Textures in slowly rotatingHe3-A

The free energy of rotating ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$ in zero magnetic field and large cylinders ($R\gg 10$ μm) is calculated for several textural configurations at slow rotation speeds ($\Omega \approx \frac{\hslash }{2m{R}^2}$). The sequence of equilibrium states with increasing $\Omega$ is studied near $T_c$. A transition from the Mermin-Ho state to one of higher circulation should occur for $\Omega \approx \frac{9.6\hslash }{2m{R}^2}$. This transition may be delayed, however, by the onset of azimuthal distortion ("swirl") in the Mermin-Ho state. A new experimental method is proposed for studying various textural configurations, based on the anistropy of negative-ion mobility. Significant and characteristic focusing should occur when ions are swept through long cylinders of length $L>\mathrm{}10R$. In addition, time-of-flight information can also help identify the textural state. Finally, the qualitative effects of weak magnetic fields and lower temperatures are discussed.