  Bremsstrahlung emission in collisions between charged nuclei is equivalent to
nuclear gamma decay between continuum states. The way the continuum spectrum
can be treated is not unique, and efficiency and accuracy of cross section
calculations depend on the chosen method. In this work we describe, relate, and
compare three different methods in practical calculations of inelastic cross
sections, that is, by (i) treating the initial and final states as pure
continuum states on the real energy axis, (ii) discretizing the continuum
states on the real energy axis with a box boundary condition, and (iii) complex
rotation of the hamiltonian(complex scaling method). The electric quadrupole
transitions, $2^+ \rightarrow 0^+$ and $4^+ \rightarrow 2^+$, in
$\alpha+\alpha$ scattering are taken as an illustration.
