Weakly interacting massive particles (WIMPs) and strangelets are two classes of exotic particles not yet discovered, and in agreement with theoretical scenarios most probably produced in different early stages of evolution of the Universe. Some peculiarities of their energy loss in the electronic and nuclear interactions with ordinary matter are investigated. For the direct detection of WIMPs the signals produced by the stopping of recoils in matter are used for their identification. The influence of the orientation of the recoil in respect to crystal axes for crystalline silicon (as material for detectors) is analysed as average quantities: energy loss, and as transient thermal effects. For strangelets, the mechanisms of picking-up neutrons during their penetration into matter and the effects on electronic and nuclear stopping are considered. The clarification of the aspects related to the stopping of these hypothetical particles in matter will permit a better interpretation of some experimental results and could also contribute to the search for new techniques or materials for their detection, if they exist.
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