Disclosed is a method for estimating a density of an earth formation penetrated by a borehole. The method includes: emitting a pulse of fast neutrons into the formation during a neutron-pulse time interval; detecting gamma-rays due to inelastic scattering and thermal capture of the emitted neutrons in the formation to provide a gamma-ray energy spectrum due to the inelastic scattering and the thermal capture during a first time interval within the neutron-pulse time interval and to provide a time spectrum of counts or count rates due to thermal capture during a second time interval occurring after the neutron-pulse time interval; determining a macroscopic capture cross section of the formation from a decay in the time spectrum of counts or count rates; determining an elemental weight fraction from the gamma-ray energy spectrum; and estimating the density of the formation using the macroscopic capture cross section and the elemental weight fraction.