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Saturation Absorption Spectroscopy
Published in Pradip Narayan Ghosh, Laser Physics and Spectroscopy, 2018
An important result is that the total angular momentum of a sub-shell with completely filled electrons is zero. In this case, for each electron with a non-zero value +ml, there is an electron with a value −me similarly, for each electron with a value +ms there is an electron with a value −ms. Thus, the total electronic angular momentum component Jz = 0. Since the only allowed value of Jz is zero, the total angular momentum of the completely filled core is zero. For rubidium atom with a single unpaired electron in the valence shell, the orbital angular momentum is L and the spin angular momentum is ½. The possible values of the total angular momentum quantum number are J = |L ±1/2|.
Electronic Magnetic Moments
Published in David Jiles, Introduction to Magnetism and Magnetic Materials, 2015
The total angular momentum quantum number j of an electron is not an independent quantum number since it is determined by l and s. However, it is a useful quantity to define, particularly since it gives a measure of the total magnetic moment of an electron. It is the vector sum of the spin and orbital angular momenta and is necessarily quantized. () pj=j(h2π)=(l+s)(h2π)
Theoretical approaches for doubly-excited Rydberg states in quasi-two-electron systems: two-electron dynamics far away from the nucleus
Published in Molecular Physics, 2021
Rydberg states are associated with electrons promoted to atomic orbitals that are much larger in size than the residual ion ‘core’. Rydberg electrons are labelled by their principal quantum number n, orbital-angular-momentum quantum number l and total-angular-momentum quantum number j. In the following, we distinguish three different types of Rydberg states: (i) singly-excited Rydberg states, in which one electron is in a Rydberg orbital and the ion core is in its electronic ground state; (ii) core-excited Rydberg states, in which one electron is in a Rydberg orbital and the ion core is in a low-lying excited electronic state; (iii) doubly-excited Rydberg states, where two electrons are in Rydberg orbitals. These three types of Rydberg states possess distinctive physical properties that are detailed below for the case of quasi-two-electron atoms.
Dissociation energy and the lowest vibrational transition in LiH without assuming the non-Born–Oppenheimer approximation
Published in Molecular Physics, 2022
Saeed Nasiri, Toreniyaz Shomenov, Sergiy Bubin, Ludwik Adamowicz
The focus of this work is the fundamental vibrational transition energy of the LiH molecule. Unlike, the standard approach used in the calculations of the molecular ro-vibrational spectra, that is based on assuming the BO approximation, the present approach does not assume this approximation. By treating the electrons and the nuclei on an equal footing, high accuracy is achieved. In the calculations, we use the variational method with the Hamiltonian obtained by separating out the kinetic energy of the centre-of-mass motion from the laboratory all-particle nonrelativistic Hamiltonian. The wave functions of the considered states are expanded in terms of single-centre ECG functions, which are eigenfunctions of the operator representing the square of the total angular momentum of the molecule with the zero total angular momentum quantum number. The total angular momentum includes the electronic angular momentum and the nuclear angular momentum. Thus the states calculated in this work can be called ‘pure vibrational states’, as they represent the ground and lowest excited internal states in the rotation-less spectrum of the system. However, as the BO approximation is not assumed in the present calculations, the terms ‘rotational’ and ‘vibrational’ that are well defined within the BO approach can only be applied loosely to the results of the present calculations. As the coupling of the electronic and nuclear motions is explicitly present in our calculations, the non-BO results are not, strictly speaking, completely equivalent to the BO results. Naturally, in the limit of infinite basis sets used to expand the BO and non-BO wave functions of the system, the non-BO description is more accurate than its BO equivalent.
Bound and scattering states of the Klein-Gordon equation for shifted Tietz-Wei potential with applications to diatomic molecules
Published in Molecular Physics, 2021
Uduakobong S. Okorie, Akpan N. Ikot, Goatsiwe J. Rampho, Michael C. Onyeaju, Millicent U. Ibezim-Ezeani, Abdel-Haleem Abdel-Aty, M. Ramantswana
The total wave function in higher dimensions is defined as with the energy eigenvalues of being given as Here, is the hyper-spherical harmonics and is the total angular momentum quantum number, both in higher dimensions.