Magnus and Iordanskii Forces in Superfluids

The total transverse force acting on a quantized vortex in a superfluid is a problem that has eluded a complete understanding for more than three decades. A recent publication by Thouless, Ao and Niu demonstrates that the vortex velocity part of this force in a homogeneous neutral superfluid is given by the usual form $\rho_s \kappa_s \times v_V$. In this letter we propose a remarkably simple argument to define the other parts of the transverse force, based on the macroscopic properties of superfluid flow. We find that the only other term in the transverse force is a superfluid velocity dependent $-\rho_s \kappa_s \times v_s$, in apparent conflict with Iordanskii's theory of the transverse force due to phonon scattering by the vortex.