We study a vortex line in superfluid He-4 on the basis of a shadow wav
e function. This allows for the first time the treatment of a quantum
vortex in He-4 with distributed vorticity and a non vanishing density
at its axis. We consider He-4 in a cylindrical bucket and by Monte Car
lo method we compute the excitation energy as a function of the radial
distance from the vortex axia and the density profile.