The paper studies the general Pauli-like equation for a Dirac fermions doublet on the background of an external non-Abelian monopole field. The variables separation has been fulfilled, the non-relativistic approximation for the radial systems has been derived. For the case of a minimal value of the conserved quantum number j = 0, the Pauli equation has been obtained in the form of one second-order differential equation. In the case j > 0, the problem has been reduced to the system of two coupled second order equations. In Bogomol'nyi-Prasad-Sommerfeld approximation, this system of equations has been solved in terms of hypergeometric functions.
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Ovsiyuk et al. (2022) studied this question.
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