Strong-potential Born calculations for electron capture

A closed-form expression for $1s-1s$ electron capture has been developed in the strong-potential Born (SPB) approximation. Terms of the order ${\left(\frac{Z_p}{v}\right)}^2$ are ignored in our expression, where $Z_p$ is the charge of the projectile and $v$ is the collision velocity. Our errors of order ${\left(\frac{Z_p}{v}\right)}^2$ are within the accuracy of the SPB approximation itself, which is valid to first order in the projectile-electron interaction $V_p$ (and all orders in the stronger target potential $V_T$). Calculations using our expression are in better agreement with experimental observations of the shape of the Thomas peak than are other calculations.