Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential

A bound state solution is a quantum state solution of a particle subjected to a potential such that the particle＇s energy is less than the potential at both negative and positive infinity. The particle＇s energy may also be negative as the potential approaches zero at infinity. It is characterized by the discretized eigenvalues and eigenfunctions, which contain all the necessary information regarding the quantum systems under consideration. The bound state problems need to be extended using a more precise method and approximation scheme. This study focuses on the non-relativistic bound state solutions to the generalized inverse quadratic Yukawa potential. The expression for the non-relativistic energy eigenvalues and radial eigenfunctions are derived using proper quantization rule and formula method, respectively. The results reveal that both the ground and first excited energy eigenvalues depend largely on the angular momentum numbers, screening parameters, reduced mass, and the potential depth. The energy eigenvalues, angular momentum numbers, screening parameters, reduced mass, and the potential depth or potential coupling strength determine the nature of bound state of quantum particles. The explored model is also suitable for explaining both the bound and continuum states of quantum systems.

Topological effects on non-relativistic eigenvalue solutions under AB-flux field with pseudoharmonic- and Mie-type potentials

In this paper,we investigate the quantum dynamics of a non-relativistic particle confined by the Aharonov-Bohm quantum flux field with pseudoharmonic-type potential in the background of topological defect produced by a point-like global monopole.We solve the radial Schrödinger equation analytically and determine the exact eigenvalue solution of the quantum system.Afterwards,we consider a Mie-type potential in the quantum system and solve the radial equation analytically and obtain the eigenvalue solution.We analyze the effects of the topological defect and the quantum flux with these potentials on the energy eigenvalue and wave function of the nonrelativistic particles.In fact,it is shown that the energy levels and wave functions are influenced by the topological defect shifted the result compared to the flat space results.In addition,the quantum flux field also shifted the eigenvalue solutions and an analogue of the Aharonov-Bohm effect for bound-states is observed.Finally,we utilize these eigenvalue solutions to some known diatomic molecular potential models and presented the energy eigenvalue and wave function.

Non-relativistic expansion of single-nucleon Dirac equation:Comparison between Foldy-Wouthuysen transformation and similarity renormalization group

By following the Foldy-Wouthuysen(FW)transformation of the Dirac equation,we derive the exact analytic expression up to the 1/M4 order for general cases in the covariant density functional theory.The results are compared with the corresponding ones derived from another novel non-relativistic expansion method,the similarity renormalization group(SRG).Based on this comparison,the origin of the difference between the results obtained with the FW transformation and the SRG method is explored.

Ground states and excitation spectra of baryons in a non-relativistic model with the anharmonic potential

In this work the mass spectra for some of the baryon resonances of the particle data group with three and four star status are obtained, and a unified description of the ground states and excitation spectra of baryons are provided in the framework of a non-relativistic potential model. For this goal we have analytically solved the radial SchrSdinger equation for three identical interacting particles with the anharmonic potential by using the Ansatz method and then we have calculated the baryon resonances spectrum by using the G/irsey Radicati mass formula （GR） and with generalized Giirsey Radicati mass formula （GGR）. The results of our model show that the calculated masses of baryon resonances by using the generalized Giirsey Radicati mass formula are found to be in good agreement with the tabulations of the Particle Data Group. The overall good description of the spectrum which we obtain shows that our model can also be used to give a fair description of the energies of the excited multiples up to 3 GeV mass and negative-parity resonance. Moreover, we have shown that our model reproduces the position of the Roper resonance of the nucleon.

Dipole (hyper)polarizabilities of neutral silver clusters

At the Douglas-Kroll-Hess （DKI4） level, the B3PW91 functional along with the all-eleclron relativistic basis sets of valence triple and quadruple zeta qualities are used to determine the structure, stability, and electronic properties of the small silver clusters （Agn, n ≤ 7）. The results presented in this study are in good agreement with the experimental data and theoretical values obtained at a higher level of theory from the literature. Static polarizability and hyperpolarizability are also reported. It is verified that the mean dipole polarizability per atom exhibits an odd-even oscillation and that the polarizability anisotropy is directly related to the cluster shape. In this article, the first study of hyperpolarizabilities of small silver clusters is presented. Except for the monomer, the second hyperpolarizabilities of the silver clusters are significantly larger than those of the copper clusters.

How do quantum numbers generally vary in the adiabatic transformation of an ideal gas?

We continue to analyse the known law of adiabatic transformation for an ideal gas PV5/3=Constant, where P isthe pressure and V is the volume, and following the approach of non-relativistic quantum mechanics which we suggested in a previous work （Yarman et al. 2010 Int. J. Phys. Sci. 5 1524）. We explicitly determine the constant for the general parallelepiped geometry of a container. We also disclose how the quantum numbers associated with molecules of an ideal gas vary through an arbitrary adiabatic transformation. Physical implications of the results obtained are discussed.

Majorana Neutrino Oscillations in Vacuum

In the context of a type I seesaw scenario which leads to get light left-handed and heavy right-handed Majorana neutrinos, we obtain expressions for the transition probability densities between two flavor neutrinos in the cases of left-handed and right-handed neutrinos. We obtain these expressions in the context of an approach developed in the canonical formalism of Quantum Field Theory for neutrinos which are considered as superpositions of mass-eigenstate plane waves with specific momenta. The expressions obtained for the left-handed neutrino case after the ultra-relativistic limit is taking lead to the standard probability densities which describe light neutrino oscillations. For the right-handed neutrino case, the expressions describing heavy neutrino oscillations in the non-relativistic limit are different respect to the ones of the standard neutrino oscillations. However, the right-handed neutrino oscillations are phenomenologically restricted as is shown when the propagation of heavy neutrinos is considered as superpositions of mass-eigenstate wave packets.

One ω-Meson Exchange Potential at Finite Temperature

On the basis of the field theory at the finite temperature,one ω-mesonexachange potential is derived.Temperature dependences of ω-meson effective massand renormalized ω-nucleon coupling constant are discussed in the non-relativistic limit.

Quantization of Newton’s Gravity

In this work we will use a recently developed non relativistic (NR) quantization methodology that successfully overcomes troubles with infinities that plague non-renormalizable quantum field theories (QFTs). The ensuing methodology is here applied to Newton’s gravitation potential. We employ here the concomitant mathematical apparatus to formulate the NR QFT discussed in the well known classical text-book by Fetter and Walecka. We emphasize the fact that we speak of non relativistic QFT. This is so because we appeal to Newton’s gravitational potential, while in a relativistic QFT one does not employ potentials. Our main protagonist is the notion of propagator. This notion is of the essence in non relativistic quantum field theory (NR-QFT). Indeed, propagators are indispensable tools for both nuclear physics and condensed matter theory, among other disciplines. In the present work we deal with propagators for both fermions and bosons.

Circular Scale of Time and Its Use in Calculating the Schrödinger Perturbation Energy of a Non-Degenerate Quantum State

The paper presents a circular scale of time—and its diagrams—which can be successfully applied in calculating the Schrödinger perturbation energy of a non-degenerate quantum state. This seems to be done in a more simple way than with the aid of any other of the perturbation approaches of a similar kind. As an example of the theory suitable to comparison is considered the Feynman diagrammatic method based on a straight-linear scale of time which represents a much more complicated formalism than the present one. All diagrams of the approach outlined in the paper can obtain as their counterparts the algebraic formulae which can be easily extended to an arbitrary Schrödinger perturbation order. The calculations and results descending from the perturbation orders N between N = 1 and N = 7 are reported in detail.

Exotic states with QQQ′Q′configuration

In the framework of a non-relativistic quark model,we have calculated the masses of the QQQ′Q′(Q=c,b,s and Q′=c,b,s)tetraquark states.Using the linear and quadratic confinement potentials inside a Cornell-type potential along with all possible spin and color configurations,the Schrodinger equation masses of these tetraquark states have been calculated.Based on our numerical analysis,linear confinement and quadratic confinement produce acceptable results.Models that use linear confinement estimate charmonium-like tetraquark mass close to experimental data,as well as bottomonium-like tetraquark mass below the threshold of their meson-meson channels.

Properties of Charmonium States in a Phenomenological Approach

We investigate the spectrum and decay rates of charmonium states within the framework of the non relativistic quark model by employing a Coulomb like potential from the perturbative one gluon exchange and the linear confining potential along with the potential derived from instanton vacuum to account for the hyperfine mass splitting of charmonium states in variational approach. We predict radiative E1, M1, two-photon, lepton and two-gluon decay rates of low lying charmonium states. An overall agreement is obtained with the experimental masses and decay widths.We have estimated the branching ratio of two gluons decaying into light hadrons.

An updated study of Υ production and polarization at the Tevatron and LHC

Following the nonrelativistic QCD factorization scheme, by taking the latest available measurements of XbJ（3P） into consideration, we present an updated study on the yield and polarization of T（1S, 2S, 3S） hadropro- duction, and the fractions of Xbj（mP） feed-down in T（nS） production at QCD next-to-leading order. In the fitting, three schemes are applied with different choices of XDj（mP） feed-down ratios and NRQCD factorization scale. The results can explain the measurements of yield very well. The polarization puzzle to T（3S） is now solved by consid- ering the XbJ（3P） feed-down contributions. The ratio of σ[Xb2（1P）]/σ[Xbl（IP）] measured by the CMS experiment can also be reproduced in our prediction. Among the different schemes, the results show little difference, but there are sizeable differences for the fitted long-distance color-octet matrix elements. This may bring large uncertainties when the values are applied in theoretical predictions for other experiments such as those at ee, ep colliders.

Quark-diquark model description for double charm baryons

We report here the mass spectrum and magnetic moments of ccq（q ∈ u,d,s） systems in the potential model framework by assuming the inter-quark potential as the colour coulomb plus power form with power index ν varying between 0.1 to 2.0.Here the two charm quarks are considered for the diquark states.The conventional one gluon exchange interaction has been employed to get the hyperfine and the fine structure between different states.We have predicted many low-lying states whose experimental verification can exclusively support the quark-diquark structure of the baryons.

η_b decay into charmonium in association with c pair

We calculate the inclusive decay rates of ηb into charmonium via double c~ pairs for S- and P-wave states ηc, J/ψ and XcJ within the framework of non-relativistic QCD （NRQCD） factorization at leading order in αs. Besides calculating the contributions of the color-singlet channels ηb → cc[2s＋1SL^（1）]＋cc, the effects of cc pair in the color-octet configurations are also considered. We find that ηb → cc[3S1^（8）] ＋cc make a small contribution to Br（ηb →J/ψ（ηc）＋cc）. While in the ηb →XcJ ＋cc case, the color octet contributions are significant, for they are of the same a 5 order as the color-singlet processes. We predict Br（ηb →J/ψ（ηc）＋cc） = 2.99（2.75） × 10^-5 Vc for S-wave states J/ψ and ηc, and Br（ηb → XcJ ＋cc） = （4.37, 3.40, 2.83） × 10^-5 （for J = 0,1, 2） for P-wave states XcJ. In the end, we also find Br（ηb → cccc） is almost saturated by ηb decay into charmonium in association with cc pair from the point of view of duality.

Λ■ production in p collis

We describe the production of Λ Λ in pp collisions using a constituent quark model which has been successfully applied to the N N system.