Metal foil targets were irradiated with 1 mum wavelength (lambda) laser pulses of 5 ps duration and focused intensities (I) of up to 4x10;{19} W cm;{-2}, giving values of both Ilambda;{2} and pulse duration comparable to those required for fast ignition inertial fusion. The divergence of the electrons accelerated into the target was determined from spatially resolved measurements of x-ray K_{alpha} emission and from transverse probing of the plasma formed on the back of the foils. Comparison of the divergence with other published data shows that it increases with Ilambda;{2} and is independent of pulse duration. Two-dimensional particle-in-cell simulations reproduce these results, indicating that it is a fundamental property of the laser-plasma interaction.