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Résumé |
Effective theories of nuclear structure must reflect the chiral global $SU(2)_L \times SU(2)_R$
symmetry of two-massless-quark QCD. Naive power counting enables
perturbation/truncation in inverse powers of $\Lambda_{\chi^{SB}} \approx 1 $GeV, with analytic operators
renormalized to all loop orders. We show that $SU(2)~\chi$PT admits a “liquid" phase,
with energy required to increase or decrease the density of constituents. "Semi-
classical Pion-less” $SU(2)~\chi$PT emerges in the chiral liquid, vastly simplifying
the derivation of saturated nuclear matter (the infinite liquid phase) and of finite
microscopic liquid drops (ground-state heavy nuclides). Static Chiral Nucleon
Liquids (Static $\chi$NL) are made entirely of nucleons, have even parity; total spin
zero; even proton number $Z$, and neutron number $N$; and are arranged so local
expectation values for spin and momenta vanish.\\
We derive the Static $\chi$NL effective Lagrangian, to order $\Lambda_{\chi^{SB}}$ and $\Lambda_{\chi^{SB}}^0$.
Static $\chi$NL motivate nuclear matter, seen as non-topological solitons at zero internal
and external pressure: the Nuclear Liquid Drop Model and Bethe-Weizsäcker Semi-
Empirical Mass Formula emerge in an explicit Thomas-Fermi construction. For
chosen nuclides, semi-classical nuclear Skyrme models are justified. We conjecture
that inclusion of $\Lambda_{\chi^{SB}}^{-1}$ and $\Lambda_{\chi^{SB}}^{-2}$ operators will result in "natural" semi-classical
Skyrme, No-Core-Shell, and non-exotic neutron star models, with approximate
liquid structure. |
