DOI: https://doi.org/10.30970/jps.02.346
TAKING INTO ACCOUNT OF SPIN-ORBIT COUPLING DURING CALCULATION OF FORMFACTORS OF NONLOCAL MODEL POTENTIAL
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Journal of Physical Studies 2(3), 346–356 (1998)
DOI: https://doi.org/10.30970/jps.02.346 TAKING INTO ACCOUNT OF SPIN-ORBIT COUPLING DURING CALCULATION OF FORMFACTORS OF NONLOCAL MODEL POTENTIAL |
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V. V. Fourman1,4, P. M. Yakibchuk1, S. O. Vakarchuk2, M. I. Zhovtanetskiy3
1The Ivan Franko State University of Lviv, Chair of Theoretical Physics,
12 Drahomanov Str., Lviv, UA–290005, Ukraine
2State University Lvivs'ka Politekhnika", Chair of Physics,
12 S. Bandera Str., Lviv, UA–290646, Ukraine
3The Ivan Franko State University of Lviv,
Chair of the Information System in Management,
18 Svobody Pr., Lviv, UA–290000, Ukraine
4E–mail: fourman@KTF.Franko.lviv.ua
The scheme that takes into account spin–orbit coupling is determined for scattering processes with the potential. The criterions of construction of nonlocal model potentials for transition and rare–earth metals on the base of the phase functions formalism, that take into account effects of spin–orbit coupling have been developed. For bound states energies, with the help of the phase functions method the criterion for finding the changes of parameters of nonlocal model potentials because of spin–orbit coupling have been obtained. Taking into account an analyticity of scattering amplitude in the presence of potential the conditions that are imposed on its structure have been analysed. The behaviour of scattering shifts was analyzed taking into account spin–orbit coupling. Phase equation with Coulomb wave functions that contain potential with spin–orbit coupling is received judging the properties of partial scattering shifts for bound states. Asymptotic solutions were found for this equation. The phase equation for partial scattering shifts in terms of Coulomb functions with partial component of potential and asymptotics that are valid for arbitrary nonlocal model potentials are presented.
The expressions for calculating model potential formfactors of transition and rare–earth metals, considering spin–orbit coupling in potential have been received. They depend on quantum defects and spectroscopic energy shifts determined through solutions of phase equations in terms of Coulomb functions.
Using obtained nonlocal model potential of 4$f$–metals and its formfactors the cohesive energy and equilibrium atomic radii have been calculated. For $4f$–metals the constant of spin–orbit coupling has been calculated too. The results of calculations are in good agreement with experimental values.