# Electron Spin Resonance (ESR) Experiment: the two peaks

I am unable to figure out how we get two peaks in the Electron Spin Resonance (ESR) experiment, in which we use Helmholtz coils as B source with modulation, and a basic unit as a source of radio waves.

• ESR is electron spin rotation? – rob Apr 29 '14 at 19:31
• electron spin resonance – kalkanistovinko Apr 29 '14 at 19:42

Assuming that the word "modulation" refers to Zeeman modulation created by superimposing a DC and AC voltage on the Helmholtz coil, and that a fixed-frequency radio wave source is used, the amplitude of the Zeeman-modulation-induced fluctuations in radio-wave intensity after passing through the sample is given by $$\Delta I\approx\frac{dI}{dH}\Delta H$$ where $I(H)$ is the absorption intensity as a function of field-strength $H$ and $\Delta H$ is the depth of the Zeeman modulation. Assuming that $\Delta H\ll\sigma$, where $\sigma$ is the width of the peaks, this means that the fluctuation signal measured is actually proportional to $dI/dH$, rather than $I(h)$.
expr = D[1/(x^2 + 1), x];