Favored one proton radioactivity within a one-parameter model*

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.     

基于折叠势的两势方法系统研究质子放射性(英文)

基于两势方法系统地研究了质子数51 ≤ Z ≤ 83质子放射性核素的衰变半衰期。总的质子-子核相互作用势包括:通过单折叠子核密度和DDM3Y有效相互作用得到的微观核势,通过单折叠子核电荷密度和质子-质子库仑相互作用得到的真实库仑势以及离心势。同时,预测了同一区域16个核的质子放射性半衰期,并且预测的质子放射性半衰期在4.11倍的范围内。此外,还研究了质子放射性的Geiger-Nuttall定律。结果表明,Geiger-Nuttall定律可以用来描述角动量相同的同位素的质子放射性。In the present work, we systematically study the half-lives of proton radioactivity for 51 ≤ Z ≤ 83 nuclei within the two-potential approach. The total emitted proton-daughter nucleus interaction potential is composed of the microscopic nuclear potential obtained by single folding the density of the daughter nucleus with the DDM3Y effective interaction, the realistic Coulomb potential obtained by single folding the charge density of the daughter nucleus with the proton-proton Coulomb interaction and the centrifugal potential. We extend our study to predict proton radioactivity half-lives of 16 nuclei in the same region within a factor of 4.11. In addition, the Geiger-Nuttall law for proton radioactivity is researched. The results indicate that the Geiger-Nuttall law can be used to describe the proton radioactivity isotopes with same angular momentum.     

质子放射性寿命的新规律

对球形核和变形核质子放射性的半衰期进行了系统的分析和研究,提出了新的计算质子放射性寿命的解析公式。 通过对公式计算寿命和实验测量值的系统比较,发现两者之间符合得非常好,说明新公式十分准确并具有良好的预言能力。 Systematic calculations on proton radioactivity half lives of both spherical and deformed nuclei are carried out. A new formula with only four parameters is proposed for proton radioactivity half lives. The half lives calculated by using the new formula are in good agreement with the experimental ones. The new formula is simple but accurate, which is very useful for further experiments.     

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.     

Theoretical study on spherical proton emission

The proton radioactivity half-lives of spherical proton emitters are 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 is calculated in the WKB approximation and the assault frequency is estimated by the quantum mechanism method considering the structure of the parent nucleus.The spectroscopic factor is taken into account in half-life calculation,which is obtained by employing the relativisti...     

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.     

利用改进的Gamow-like模型研究原子核的α衰变和质子放射性

通过引入离心势和静电屏蔽效应对Gamow-like模型进行了改进，并将其用于α衰变和质子放射性研究，发现改进的Gamow-like模型能更好地符合实验数据。另外，还利用改进的Gamow-like模型预言了16个丰质子核的质子放射性的半衰期以及7个$Z=120$超重核素($^{296-308}120$)α衰变链上原子核的α衰变的半衰期，为将来在大科学装置上合成和鉴别这些新核素提供重要的理论参考。     

Theoretical Analysis and New Formulae for Half-Lives of Proton Emission

The proton radioactivity hMf-lives of spherical proton emitters are calculated by the cluster model with the con- tribution of a centrifugal potential barrier considered separately. The results are compared with the experimental data and other theoretical data, and good agreement is found for most nuclei. In addition, two formulae are pro- posed for the proton decay half-life of spherical proton emitters through the least squares fit to the experimental data available, and could reproduce the experimental half-lives successfully.     

有效液滴模型对超铅区结团放射性的研究

利用有效液滴模型计算了超铅区结团放射半衰期.在计算Gamow势垒穿透因子时采用了碎块体积不守恒以及有效惯性系数因子,并用有效的核半径常数公式代替原来的经验公式.理论计算得到的结团放射半衰期和实验值符合得很好,其半衰期对数值的均方差只有0.895.理论结果表明,有效液滴模型能充分反映N=126和Z=82的壳效应,并且在奇数结团25Ne,29Mg中出现了明显的奇偶质量摆动现象.另外,理论计算得到的结团半衰期基本符合盖革-努塔尔定律,并基于理论结果得到了一些关于盖革-努塔尔定律的有意义的结论.     

A formula for half-life of proton radioactivity

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.     

Two-proton radioactivity of ground and excited states within a unified fission model

A unified fission model is extended to study two-proton radioactivity of the ground states of nuclei, and a good agreement between the experimental and calculated half-lives is found. The two-proton radioactivity half-lives of the ground states of some probable candidates are predicted within this model by inputting the released energies taken from the AME2020 table. It is shown that the predictive accuracy of the half-lives is comparable to those of other models. Then, two-proton radioactivity of the excited states of ¹⁴O, ^17,18Ne, ²²Mg, ²⁹S, and ⁹⁴Ag is discussed within the unified fission model and two analytical formulas. It is found that the experimental half-lives of the excited states are reproduced better within the unified fission model. Furthermore, the two formulas are not suitable for the study of two-proton radioactivity of excited states because their physical appearance deviates from the mechanism of quantum tunneling, and the parameters involved are obtained without including experimental data from the excited states.     

New approach for alpha decay half-lives of superheavy nuclei and applicability of WKB approximation

The α decay half-lives of recently synthesized superheavy nuclei (SHN) are calculated by applying a new approach which estimates them with the help of their neighbors based on some simple formulas. The estimated half-life values are in very good agreement with the experimental ones, indicating the reliability of the experimental observations and measurements to a large extent as well as the predictive power of our approach. The second part of this work is to test the applicability of the Wentzel-Kramers-Brillouin (WKB) approximation for the quantum mechanical tunneling probability. We calculated the accurate barrier penetrability for alpha decay along with proton and cluster radioactivity by numerically solving Schrödinger equation. The calculated results are compared with those of the WKB method to find that WKB approximation works well for the three physically analogical decay modes.     

Two-proton radioactivity within Coulomb and proximity potential model

Considering the preformation probability of the two emitted protons in the parent nucleus, we extend the Coulomb and proximity potential model (CPPM) to systematically study two-proton (2p) radioactivity half-lives of the nuclei close to proton drip line. The proximity potential chosen is Prox. 81 proposed by Blocki et al. in 1981. Furthermore, we apply this model to predict the half-lives of possible 2p radioactive candidates whose 2p radioactivity is energetically allowed or observed but not yet quantified in the evaluated nuclear properties table NUBASE2016. The predicted results are in good agreement with those from other theoretical models and empirical formulas, namely the effective liquid drop model (ELDM), generalized liquid drop model (GLDM), Gamow-like model, Sreeja formula and Liu formula.     

Proton emission from the drip-line nuclei I-Bi using the WKB approximation with relativistic mean-field densities

crucial application to the existence of exotic nuclei. The effective relativistic meanfield formalism(E-RMF), with NL3, FSUGarnet, G3 and IOPB-I interactions, is adopted for analysis of the ground state properties of proton emitters. Furthermore, in the E-RMF background, the Wentzel-Karmers-Brillouin(WKB)barrier penetration method is used for the calculation of proton emission half-lives. It is found that the calculated halflives are in good agreement with the experimental results for all emitters considered in this study.     

Comprehensive decay law for emission of charged particles and exotic cluster radioactivity

A general decay formula for the emission of charged particles from metastable nuclei is developed based on the basic phenomenon of resonances occurring in quantum scattering process under Coulomb-nuclear potential. It relates the half-lives of radioactive decays with the Q values of the outgoing elements with masses and charges of the nuclei involved in the decay. The relation is found to be a generalization of the Geiger–Nuttall law in α radioactivity and explains well all the known emissions of charged particles including clusters, alpha and proton.     

Empirical formulas for proton decay half-lives:Role of nuclear deformation and Q-value

Two empirical formulas for the proton decay half-lives including nuclear deformation are proposed. The formula with parameter set I gives the logarithm of the proton decay half-lives as an explicit function of the orbital angular momentum with eight adjustable parameters, whereas that with set II represents the logarithm of the reduced half-lives as an implicit function of the angular momentum with seven adjustable parameters. Experimental data for the half-lives of 44 proton emitters in the ground state or isomeric state were used to obtain the parameters. The experimental and calculated Q values were used. Different sets of parameters were obtained for the ground state transition, isomeric state transition, and all transitions for both deformed and spherical nuclei. The best agreement with experimental data was observed for set I for deformed proton emitters with experimental Q values.     

T-REX

The potential barrier impeding the spontaneous emission of protons in the proton radioactive nuclei is calculated as the sum of nuclear, Coulomb and centrifugal contributions. The nuclear part of the proton-nucleus interaction potential is obtained in the energy density formalism using the Skyrme effective interaction that results into a simple algebraic expression. The half-lives of the proton emitters are calculated for the different Skyrme sets within the improved WKB framework. The results are found to be in reasonable agreement with the earlier results obtained for more complicated calculations involving finite-range interactions.     

Heavy-particle radioactivity of superheavy nuclei

The concept of heavy-particle radioactivity (HPR) is changed to allow emitted particles with Z(e) > 28 from parents with Z > 110 and daughter around (208)Pb. Calculations for superheavy (SH) nuclei with Z = 104-124 are showing a trend toward shorter half-lives and larger branching ratio relative to α decay for heavier SHs. It is possible to find regions in which HPR is stronger than alpha decay. The new mass table AME11 and the theoretical KTUY05 and FRDM95 masses are used to determine the released energy. For 124 we found isotopes with half-lives in the range of ns to ps.     

低能质子束产生感生放射性的蒙特卡罗模拟

质子束轰击探测器产生的感生放射性核素,将使探测器成为一个典型的外照射辐射源,针对感生放射性核素种类、活度的计算有利于辐射防护工作的开展。使用FLUKA蒙特卡罗程序,研究了低能质子束（20 MeV以内）轰击三种探头材料（铜、钽、钨）产生的感生放射性问题,得到探头材料在一定照射时间下的放射性核素活度及指定冷却时间后的剂量水平。研究结果表明,质子束轰击铜探头产生感生放射性的能量阈值最低（4~5 MeV）,而钨、钽探头与质子束产生感生放射性的能量阈值较高。相同照射时间下的钨、钽探头产生感生放射性总活度远低于铜探头,在冷却1 h后其放射性总活度降至最低。     

Nonlinear Control of Beam Halo-Chaos in Accelerator-Driven Clean Nuclear Power System

Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry, medicine, and national defense. Some general engineering methods for chaos control have been developed in recent years, but they generally are unsuccessful for beam halo-chaos suppression due to many technical constraints. Beam halo-chaos is essentially a spatiotemporal chaotic motion within a high power proton accelerator. In this paper, some efficient nonlinear control methods, including wavelet function feedback control as a special nonlinear control method, are proposed for controlling beam halo-chaos under five kinds of the initial proton beam distributions (i.e., Kapchinsky-Vladimirsky, full Gauss,3-sigma Gauss, water-bag, and parabola distributions) respectively. Particles-in-cell simulations show that after control of beam halo-chaos, the beam halo strength factor is reduced to zero, and other statistical physical quantities of beam halo-chaos are doubly reduced. The methods we developed is very effective for suppression of proton beam halo-chaos in a periodic focusing channel of accelerator. Some potential application of the beam halo-chaos control in experiments is finally pointed out.