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During polar-cap absorption events, which are caused by the incidence ofenergetic solar protons, the high-latitude ionospheric D region is extendeddown to relatively low altitudes. While the incoming proton fluxes may bemonitored by satellite-borne detectors, and the resulting radio-waveabsorption with a ground-based riometer, the enhancement of electron densityat a given altitude is less easily determined. Direct measurements byincoherent-scatter radar are infrequent and they tend to lack the necessarysensitivity at the lower levels. Computations of the electron density fromthe observed particle fluxes are handicapped by uncertainties in the heightprofile of the effective recombination coefficient.<P  style="line-height: 20px;">This paper describes a new approach based on finding the best-fit solutionto an over-determined set of equations. The D region is treated as a set ofslabs, each contributing to the total radio absorption, and the methodrelies on the fact that the proton spectrum varies during the event. Theanalysis produces a set of coefficients relating the absorption increment inthe slab to the square root of the production rate, as a function of height.Values of effective recombination coefficient are also deduced over a rangeof heights, and these agree with previous estimates (Gledhill, 1986) towithin a factor of 2. However, whereas the latter do not generally go below60km altitude the new determination extends the values down to 40km.<P  style="line-height: 20px;">The new method provides a measurement of the height profile of theabsorption in PCA events. It is shown that the slabs centred from45 to 65km typically account for 80% of the total daytime absorption, and thatless than 1% of the total arises above 80km or below 30km. At nightmost of the absorption comes from the slabs at 75 and 80km, with nosignificant contribution from slabs below 75 or above 85km. These resultswould not differ significantly from estimates based on the Gledhill profilesif extrapolated downward.<P  style="line-height: 20px;">Predictions based on the coefficients generated by the procedure arecompared with the polar-cap absorption observed during some recent events.Typical electron-density values are derived, and the study provides anindependent confirmation that the electron density and the production rateare related by a square-root law

A new method of studying the relation between ionization rates and radio-wave absorption in polar-cap absorption events