The orientational phase transition at a vortex in³He-B

The orientational phase transition in the vicinity of a single vortex in³He-B is studied. It is the phase transition from a uniform n-texture with n parallel to the magnetic field and the vortex line to an n-texture that is nonuniform near the vortex. The problem of the instability of the the uniform n-texture is equivalent to the quantum mechanical two-dimensional problem of a bound state in a field with an attractive potential 1/r². The orientational phase transition at a vortex array is also considered. In the limit of large vortex density the orientational phase transition transforms to the phase transition studied by Gongadze et al. The theoretical results are compared with the observed phase transition at a vortex in³He-B.