*2.2. Gamow Shell Model with Phenomenological Nuclear Potential*

Within the Gamow shell model with phenomenological nuclear potential, the nucleus is assumed to be a system of *Nv* valence particles outside a frozen closed core, from which, core polarization is absent [5,36,37,49]. The GSM Hamiltonian, expressed with intrinsic nucleon-core cluster-orbital shell model coordinates [64], writes

$$H = \sum\_{i=1}^{N\_{\mathcal{V}}} \left[ \frac{\mathbf{p}\_i^2}{2\mu\_i} + \mathcal{U}\_{\text{core}}(i) \right] + \sum\_{i$$

where *<sup>p</sup><sup>i</sup>* is the nucleon momentum in cluster-orbital shell model frame, *<sup>U</sup>*core is the singleparticle nucleon-core potential, and *V* is the phenomenological NN interaction between valence nucleons. *μ<sup>i</sup>* and *M*core stand for the reduced mass of the nucleon and the mass of the core, respectively. The *<sup>p</sup><sup>i</sup> <sup>p</sup><sup>j</sup> <sup>M</sup>*core term accounts for the two-body recoil term. As seen in Equation (15), the GSM has two components: the one-body part Hamiltonian *H*<sup>0</sup> = ∑*Nv i*=1 *p*2 *i* <sup>2</sup>*μ<sup>i</sup>* + *<sup>U</sup>*core(*i*) and the two-body part Hamiltonian *HI* = ∑*Nv i*<*j*=1 *V*(*i*, *j*) + *<sup>p</sup><sup>i</sup> <sup>p</sup><sup>j</sup> <sup>M</sup>*core . The core-valence particle potential *U*core is usually a WS potential, in which a spin-orbit term is included. The NN interaction *V* takes the form of an effective phenomenological NN interaction, such as Minnesota [65], Furutani-Horiuchi-Tamagaki (FHT) [66,67], or effective field theory (EFT) [18,56] interactions. The parameters within the effective Hamiltonian in Equation (15), both one- and two-body interactions, need to be optimized to reproduce experimental data. For optimizations, the *χ*<sup>2</sup> optimization method is employed, where one uses the Gauss–Newton algorithm augmented by the singular value decomposition technique to calculate the Jacobian pseudo-inverse [43].
