Near-threshold ionization of He has been studied by using a uniform semicla
ssical wavefunction for the two outgoing electrons in the final channel. Th
e quantum mechanical transition amplitude for the direct and exchange scatt
ering derived earlier by using the Kohn variational principle has been used
to calculate the triple differential cross sections. Contributions from si
nglets and triplets are critically examined near the threshold for coplanar
asymmetric geometry with equal energy sharing by the two outgoing electron
s. It is found that in general the tripler contribution is much smaller com
pared to its singlet counterpart. However, at unequal scattering angles suc
h as theta (1) = 60 degrees, theta (2) = 120 degrees the smaller peaks in t
he triplet contribution enhance both primary and secondary TDCS peaks. Sign
ificant improvements of the primary peak in the TDCS are obtained for the s
inglet results both in symmetric and asymmetric geometry indicating the nee
d to treat the classical action variables without any approximation. Conver
gence of these cross sections are also achieved against the higher partial
waves. Present results are compared with absolute and relative measurements
of Rosel et al (1992 Phys. Rev. A 46 2539) and Selles et al (1987 J. Phys.
B. At. Mel. Phys. 20 5195) respectively.