions of the Skyrme interactions. The calculated results indicate that the SLy7 Skyrme interaction gives the lowest r.m.s. deviation in the description of the experimental data of the spherical proton emitters among all the different versions of the Skyrme interactions. In addition, we use this model with the SLy7 Skyrme interaction to predict the proton radioactivity half-lives of 7 spherical nuclei in the same region, whose proton radioactivity is energetically allowed or has been observed but is not yet quantified.

Half-lives of proton emitters studied with the KDE0v1 Skyrme interaction

The half-lives of proton radioactivity of proton emitters are investigated theoretically by using KDE0v1 Skyrme interaction. The total barrier potential in the proton radioactive nuclei is calculated as the sum of the nuclear, Coulomb and centrifugal contributions. The Hartree-Fock nuclear density distributions is used in calculating the nuclear as well as the Coulomb interaction potentials. The quantum mechanical tunneling probability is calculated within the WKB approximation. These calculations provide reasonable estimates for the observed proton radioactivity lifetimes.

New Geiger-Nuttall law for proton radioactivity

In the present work considering the contributions of the daughter nuclear charge and the orbital angular momentum taken away by the emitted proton, we propose a two-parameter formula of new Geiger-Nuttall law for proton radioactivity. A set of universal parameters of this law is obtained by fitting 44 experimental data of proton emitters in the ground state and isomeric state. The calculated results can reproduce the experimental data well. For a comparison, the calculations performed using other theoretical methods, such as UDLP proposed by Qi et al. (Phys. Rev. C 85, 011303(R) (2012)), the CPPM-Guo2013 analyzed by our previous work (Deng et al., Eur. Phys. J. A 55, 58 (2019)) and the modified Gamow-like model proposed by us (Chen et al., J. Phys. G: Nucl. Part. Phys. 96, 065107 (2019)) are also included. Meanwhile, we extend this new Geiger-Nuttall law to predict the proton radioactivity half-lives for $ 51 \leq Z \leq 91$ nuclei, whose proton radioactivity is energetically allowed or observed but not yet quantified in NUBASE2016.

Systematic study of proton radioactivity based on Gamow-like model with a screened electrostatic barrier

In the present work we systematically study the half-lives of proton radioactivity for 51 ≤ Z ≤ 83 nuclei based on the Gamow-like model with a screened electrostatic barrier. In this model there are two parameters while considering the screened electrostatic effect of Coulomb potential with the Hulthen potential, i.e. the effective nuclear radius parameter r0 and the screening parameter a. The calculated results can reproduce the experimental data well. In addition, we extend this model to predict the proton radioactivity half-lives of 16 nuclei in the same region within a factor of 2.94, whose proton radioactivity are energetically allowed or observed but not yet quantified. Meanwhile, studying of the proton radioactivity half-life by a type of universal decay law has been done. The results indicate that the calculated half-lives are linearly dependent on Coulomb parameter with the same orbital angular momentum.

Systematic study of proton radioactivity of spherical proton emitters within various versions of proximity potential formalisms

In this work we present a systematic study of the proton radioactivity half-lives of spherical proton emitters within the Coulomb and proximity potential model. We investigate 28 different versions of the proximity potential formalisms developed for the description of proton radioactivity, $\mathcal{\alpha}$ decay and heavy particle radioactivity. It is found that 21 of them are not suitable to deal with the proton radioactivity, because the classical turning points $r_{\text{in}}$ cannot be obtained due to the fact that the depth of the total interaction potential between the emitted proton and the daughter nucleus is above the proton radioactivity energy. Among the other 7 versions of the proximity potential formalisms, it is Guo2013 which gives the lowest rms deviation in the description of the experimental half-lives of the known spherical proton emitters. We use this proximity potential formalism to predict the proton radioactivity half-lives of 13 spherical proton emitters, whose proton radioactivity is energetically allowed or observed but not yet quantified, within a factor of 3.71.

Calculation of proton radioactivity half-lives

We have investigated the proton radioactivity half-lives of 45 proton emitters within the framework of the Wentzel–Kramers–Brillouin (WKB) method by considering the Bohr–Sommerfeld quantization condition. The orientation angle dependent Woods–Saxon, Coulomb, and spin–orbit potentials and centrifugal potential have been used in calculations. We observed that using the orientation angle dependent formalism decreases the values of calculated half-lives.

A formula for half-life of proton radioactivity**Supported by National Natural Science Foundation of China (11435014, 11405223, 11675265, 11575112), the 973 Program of China (2013CB834401, 2013CB834405), National Key Program for S&T Research and Development (2016YFA0400501), the Knowledge Innovation Project (KJCX2-EW-N01) of Chinese Academy of Sciences, the Funds for Creative Research Groups of China (11321064) and the Youth Innovation Promotion Association of Chinese Academy of Sciences

We present a formula for proton radioactivity half-lives of spherical proton emitters with the inclusion of the spectroscopic factor. The coefficients in the formula are calibrated with the available experimental data. As an input to calculate the half-life, the spectroscopic factor that characterizes the important information on nuclear structure should be obtained with a nuclear many-body approach. This formula is found to work quite well, and in better agreement with experimental measurements than other theoretical models. Therefore, it can be used as a powerful tool in the investigation of proton emission, in particular for experimentalists.

Competition between α decay and proton radioactivity of neutron-deficient nuclei

The $\ensuremath{\alpha}$ decay and proton radioactivity half-lives of some neutron-deficient nuclei are calculated using an effective liquid drop model (ELDM). It is found that the experimental half-lives of the two decay modes and the dominant decay mode can be well reproduced by the ELDM. Moreover, the predicted penetration probabilities ($P$) of proton radioactivity by the ELDM are in agreement with those by a microscopic model (MM). This allows us to make predictions on the competition of the two decay modes for nuclei whose experimental data are not available, which are useful for future measurements. In addition, the comparison between the predicted reduced proton radioactivity half-lives by the ELDM and the ones by a standard formula suggests that one is unlikely to observe large angular momentum transfers for nuclei with a very large Coulomb parameter $\ensuremath{\chi}$. Last, we find that in most isotope chains the proton radioactivity is the dominant decay mode for nuclei that are very close to the proton drip line. But with increasing neutron number $N$ the main decay mode is changed into $\ensuremath{\alpha}$ decay. With the decay energies the decay mode anomaly of $^{184}\mathrm{Bi}$ is discussed.

Investigation of proton radioactivity with the effective liquid drop model**Supported by National Natural Science Foundation of China (11247001), Natural Science Foundation of the Higher Education Institutions of Anhui Province, China (KJ2012A083, KJ2013Z066) and Anhui Provincial Natural Science Foundation (1408085MA05)

Proton radioactivity has been investigated using the effective liquid drop model with varying mass asymmetry shapes and effective inertial coefficients. An effective nuclear radius constant formula replaces the old empirical one in the calculations. The theoretical half-lives are in good agreement with the available experimental data. All the deviations between the calculated logarithmic half-lives and the experimental values are less than 0.8. The root-mean-square (rms) deviation is 0.523. Predictions for the half-lives of proton radioactivity are made for elements across the periodic table. From the theoretical results, there are 11 candidate nuclei for proton radioactivity in the region Z<51. In the region Z>83, no nuclei are suggested as probable candidate nuclei for proton radioactivity within the selected range of half-lives studied.

Analysis of proton radioactivity of nuclei by using proximity potential with a new universal function

The nuclear potential between proton and the daughter nuclei is calculated in the frame of the proximity potential with a new universal function. We obtained and analyzed the half-lives of proton radioactivity of the mother nuclei. By comparing to the experimental data and the other calculation results of ground and isomer states of proton emitters, it is found that the present calculation results can reproduce the order of magnitude of the experimental data well. It indicates that the proximity potential with a new universal function can estimate the half-life of proton radioactivity.

Competition between α-decay and proton radioactivity within a generalized liquid drop model

The α-decay and proton radioactivity half-lives of a number of spherical nuclei in the proton range Z = 51–83 were investigated within a generalized liquid drop model (GLDM), including the proximity effects between nuclei in a neck and the mass and charge asymmetry. The penetrability on potential barrier constructed by the GLDM is calculated by the WKB approximation for the two decay modes. The spectroscopic factors (Sp) evaluated by the relativistic mean field theory combined with the BCS method for the proton radioactivity. The agreement between theoretical results and experimental data is satisfactory for both α and proton emission, which allows us to make predictions about the half-lives of the two decay modes for some unstable nuclei in the same theoretical framework.

Proton radioactivity with a Yukawa effective interaction

The half-lives of proton radioactivity of proton emitters are investigated theoretically. Proton-nucleus interaction potentials are obtained by folding the densities of the daughter nuclei with a finite-range effective nucleon-nucleon interaction having Yukawa form. The Wood-Saxon density distributions for the nuclei used in calculating the nuclear as well as the Coulomb interaction potentials are predictions of the interaction. The quantum mechanical tunneling probability is calculated within the WKB framework. These calculations provide reasonable estimates for the observed proton radioactivity lifetimes. The effects of neutron-proton effective mass splitting in neutron-rich asymmetric matter as well as the nuclear matter incompressibility on the decay probability are investigated.