Linear Rayleigh and Raman scattering to the second order: Analytical results for light scattering by any scatterer of size <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mi>d</mml:mi><mml:mo>≲</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:math>

We extend the usual multipolar theory of linear Rayleigh and Raman scattering to include the second-order correction. These terms promise a wealth of information about the shape of a scatterer and yet are insensitive to the scatterer's chirality. Our extended theory might prove especially useful for analyzing samples in which the scatterers have nontrivial shapes but no chiral preference overall, as the zeroth-order theory offers little...