A newly developed "intense-field many-body S-matrix" theory (or IMST) for i
nvestigating highly nonperturbative interaction of strong laser pulses with
many-electron atomic and molecular systems is briefly presented and the us
efulness of the theory is demonstrated by direct calculations of (i) "hot e
lectron plateaus" in ATI spectra of He, (ii) intensity dependence of double
ionization yields of He, and (iii) multiple ionization yields of Xe, (iv)
"enhanced ionization" of a diatomic molecule, H-2, and (v) of the polyatomi
c molecules benzene C6H6 and its cation C6H6+. The ATI spectra of He and th
e associated double ionization yields, as well as the multiple ionization y
ields of Xe, in the presence of intense femtosecond laser pulses, have been
measured recently. The results of theoretical calculations are found to ag
ree remarkably well with these experimental data. They confirm the crucial
role of rescattering for the formation of the hot electron plateaus, and th
at of the "internal e-ne" process for the nonsequential double and multiple
ionization of noble gases. The phenomenon of "enhanced ionization" at a sp
ecific internuclear distance for the diatomic molecular hydrogen, studied b
y previous authors, is confirmed and that for the polyatomic benzene molecu
le and its cation are predicted.