Nuclear matter density distributions of "4He and the neutron-rich nuclei "6He and "8He were studied via intermediate-energy proton nucleus scattering in inverse kinematics using the recoil detector IKAR. For these nuclei, differential cross sections for elastic scattering at low momentum transfer were measured with an accuracy of 2% on absolute normalization. The experimental method and the procedure of data analysis are described. Phenomenological and microscopically calculated nuclear matter distributions were related to the measured cross sections with the aid of the Glauber multiple scattering theory. (orig.)13 refs.Available from TIB Hannover: RO 801(95-33) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman