We investigate the α-decay of a spherical nucleus under the influence of an ultra-intense laser field for the case where the radius vector joining the centre-of-masses of the α-particle and the daughter is aligned with the direction of the external field. The time-independent part of the α-daughter interaction is taken from elastic scattering compilations whereas the time-varying part describes the interaction between the decaying system with the laser field. The time-dependent Schr?dinger equation is solved numerically by appealing to a modified scheme of the Crank-Nicolson type where an additional first-order time derivative appears compared to the field-free case. The tunnelling probability of the α-cluster and derived quantities (decay rate, total flux) is determined for various laser intensities and frequencies for either continuous waves or few-cycle pulses of envelope function F(t) = 1. We show that in the latter case pulse sequences containing an odd number of half-cycles determine an enhancement of the tunnelling probability when compared to the field-free case and the continuous wave case. The present study is carried out using the alpha decaying nucleus 106Te as an example.
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