Neutron diffraction measurements and theoretical calculations of the struct
ure Factor S(k) of liquid Kr are extended to small k values (k < 4 nm(-1)).
The results show that many-body interaction contributions have an increasi
ng effect on S(k) as k --> 0, reaching at least 40% of the measured intensi
ty. Both the phase diagram and the low-k structural data of dense Kr turn o
ut to be closely reproduced by the hierarchical reference theory if additio
nal many-body forces are taken into account by an augmented strength of the
Axilrod-Teller triple-dipole potential. The experimental density derivativ
e of S(k) is also used for a very sensitive test of the theories and intera
ction models considered here.