A process for preparing ethylene homopolymers and copolymers in a tubular reactor having two or more polymerization zones at temperatures of between 150° C. and 350° C. and pressures in the range from 500 to 5000 bar, using oxygen as initiator, which comprises using, as molar mass regulator, one or more aliphatic ketones of the formula I, where the variable R1 is a C1-C6-alkyl or C3-C12-cycloalkyl, ethylene homopolymers and copolymers obtainable therefrom and their user for producing injection-molded products in the cosmetics, medical and food sectors are described.