Simple Harmonic Oscillator Wave Functions Research Articles

Transition form factors and angular distributions of the Λb→Λ(1520)(→NK¯)ℓ+ℓ− decay supported by baryon spectroscopy

We calculate the weak transition form factors of the $\Lambda_b\to\Lambda(1520)$ transition, and further calculate the angular distributions of the rare decays $\Lambda_b\to\Lambda(1520)(\to N\bar{K})\ell^{+}\ell^{-}$ ($N\bar{K}=\{pK^-,n\bar{K}^0\}$) with unpolarized $\Lambda_b$ and massive leptons. The form factors are calculated by the three-body light-front quark model with the support of numerical wave functions of $\Lambda_b$ and $\Lambda(1520)$ from solving the semirelativistic potential model associated with the Gaussian expansion method. By fitting the mass spectrum of the observed single bottom and charmed baryons, the parameters of the potential model are fixed, so this strategy can avoid the uncertainties arising from the choice of a simple harmonic oscillator wave function of the baryons. With more data accumulated in the LHCb experiment, our result can help for exploring the $\Lambda_b\to\Lambda(1520)\ell^+\ell^-$ decay and deepen our understanding on the $b\to s\ell^+\ell^-$ processes.

Mass Spectrum and Decay Constants of Heavy Quarkonia

In this paper, a non-relativistic potential model is used to find the solution of radial Schrodinger wave equation by using Crank Nicolson discretization for heavy quarkonia ( ̅, ̅). After solving the Schrodinger radial wave equation, the mass spectrum and hyperfine splitting of heavy quarkonia are calculated with and without relativistic corrections. The root means square radii and decay constants for S and P states of c ̅ and ̅ mesons by using the realistic and simple harmonic oscillator wave functions. The calculated results of mass, hyperfine splitting, root means square radii and decay constants agreed with experimental and theoretically calculated results in the literature.

Non-Perturbative Treatment of Quantum Mathieu Oscillator

We study the evolution in time of the quantum Mathieu oscillator (QMO), according to the motion of a charged particle in a radio frequency Paul trap. We adopt non-perturbative treatment based on the quantized Floquet formalism together with the resonating averages method (RAM). We prove that we can develop solutions of the time-dependent Schrödinger equation of such a system, in terms of the simple harmonic oscillator wave functions. Numerical simulations of the analytical results are performed to show the coherence and the squeezed proprieties of the wave-packet of this system.

Pionic transition from Y(4260) to Zc(3900) in a hadronic molecular scenario

We study the pionic transition from Y(4260) to Z c(3900), where Y(4260) and Z c(3900) are regarded as the weakly bound states of D $\bar{D}_{1}$ (2420) + H.c. and D $\bar{D}^{\ast}$ + H.c., respectively. The partial width of Y(4260) $ \rightarrow$ Z c(3900) $\pi$ is estimated to be of the order of MeV with the wave functions of the bound states, where the wave functions are simulated by the simple harmonic oscillator wave functions with equivalent root-mean-square radii.

Two-body strong decay of light mesons with Gaussian expansion method

In this paper, we survey the radial and orbital excitations of I = 0 and [Formula: see text] systems anticipated up to 2.0 GeV in the framework of the chiral quark model. The Schrödinger equation is solved by using Gaussian expansion method. And using the wave functions obtained, instead of the simple harmonic oscillator wave functions, we study systematically the two-body strong decay (limited to S + S modes) of the systems. By comparing with the experimental data, we try to identify the normal states and exotic states.

Electroweak form factors of heavy-light mesons: A relativistic point-form approach

We present a general relativistic framework for the calculation of the electroweak structure of heavy-light mesons within constituent-quark models. To this aim the physical processes in which the structure is measured, i.e., electron-meson scattering and semileptonic weak decays, are treated in a Poincar\'e-invariant way by making use of the point form of relativistic quantum mechanics. The electromagnetic and weak meson currents are extracted from the $1\mathrm{\text{\ensuremath{-}}}\ensuremath{\gamma}$- and $1\mathrm{\text{\ensuremath{-}}}W$-exchange amplitudes that result from a Bakamjian-Thomas type mass operator for the respective systems. The covariant decomposition of these currents provides the electromagnetic and weak (transition) form factors. Problems with cluster separability, which are inherent in the Bakamjian-Thomas construction, are discussed and it is shown how to keep them under control. It is proved that the heavy-quark limit of the electroweak form factors leads to one universal function, the Isgur-Wise function, confirming that the requirements of heavy-quark symmetry are satisfied. A simple analytical expression is given for the Isgur-Wise function and its agreement with a corresponding front-form calculation is verified numerically. Electromagnetic form factors for ${B}^{\ensuremath{-}}$ and ${D}^{+}$ and weak $B\ensuremath{\rightarrow}{D}^{(*)}$ decay form factors are calculated with a simple harmonic-oscillator wave function and heavy-quark symmetry breaking due to finite masses of the heavy quarks is discussed.

Nucleon Meson Form Factors and Coupling Constants

The nucleon-nucleon (NN) interaction has been an object of active study for over fifty years. In the past decade high precision potentials based on one boson exchange (OBE) were developed: Argonne 18, Nijmegen '93, CD Bonn, etc. Unfortunately they are highly parametrized (≈ 40 parameters) and less theoretically sound than their predecessors: Bonn B, Nijmegen '78, Paris, etc. Historically OBE potentials parametrize the coupling constants/form factors of an effective Lagrangian. We have calculated these form factors using quark model simple harmonic oscillator wave functions and the 3P0 model of hadronic decays. We present preliminary results for phase shifts of a toy nuclear interaction model, pion (π) and scalar/iso- scalar (σ) exchange. Prospects for future work, including self-consistently extending this work to non-zero strangeness hadrons, are discussed.

Integrating products of displacedSHO wave functions

Integrals of products ofn-dimensional, displaced, simple harmonic-oscillator (SHO) wave functions are evaluated. Each of thep different wave functions may be displaced in both representation and momentum space. Each SHO wave function may be an eigensolution of a different integral or differential equation. These integrals occur in quantum mechanics, coherent optics and nonlinear optics. In addition, the notation and formalism introduced in this work may prove useful in other areas of mathematical physics. We provide a more powerful and versatile alternative to the Einstein summation convention. The coherent-state representation of Glauber is adapted to the discussion of the above integrals.

Correlation structure of 6Li

We use a simplified scheme of incorporating the residual potentials and nucleon-nucleon correlation effects in the independent particle shell-model (IPSM) wave functions of nuclei. This method is particularly convenient for nuclei with two valence nucleons (or holes). We apply this scheme to calculate the energy spacings and electron scattering form factor of 6Li. Using the variational principle we reproduce the correct energy spacings and report the values of the parameters for several potential functions. We have also calculated the 6Li form factors as obtained from the electron scattering using the simple harmonic oscillator wave functions with and without the correlation term. The correlated form factors show considerable improvement over the uncorrelated result both qualitatively and quantitatively when compared with the experimental data. This work also concludes the clustering effect of the valence nucleons.

A semi-emphirical study of the shell model proton-neutron interaction

The effective proton-neutron interaction in nuclei is approximated by an extreme short-range force with an ordinary and a spin-dependent component. This interaction is applied to several odd nuclei with two nucleons (or holes) outside of closed shells throughout the periodic table. Simple harmonic oscillator wave functions are used to evaluate the radial integrals. The interaction strength and the ratio of spin-dependent to ordinary force are determined empirically. It is found that the simple model reproduces the interaction with about 30% accuracy. It also indicates that a larger interaction constant should be used when the proton and neutron are in the same single-particle state than when they are in different states.