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arXiv · 2307.13103

Effective Field Theory for the Bound States and Scattering of a Heavy Charged Particle and a Neutral Atom

Daniel Odell·Daniel R. Phillips·Ubirajara van Kolck
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Abstract

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 $1/r^4$ induced dipole potential determines the long-distance/low-energy wave functions. The $1/r^4$ 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 $\pi^+$-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.

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Daniel Odell, Daniel R. Phillips, Ubirajara van Kolck. 2023-07-24. Effective Field Theory for the Bound States and Scattering of a Heavy Charged Particle and a Neutral Atom. https://arxiv.org/abs/2307.13103

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