Complete flavour decompositions of the scalar, axial and tensor charges of the proton, deuteron, diproton and $^3$He at SU(3)-symmetric values of the quark masses corresponding to a pion mass $m_pisim806$ MeV are determined using lattice QCD. At the physical quark masses, the scalar charges constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor charges of nuclei constrain their spin content, integrated transversity and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elements of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. Significant nuclear modifications are found, with particularly large, O(10%), effects in the scalar charges. Typically, these nuclear effects reduce the effective charge of the nucleon (quenching), although in some cases an enhancement is not excluded. Given the size of the nuclear modifications of the scalar charges resolved here, contributions from correlated multi-nucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.
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