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Register a new user$Xi$ hyperons in the nuclear medium described by chiral NLO interactions
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Authors
M. Kohno
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Properties of the baryon-baryon interactions in the strangeness $S=-2$ sector of chiral effective field theory at the next-to-leading order (NLO) level are explored by calculating $Xi$ single-particle potentials in symmetric nuclear matter. The results are transformed to the $Xi$ potential in finite nuclei by a local-density approximation with convolution by a Gaussian form factor to simulate finite-range effects. The $Xi$ potential is repulsive in a central region, and attractive in a surface area when the $Xi$ energy is low. The attractive pocket can lower the $Xi^-$ $s$ and $p$ atomic states. The obtained binding energies in $^{12}$C and $^{14}$N are found to be conformable with those found in emulsion experiments at Japans National Laboratory for High Energy Physics (KEK). $K^+$ spectra of $(K^-, K^+)$ $Xi$ production inclusive processes on $^9$Be and $^{12}$C are also evaluated, using a semi-classical distorted wave method. The absolute values of the cross section are properly reproduced for $^9$Be, but the peak locates at a lower energy position than that of the experimental data. The calculated spectrum of $^{12}$C should be compared with the forthcoming result from the new experiments recently carried out at KEK with better resolution than before. The comparison would be valuable to improve the understanding of the $Xi N$ interaction, the parametrization of which has still large uncertainties.
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The $Xi$ single-particle potential obtained in nuclear matter with the next-to-leading order baryon-baryon interactions in chiral effective field theory is applied to finite nuclei by an improved local-density approximation method. As a premise, phase shifts of $Xi N$ elastic scattering and the results of Faddeev calculations for the $Xi NN$ bound state problem are presented to show the properties of the $Xi N$ interactions in the present parametrization. First, the $Xi$ states in $^{14}$N are revisited because of the recent experimental progress, including the discussion on the $Xi N$ spin-orbit interaction that is relevant to the location of the $p$-state. Then the $Xi$ levels in $^{56}$Fe are calculated. In particular, the level shift which is expected to be measured experimentally in the near future is predicted. The smallness of the imaginary part of the $Xi$ single-particle potential is explicitly demonstrated.
Chiral expansions of the two-pion exchange components of both two- and three-nucleon forces are reviewed and a discussion is made of the predicted pattern of hierarchies. The strength of the scalar-isoscalar central potential is found to be too large and to defy expectations from the symmetry. The causes of this effect can be understood by studying the nucleon scalar form factor.
Total and reaction cross sections are derived self consistently from the attenuation cross sections measured in transmission experiments at the AGS for K^+ on Li^6, C, Si and Ca in the momentum range of 500-700 MeV/c by using a V_{opt}=t_{eff}(rho)rho optical potential. Self consistency requires, for the KN in-medium t matrix, that Im t_{eff}(rho) increases linearly with the average nuclear density in excess of a threshold value of 0.088+-0.004 fm^-3. The density dependence of Re t_{eff}(rho) is studied phenomenologically, and also applying a relativistic mean field approach, by fitting the integral cross sections. The real part of the optical potential is found to be systematically less repulsive with increasing energy than expected from the free-space repulsive KN interaction. When the elastic scattering data for Li^6 and C at 715 MeV/c are included in the analysis, a tendency of Re V_{opt} to generate an attractive pocket at the nuclear surface is observed.
We propose a new stochastic method to describe low-lying excited states of finite nuclei superposing multiple Slater determinants without assuming generator coordinates a priori. We examine accuracy of our method by using simple BKN interaction.
Adopting hyperon-nucleon and hyperon-nucleon-nucleon interactions parametrized in chiral effective field theory, single-particle potentials of the $Lambda$ and $Sigma$ hyperons are evaluated in symmetric nuclear matter and in pure neutron matter within the framework of lowest order Bruckner theory. The chiral NLO interaction bears strong $Lambda$N-$Sigma$N coupling. Although the $Lambda$ potential is repulsive if the coupling is switched off, the $Lambda$N-$Sigma$N correlation brings about the attraction consistent with empirical data. The $Sigma$ potential is repulsive, which is also consistent with empirical information. The interesting result is that the $Lambda$ potential becomes shallower beyond normal density. This provides the possibility to solve the hyperon puzzle without introducing ad hoc assumptions. The effects of the $Lambda$NN-$Lambda$NN and $Lambda$NN-$Sigma$NN three-baryon forces are considered. These three-baryon forces are first reduced to normal-ordered effective two-baryon interactions in nuclear matter and then incorporated in the $G$-matrix equation. The repulsion from the $Lambda$NN-$Lambda$NN interaction is of the order of 5 MeV at the normal density, and becomes larger with increasing the density. The effects of the $Lambda$NN-$Sigma$NN coupling compensate the repulsion at normal density. The net effect of the three-baryon interactions to the $Lambda$ single-particle potential is repulsive at higher densities.
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