From a point-like to an arbitrarily shaped sample: A survey of equations for electron paramagnetic resonance signal intensity calculations

A set of original, analytical equations useful for theoretical calculation of the electron paramagnetic resonance (EPR) signal intensity are presented for the multitude of sample shapes, which range from point-like, line-like, planar, rectangular, cubical, circular, cylindrical, spherical to an irregularly shaped sample. The samples can be situated at any available position within the prescribed part of the microwave cavity (a central cylinder of diameter 11 mm and length 23.5 mm, in either a Bruker single TE₁₀₂ or double TE₁₀₄ rectangular cavity, with the modulation coils situated in the left and right side cavity walls, which is connected to a X-band, field-modulated CW Bruker EPR spectrometer). The theoretical computations of EPR signal intensity can be used in the computer simulations in which: (i) the EPR signal intensity profiles are constructed; (ii) the optimal sample positions in the cavity to give a maximum value of signal intensity are found; (iii) the errors associated with sample positioning within the cavity when compared to a second sample of a different size, shape or position are studied.