Quark Pauli principle and the transmutation of nuclear matter

The phase space density, ${\ensuremath{\rho}}^{Q}$, of quarks in nuclei is studied using realistic models of unintegrated quark distributions, known as transverse momentum densities (TMDs). If this density exceeds unity for matter at normal nuclear densities, the effects of the quark Pauli principle must play a role in nuclei, and models in which the nucleon density at low momentum is small (quarkyonic matter) may become a starting point for an entirely new description of nuclei. We denote the nuclear density for which ${\ensuremath{\rho}}^{Q}=1$ to be a transmutation density, ${n}_{T}$, because quark degrees of freedom must be relevant at that density. Including the TMDs of [G. F. de Teramond et al., Phys. Rev. Lett. 120, 182001 (2018)] for the valence quarks and phenomenological TMDs for the sea quarks, we find that ${n}_{T}=0.17\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.28em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$, a density range that includes current determinations of the density of normal nuclear matter, $0.16\ifmmode\pm\else\textpm\fi{}0.01\phantom{\rule{0.28em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$. Some of the implications of this finding are discussed.