Energies of symmetric nuclear matter and neutron matter are evaluated in the lowest order Bruekner theory using the Ch-EFT potential including effects of the three-nucleon force (3NF). The 3NF is first reduced to density-dependent nucleon-nucleon (NN
) force by folding single-nucleon degrees of freedom in infinite matter. Adding the reduced NN force to the initial NN force and applying a partial-wave expansion, we perform $G$-matrix calculations in pure neutron matter as well as in symmetric nuclear. We obtain the saturation curve which is close to the empirical one. It is explicitly shown that the cutoff-energy dependence of the calculated energies is substantially reduced by including the 3NF. Characters of the 3NF contributions in separate spin and isospin channels are discussed. Calculated energies of the neutron matter are very similar to those used in the literature for considering neutron star properties.
The contribution of a chiral three-nucleon force to the strength of an effective spin-orbit coupling is estimated. We first construct a reduced two-body interaction by folding one-nucleon degrees of freedom of the three-nucleon force in nuclear matte
r. The spin-orbit strength is evaluated by a Scheerbaum factor obtained by the $G$-matrix calculation in nuclear matter with the two-nucleon interaction plus the reduced two-nucleon interaction. The problem of the insufficiency of modern realistic two-nucleon interactions to account for the empirical spin-orbit strength is resolved. It is also indicated that the spin-orbit coupling is weaker in the neutron-rich environment. Because the spin-orbit component from the three-nucleon force is determined by the low-energy constants fixed in the two-nucleon sector, there is little uncertainty in the present estimation.
The reformulated coupled-cluster method (CCM), in which average many-body potentials are introduced, provides a useful framework to organize numerous terms appearing in CCM equations, which enables us to clarify the structure of the CCM theory and ph
ysical importance of various terms more easily. We explicitly apply this framework to $^4$He, retaining one-body and two-body correlations as the first illustrating attempt. Numerical results with using two modern nucleon-nucleon interactions (AV18 and CD-Bonn) and their low-momentum interactions are presented. The characters of short-range and many-body correlations are discussed. Although not considered explicitly, the expression of the ground-state energy in the presence of a three-nucleon force is given.
Hyperon-nucleons interactions constructed by two frameworks, the Kyoto-Niigata SU$_6$ quark model and the chiral effective field theory, are compared by investigating equivalent interactions in a low-momentum space and in addition by calculating hype
ron single-particle potentials in the lowest-order Brueckner theory in symmetric nuclear matter. Two descriptions are shown to give similar matrix elements in most channels after renormalizing high momentum components. Although the range of the $Lambda N$ interaction is different in two potentials, the $Lambda$ single-particle potential in nuclear matter is very similar. The $Sigma$-nucleus and $Xi$-nucleus potentials are also found to be similar. These predictions are to be confronted with forthcoming experimental data.
The $(K^-,K^+)$ $Xi^-$ production inclusive spectrum is reinvestigated in view of the very weak $Xi$-nucleus potential predicted by microscopic calculations with the SU$_6$ quark-model baryon-baryon interaction. The inclusive spectrum is evaluated by
the semiclassical distorted wave (SCDW) method. The explicit comparison of the strength function with that of the Green-function method demonstrates the quantitative reliability of the SCDW approximation. It is presumed that the presently available data at the $Xi$ production threshold region does not necessarily imply the attractive strength of about 15 MeV for the $Xi$-nucleus potential in a conventional Woods-Saxon form. Instead, an almost zero potential is preferable.
Equivalent interactions in a low-momentum space for the $Lambda N$, $Sigma N$ and $Xi N$ interactions are calculated, using the SU$_6$ quark model potential as well as the Nijmegen OBEP model as the input bare interaction. Because the two-body scatte
ring data has not been accumulated sufficiently to determine the hyperon-nucleon interactions unambiguously, the construction of the potential even in low-energy regions has to rely on a theoretical model. The equivalent interaction after removing high-momentum components is still model dependent. Because this model dependence reflects the character of the underlying potential model, it is instructive for better understanding of baryon-baryon interactions in the strangeness sector to study the low-momentum space $YN$ interactions.
