Production cross sections for neutron-rich nuclei from the fragmentation of a 76Ge beam at 132 MeV/u were measured. The longitudinal momentum distributions of 34 neutron-rich isotopes of elements 13 <= Z <= 27 were scanned using a novel experimental approach of varying the target thickness. Production cross sections with beryllium and tungsten targets were determined for a large number of nuclei including 15 isotopes first observed in this work. These are the most neutron-rich nuclides of the elements 17 <= Z <= 25 (50Cl, 53Ar, 55,56K, 57,58Ca, 59,60,61Sc, 62,63Ti, 65,66V, 68Cr,70Mn). A one-body Qg systematics is used to describe the production cross sections based on thermal evaporation from excited prefragments. Some of the fragments near 58Ca show anomalously large production cross sections.