Quark Phase Space Distributions in Nuclei

In [PRC 110, 025201], the authors construct a model for nuclear matter which features a quarkyonic phase. A main feature in this model is that the nucleon occupation is strongly reduced at small momenta. Somewhat surprisingly, this result is supported by data for electron scattering from nuclear matter, where a reduction of the cross section consistent with suppression of nucleons with small momenta is seen. Since nuclear matter data are obtained by extrapolation of electron scattering data on increasingly heavier systems, this feature should manifest at least to some degree in heavy nuclei. To check if this is plausible we extend the approach of [PRC 110, 025201] to finite nuclei by considering the nuclear Wigner distribution. We use non-relativistic and relativistic independent particle models to determine the nuclear Wigner distribution, in addition to the local-density approximation (LDA). Phase-space distributions of quarks are obtained as a convolution of the Wigner distribution with a quark momentum distribution. We highlight some properties of the Wigner distribution in spherical systems, which can spoil the interpretation of the quark phase-space distribution as occupation numbers in the Fermi sea. On the other hand, we show that large systems behave essentially like infinite nuclear matter in their interior, and that LDA and full results are quantitatively similar for large A. We then compute the fraction of baryons that would be in a quarkyonic phase in the same sense as in [PRC 110, 025201] for a set of nuclei with mass $12 \leq A \leq 238$. We find that this fraction systematically tends to a constant at large $A$. It is hence plausible that the suppression seen in the nuclear matter data is a genuine feature, present in large finite nuclei. This result is counter-intuitive and we discuss possible electron scattering measurements that could rule out this model.