The symbol | | indicates that the absolute value (L -S) is employed, i.e., no regard is paid to ± sign. Thus for L = 2 and S = 1, the possible J states are 3, 2 and 1 in units of h/2 .The individual spin angular momentum, si and the individual orbital angular momentum, li, couple to give total individual angular momentum, ji. This scheme of coupling is known as spin-orbit coupling or j -j coupling.
Term symbols
Spectroscopic terms for free ion ground statesThe rules governing the term symbol for the ground state according to L-S coupling scheme are given below: a. The spin multiplicity is maximized i.e., the electrons occupy degenerate orbitals so as to retain parallel spins as long as possible (Hund's rule). b. The orbital angular momentum is also maximized i.e., the orbitals are filled with highest positive m values first. c. If the sub-shell is less than half-filled, J = L-S and if the sub-shell is more than halffilled, J = L +S.The term symbol is given by 2S+1 LJ. The left-hand superscript of the term is the spin multiplicity, given by 2S+1 and the right-hand subscript is given by J. It should be noted that S is used to represent two things-(a) total spin angular momentum and (b) and total angular momentum when L = 0. The above rules are illustrated with examples.
The present paper deals with the thermo physical properties of a Casson fluid through an oscillating vertical wall embedded through porous medium under the influence transverse magnetic field, radiation, constant heat source and first order chemical reaction. The radiative heat loss is modelled by using Rosseland approximation. Similarity variables were used to convert the partial differential equations into ordinary differential equation. The transformed ordinary differential equations are solved numerically using Runge-Kutta-Fehlberg method with shooting technique. In order to get perfect perception of the flow pattern we obtain the graphs of axial velocity, temperature and concentrations profiles for various governing parameters viz. Casson parameter, Wall dilation ratio, Reynolds number, Grashoff numbers, Magnetic field parameter, Porous parameter, Radiation parameter, Prandtl number, Heat source parameter, Schmidt's number, Soret number, Chemical reaction parameter. Influence of Skin friction coefficient, Nusselt number, and Sherwood number on both walls are discussed and presented through tabular form.
In this paper, we discuss the Soret and Dufour effects on an MHD micropolar fluid flow over a linearly stretching sheet, through a non-Darcy porous medium, where stretching velocity of the sheet varies linearly with distance from the origin, and, temperature and concentration vary non-linearly in the boundary layer region. By suitable similarity transformations, the governing boundary layer equations are transformed to ordinary differential equations. These equations are solved by numerical computations with bvp4c along with the shooting technique method. The effects of the magnetic parameter, Soret number and Dufour number on velocity profiles, microrotation profile, heat transfer, and concentration, skin-friction, Nusselt number and Sherwood number are computed, discussed and analysed numerically and presented through tables and graphs.
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