Linearizing the Navier-Stokes equations with a magnetic field for a velocity field of a plasma with axial symmetry, the axial and the azimuthal components of the velocity can be eliminated at the expense of a rational dependence on the eigenvalue parameter in the equation for the remaining velocity component. Corresponding eigenvalue problems such as \[ y''+ \left(\lambda- p+{q\over u-\lambda} \right)y=0,\;y(0)=y(1)=0, \] have extensively been studied, notably by H. Langer and the Regensburg school around R. Mennicken, using the theory of block operator matrices. Let \(p\) be a real-valued and \(q\) a nonnegative function in \(L^2(0,1)\). If \(u\) is real-valued and bounded, the point spectrum consists of eigenvalues accumulating at infinity and possibly of eigenvalues below \(\sup u\), while the essential spectrum is determined by the range of \(u\). In the present paper, slightly stronger assumptions are used to show that the essential spectrum of \[ \widetilde A:=\left(\begin{matrix} A & q^{1/2} \\ q^{1/2} & u\end{matrix} \right)\text{ in }L^2(0,1) \oplus L^2(0,1) \] \((A\) the operator \(-y''+py\) with Dirichlet boundary conditions) is in fact purely absolutely continuous, and the spectral density can be expressed in terms of a Titchmarsh-Weyl \(m\)-function. Moreover, the generalized Fourier transform which provides the unitary equivalence between the absolutely continuous part of \(\widetilde A\) and the operator of multiplication by the independent variable is explicitly given.