Calibration method in isotopic carbon analysis

Unlike neutrons or gamma-rays, charged particles readily lose energy when they penetrate matter; thus, the main difficulty in its calculation is, perhaps, the complication introduced in its mathematical treatment. In our experiments, determination of ¹³C in breath test samples by proton-induced gamma-ray emission, interesting regularities were found that allowed drastic simplification in the theoretical treatment of the problem, and led to the derivation from first principles of a simple, sufficiently accurate basic equation which proved reliable for the determination of the isotopic abundance ratio ${}^{13}\text{C}{}^{12}\text{C}$ by low-energy proton bombardment of biological samples with simultaneous prompt gamma spectrometry.