Analytical distance distributions in systems of spherical symmetry with applications to double electron-electron resonance

► Analytical expressions of the probability density functions (pdfs) of distance. ► Valid for homogeneously distributed probes in spherical aggregates with shell structure. ► Well-suited to analyze DEER data of disordered nanometer-sized spin clusters. ► Provides building blocks for distance distributions in arbitrary spherically symmetric objects. ► Applied to derive spin probe distributions in SDS micelles from DEER data.