Energy Levels Of Neutral Atoms Research Articles

A Theoretical Model of Deformed Klein–Gordon Equation with Generalized Modified Screened Coulomb Plus Inversely Quadratic Yukawa Potential in RNCQM Symmetries

In this work, we present approximate and analytical solutions of the deformed Klein–Gordon containing an interaction of the equal vector and scalar potential newly generalized modified screened Coulomb plus inversely quadratic Yukawa potential. To overcome the centrifugal barrier, we employed the well-known Greene and Aldrich approximation scheme. This study is realized in the relativistic noncommutative 3-dimensional real space symmetries. This potential is suggested to compute bound-state normalizations and the energy levels of neutral atoms. Furthermore, it is considered a good potential in studying Hydrogen-like atoms. Both ordinary Bopp’s shift method, perturbation theory, and the Greene–Aldrich approximation method of handling centrifugal barriers are surveyed to get generalized excited states energy $$E_{r-nc}^{sip} \left( {V_{0} ,\,V_{1} ,\,k\left( {j,l,s} \right) ,\,\alpha ,\,n,\,j,\,l,\,m,\,s} \right) $$ , as a function of the shift energy, the energy of the modified screened Coulomb plus inversely quadratic Yukawa potential, the discreet atomic quantum numbers $$(j,\,l,\,s,\,m)$$ , the potential parameters ( $$V_{0} ,\,V_{1} ,\,\alpha )$$ and the infinitesimal noncommutativity parameters ( $$\theta $$ and $$\sigma $$ ). We have shown that the degeneracy of the initial spectral under the potential in the relativistic commutative quantum mechanics RCQM is broken and replaced by newly degeneracy of energy levels; this gives more precisions in measurement and better off compared to results of ordinary RCQM.

Estimation Using an Enhancement Factor on Non Local Thermodynamic Equilibrium Behavior of High-lying Energy Levels of Neutral Atom in Argon Radio-Frequency Inductively-Coupled Plasma.

This paper describes a plasma-diagnostic method using an enhancement factor on the Boltzmann distribution among emission lines of iron atom in an argon radio-frequency inductively-coupled plasma (ICP). It indicated that Boltzmann plots of the atomic lines having lower excitation energies (3.4 to 4.8 eV) were well fitted on a straight line while those having more than 5.5 eV deviated upwards from a linear relationship. This observation could be explained by the fact that ICP is not in a complete thermodynamic equilibrium between direct excitation to energy levels of iron atom, ionization of iron atom, and radiative decay processes to the ground state. Especially, the recombination of iron ion with captured electron should accompany cascade de-excitations between closely-spaced excited levels just below the ionization limit, the rates of which become slower as a whole; as a result, these high-lying levels might be more populated than the low-lying levels as if a different LTE condition coexists on the high energy side. This overpopulation could be quantitatively estimated using an enhancement factor (EF), which was a ratio of the observed intensity to the expected value extrapolated from the normal distribution on the low energy side. The EFs were generally small (less than 3); therefore, the cascade de-excitation process would slightly contribute to the population of these excited levels. It could be considered from variations of the EF that the overpopulation proceeded to a larger extent at lower radio-frequency forward powers, at higher flow rates of the carrier gas, or at higher observation heights. The reason for this is that the kinetic energy of energetic particles, such as electrons, becomes reduced under all of these plasma conditions, thus enabling the high-lying levels to be more populated by cascade de-excitation processes from iron ion rather than by collisional excitation processes with the energetic particles. A similar Boltzmann analysis using the EF was also carried out in emission lines of nickel atom, which confirmed the conclusion concerning the atomic lines of iron.

Approximate Bound States Solution of the Hellmann Potential

The Hellmann potential, which is a superposition of an attractive Coulomb potential −a/r and a Yukawa potential b e−δr/r, is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov—Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schrödinger equation (SE) for the Hellmann potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented, which show good agreement with a numerical amplitude phase method and also those previously obtained by other methods. As a particular case, we find the energy levels of the pure Coulomb potential.

Approximate Analytical Solution of the Yukawa Potential with Arbitrary Angular Momenta

The Yukawa potential is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov method, we obtain approximate analytical solutions of the radial Schrödinger equation for the Yukawa potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented and show that these results are in good agreement with those obtained previously by other methods. Also, we find the energy levels of the familiar pure Coulomb potential energy levels when the screening parameter of the Yukawa potential goes to zero.

A PERTURBATIVE TREATMENT FOR THE ENERGY LEVELS OF NEUTRAL ATOMS

Energy levels of neutral atoms have been reexamined by applying an alternative perturbative scheme in solving the Schrödinger equation for the Yukawa potential model with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number Z up to 84 and compare very well with those obtained within the framework of hypervirial-Padé scheme and the method of shifted large-N expansion. It is observed that the new perturbative method may also be applied to the other areas of atomic physics.

Yukawa potentials for atomic negative ions

For the purpose of calculating bound-state properties (e.g., energy levels) and scattering properties (e.g., cross sections) of atomic systems, we seek a precise independent-particle model (IPM) for electrons in atomic negative ions from Z=3 up to Z=85. The IPM potential is a combination of two Yukawa potentials whose strengths and ranges are functions of two adjustable parameters. The parameters are varied until the inner energy levels are close to the experimental energy levels of neutral atoms, and the last electron eigenvalue is precisely equal to the electron affinity of negative ions. Systematic trends in the parameters are determined.

Shifted large-N expansion for the energy levels of neutral atoms

Energy levels of neutral atoms have been re-examined by applying the method of shifted large-N expansion (whereN is the number of spatial dimensions) to the model Yukawa potential with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number Z up to 84 and compare very well with those obtained within the framework of hypervirial-Pade scheme. It is observed that the large-N technique which is hitherto used in different contexts may also be applied to other areas of atomic physics.

On the energy levels of neutral atoms

By applying the hypervirial-Pade calculation to the model Yukawa potential with a modified screening parameter, we obtain the shell binding energies of neutral atoms which yield accurate results over the entire range of the atomic number.

An analytic approximation for the energy levels of neutral atoms

Using a screened coulomb potential, a simple formula is obtained for the shell binding energyEns of a neutral atom which gives accurate results over the entire range of the atomic number upto 84.