We experimentally and numerically investigated the impact of input pump pulse duration on the near-infrared bandwidth of supercontinuum generation in a photonic crystal fiber. We continuously stretched the temporal duration of the input pump laser (centered at 1030 nm) pulses from 500 fs up to 10 ps, while keeping fixed the pump peak power. We observed that the long-wavelength edge of the supercontinuum spectrum is increased by 200 nm as the pump pulse duration grows from 500 fs to 10 ps. We provide a quantitative fit of the experimental results by means of numerical simulations. Moreover, we have explained the observed spectral broadening enhancement induced by pump pulse energy by developing an approximate yet fully analytical model for soliton energy exchange through a series of collisions in the presence of stimulated Raman scattering.