## The Gibbs phenomenon leads to the appearance of discontinuities near the threshold energy in the partial cross section from the *v* = 2 level of the *b* ^{3}Σ^{+} state towards the H^{+} + He(1s2p ^{3}P^{o}) fragments (full line, black), while the total cross section as obtained through the Fourier transform of the autocorrelation function for short propagation times is perfectly smooth (dashed line)

**Figure 3.** The Gibbs phenomenon leads to the appearance of discontinuities near the threshold energy in the partial cross section from the *v* = 2 level of the *b* ^{3}Σ^{+} state towards the H^{+} + He(1s2p ^{3}P^{o}) fragments (full line, black), while the total cross section as obtained through the Fourier transform of the autocorrelation function for short propagation times is perfectly smooth (dashed line). Thanks to this, the correct form of the partial cross section can be deduced (full line, red).

**Abstract**

We illustrate some of the difficulties that may be encountered when computing photodissociation and radiative association cross sections from the same time-dependent approach based on wavepacket propagation. The total and partial photodissociation cross sections from the 33 vibrational levels of the *b* ^{3}Σ^{+} state of HeH^{+} towards the nine other ^{3}Σ^{+} and 6 ^{3}Π *n* = 2, 3 higher lying electronic states are calculated, using the autocorrelation method introduced by Heller (1978 *J. Chem. Phys.* **68** 3891) and the method based on the asymptotic behaviour of wavepackets introduced by Balint-Kurti *et al* (1990 *J. Chem. Soc. Faraday Trans.* **86** 1741). The corresponding radiative association cross sections are extracted from the same calculations, and the photodissociation and radiative association rate constants are determined.