The peakedness of the density profile in source-free MHD-quiescent L-mode plasmas with lower hybrid current drive is observed to decrease with decreasing peaking of the current profile. For the discharges investigated, which include normal and reversed magnetic shear plasmas, the relationship can be summarized as n(e0)/ congruent to 1.2l(i), where l(i) is the normalized internal inductance. Density profiles are monotonically peaked at negative shear. Since density profiles remain peaked at zero loop voltage and negligible core particle source, the effect is attributed to an anomalous process of inward convection. No significant evidence was found for a correlation of density peaking with collisionality, nor of a dependence on temperature peaking within the parameter range investigated. The peaking, of-the temperature profiles and of the current profiles is uncorrelated in this dataset, allowing, for the first time, an experimental distinction between their effects on the density profile. The results are supportive of theories explaining particle convection by the anomalous curvature pinch or turbulent equipartition by trapped electrons, rather than by anomalous thermodiffusion.