Neutron production from a thin deuterium–tritium (D–T) foil irradiated by two intense femtosecond laser pulses from opposite sides with zero phase difference is studied analytically and numerically. For the interaction of a laser pulse of amplitude $a=7$, focal area 100 $\mu$m$^2$ and areal density $4.4\times 10^{18}$ cm$^{-2}$ with a D–T plasma foil, about $1.17\times 10^{21}$ neutron s$^{-1}$ can be obtained, much more than from other methods. The profiles of the ion and electron densities are also calculated.