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.     

Proton radioactivity with analytically solvable potential

The phenomenon of proton emission is treated as a process of asymmetric fission through a one-dimensional potential barrier developed due to combined effects of the Coulomb potential, centrifugal potential and various renormalization processes. The barrier is simulated to an asymmetric, smooth and analytically solvable potential with adjustable depth, shape and range. The half-lives of proton emitters in the mass range A = 105–171 have been calculated using exact expression for the transmission coefficients. Good agreement with the experimental data is obtained by the adjustment of just one parameter in all the cases.      

Systematic study of two-proton radioactivity half-lives using the two-potential and Skyrme-Hartree-Fock approaches

In this work, we systematically study the two-proton (\begin{document}$2p$\end{document}) radioactivity half-lives using the two-potential approach, and the nuclear potential is obtained using the Skyrme-Hartree-Fock approach and the Skyrme effective interaction of SLy8. For true \begin{document}$2p$\end{document} radioactivity (\begin{document}$Q_{2p}$\end{document} \begin{document}$>$\end{document} 0 and \begin{document}$Q_p$\end{document} \begin{document}$< $\end{document}0, where \begin{document}$Q_p$\end{document} and \begin{document}$Q_{2p}$\end{document} are the released energies of the one-proton and two-proton radioactivity, respectively), the standard deviation between the experimental half-lives and our theoretical calculations is 0.701. In addition, we extend this model to predict the half-lives of 15 possible \begin{document}$2p$\end{document} radioactivity candidates with \begin{document}$Q_{2p}$\end{document} \begin{document}$>$\end{document} 0 obtained from the evaluated atomic mass table AME2016. The calculated results indicate a clear linear relationship between the logarithmic \begin{document}$2p$\end{document} radioactivity half-lives (\begin{document}${\log}_{10}T_{1/2}$\end{document}) and coulomb parameters [(\begin{document}$Z_{d}^{0.8}$\end{document}+\begin{document}${l}^{\,0.25}$\end{document})\begin{document}$Q_{2p}^{-1/2}$\end{document}] considering the effect of orbital angular momentum proposed by Liu \begin{document}$et$\end{document} \begin{document}$al.$\end{document} [Chin. Phys. C 45, 024108 (2021)]. For comparison, the generalized liquid drop model (GLDM), effective liquid drop model (ELDM), and Gamow-like model are also used. Our predicted results are consistent with those obtained using other relevant models.     

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.     

Coulomb bound potential quantum rod qubit

We study the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to LO-phonon in a quantum rod with a hydrogen-like impurity at the center by using the variational method of Pekar type. This quantum rod system may be used as a two-level quantum qubit. When the electron is in the superposition state of the ground and the first-excited states, the probability density of the electron oscillates in the quantum rod. It is found that the probability density and the oscillation period are individually increased and decreased due to the presence of the Coulomb interaction between the electron and the hydrogen-like impurity. The oscillation period is an increasing function of the ellipsoid aspect ratio and the effective confinement lengths of the quantum rod, whereas it is a decreasing one of the electron–phonon coupling strength.     

The decoherence of the triangular and Coulomb bound potential quantum dot qubit

We study the eigenenergies and eigenfunctions of the ground and first-excited states of an electron which is strongly coupled to an LO-phonon in a quantum dot with a triangular bound potential and Coulomb bound potential by using the Pekar variational method. This system may be used as a two-level qubit. Phonon spontaneous emission causes the decoherence of the qubit. Numerical calculations are performed on the decoherence rate as a function of the polar angle, the Coulomb binding parameter, the coupling strength, the confinement length of the quantum dot and the dispersion coefficient.     

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.     

Solutions of the two-body Salpeter equation under the Coulomb and exponential potential for any l state with Laplace approach

In this paper we have solved the two-body spinless-Salpeter (SS) equation under the Coulomb and exponential type potentials. We have applied an approximation for the centrifugal term in our calculations. The energy eigenvalues and the corresponding eigenfunctions are reported by using the Laplace transform approach for any n, l states.     

Concise presentation of the Coulomb electrostatic potential of a uniformly charged cube

We use a novel method to calculate in closed form the Coulomb electrostatic potential created by a uniformly charged cube at an arbitrary point in space. We apply a suitable transformation of variables that allows us to obtain a simple presentation of the electrostatic potential in one-dimensional integral form. The final concise closed form expression of the Coulomb electrostatic potential of the uniformly charged cube is obtained after completing the calculation of the resulting one-dimensional integrals. Such integrals consist of combinations of products of error functions and power functions that can be solved exactly despite their intimidating appearance. The exact analytic formula for the Coulomb electrostatic potential that we derive reflects the symmetry of the cube and is easy to implement. We illustrate its use by calculating the exact values of the electrostatic potential at some points of symmetry such as the center of cube, center of face of cube, center of edge of cube and corner of cube.     

库仑势加新环形势的相对论束缚态

在标量势等于矢量势的条件下，获得了库仑势加新环形势的Klein-Gordon方程和Dirac方程的束缚态的精确解. 对于Klein-Gordon方程，获得了精确的能谱方程和归一化的波函数. 对于Dirac方程，给出了精确的能谱方程和归一化的旋量波函数. 关键词： 库仑势加新环形势 束缚态 精确解     

Effective Kratzer and Coulomb potentials as limit cases of a multiparameter exponential-type potential

We show that the effective Kratzer and Coulomb potentials can be obtained by taking particular limits of a multiparameter exponential potential that was studied recently. Moreover, we demonstrate that the bound state solutions of the exponential potential reduce correctly to their well-known counterparts associated with the Kratzer and Coulomb potentials. As a byproduct, we obtain a new limit relation for the hypergeometric function.     

Pseudospin and spin symmetries in 1+1 dimensions: The case of the Coulomb potential

The problem of fermions in 1+1 dimensions in the presence of a pseudoscalar Coulomb potential plus a mixing of vector and scalar Coulomb potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. We show the relation between spin and pseudospin symmetries by means of charge-conjugation and γ⁵${\gamma }^5$ chiral transformations. The cases of pure pseudoscalar and mixed vector–scalar potentials, already analyzed in previous works, are obtained as particular cases. The results presented can be extended to 3+1 dimensions.     

Bound states of the SchrSdinger equation for the PSschl-Teller double-ring-shaped Coulomb potential

Poschl-Teller double-ring-shaped Coulomb （PTDRSC） potential, the Coulomb potential surrounded by PSschl- Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ,θ and τ coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schr6dinger equation with PTDRSC potential are presented. The normalized φ,θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.     

双环形Coulomb势Schr?dinger方程束缚态的精确解

双环形Coulomb势是指在氢原子势外面再加上一个双环形平方反比势,该模型势是在讨论类似于苯环分子结构的基础上提出的,该模型势在分子和原子物理中有着广泛的应用.本文研究了双环形Coulomb势Schr(o)dinger方程的束缚态精确解, 所采用的方法是首先对双环形Coulomb势的Schr(o)dinger方程在球坐标系中进行分离变量,得到相应的角向方程和径向方程;证明双环形 Coulomb势在角向和径向具有超对称性和形不变性;根据超对称性和形不变性的性质,获得了角动量量子化条件和束缚态的能谱方程,并将归一化角向波函数用Jacobi多项式表示,将归一化径向波函数用Laguerre多项式函数表示.体系的波函数和束缚态能谱性质由三个量子数n、m和s及势参数α,a和 b 描述.本文说明量子物理中一些具有对称性的非中心势有精确解,用超对称性和形不变性方法还可以讨论其他形式的非中心势.     

双环形Coulomb势Schroedinger方程束缚态的精确解

双环形Coulomb势是指在氢原子势外面再加上一个双环形平方反比势。该模型势是在讨论类似于苯环分子结构的基础上提出的，该模型势在分子和原子物理中有着广泛的应用．本文研究了双环形Coulomb势Schroedinger方程的束缚态精确解，所采用的方法是首先对双环形Coulomb势的Schroedinger方程在球坐标系中进行分离变量，得到相应的角向方程和径向方程；证明双环形Coulomb势在角向和径向具有超对称性和形不变性；根据超对称性和形不变性的性质，获得了角动量量子化条件和束缚态的能谱方程，并将归一化角向波函数用Jacobi多项式表示，将归一化径向波函数用Laguerre多项式函数表示．体系的波函数和束缚态能谱性质由三个量子数n、m和s及势参数a，a和b描述．本文说明量子物理中一些具有对称性的非中心势有精确解．用超对称性和形不变性方法还可以讨论其他形式的非中心势．     

Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics

The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.     

声子和杂质对三角束缚势量子点量子比特性质的影响

本文以含有类氢杂质的三角束缚势量子点为基础,应用Peker变分方法,电子与体纵光学声子强耦合的条件下得出了电子的基态和第一激发态的本征能量及基态和第一激发态的波函数,量子点中这样的二能级体系可作为一个量子比特。讨论了能量与库仑结合参数,耦合强度,受限长度以及极角的变化关系.     

Coulomb system equivalent to the energy spectrum of the Calogero-Sutherland-Moser (CSM) model

The purpose of this paper is to prove an equivalence between the energy spectrum of the CSM model and the electrostatic energy of a one-dimensional lattice of quantized point charges interacting via Coulomb potential with Dirichlet boundary conditions. This paper is dedicated to B. Jancovici in honor of his 65th birthday.     

Released energy formula for proton radioactivity based on the liquid-drop model

In this work, based on the liquid-drop model and considering the shell correction, we propose a simple formula to calculate the released energy of proton radioactivity(Q_p). The parameters of this formula are obtained by fitting the experimental data of 29 nuclei with proton radioactivity from ground state. The standard deviation between the theoretical values and experimental ones is only 0.157 Me V. In addition, we extend this formula to calculate 51 proton radioactivity candidates in region 51≤Z≤83 taken from the latest evaluated atomic mass table AME2016 and compared with the Q_p calculated by WS4 and HFB-29. The calculated results indicate that the evaluation ability of this formula for Q_p is inferior to WS4 while better than HFB-29.