A new parameter to describe light scattering by an arbitrary sphere

We consider light scattering by uniform spheres of arbitrary size R and refractive index m. A new internal coupling parameterρ'=2kR|(m2−1)/(m2+2)| where k=2π/λ and λ is the wavelength is proposed that has a superior ability to determine the asymptotic regimes of small size, weakly refractive and large size, refractive than the parameter ρ=2kR(m−1). It also has superior ability as a parameter to organize patterns in light scattering from spheres.