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Register a new user$Xi$ hyper-nuclear states predicted by NLO chiral baryon-baryon interactions
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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.
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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.
We report on the recent studies of leading order baryon-baryon interactions in covariant baryon chiral perturbation theory. In the strangeness $S=0$ sector, one can achieve a rather good description of the Nijmegen $np$ phase shifts with angular momenta $Jleq 1$, particularly the $^1S_0$ and $^3P_0$ partial waves, comparable with the next-to-leading order (NLO) heavy baryon approach. In the strangeness $S=-1$ hyperon-nucleon sector, the best fit of the 36 scattering data is similar to the sophisticated phenomenological models and the NLO heavy baryon approach.
In this talk, we report on two recent studies of relativistic nucleon-nucleon and hyperon-nucleon interactions in covariant chiral perturbation theory, where they are constructed up to leading order. The relevant unknown low energy constants are fixed by fitting to the nucleon-nucleon and hyperon-nucleon scattering data. It is shown that these interactions can describe the scattering data with a quality similar to their next-to-leading order non-relativistic counterparts. These studies show that it is technically feasible to construct relativist baryon-baryon interactions, and in addition, after further refinements, these interactions may provide important inputs to {it ab initio} relativistic nuclear structure and reaction studies and help improve our understanding of low energy strong interactions.
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.
In-medium ${bar K}N$ scattering amplitudes developed within a new chirally motivated coupled-channel model due to Cieply and Smejkal that fits the recent SIDDHARTA kaonic hydrogen 1s level shift and width are used to construct $K^-$ nuclear potentials for calculations of $K^-$ nuclear quasi-bound states. The strong energy and density dependence of scattering amplitudes at and near threshold leads to $K^-$ potential depths $-Re V_K approx 80 -120$ MeV. Self-consistent calculations of all $K^-$ nuclear quasi-bound states, including excited states, are reported. Model dependence, polarization effects, the role of p-wave interactions, and two-nucleon $K^-NNrightarrow YN$ absorption modes are discussed. The $K^-$ absorption widths $Gamma_K$ are comparable or even larger than the corresponding binding energies $B_K$ for all $K^-$ nuclear quasi-bound states, exceeding considerably the level spacing. This discourages search for $K^-$ nuclear quasi-bound states in any but lightest nuclear systems.
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