A new use of the kronig-kramers relations in nuclear magnetic resonance

Abstract

Many weak or readily saturable nuclear magnetic resonances can be detected only by the use of the dispersion mode in a nuclear induction system, and dispersion records of complicated or partially resolved spectra may be difficult to interpret. However, it is shown in this paper that, for systems obeying Bloch or Redfield equations, the Kronig-Kramers (K-K) relations may justifiably be used to transform a dispersion record taken in the presence of saturation, under slow modulation conditions, into the more readily interpretable absorption record. The K-K relations are shown to apply to the derivatives of the absorption and dispersion line shapes, which are the quantities usually recorded, and to transform a modulation-broadened dispersion curve into the appropriate modulation-broadened absorption curve. The relations hold for derivatives of any order and may, therefore, be applied to records from an apparatus employing phase-sensitive detection at any harmonic of the modulation frequency. Results are presented for some analytical cases, and details of the computational method are given. Simple trapezoidal integration is found to yield high accuracy. The resonance of ⁹Be in beryl is used to confirm the applicability of the K-K relations in the presence of saturation.