Simulation of nonperturbative interactions between electric fields and real three-dimensional atoms is demanding. For this reason, many proof-of-principle and method studies replace three-dimensional atoms by suitable one-dimensional soft-core models. Soft-core potentials may be classified by their curvature at the nucleus that can be either infinite, finite, or vanishing. Within each class, models with analytical ground states and correct $1s$ binding energy exist. In this work we examine if the agreement with real atoms extends to perturbations by electric fields for such models. We demonstrate that the static polarizability is generally overestimated. Accordingly, we construct an improved soft-core potential, for which both $1s$ binding energy and polarizability agree with three-dimensional values. Additionally, the hyperpolarizability of this model deviates by as little as 3% from three-dimensional hydrogen, and field-induced ionization is correctly captured. Finally, we show that the new potential leads to significantly improved response to time-dependent fields.

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• Nonlinear optics
• Perturbation theory
• Polarizability