Two Types of Potential Oscillation During the Reduction of Dichromate on Gold Electrode in H2SO4 Solution

Two different types of potential oscillations have been identified for the first time during dichromate reduction on a gold electrode in a solution of dilute sulfuric acid. One occurs before hydrogen evolution due to the formation and dissolution of passivating films of low-valence chromium oxides, and the other generates, accompanying periodic hydrogen evolution, from the coupling of electrochemical reactions with diffusive and convective mass transport. More interestingly, these two types of oscillations correspond to two crossing loops in the cyclic voltammogram （CV）. Such a relation of oscillations with crossed CVs will provide a new way to find electrochemical oscillatory systems systematically and rapidly.

Solving Dirac Equation with New Ring-Shaped Non-Spherical Harmonic Oscillator Potential

A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.

Modulation of Electrochemical Oscillations by Specific Adsorption of Cl- during the Electrooxidation of Methanol on Pt Electrode

Potential oscillation during the electrocatalytic oxidation of methanol can be modulated by the specific adsorption of Cl- on the platinum electrode, which suppresses the electrocatalytic oxidation of methanol, and makes the cross cycle in the cyclic voltammogram become smaller and finally disappear with the increase of Cl- concentration. The method is also applicable to the electrocatalytic oxidation of other small organic molecules.

Quantum and semiclassical studies on photodetachment cross sections of H^- in a harmonic potential

The photodetachment cross section of H- in a linear harmonic oscillator potential is investigated. This system pro- vides a rare example that can be studied analytically by both quantum and semiclassical methods with some approxi- mations. The formulas of the cross section for different laser polarization directions are explicitly derived by both the traditional quantum approach and closed-orbit theory. In the traditional quantum approach, we calculate the cross sections in coordinate representation and momentum representation, and get the same formulas. We compare the quantum formulas with closed-orbit theory formulas, and find that when the detachment electron energy is larger than hco, where co is the frequency of the oscillator potential, the quantum results are shown to be in good agreement with the semiclassical results.

Quantum photodetachment of hydrogen negative ion in a harmonic potential subjected to static electric field

Photodetachment of negative ions has attracted immense interest owing to its fundamental nature and practical implications with regard to technology. In this study, we explore the quantum dynamics of the photodetachment cross section of negative ion of hydrogen H-in the perturbed one dimensional linear harmonic potential via static electric field. To this end,the quantum formula for total photodetachment cross section of the H-ion is derived by calculating the dipole matrix element in spherical coordinates. In order to obtain the detached electron wave function, we have solved the time-independent Schr¨odinger wave equation for the perturbed Hamiltonian of the harmonic oscillator in momentum representation. To acquire the corresponding normalized final state detached electron wave function in momentum space, we have employed an approach analogous to the WKB(Wenzel–Kramers–Brillouin) approximation. The resulting analytical formula of total photodetachment cross section depicts interesting oscillator structure that varies considerably with incident-photon energy,oscillator potential frequency, and electric field strength as elucidated by the numerical results. The current problem having close analogy with the Stark effect in charged harmonic oscillator may have potential implications in atomic and molecular physics and quantum optics.

Steady and oscillatory plasma properties in the near-field plume of a hollow cathode

Hollow cathodes serve as electron sources in Hall thrusters,ion thrusters and other electric propulsion systems.One of the vital problems in their application is the cathode erosion.However,the basic erosion mechanism and the source of high-energy ions cause of erosion are not fully understood.In this paper,both potential measurements and simulation analyses were performed to explain the formation of high-energy ions.A high-speed camera,a single Langmuir probe and a floating emissive probe were used to determine the steady and oscillatory plasma properties in the near-field plume of a hollow cathode.The temporal structure,electron temperature,electron density,and both static and oscillation of plasma potentials of the plume have been obtained by the diagnostics mentioned above.The experimental results show that there exists a potential hill（about 30 V） and also severe potential oscillations in the near-plume region.Moreover,a simple 2 D particle-in-cell model was used to analyze the energy transition between the potential hill and/or its oscillations and the ions.The simulation results show that the energy of ions gained from the static potential background is about 20 e V,but it could reach to 60 e V when the plasma oscillates.

Effects of external fields on a two-dimensional Klein-Gordon particle under pseudo-harmonic oscillator interaction

We study the effects of the perpendicular magnetic and Aharonov-Bohm （AB） flux fields on the energy levels of a two-dimensional （2D） Klein Gordon （KG） particle subjected to an equal scalar and vector pseudo-harmonic oscillator （PHO）. We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential param- eter, magnetic field strength, AB flux field, and magnetic quantum number by means of the Nikiforov Uvarov （NU） method. The non-relativistic limit, PHO, and harmonic oscillator solutions in the existence and absence of external fields are also obtained.

An improved simple model for α decay half-lives

In this paper,using theαparticle preformation probabilities Pαfrom Xu et al.[Xu and Ren,Nucl.Phys.A 760,303(2005)],which were extracted by fitting experimental half-lives ofαdecay,based on a phenomenological harmonic oscillator potential model(HOPM)[Bayrak,J Phys G 47,025102(2020)],refitting 178αdecay half-lives of even-even nuclei obtained from the latest nuclear property table NUBASE2020,we obtain the only one adjustable parameter V0-162.6 MeV in the HOPM,i.e.,the depth of nuclear potential.The corresponding root-mean-square(rms)deviation isσ-0.322.Furthermore,to consider the contribution of centrifugal potential to unfavoredαdecay half-lives,adding a new term■(d and l are the adjustable parameter and orbital angular momentum carried away by emittedαparticle)to the logarithmic form of favoredαdecay half-lives under the HOPM framework,we propose an improved simple model(ISM)for calculating favored and unfavoredαdecay half-lives.Fitting the experimental half-lives of 205 unfavoredαdecay,we obtain d-0.381.The ISM is used to calculate the unfavoredαdecay half-lives of 128 odd-A and 77 odd-odd nuclei.The results improve by 54.2%and 53.6%,respectively,compared with HOPM.In addition,we extend the ISM to predict theαdecay half-lives of 144 nuclei with Z=117,118,119,and 120.For comparison,the improved model with eight parameters(DUR)proposed by Deng et al.[Deng,Phys.Rev.C 101,034307(2020)]and the modified universal decay law(MUDL)proposed by Soylu et al.[Soylu,Nucl.Phys.A 1013,122221(2021)]are also used.The predictions of these models and/or formulas are generally consistent with each other.

Boundedness of Solutions for a Class of Oscillating Potentials without the Twist Condition

In this paper, we prove that the second order differential equation d^2x/dt^2＋x^2n_1f（x）＋p（t）=0with p（t ＋ 1） = p（t）, f（x ＋ T） = f（x） smooth and f（x） 〉 0, possesses Lagrangian stability despite of the fact that the monotone twist condition is violated.

Multiquark cluster form factors in the relativistic harmonic oscillator model

A QCD multiquark cluster system is studied in the relativistic harmonic oscillator potential model （RHOPM）, and the electromagnetic form factors of the pion, proton and deuteron in the RHOPM are predicted. The calculated theoretical results are then compared with existing experimental data, finding very good agreement between the theoretical predictions and experimental data for these three target particles. We claim that this model can be applied to study QCD hadronic properties, particularly neutron properties, and to find six-quark cluster and/or nine-quark cluster probabilities in light nuclei such as helium 3He and tritium 3H. This is a problem of particular importance and interest in quark nuclear physics.