+ {\operatorname{Re}}U_{B_i}(p)~,\end{aligned}$$ where $M_i$ is the mass of baryon $B_i$. Hence, the energy denominator $e(\omega)$ (see appendix A) requires the single-particle potentials for both hyperons and nucleons as an input.

In Brueckner-Hartree-Fock approximation the single-particle potential for a baryon $B_1\in\{\Lambda,\Sigma^+,\Sigma^0,\Sigma^-,p,n\}$ interacting with the Fermi sea of nucleons $B_2\in\{p,n\}$ is then given by: $$\begin{aligned}
&U_{B_1}(p_1) = 
\sum_{\alpha}\left[1+\delta_{B_1B_2}(-1)^{L+S}\right]\frac{(1+M_2/M_1)^3}{2}~\times\nonumber \\
& \sum_{J}(2J+1)
\int_{k_\mathrm{min}}^{k_\mathrm{max}}\! \frac{\mathrm dk\, k^2}{(2\pi)^3}\,W(p_1,k) \, G_{\alpha\alpha}^{J}(k,k;\bar P,\omega) \,.
{\addtocounter{equation}{1}\tag{\theequation}}\label{eq:U}\end{aligned}$$ The weight function $W(p_1,k)$ resulting from the angular averaging procedure is specified in appendix A, together with the integration boundaries $k_\mathrm{min}$ and $k_\mathrm{max}$. Evidently, the calculation of the single-particle potentials depends on the single-particle potentials themselves as they appear in the energy denominator. Therefore eqs.  and must be solved self-consistently by iteration until convergence is reached. For the nucleon sector itself the $NN$ input potential is taken from ref.[@Entem2003], employing SU(2) chiral perturbation theory at fourth order (N3LO). Chiral three-nucleon forces at order N2LO are also included.

The computations are carried out using the so-called continuous choice, where single-particle potentials enter the energy denominator of intermediate states for all momenta, below and above the Fermi sea). From previous work [@Schulze1998] it is known that the continuous choice for intermediate states is preferable 