An apparatus can measure characteristics of a formation surrounding a borehole. The apparatus includes a tool body having a neutron measurement section and a density measurement section. The neutron measurement section includes a neutron source and a neutron detector arrangement spaced in an axial direction from the neutron source. The density measurement section includes a gamma ray source and a gamma ray detector arrangement spaced in an axial direction from the gamma ray source. The neutron measurement section and the density measurement section are positioned in the tool body so that the sections overlap in the axial direction and are azimuthally spaced apart in the tool body. The tool body also includes shielding to block a direct signal path from the neutron source to the gamma ray detector arrangement and to block a direct signal path from the gamma ray source to the neutron detector arrangement.