Hyperonic Softening Versus Nucleonic Three-Body Repulsion in Hypernuclear Matter Within a Microscopic Approach

We investigate cold homogeneous matter composed of neutrons, protons, and Λ hyperons within our hyperonic extension of the lowest-order constrained variational (LOCV) method, hereafter denoted LOCVY. Our earlier LOCVY calculation, based on two-baryon interactions, is extended by supplementing the Argonne v18 nucleonic interaction with the Urbana IX three-nucleon force, reduced within the variational framework to a correlation-weighted density-dependent effective two-nucleon interaction. The NΛ and ΛΛ interactions are kept unchanged, allowing the present calculation to isolate the competition between hyperon-induced softening and nucleonic three-body repulsion. The energy per baryon is calculated for fixed Λ fractions YΛ=0, 0.1, and 0.2 in matter with a symmetric nucleonic component and in the proton-free neutron–Λ limit. Direct differences between calculations with and without the three-body force quantify its density-dependent contribution, while a complementary decomposition into NN, NΛ, and ΛΛ terms identifies the microscopic origin of the stiffening. For matter with a symmetric nucleonic component, the nucleonic three-body force contribution becomes increasingly repulsive at high densities and can dominate the energy change associated with a Λ admixture in the two-body calculation. This comparison uses rest-mass-subtracted energies at fixed composition and does not determine the equilibrium hyperon content. We further investigate the saturation properties for several prescribed Λ fractions, with and without the nucleonic three-body force, to clarify how strangeness and many-body interactions modify the saturation point and the agreement with empirical nuclear-matter properties.