The nucleus of atoms are surrounded by electrons, which are all negatively charged effectively making atoms miniature magnetic monopoles (magnet with only one side). So all atoms repel each other, when you touch something you’re really feeling the electrons in the atoms of your hand repelling the electrons of the atoms of the thing you’re touching. So nuclei never touch.
Touch is a relative/fuzzy concept at atomic scales.
(Note; this doesn’t include atoms reacting with one another where they form bonds and could by some definitions be considered touching).
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