The generalized oscillator strength (GOS) is an important property of the a
tom which manifests the atomic wavefunction directly. GOSs for the potassiu
m resonance transition have been investigated using the spin-polarized tech
nique of the random-phase approximation with exchange (RPAE) and,the Hartre
e-Fock approximation (HFA). Two minima are predicted by both calculations.
The first minimum, which is narrower and has never been measured before, is
predicted by the RPAE at a momentum transfer value of K = 0.8838 au, while
the second is the well measured one at 2.907 au. The positions of the mini
ma are found to be influenced by inter-shell correlations significantly. We
recommend a careful experimental search for the first minimum around the p
redicted value.