A modified hypernetted-chain theory is applied to calculate the static liquid structure factor for simple liquid metals during rapid cooling. With a proper choice of bridge function, it is found that this integral-equation theory is capable of yielding a reasonably accurate liquid structure factor in the supercooled liquid region. To exploit the usefulness of the calculated liquid structure, we combine these structure data with mode-coupling theory to investigate the dynamics of the beta-relaxation process. It is demonstrated in this work that the critical temperatures for an ideal glass transition predicted here for liquid metals Na and K are slightly lower than those determined previously by us using computer-simulated structure factors. In particular, we show that the material-dependent exponent parameter lambda, which is used widely in the literature as a fitting parameter in the analysis of light scattering experiments, can be given more physical significance if one correlates the change of lambda, with the microscopic interaction of particles specifically for the liquid metal, Lennard-Jones fluid and hard-sphere systems. The implications of the present results, and the possibility of extracting useful information for more complicated systems, is discussed in the text.