Effective field theory for the bound states and scattering of a heavy charged particle and a neutral atom

We show the system of a heavy charged particle and a neutral atom can be described by a low-energy effective field theory where the attractive 1/r4 induced dipole potential determines the long-distance, low-energy wave functions. The 1/r4 interaction is renormalized by a contact interaction at leading order. Derivative corrections to that contact interaction give rise to higher-order terms. We show that this "induced-dipole EFT"(ID-EFT) reproduces the π+-hydrogen phase shifts of a more microscopic potential, the Temkin-Lamkin potential, over a wide range of energies. Already at leading order it also describes the highest-lying excited bound states of the pionic-hydrogen ion. Lower-lying bound states receive substantial corrections at next-to-leading order, with the size of the correction proportional to their distance from the scattering threshold. Our next-to-leading order calculation shows that the three highest-lying bound states of the Temkin-Lamkin potential are well described in ID-EFT.