Analytical solution for the inverting pulses with constant adiabaticity

[Display omitted] •Analytical solution for the inverting pulses with constant adiabaticity.•Comparison with other adiabatic EPR pulses.•Design of new inverting pulses with constant adiabaticity. The exact solution was found for inverting pulses with constant adiabaticity for spin ½. The analytical relationship between the time-varying frequency of the microwave resonant field (or RF field in the case of NMR) and its amplitude time dependence such that the adiabaticity parameter remains constant for the single isochromat throughout the pulse is found. Comparison with EPR (hyperbolic tangent)-(hyperbolic secant) pulse method was carried out. On the basis of the analytical solution the pulses with different dependences of the microwave field amplitude conserving the constant adiabaticity have been constructed. The pulses exhibit rather sharp inversion selectivity that can be used in the field of EPR, NMR and MRI.