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International Journal of Trend in Scientific Research and Development

Study on the Energy Level Splitting of the Francium Atom Fr in an External Magnetic Field

Win Moe Thant

Published Jul 22, 2019• 0 citations
Publisher

Abstract

In This paper the normal Francium atom is considered with the use of non relativistic quantum mechanical approach and the Bohrs atomic model. We study the energy shift values of a Francium atom by the external magnetic fields effect we considered the two cases that effect without external magnetic fields and those of with the external magnetic fields. Win Moe Thant "Study on the Energy Level Splitting of the Francium Atom (Fr) in an External Magnetic Field" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26730.pdf

DOI
10.5281/zenodo.3591339

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Physical Review A•Jul 1, 1997•10 citations
In This paper the normal Francium atom is considered with the use of non relativistic quantum mechanical approach and the Bohrs atomic model. We study the energy shift values of a Francium atom by the external magnetic fields effect we considered the two cases that effect without external magnetic fields and those of with the external magnetic fields. Win Moe Thant "Study on the Energy Level Splitting of the Francium Atom (Fr) in an External Magnetic Field" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26730.pdf
Within the Sommerfeld atomic model the quantization of magnetic flux through the electronic orbits is investigated together with its dependency on additional sources of magnetic fields. These sources alter the magnetic flux through the atomic orbits and in consequence are causing energy shifts. This effect is investigated for the cases, where the source is an external magnetic field, the magnetic moment of the nucleus or the magnetic moment of the electron. The energy shifts due to external magnetic fields, the magnetic dipole contribution of the hyperfine splitting and the spin-orbit coupling can be reproduced very well. The meaning of 'spin', however, changes within this approach drastically. The unusual Landé g-factor of 2 for the electron is a result of the orbital motion and the magnetic moment of the electron rather than it is an intrinsic property of the electron.
Interaction of alkali atoms with external magnetic field induced a splitting and a shift of their energy levels. We have studied this interaction for external field from 0 to 5000 Gauss when the alkali vapor is confined in submicron thin vapor cell with thickness L = λ /2. Rubidium and Sodium vapors have been studied. The Hamiltonian can be expressed as the sum of the unperturbated atomic Hamiltonian and the so-called Zeeman Hamiltonian. The probability of a transition, induced by the laser electric field is proportional to the square of the transfer coefficients modified by the presence of the magnetic field. We will show that the strong nonlinearity of the transition intensities versus the external magnetic field intensity is obvious for B > 100 G. Some possible applications for Laser Spectroscopy of the Rb and the Na atoms are presented.
Interaction of alkali atoms with external magnetic field induced a splitting and a shift of their energy levels. We have study this interaction for external field from 0 to 5000 Gauss when the alkali vapor is confined in submicron thin vapor cell with thickness L = λ/2. Rubidium and Sodium vapors have been studied. The Hamiltonian can be expressed as the sum of the unperturbated atomic Hamiltonian and the so-called Zeeman Hamiltonian. The probability of a transition, induced by the laser electric field is proportional to the square of the transfer coefficients modified by the presence of the magnetic field. We will show that the strong nonlinearity of the transition intensities versus the external magnetic field intensity is obvious for B<1500 G. Some possible application for Laser Spectroscopy of the Rb and the Na atoms will be presented.
We extend a recent classical mechanical analog of Bohr's atom consisting of a scalar field coupled to a massive point-like particle [P. Jamet and A. Drezet, "A mechanical analog of Bohr's atom based on de Broglie's double-solution approach," Chaos 31, 103120 (2021)] by adding and studying the contribution of a uniform weak magnetic field on their dynamics. In doing so, we are able to recover the splitting of the energy levels of the atom called Zeeman's effect within the constraints of our model and in agreement with the semiclassical theory of Sommerfeld. This result is obtained using Larmor's theorem for both the field and the particle, associating magnetic effects with inertial Coriolis forces in a rotating frame of reference. Our work, based on the old "double solution" theory of de Broglie, shows that a dualistic model involving a particle guided by a scalar field can reproduce the normal Zeeman effect.
Abstract Attempts to understand the behaviour of various quantum systems are still become interest for many researchers in recent years. While experimentation is too complicated to be done, analytical mathematical approach is become a reliable choice. This approach is using potential functions or models as representations of the real quantum system, such as physical force interactions within a molecule. In this study, the new combination model of screened Kratzer and screened Eckart potentials is investigated under the non-relativistic quantum mechanics framework. These potentials are well-suited for modelling atomic interactions in diatomic molecules. The primary objective is to examine how these interactions are affected by the presence of external magnetic fields. Using a specific form of the Schro dinger equation, both the energy eigenfunction and the wave function have been derived. The Nikiforov-Uvarov Functional Analysis (NUFA) method was employed for this derivation. Additionally, several thermodynamic properties were obtained from the energy equation using numerical methods. Selected diatomic molecule data were used in the computations to demonstrate the effect of the magnetic field. A detailed analysis was performed through graphical representations, revealing that an increase in the magnetic field or the associated Aharonov-Bohm (AB) flux enhances and splits the energy spectra. The effects on thermodynamic properties vary across different molecules and conditions, but overall, the magnetic field increases the thermodynamic properties of the molecules.
To enhance the current understanding of mechanisms contributing to magnetic hyperfine interactions in excited states of atomic systems, in particular, alkali-metal atom systems, the hyperfine fields in the excited 52S1/2−−82S1/25{}^{2}{S}_{1/2}--8{}^{2}{S}_{1/2}52S1/2​−−82S1/2​ states of potassium and 82S1/2−−122S1/28{}^{2}{S}_{1/2}--12{}^{2}{S}_{1/2}82S1/2​−−122S1/2​ states of francium atoms have been studied using the relativistic linked-cluster many-body perturbation procedure. The net theoretical values of the hyperfine fields for the excited states studied are in excellent agreement with available experimental data for both atoms. There is a significant decrease in importance of the correlation contribution in going from the ground state to the excited states, the correlation contributions as ratios of the direct contribution decreasing rapidly as one moves to the higher excited states. However, the contribution from the exchange core polarization (ECP) effect is nearly a constant fraction of the direct effect for all the excited states considered. Physical explanations are offered for the observed trends in the contributions from the different mechanisms. A comparison is made of the different contributing effects to the hyperfine fields in potassium and francium to those in the related system, rubidium, studied earlier. Extrapolating from our results to the highly excited states of alkali-metal atoms, referred to as the Rydberg states, it is concluded that in addition to the direct contribution from the excited valence electron to the hyperfine fields, a significant contribution is expected from the ECP effect arising from the influence of exchange interactions between electrons in the valence and core states.