Rashba coupling in three-electron-quantum dot under cylindrical symmetry: An exact solution

The application of quantum dots in advanced technology goes beyond doubt. Here, based on an analytical methodology, investigate a three-electron-quantum dot in the presence of Rashba spin–orbit interaction under cylindrical symmetry. Both eigenvalues and eigenfunctions of the system are reported and the problem is numerically discussed.     

Rashba coupling in three-electron-quantum dot: A numerical solution

We present a numerical solution of a Schrödinger equation for three electrons in a quantum dot with hard-wall confining potential in the presence Spin-Orbit coupling. After separation of the problem by some hyperspherical technique, we have solved the resulting equations by using a novel finite difference method. Then a study of the wave functions, eigen-energies and accuracy of the method is done.     

Estimation of the offspring mean in a supercritical branching process with non-stationary immigration

In this paper, we consider the conditional least squares estimator (CLSE) of the offspring mean of a branching process with non-stationary immigration based on the observation of population sizes. In the supercritical case, assuming that the immigration variables follow known distributions, conditions guaranteeing the strong consistency of the proposed estimator will be derived. The asymptotic normality of the estimator will also be proved. The proofs are based on direct probabilistic arguments, unlike the previous papers, where functional limit theorems for the process were used.     

Arbitrary-state solutions of the Dirac equation for a Möbius square potential using the Nikiforov-Uvarov method

We inquire into spin and pseudospin symmetries of the Dirac equation under a Mbius square-type potential using the Nikiforov-Uvarov method to calculate the bound state solutions. We numerically discuss the problem and include various explanatory figures.     

Synthesis and study of nonionic surfactants based on propylene oxide and lauric acid

Nonionic surfactants were synthesized at various molar ratios of propylene oxide and lauric acid. Propoxylation products were identified by a number of physico-chemical analytical methods. The tensiometric method was used to measure the surface tension of aqueous solutions of the products at interface with air, find their high surface activity, and determine certain colloidal-chemical parameters (critical micelle concentration, surface pressure, maximum adsorption, minimum cross-sectional area of a molecule, change in the Gibbs free energy in micelle-formation and adsorption processes). Laboratory studies of the oil-collecting capacity of these substances were carried out for the example of a thin oil film on the surface of water with varied degree of mineralization.     

Bootstrap of the offspring mean in the critical process with a non-stationary immigration

In applications of branching processes, usually it is hard to obtain samples of a large size. Therefore, a bootstrap procedure allowing inference based on a small sample size is very useful. Unfortunately, in the critical branching process with stationary immigration the standard parametric bootstrap is invalid. In this paper, we consider a process with non-stationary immigration, whose mean and variance vary regularly with nonnegative exponents α and β, respectively. We prove that 1+2α is the threshold for the validity of the bootstrap in this model. If β<1+2α, the standard bootstrap is valid and if β>1+2α it is invalid. In the case β=1+2α, the validity of the bootstrap depends on the slowly varying parts of the immigration mean and variance. These results allow us to develop statistical inferences about the parameters of the process in its early stages.     

Deng-Fan Potential for Relativistic Spinless Particles—an Ansatz Solution

Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems.On the contrary to the ground state of one-dimensional Schro¨dinger equation,this potential fails to admit exact analytical solutions for arbitrary quantum number in both relativistic and nonrelativistic regime.Because of this complexity,there exists only few papers,which discuss this interesting problem.Here,using an elegant ansatz,we have calculated the system spectra as well as the eigenfunctions in the general case of unequal vector and scalar potentials under Klein-Gordon equation.     

Alpha Decay Half-Lives of Some Nuclei from Ground State to Ground State with Yukawa Proximity Potential

We study the half-lives of some nuclei via the alpha-decay process from ground state to ground state. To go through the problem, we have considered a potential model with Yukawa proximity potential and have thereby calculated the half-lives. The comparison with the existing data is motivating.     

Approximate any 1-state solutions of the Dirac equation for modified deformed Hylleraas potential by using the Nikiforov-Uvarov method

<正>We investigate the spin and pseudospin symmetries of the Dirac equation under modified deformed Hylleraas potential via a Pekeris approximation and the Nikiforov-Uvarov technique.A tensor interaction of Coulomb form is considered and its degeneracy-removing role is discussed in detail.The solutions are reported for an arbitrary quantum number in a compact form and useful numerical data are included.     

An alternative method for spectrum of a three-electron-quantum dot

We consider the Hamiltonian of a three-electron-quantum dot composed of parabolic confinement plus Coulomb terms. Instead of using the Jacobi coordinates, we apply a unitary transformation to this system. To avoid the complexity, the Taylor expansion of the effective potential is introduced into the problem and thereby a solution is found for the eigenvalues of the corresponding three-body Schrödinger equation in terms of the Wigner parameter.