We report high-resolution spectroscopic observations of the NLTE H alp
ha core in 28 DA white dwarfs. From a comparison with theoretically br
oadened NLTE models projected rotation velocities can be determined. T
he majority of objects are found to be compatible with zero or very sm
all rotation with typical upper limits for v sin i of 15 km/s, corresp
onding to periods of hours or longer. The implications for the loss of
angular momentum during the evolution of the progenitors is discussed
. Three new magnetic white dwarfs are detected with very small tangent
ial fields in the range of 30 to 50 kG. In two more magnetic objects k
nown before we found field strengths significantly larger than the mea
n longitudinal fields determined from the circular polarization. Very
puzzling is the result for three ZZ Ceti stars in the sample, which al
l seem to have projected rotational velocities between 30 and 45 km/s,
in conflict with asteroseismological results.