We have mapped the dense dark core L 1544 in { H ^ { 13 } CO } ^ { + } ( 1–0 ) , { DCO } ^ { + } ( 2–1 ) , { DCO } ^ { + } ( 3–2 ) , { N } _ { 2 } { H } ^ { + } ( 1–0 ) , { N } _ { 2 } { H } ^ { + } ( 3–2 ) , { N } _ { 2 } { D } ^ { + } ( 2–1 ) , { N } _ { 2 } { D } ^ { + } ( 3–2 ) , { C } ^ { 18 } { O } ( 1–0 ) , and { C } ^ { 17 } { O } ( 1–0 ) using the IRAM 30–m telescope . We have obtained supplementary observations of { HC ^ { 18 } O } ^ { + } ( 1–0 ) , { HC ^ { 17 } O } ^ { + } ( 1–0 ) , and { D ^ { 13 } CO } ^ { + } ( 2–1 ) . Many of the observed maps show a general correlation with the distribution of dust continuum emission in contrast to { C } ^ { 18 } { O } ( 1–0 ) and { C } ^ { 17 } { O } ( 1–0 ) which give clear evidence for depletion of CO at positions close to the continuum peak . In particular { N } _ { 2 } { D } ^ { + } ( 2–1 ) and ( 3–2 ) and to a lesser extent { N } _ { 2 } { H } ^ { + } ( 1–0 ) appear to be excellent tracers of the dust continuum . Our { DCO } ^ { + } maps have the same general morphology as the continuum while { H ^ { 13 } CO } ^ { + } ( 1–0 ) is more extended . We find also that many apparently optically thin spectral lines such as { HC ^ { 18 } O } ^ { + } and { D ^ { 13 } CO } ^ { + } have double or highly asymmetric profiles towards the dust continuum peak . We have studied the velocity field in the high density nucleus of L 1544 putting particular stress on tracers such as { N } _ { 2 } { H } ^ { + } and { N } _ { 2 } { D } ^ { + } which trace the dust emission and which we therefore believe trace the gas with density of order of 10 ^ { 5 } \hbox { { cm } } ^ { -3 } . We find that the tracers of high density gas ( in particular { N } _ { 2 } { D } ^ { + } ) show a velocity gradient along the minor axis of the L 1544 core and that there is evidence for larger linewidths close to the dust emission peak . We interpret this using the model of the L 1544 proposed by [ Ciolek and Basu 2000 ] and by comparing the observed velocities with those expected on the basis of their model . The results show reasonable agreement between observations and model in that the velocity gradient along the minor axis and the line broadening toward the center of L 1544 are predicted by the model . This is evidence in favour of the idea that amipolar diffusion across field lines is one of the basic processes leading to gravitational collapse . However , the double–peaked nature of the profiles is reproduced only at the core center and if a “ hole ” in the molecular emission , due to depletion , is present . Moreover , line widths are significantly narrower than observed and are better reproduced by the [ Myers & Zweibel 2001 ] model which considers the quasistatic vertical contraction of a layer due to dissipation of its Alfvénic turbulence , indicating the importance of this process for cores in the verge of forming a star .