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Physical Review A

Quantum states of neutrons bound in the magnetic field of a rectilinear current

R. Blümel, Klaus Dietrich

Published Jan 1, 1991• 98 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.43.22

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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.
A first experimental demonstration of a new type of magnetic trap for ultra-cold neutrons is presented. High-field seeking spin-states are trapped in a potential formed by the magnetic field of a straight wire and a repulsive coating on the wire surface. Life-times of the trapped neutrons of 60 s could be observed. This configuration can in principle be used to form bound states of the wave function on the surface of the wire to probe new forces at short distances. Further applications include the use as a guide and selector for perfectly polarized neutrons.
A first experimental demonstration of a new type of magnetic trap for ultra-cold neutrons is presented. High-field seeking spin-states are trapped in a potential formed by the magnetic field of a straight wire and a repulsive coating on the wire surface. Life-times of the trapped neutrons of 60 s could be observed. This configuration can in principle be used to form bound states of the wave function on the surface of the wire to probe new forces at short distances. Further applications include the use as a guide and selector for perfectly polarized neutrons.
We consider a waveguide for cold neutral atoms with a magnetic moment proportional to their spin angular momentum. The waveguide consists of a thin wire carrying a constant current. For the spin-1 case, we find bound states for the two-dimensional part of the motion around the wire, and present numerical and approximate analytic results for these bound states. In an experiment, the bound states can decay due to various effects, and we calculate the time scales involved. \textcopyright{} 1996 The American Physical Society.
The energy spectrum of a neutral atom bound in the magnetic field created by a straight line direct current is given by the Rydberg formula for particles with spin less than 3/2. An adiabatic representation leads to a natural understanding of this spectrum and provides a good approximation to the bound state energy levels. A more accurate finite element method is applied to directly solve the time-independent Schr\"odinger equation for neutral particles with arbitrary spin. A combination of the finite element method with multichannel quantum defect theory provides a more efficient method to calculate the bound state energies. In addition, new spectral features arise for particles with spin greater than 1. \textcopyright{} 1996 The American Physical Society.
The problem of the neutron scattering in the magnetic field of a linear current has been formulated and solved quantum mechanically exactly. The SSS matrix has been derived in the adiabatic representation and the closed analytical expression for the differential cross section has been obtained. The results reveal the topological phase part at the nonadiabatic collisions.