We present results of an extensive mapping survey of N _ { 2 } H ^ { + } ( 1–0 ) in about 60 low mass cloud cores already mapped in the NH _ { 3 } ( 1,1 ) inversion transition line . The survey has been carried out at the FCRAO antenna with an angular resolution of 54 ^ { \prime \prime } , about 1.5 times finer than the previous ammonia observations made at the Haystack telescope . The comparison between N _ { 2 } H ^ { + } and NH _ { 3 } maps shows strong similarities in the size and morphology of the two molecular species indicating that they are tracing the same material , especially in starless cores . Cores with stars typically have map sizes about a factor of two smaller for { N } _ { 2 } { H } ^ { + } than for NH _ { 3 } , indicating the presence of denser and more centrally concentrated gas compared to starless cores . The mean aspect ratio is \sim 2 . Significant correlations are found between { NH } _ { 3 } and { N } _ { 2 } { H } ^ { + } column densities and excitation temperatures in starless cores , but not in cores with stars , suggesting a different chemical evolution of the two species . Starless cores are less massive ( < M _ { vir } > \simeq 3 M _ { \odot } ) than cores with stars ( < M _ { vir } > \simeq 9 M _ { \odot } ) . Velocity gradients range between 0.5 and 6 km/s/pc , similar to what has been found with NH _ { 3 } data , and the ratio \beta of rotational kinetic energy to gravitational energy have magnitudes between \sim 10 ^ { -4 } and 0.07 , indicating that rotation is not energetically dominant in the support of the cores . “ Local ” velocity gradients show significant variation in both magnitude and direction , suggesting the presence of complex motions not interpretable as simple solid body rotation . Integrated intensity profiles of starless cores present a “ central flattening ” and are consistent with a spherically symmetric density law n \propto r ^ { - \alpha } where \alpha = 1.2 for r < r _ { break } and \alpha = 2 for r > r _ { break } , where r _ { break } \sim 0.03 pc . Cores with stars are better modelled with single density power laws with \alpha \geq 2 , in agreement with observations of submillimeter continuum emission . Line widths change across the core but we did not find a general trend : there are cores with significant positive as well as negative linear correlations between \Delta v and the impact parameter b . The deviation in line width correlates with the mean line width , suggesting that the line of sight contains \sim 10 coherence lengths . The corresponding value of the coherence length , \sim 0.01 pc , is similar to the expected cutoff wavelength for MHD waves . This similarity may account for the increased “ coherence ” of line widths on small scales . Despite of the finer angular resolution , the majority of { N } _ { 2 } { H } ^ { + } and { NH } _ { 3 } maps show a similar “ simple ” structure , with single peaks and no elongation .