In heavy-fermion superconductors, it is widely believed that the superconducting gap function has sign-reversal due to the strong electron correlation. However, recently discovered fully-gapped s-wave superconductivity in CeCu₂Si₂ has clarified that strong attractive pairing interaction can appear even in heavy-fermion systems. To understand the origin of attractive force, we develop the multipole fluctuation theory by focusing on the inter-multipole many-body interaction called the vertex corrections. By analyzing the periodic Anderson model for CeCu₂Si₂, we find that hexadecapole fluctuations mediate strong attractive pairing interaction. Therefore, fully-gapped s-wave superconductivity is driven by pure on-site Coulomb repulsion, without introducing electron–phonon interactions. The present theory of superconductivity will be useful to understand rich variety of the superconducting states in heavy fermion systems.

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