The calculation of spin-dependent matrix elements relevant to scattering of weakly interacting massive particles (WIMP) on nuclei is reviewed. A comprehensive list, to our knowledge, of the proton and neutron total spin expectation values (< S _p > and < S _n > ) calculated within different nuclear models is presented. These values allow a conclusion about the event rate expected in direct dark matter search experiments due to spin-dependent neutralino-nucleon interaction, provided neutralino is a dark matter particle.

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