The spectrum and the wave functions of neutrons bound in the magnetic field of a thin rectilinear current filament are calculated analytically by solving a fourth-order Hamburger equation. Finite current cross sections are treated numerically: the bound states persist---a necessary prerequisite in view of possible experimental verifications of the theory. Two setups [(i) a superconducting wire and (ii) a Church trap] are proposed for obtaining these states experimentally. Some results on spin-1 magnetic surface states are presented.
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Blümel et al. (1991) studied this question.
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