Casimir–Polder non-retarded limit

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Reference
Casimir–Polder non-retarded limit
Kind
analytic: a closed form, limit or conservation law: independent of any code
Calculated
potential
Agreement
1e-12
An atom near a 200 nm Drude sphere: the Casimir–Polder potential against the non-retarded limit −C₃/d³ Within a nanometre the potential is the flat-surface, non-retarded −C₃/d³ with C₃ = (ħ/4π)∫α(iξ)(ε − 1)/(ε + 1) dξ; further out retardation and the sphere's curvature weaken it, so the curves part by design: 0.3% at 0.5 nm, 3% at 5 nm, 37% at 50 nm.
102030405010⁻²⁷10⁻²⁶10⁻²⁵10⁻²⁴10⁻²³10⁻²²10⁻²¹10⁻²⁰10⁻¹⁹distance from the surface [nm]|U| [J]
|U|, PyStratify C₃/d³, non-retarded limit
Hover to read values.
  • relative difference within 0.6 nm: 0.00337399
  • PyStratify the lines, the reference the circles

Run it yourself: sphere_emitter_checks.py · test_casimir.py · figures.py · SPHERE_EMITTER_CHECKS.md on GitHub, PyStratify 97e52a9