Hypercentral Potential Research Articles

Accuracy of ground-state solutions of boson systems in the revised few-body integrodifferential equations approach

In this work, the traditional two-variable few-body integrodifferential equations approach is reviewed. Boundary conditions are implemented in both the hyperradial and hyperangular domains. A novel procedure of including effects of higher partial waves of the interaction potential is introduced. The new approach reproduces results obtained by an exact method for boson systems. These results suggest that many-body correlations are negligibly small in systems with short-range interactions and that effect of higher partial waves are adequately accounted for by the revised hypercentral potential.

Determination of hyperon properties through the variational method considering the hyperfine interaction

Performing a fit procedure on the hyperon masses, we first determine the free parameters in the Cornell-like hypercentral potential between the constituent quarks of hyperons in their ground state. To this end, using the variational principle, we apply the hyperspherical Hamiltonian including the Cornell-like hypercentral potential and the perturbation potentials due to the spin–spin, spin–isospin and isospin–isospin interactions between constituent quarks. In the following, we compute the hyperon magnetic moments as well as radiative decay widths of spin-3/2 hyperons using the spin-flavor wave function of hyperons. Our analysis shows acceptable consistencies between theoretical results and available experimental data. This leads to reliable wave functions for hyperons at their ground state.

An efficient method for obtaining the ground and excited states mass spectrum of doubly heavy $ \Omega$ Ω baryons

In this paper, we obtained the ground state masses and the positive and negative parity excited state masses of doubly heavy $ \Omega$ baryons. For this goal we have analytically solved the radial Schrodinger equation for three identical particles with the hypercentral potential by using the ansatz method. In this study the hypercentral potential is regarded as a combination of the color Coulomb plus linear confining term and the six-dimensional harmonic oscillator potential which has a two-body character and turns out to be exactly hypercentral. We also added the first-order correction and the spin-dependent part contains three types of interaction terms (the spin-spin term, spin-orbit term and tensor term) to the hypercentral potential. Our calculations have been performed for the radial excited states as well as orbital excited states for $ \Omega_{cc}$ , $ \Omega_{bb}$ and $ \Omega_{bc}$ systems. The masses obtained are compared with other theoretical reports, which could be a benefit tool for the interpretation of experimentally unknown doubly heavy baryons spectrum. The doubly heavy baryons masses are experimentally unknown so that the Regge trajectories are plotted using calculated masses to assign the quantum numbers of baryons unknown states.

A New Model for Calculating the Ground and Excited States Masses Spectra of Doubly Heavy Ξ Baryons

Since the doubly heavy baryons masses are experimentally unknown (except Ξcc+ and Ξcc++), we present the ground state masses and the positive and negative parity excited state masses of doubly heavy Ξ baryons. For this purpose, we have solved the six-dimensional hyperradial Schrödinger equation analytically for three particles under the hypercentral potential by using the ansatz approach. In this paper, the hypercentral potential is regarded as a combination of the color Coulomb plus linear confining term and the six-dimensional harmonic oscillator potential. We also added the first-order correction and the spin-dependent part contains three types of interaction terms (the spin-spin term, spin-orbit term, and tensor term) to the hypercentral potential. Our obtained masses for the radial excited states and orbital excited states of Ξccd, Ξccu, Ξbbd, Ξbbu, Ξbcd, and Ξbcu systems are compared with other theoretical reports, which could be a beneficial tool for the interpretation of experimentally unknown doubly heavy baryons spectrum.

Electromagnetic Coupling of Negative Parity Nucleon Resonances N (1535) Based on Nonrelativistic Constituent Quark Model

The electromagnetic transition between the nucleon and excited baryons has long been recognized as an important source of information for understanding strong interactions in the domain of quark confinement. We study the electromagnetic properties of the excitation of the negative parity the N*(1535) resonances in the nonrelativistic constituent quark model at large momentum transfers and have performed a calculation the longitudinal and transverse helicity amplitudes. Since the helicity amplitudes depend strongly on the quark wave function in this paper, we consider the baryon as a simple, non-relativistically three-body quark model and also consider a hypercentral potential scheme for the internal baryon structure, which makes three-body forces among three quarks. Since the hyper central potential depends only on the hyper radius, therefore, the Cornell potential which is a combination of the Coulombic-like term plus a linear confining term is considered as the potential for interaction between quarks. In our work, in solving the Schrodinger equation with the Cornell potential, the Nikiforov–Uvarov method employed, and the analytic eigen-energies and eigen-functions obtained. By using the obtained eigen-functions, the transition amplitudes calculated. We show that our results in the range lead to an overall better agreement with the experimental data in comparison with the other three non-relativistic quark models.

Electromagnetic transitions of the Roper resonance $\gamma^{\ast} p \rightarrow p_{11}(1440)$ γ * p → p 11 ( 1440 ) within the nonrelativistic quark model

The Roper resonance, or ( $ \gamma^{\ast}p \rightarrow p_{11} (1440)$ ), is the lowest excited state of the nucleon. We study the scalar and transverse helicity amplitudes for the electroexcitation of the Roper resonance and obtain the $ Q^{2}$ dependence of the helicity amplitudes of the Roper resonance. The helicity amplitudes depend strongly on the quark wave function. In this paper, we consider the baryon as a simple, nonrelativistic three-body quark model and we also consider a hypercentral potential scheme for the internal baryon structure which makes three-body forces among three quarks. The hypercentral potential depends only on the hyperradius which itself is a function of Jacobi relative coordinates that are functions of particle positions ( $ r_{1}$ , $ r_{2}$ , and $ r_{3}$ ). For this purpose, the Cornell potential is regarded as a combination of the Coulombic-like term plus a linear confining term in our work. In solving the Schrodinger equation with the Cornell potential, the Nikiforov-Uvarov (NU) method is employed, and the analytic eigenenergies and eigenfunctions are obtained. By using the obtained eigenfunctions, the transition amplitudes are calculated. Presenting our results in the range $ 0\le Q^{2} (GeV^{2}) \le 5$ in comparison with the predictions obtained in other non-relativistic quark models, our results lead to an overall better agreement with the experimental data, especially in the medium $ Q^{2}$ range.

Study of Baryon Spectroscopy Using a New Potential Form

In the present work, the nonrelativistic quark model is applied to study baryon systems, where the constituent quarks are bound by a suitable hyper central potential. We proposed a new phenomenological form of the interaction potential, digamma-type potential. Using the Jacobi coordinates, the three-body wave equation is solved numerically to calculate the resonance states of theN, Δ, Λ, andΣbaryon systems. The present model contains only two adjustable parameters in addition to the quark masses. Our theoretical calculations are compared to the available experimental data and Cornell potential results. The description of the spectrum shows that the ground states of the considered light and strange baryon spectra are in general well reproduced.

The light and strange baryon spectrum in a non-relativistic hypercentral quark potential model and algebraic framework

In this paper, we studied the baryon resonances spectrum within a non-relativistically quark model using a simple approach based on the Gursey-Radicati mass formula (GR). The average energy value of each SU(6) multiplet is described using the SU(6) invariant interaction given by a hypercentral potential. In this paper the hypercentral potential is composed of four components: the oscillatory potential, color charge, the intraction quark and neutral gluon and the dipole-dipole electromagnetic interaction. The results of our model (the combination of our proposed hypercentral potential and the generalized GR mass formula to the description of the spectrum) show that the light and strange baryons spectrum are in general fairly well reproduced. 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 multiplets with more than 2GeV mass and negative-parity resonance.

A new method for obtaining the spectrum of baryon resonances in the Killingbeck potential

In this paper, we investigate the spin- and flavor-dependent SU(6) violations in the baryon resonances spectrum using a simple approach based on the Gürsey–Radicati (GR) mass formula. The relativistic energy spectrum has some very important features that makes it vastly superior to the nonrelativistic one; so, in order to obtain the average energy value of each SU(6) multiplet, we have exactly solved the Dirac equation for the Killingbeck potential analytically by using the wave function ansatz method. The results of our model (the combination of our proposed hypercentral potential and the generalized GR mass formula for the description of the spectrum) show that the strange and nonstrange baryon spectra are, in general, fairly well reproduced. 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 multiplets with more than 2 GeV mass and negative-parity resonance. Moreover, we have shown that our model reproduces the position of the Roper resonance of the nucleon. Finally, we compare the results obtained by the Dirac equation for the Killingbeck potential with the corresponding results of the Schrödinger equation for the Cornell potential and we find that our model has improved the results of the nonrelativistic model.

A relativistic model for the light baryon masses in hypercentral potential and spin-flavor dependence

In this paper, we studied the light baryon resonances spectrum within a relativistically quark model based on Dirac equation and generalized Gursey Radicati mass formula (GR). For exact solving of the Dirac equation for our proposed hypercentral confining potential analytically, we used the Ansatz approach. The results of our model show that the light baryons spectrums are fairly well reproduced, thanks to the flavor-dependent interaction. The overall good description of the spectrums which we obtain shows that our model can also be used to give a fair description of the energies of the negativeparity resonance and excited multiplets, at least up to 3 GeV. Eventually, we compare the results obtained from our model with the corresponding results of the Schrodinger equation for the Coulombiclike term plus a linear confining term and we found out that our model has certainly improved the results of the non-relativistic model.

Spectrum of strange and nonstrange baryons by using generalized guersey radicati mass formula and hypercentral potential

Spectrum of strange and nonstrange baryons by using generalized guersey radicati mass formula and hypercentral potential

PROTON STATIC PROPERTIES BY USING HYPERCENTRAL CONSTITUENT QUARK MODEL AND ISOSPIN

The static properties of protons are useful for understanding the quark structure of the proton. In his work we have introduced the hypercentral constituent quark model and isospin dependent potentials. Here constituent quarks interact with each other via a potential in which we have taken into account the three-body force effect and the standard two-body potential contributions. According to our model the static properties of protons containing u and d quarks are better than the other models and closer to experimental results. The two key ingredients of this improvement are the effective quark–gluon hypercentral potentials, and hyperfine interaction and isospin dependence potential. Recently, Schrödinger equation has been solved by Giannini but we have solved the Dirac equation exact analytically and we have shown that a considerable improvement in the description of the static properties of proton is obtained with an isospin dependent potential and the complete interaction including spin and isospin terms reproduces the position of the quark.

HYPERSPHERICAL APPROACH TO STUDY THE SCHRÖDINGER EQUATION FOR AN N-PARTICLE SYSTEM

In the present work we give an exact analytical solution of the Schrödinger equation for an N-particle system by using the hyperspherical approach, in the presence of the hypercentral potential of form V(R) = a1R2+b1R-4+c1R-6 for both the ground state and the excited states.

Partonic transverse momenta in non-relativistic hyper-central quark potential models

We investigate the impact of three-body forces on the transverse-momentum distribution of partons inside the proton. This is achieved by considering the three-body problem in a class of hyper-central quark potential models. Solving the corresponding Schrödinger equation, we determine the quark wave function in the proton and with appropriate transformations and projections we find the transverse-momentum distribution of a single quark. In each case the parameters of the quark potentials are adjusted in order to sufficiently describe observable properties of the proton. Using a factorization ansatz, we incorporate the obtained transverse-momentum distribution in a perturbative QCD scheme for the calculation of the cross-section for prompt photon production in pp collisions. A large set of experimental data is fitted using as a single free parameter the mean partonic transverse momentum. The dependence of 〈k T〉 on the collision characteristics (initial energy and transverse momentum of the final photon) is much smoother when compared with similar results found in the literature using a Gaussian distribution for the partonic transverse momenta. Within the considered class of hyper-central quark potentials the one with the weaker dependence on the hyper-radius is preferred for the description of the data since it leads to the smoothest mean partonic transverse-momentum profile. We have repeated all the calculations using a two-body potential of the same form as the optimal (within the considered class) hyper-central potential in order to check if the presence of three-body forces is supported by the experimental data. Our analysis indicates that three-body forces influence significantly the form of the parton transverse-momentum distribution and consequently lead to an improved description of the considered data.

Masses and magnetic moments of heavy flavour baryons in the hyper central model

Heavy flavour baryons containing one or two charm (beauty) quarks with light flavour combinations are studied using the hyper central description of the three-body system. The confinement potential is assumed as hyper central Coulomb plus power potential with a power index p. The ground state ( and ) masses of heavy flavour baryons are computed for different power indices, p starting from 0.5 to 2.0. The predicted masses are found to attain a saturated value with respect to the variation in p beyond the power index p > 1.0. Using the spin-flavour structure of the constituting quarks and by defining the effective mass of the confined quarks within the baryons, the magnetic moments are computed with no additional free parameters. The masses and magnetic moments of the single heavy and double heavy flavour baryons are found to be in accordance with other model predictions.

A Method to Solve the Schrödinger Equation for Any PowerHypercentral Potentials

An exact closed form of solution to the hyperradialSchrödinger equation is constructed for any general casecomprising any hypercentral power and inverse-power potential.The hypercentral potential depends only on thehyperradius, which itself is a function of Jacobi relativecoordinates that are functions of particle positions(r1,r2,…, rN). Thisarticle is mainly devoted to the dernonstrat of the fact that anyψ of the form ψ = powerseries×exp(polynomial) = [f(x)exp (g(x))]is potentially a solution of the Schrödingerequation, where the polynomial g(x) is an ansatz depending on theinteraction potential.

Calculation of the Eigenstates and Eigenvalues for the Power and Inverse-Power Hypercentral Potentials

The bound-state solutions to the hyperradial Schrodinger equation is constructed for any general case comprising any hypercentral power and inverse-power potentials. The hypercentral potential depends only on the hyperradius which itself is a function of Jacobi relative coordinates that are functions of particle positions (r 1,r 2, … , and r N ). This paper is mainly devoted to the demonstration of the fact that any ψ of the form ψ = power series × exp(polynomial) = [f(x) exp (g(x))] is potentially a solution of the Schrodinger equation, where the polynomial g(x) is an ansatz depending on the interaction potential.

Bound States for Hypercentral Singular and Exponential Potentials

With a view to obtaining an exact closed form solution to theSchrödinger equation for a variety of hypercentral potentials, weinvestigate further application of an ansatz. This method is good enough formany kinds of potentials, but in this article it applies to a type of thehypercentral singular potentials V(x) = ax2+bx−4+cx−6and exponential hypercentral Morse potential U(x) = U0(e−2ax−2e−ax) for three interacting particles. The Morse potential is used fordiatomic molecule while this method will be successfully used for manyatomic molecules. The three-body potentials are more easily introduced andtreated within the hyperspherical harmonic formalism. The internal particlemotion is usually described by means of Jacobi relative coordinatesρ, λ, and R, in terms of three particle positionsr1, r2, and r3. We discuss some results obtained by usingharmonic and anharmonic oscillators, however the hypercentralpotential can be easily generalized in order to allow a systematicanalysis, which admits an exact solution of thewave equation. This method is also applied to some other types ofthree-body, four-body, …, interacting potentials.

A new application of the Gürsey and Radicati mass formula

We study the spin- and flavour-dependent SU(6) violations in the baryon spectrum by means of a Gürsey-Radicati mass formula. The average energy of each SU(6) multiplet is described using the SU(6)-invariant interaction given by a hypercentral potential containing a linear and a hyper-Coulomb term. We show that the nonstrange- and strange-baryon masses are, in general, fairly well reproduced and moreover that the Gürsey-Radicati formula holds in a satisfactory way also for the excited states up to 2 GeV.

Proton dipole form factor quark model

The dipole-shaped electromagnetic form factors of the proton may imply an exponential radial dependence of the wave function describing the charged constituents of the proton. The hypercentral potential required by the three-body Dirac equation to produce such an exponential radial wave function for three bound quarks is found to have a linear confining potential plus an attractive Coulombic central diagonal part. The configuration assumed for the quark constituents is the (1/2+)3 positive parity configuration, coupled to the spin of the proton. Assuming equal-mass Dirac quarks with no anomalous magnetic moments, we find the largest magnetic moment for this wave function to be 2.763 nuclear magnetons, close to, but less than the experimental value of 2.793. The hypercentral potential is mostly the sum of three quark-quark potentials, but a small three-body potential is required.