Background: In a previous series of papers we investigated the domain of applicability of chiral potentials to the construction of a microscopic optical potential (OP) for elastic nucleon-nucleus scattering. The OP was derived at the first order of the spectator expansion of the Watson multiple scattering theory and its final expression was a folding integral between the nucleon-nucleon ($NN$) $t$ matrix and the nuclear density of the target. In the calculations $NN$ and three-nucleon ($3N$) chiral interactions were used for the target density and only the $NN$ interaction for the $NN t$ matrix.

Purpose: The purpose of this work is to achieve another step towards the calculation of a more consistent OP introducing the $3N$ force also in the dynamic part of the OP.

Methods: The full treatment of the $3N$ interaction is beyond our present capabilities. Thus, in the present work it is approximated with a density dependent $NN$ interaction obtained after the averaging over the Fermi sphere. In practice, in our model the $3N$ force acts as a medium correction of the bare $NN$ interaction used to calculate the $t$ matrix. Even if the $3N$ force is treated in an approximate way, this method naturally extends our previous model of the OP and allows a direct comparison of our present and previous results.

Results: We consider as case studies the elastic scattering of nucleons off ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$. We present results for the differential cross section and the spin observables for different values of the projectile energy. From the comparison with the experimental data and with the results of our previous model we assess the importance of the $3N$ interaction in the dynamic part of the OP.

Conclusions: Our analysis indicates that the contribution of the $3N$ force in the $t$ matrix is small for the differential cross section and it is sizable for the spin observables, in particular, for the analyzing power. We find that the two-pion exchange term is the major contributor to the $3N$ force. A chiral expansion order-by-order analysis of the scattering observables confirms the convergence of our results at the next-to-next-to-next-to-leading-order, as already established in our previous work.

It is believed that in noncentral relativistic heavy-ion collisions a very strong magnetic field is formed. There are several studies of the effects of this field, where $\vec{B}$ is calculated with the expressions of classical electrodynamics. A quantum field may be approximated by a classical one when the number of field quanta in each field mode is sufficiently high. This may happen if the field sources are intense enough. In heavy-ion physics the validity of the classical treatment was not investigated. In this work we propose a test of the quality of the classical approximation. We calculate an observable quantity using the classical magnetic field and also using photons as input. If the results of both approaches coincide, this will be an indication that the classical approximation is valid. More precisely, we focus on the process in which a nucleon is converted into a delta resonance, which then decays into another nucleon and a pion, i.e., $N\to \mathrm{\Delta }\to N^{\prime }\pi$. In ultraperipheral relativistic heavy-ion collisions this conversion can be induced by the classical magnetic field of one of the ions acting on the other ion. Alternatively, we can replace the classical magnetic field by a flux of equivalent photons, which are absorbed by the target nucleons. We calculate the cross sections in these two independent ways and find that they differ from each other by $\simeq 10$ % in the considered collision energy range. This suggests that the two formalisms are equivalent and that the classical approximation for the magnetic field is reasonable.

The strangeness $S=-3$ and $-4$ baryon-baryon interactions are investigated in the relativistic chiral effective-field theory at leading order. First, the 12 tree-level low-energy constants contributing to the $S=-1$ hyperon-nucleon interaction are fixed by fitting to the 36 hyperon-nucleon scattering data. Then the $S=-3$ and $-4$ baryon-baryon interactions are derived from that of $S=-1$ assuming that the corresponding low-energy constants are related to each other via SU(3) flavor symmetry. The comparison with the state-of-the-art lattice QCD simulations, show, however, that SU(3) flavor symmetry-breaking effects cannot be neglected. To take into account these effects, we redetermine two sets of low-energy constants by fitting to the lattice QCD data in the $\mathrm{\Xi }\mathrm{\Sigma }$ and $\mathrm{\Xi }\mathrm{\Xi }$ channels, respectively. The fitting results demonstrate that the lattice QCD $S$-wave phase shifts for both channels can be described rather well. Without any additional free low-energy constants, the predicted phase shifts for the ${}^{3}D_1$ channel and the mixing angle ${\varepsilon }_1$ are also in qualitative agreement with the lattice QCD data for the $S=-3$ channel, while the results for the $S=-4$ channel remain to be checked by future lattice QCD simulations. With the so-obtained low-energy constants, the $S$-wave scattering lengths and effective ranges are calculated for these two channels at the physical point. Finally, in combination with the $S=0$ and $-2$ results obtained in our previous works, we study the evolution of the irreducible representation “27” in the baryon-baryon interactions as a function of increasing strangeness. It is shown that the attraction decreases dramatically as strangeness increases from $S=0$ to $S=-2$, but then remains relatively stable until $S=-4$. The results indicate that the existence of bound states in the $\mathrm{\Xi }\mathrm{\Sigma }$ and $\mathrm{\Xi }\mathrm{\Xi }$ channels is rather unlikely.

We conduct a dynamical calculation of pentaquark systems with quark contents $sssu\overline{u}$ in the framework of two quark models: the chiral quark model (ChQM) and quark delocalization color screening model (QDCSM). The effective potentials between baryon and meson clusters are given, and the possible bound states are also investigated. Also, the study of the scattering process of the open channels is performed to look for any resonance state. The results show that the $\mathrm{\Omega }\left(2012\right)$ is not suitable for the interpretation as a ${\mathrm{\Xi }}^{*}\overline{K}$ molecular state in present quark models. Two resonance states: the ${\mathrm{\Xi }}^{*}{\overline{K}}^{*}$ with $I{J}^P=0{\frac{3}{2}}^{-}$ ($M=2328$–$2374\mathrm{MeV}, \mathrm{\Gamma }=57$–$65.5\mathrm{MeV}$) and $I{J}^P=1{\frac{3}{2}}^{-}$ ($M=2341$–$2386\mathrm{MeV}, \mathrm{\Gamma }=31.5$–$100\mathrm{MeV}$) are obtained in both QDCSM and ChQM, which indicates that these two states are more likely to exist and worthy of being sought by future experiments.

The equation of state and phase diagram of strongly interacting matter composed of $\alpha$ particles are studied in the mean-field approximation. The particle interactions are included via a Skyrme-like mean field, containing both attractive and repulsive terms. The model parameters are found by fitting the values of binding energy and baryon density in the ground state of $\alpha$ matter, obtained from microscopic calculations by Clark and Wang [Ann. Phys. (NY) 40, 127 (1966)]. Thermodynamic quantities of $\alpha$ matter are calculated in the broad domains of temperature and baryon density, which can be reached in heavy-ion collisions at intermediate energies. The model predicts both first-order liquid-gas phase transition and Bose-Einstein condensation of $\alpha$ particles. We present the profiles of scaled variance, sound velocity, and isochoric heat capacity along the isentropic trajectories of $\alpha$ matter. Strong density fluctuations are predicted in the vicinity of the critical point at temperature $T_c\approx 14\text{MeV}$ and density $n_c\approx 0.012{\text{fm}}^{-3}$.

High-spin states of ${}^{110}\mathrm{Ag}$ have been studied by in-beam $\gamma$-ray spectroscopic techniques using the fusion-evaporation reaction ${}^{110}\mathrm{Pd}$(${}^7\mathrm{Li}, \alpha 3\mathrm{n}$)${}^{110}\mathrm{Ag}$ at a beam energy of 46 MeV. The previously known level scheme of ${}^{110}\mathrm{Ag}$ is significantly extended and modified with the addition of 50 new $\gamma$ transitions and 21 new levels. In total, four new rotational bands are observed, among which two negative-parity coupled bands are assigned to the four-quasiparticle $\pi g_{9/2}^{-1}\otimes \nu h_{11/2}{(g_{7/2}/d_{5/2})}^2$ configuration based on the quasiparticle alignment analysis and cranked shell model calculations. The properties of both bands show general agreement with the fingerprints of chiral rotation, and thus such two negative-parity bands are suggested to be candidates for near degenerate chiral doublet bands. A new decoupled $\mathrm{\Delta }I=2$ band decaying directly to the yrast band is established, and probably results from one-particle-one-hole (1p-1h) proton excitation from the $g_{9/2}$ orbital to the $g_{7/2}$ orbital across the large $Z=50$ shell gap, i.e., the 2p2h $\pi g_{9/2}^{-2}{g}_{7/2}\otimes \nu h_{11/2}$ configuration. In addition to, a weak positive-parity sequence consisting of magnetic dipole $\left(M1\right)$ and no $E2$ crossover transitions is also identified in the present work.

Significant transition strength in light $\alpha$-conjugate nuclei at low energy, typically below 10 MeV, has been observed in many experiments. In this work the isoscalar low-energy response of $N=Z$ nuclei is explored using the finite amplitude method based on the microscopic framework of nuclear energy density functionals. Depending on the multipolarity of the excitation and the equilibrium deformation of a particular isotope, the low-energy strength functions display prominent peaks that can be attributed to cluster mode structures: $\alpha +{}^{12}\mathrm{C}+\alpha$ and $\alpha +{}^{16}\mathrm{O}$ in ${}^{20}\mathrm{Ne}, {}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ in ${}^{24}\mathrm{Mg}, 4\alpha +{}^{12}\mathrm{C}$ in ${}^{28}\mathrm{Si}$, etc. Such cluster modes are favored in light nuclei with large deformation.

Differential cross sections of $(p,n)$ and $({}^3\mathrm{He},t)$ charge-exchange reactions leading to the excitation of the isobaric analog state (IAS) of the target nucleus are calculated with the distorted wave Born approximation. The $G$-matrix double-folding method is employed to determine the nucleus-nucleus optical potential within the framework of the Lane model. $G$ matrices are obtained from a Brueckner-Hartree-Fock calculation using the Argonne Av18 nucleon-nucleon potential. Target densities have been taken from Skyrme-Hartree-Fock calculations which predict values for the neutron skin thickness of heavy nuclei compatible with current existing data. Calculations are compared with experimental data of the reactions $(p,n)\mathrm{IAS}$ on ${}^{14}\mathrm{C}$ at $E_{\mathrm{lab}}=135$ MeV and ${}^{48}\mathrm{Ca}$ at $E_{\mathrm{lab}}=134$ MeV and $E_{\mathrm{lab}}=160$ MeV, and $({}^3\mathrm{He},t)\mathrm{IAS}$ on ${}^{58}\mathrm{Ni},$ ${}^{90}\mathrm{Zr},$ and ${}^{208}\mathrm{Pb}$ at $E_{\mathrm{lab}}=420$ MeV. Experimental results are well described without the necessity of any rescaling of the strength of the optical potential. A clear improvement in the description of the differential cross sections for the $({}^3\mathrm{He},t)\mathrm{IAS}$ reactions on ${}^{58}\mathrm{Ni}$ and ${}^{90}\mathrm{Zr}$ targets is found when the neutron excess density is used to determine the transition densities. Our results show that the density and isospin dependences of the $G$ matrices play a non-negligible role in the description of the experimental data.

Neutron kinetic energy spectra in coincidence with low-energy $\gamma$-ray multiplicities have been measured around $A\approx 110$ in the ${}^{16}\mathrm{O}+{}^{93}\mathrm{Nb}$ and ${}^{20}\mathrm{Ne}+{}^{93}\mathrm{Nb}$ reactions in a compound nuclear excitation energy range of $\approx 90–140$ MeV. The excitation energy (temperature) dependence and the angular momentum (spin) dependence of the inverse level density parameter $k$ have been investigated by comparing the experimental data with statistical Hauser-Feshbach calculations. In contrast to the available systematic in this mass region, the inverse level density parameter showed an appreciable increase as a function of the excitation energy. The extracted $k$ values at different angular momentum regions, corresponding to different $\gamma$ multiplicities, also showed an overall increase with the average nuclear spins. The experimental results have been compared with a microscopic statistical-model calculation and found to be in reasonable agreement with the data. The results provide useful information to understand the variation of nuclear level density at high temperature and spins.

Background: The band structure of the negative-parity states of ${}^{24}\mathrm{Mg}$ has not yet been clarified. The $K^{\pi }=0^{-}$, $K^{\pi }=1^{-}$, and $K^{\pi }=3^{-}$ bands have been suggested, but the assignments have been inconsistent between experiments and theories.

Purpose: Negative-parity states of ${}^{24}\mathrm{Mg}$ are investigated by microscopic structure and reaction calculations via proton and $\alpha$ inelastic scattering to clarify the band assignment for the observed negative-parity spectra.

Method: The structure of ${}^{24}\mathrm{Mg}$ was calculated using the antisymmetrized molecular dynamics (AMD). Proton and $\alpha$ inelastic reactions were calculated using microscopic coupled-channel (MCC) calculations by folding the Melbourne $g$-matrix $NN$ interaction with the AMD densities of ${}^{24}\mathrm{Mg}$.

Results: The member states of the $K^{\pi }=0^{+}$, $K^{\pi }=2^{+}$, $K^{\pi }=0^{-}$, $K^{\pi }=1^{-}$, and $K^{\pi }=3^{-}$ bands of ${}^{24}\mathrm{Mg}$ were obtained through the AMD result. In the $\mathrm{MCC}+\mathrm{AMD}$ results for proton and $\alpha$ elastic and inelastic cross sections, reasonable agreements were obtained with existing data, except in the case of the $4_1^{+}$ state.

Conclusions: The $3^{-}$ state of the $K^{\pi }=3^{-}$ band and the $1^{-}$ and $3^{-}$ states of the $K^{\pi }=0^{-}$ bands were assigned to the $3_1^{-}$(7.62 MeV), $1_1^{-}$(7.56 MeV), and $3_2^{-}$(8.36 MeV) states, respectively. The present AMD calculation is the first microscopic structure calculation to reproduce the energy ordering of the $K^{\pi }=0^{-}$, $K^{\pi }=1^{-}$, and $K^{\pi }=3^{-}$ bands of ${}^{24}\mathrm{Mg}$.

The system size dependence of baryon-strangeness (BS) correlation ($C_{BS}$) is investigated with a multiphase transport (AMPT) model for various collision systems from ${}^{10}\mathrm{B}+{}^{10}\mathrm{B}$, ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$, ${}^{20}\mathrm{Ne}+{}^{20}\mathrm{Ne}$, ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$, ${}^{96}\mathrm{Zr}+{}^{96}\mathrm{Zr}$, and ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ at Relativistic Heavy Ion Collider energies $\sqrt{s_{NN}}$ of 200, 39, 27, 20, and 7.7 GeV. Both effects of hadron rescattering and a combination of different hadrons play a leading role in baryon-strangeness correlation. When the kinetic window is limited to absolute rapidity $\left|y\right|>3$, these correlations tend to be constant after the final-state interaction, whatever kind of hadron subset we choose based on the AMPT framework. The correlation is found to smoothly increase with baryon chemical potential ${\mu }_B$, corresponding to the collision system or energy from the quark-gluon-plasma-like phase to the hadron-gas-like phase. In addition, the influence of initial nuclear geometric structures of $\alpha$-clustered nuclear collision systems of ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ as well as ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ collisions is discussed but the effect is found negligible. The current model studies provide baselines for searching for the signals of the quantum chromodynamics phase transition and critical point in heavy-ion collisions through the BS correlation.

Background: Isobaric quintets provide the best test of the isobaric multiplet mass equation (IMME) and can uniquely identify higher order corrections suggestive of isospin symmetry breaking effects in the nuclear Hamiltonian. The generalized IMME (GIMME) is a novel microscopic interaction theory that predicts an extension to the quadratic form of the IMME. Only the $A=20,32$ $T=2$ quintets have the exotic $T_z=-2$ member ground state mass determined to high precision by Penning trap mass spectrometry.

Purpose: We aim to establish $A=36$ as the third $T=2$ isobaric quintet with the $T_z=-2$ member ground state mass measured by Penning trap mass spectrometry and provide the first test of the predictive power of the GIMME.

Method: A radioactive beam of neutron-deficient ${}^{36}\mathrm{Ca}$ was produced by projectile fragmentation at the National Superconducting Cyclotron Laboratory. The beam was thermalized and the masses of ${}^{36}\mathrm{Ca}^{+}$ and ${}^{36}\mathrm{Ca}^{2+}$ were measured by the time-of-flight ion cyclotron resonance method in the LEBIT 9.4 T Penning trap.

Results: We measure the mass excess of ${}^{36}\mathrm{Ca}$ to be $\mathrm{ME}=-6483.6\left(56\right)$ keV, an improvement in precision by a factor of 6 over the literature value. The new datum is considered together with evaluated nuclear data on the $A=36$, $T=2$ quintet. We find agreement with the quadratic form of the IMME given by isospin symmetry, but only coarse qualitative agreement with predictions of the GIMME.

Conclusion: A total of three isobaric quintets have their most exotic members measured by Penning trap mass spectrometry. The GIMME predictions in the $T=2$ quintet appear to break down for $A=32$ and greater.

We report here the results of a study of the $\beta$ decay of the proton-rich Ge isotopes, ${}^{60}\mathrm{Ge}$ and ${}^{62}\mathrm{Ge}$, produced in an experiment at the RIKEN Nishina Center. We have improved our knowledge of the half-lives of ${}^{62}\mathrm{Ge}$ [73.5(1) ms] and ${}^{60}\mathrm{Ge}$ [25.0(3) ms] and its daughter nucleus, ${}^{60}\mathrm{Ga}$ [69.4(2) ms]. We measured individual $\beta$-delayed proton and $\gamma$ emissions and their related branching ratios. Decay schemes and absolute Fermi and Gamow-Teller transition strengths have been determined. The mass excesses of the nuclei under study have been deduced. A total $\beta$-delayed proton-emission branching ratio of 67(3)% has been obtained for ${}^{60}\mathrm{Ge}$. New information has been obtained on the energy levels populated in ${}^{60}\mathrm{Ga}$ and on the ${1/2}^{-}$ excited state in the $\beta p$ daughter ${}^{59}\mathrm{Zn}$. We extracted a ground state–to–ground state feeding of 85.3(3)% for the decay of ${}^{62}\mathrm{Ge}$. Eight new $\gamma$ lines have been added to the deexcitation of levels populated in the ${}^{62}\mathrm{Ga}$ daughter.

Empirical energy density functionals (EDFs) are generally successful in describing nuclear properties across the table of nuclides. But their limitations motivate using the density-matrix expansion (DME) to embed long-range pion interactions into a Skyrme functional. Recent results on the impact of the pion were both encouraging and puzzling, necessitating a careful re-examination of the DME implementation. Here we take the first steps, focusing on two-body scalar terms in the DME. Exchange energies with long-range one-pion contributions are well approximated by all DME implementations considered, with preference for variants that do not truncate at two derivatives in every EDF term. The use of the DME for chiral pion contributions is therefore supported by this investigation. For scalar-isovector energies it is important to treat neutrons and protons separately. The results are found to apply under broad conditions, although self-consistency is not yet tested.

The pion production mechanism is explored based on the ultrarelativistic quantum molecular dynamics model (UrQMD) in which the $\mathrm{\Delta }$-mass dependence of the $\mathcal{M}$ matrix and $\mathrm{\Delta }$-mass dependence of the momentum $p_{N\mathrm{\Delta }}$ in $N\mathrm{\Delta }\to NN$ cross sections are taken into account. By analyzing the time evolution of the pion production rate and the density in the overlapped region for the reaction of Au+Au at the beam energy of $0.4A$ GeV, we find that characteristic density of pion observable is in the region of 1–2 times normal density. The process of pion production in the reaction is tracked, including the loops of $NN\leftrightarrow N\mathrm{\Delta }$ and $\mathrm{\Delta }\leftrightarrow N\pi$, and our calculations show that the sensitivity of ${\pi }^{-}/{\pi }^{+}$ to symmetry energy is weakened after 4–5 $N\text{−}\mathrm{\Delta }\text{−}\pi$ loops in the pion production path. The ${\pi }^{-}/{\pi }^{+}$ ratio in the reaction near the threshold energies retains its sensitivity to the symmetry energy, and it is insensitive to the nuclear incompressibility $K_0$ and effective mass when their values are selected in the commonly accepted range. By comparing the UrQMD calculations to the FOPI data at $0.4A$ GeV and considering the constraint of symmetry energy from neutron star properties, the slope of symmetry energy $L=54–91$ MeV and the symmetry energy at two times normal density $S\left(2{\rho }_0\right)=48–59$ MeV are deduced, and they are also consistent with the constraint from the ASY-EOS flow data.

We explore parton collisional effects on the conversion of geometry eccentricities into azimuthal anisotropies in $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s_{NN}}=5.02$ TeV using a multiphase transport model. The initial eccentricity ${\varepsilon }_n(n=2,3)$ and flow harmonics $v_n(n=2,3)$ are investigated as a function of the number of parton collisions ($N_{\mathrm{coll}}$) during the source evolution of partonic phase. It is found that partonic collisions leads to generate elliptic flow $v_2$ and triangular flow $v_3$ in $\mathrm{Pb}+\mathrm{Pb}$ collisions. On the other hand, partonic collisions also result in an evolution of the eccentricity of geometry. The collisional effect on the flow conversion efficiency is therefore studied. We find that the partons with larger $N_{\mathrm{coll}}$ show a lower flow conversion efficiency, which reflects differential behaviors with respect to $N_{\mathrm{coll}}$. It provides an additional insight into the dynamics of the space-momentum transformation during the QGP evolution from a transport model point of view.

The exotic $\beta -\gamma -\alpha$ decay mode of ${}^{20}\mathrm{Na}$ has been directly observed for the first time in the Day-one experiment at the Beijing Radioactive Ion-beam Facility. The ${}^{20}\mathrm{Na}$ source was produced by using a 100-MeV proton beam bombarding a stack of microporous MgO thick target and delivered as an intense mass separated beam after online ionization. A high-efficiency simultaneous measurement of $\beta , \gamma$, and $\alpha$ transitions enables the $\beta$-delayed $\gamma -\gamma$ and $\alpha -\gamma$ coincidence spectroscopy. Three $\beta -\gamma -\alpha$ exotic decay sequences in ${}^{20}\mathrm{Na}$ are discovered, which expands the rare decay modes observed in $\beta$ decay. Moreover, a $\beta -\alpha$–decay sequence to the 6130-keV $3^{-}$ state of ${}^{16}\mathrm{O}$ is observed, which is likely through the $12367$-keV $1^{+}$ state in ${}^{20}\mathrm{Ne}$. The experimentally deduced $B\left(F\right)$ and $B\left(GT\right)$ are compared to the shell-model calculation, the allowed $\beta$ transition strengths can be well accounted for by using $sd$ shell-model space interactions.

We present recent results on the structure of the one-valence-particle ${}^{41}\mathrm{Ca}$ and ${}^{49}\mathrm{Ca}$ nuclei and the one-valence-hole ${}^{47}\mathrm{Ca}$ nucleus. The isotopes of interest were populated via the cold-neutron-capture reactions ${}^{40}\mathrm{Ca}(n,\gamma ), {}^{48}\mathrm{Ca}(n,\gamma )$, and ${}^{46}\mathrm{Ca}(n,\gamma )$, respectively. The experiments were performed at the Institut Laue-Langevin, within the EXILL campaign, which employed a large array of high-purity germanium (HPGe) detectors. The $\gamma$ decay and level schemes of these nuclei were investigated by $\gamma$-ray coincidence relationships, leading to the identification of 41, 10, and 6 new transitions in ${}^{41}\mathrm{Ca}, {}^{47}\mathrm{Ca}$, and ${}^{49}\mathrm{Ca}$, respectively. Branching ratios and intensities were extracted for the $\gamma$ decay from each state, and $\gamma$-ray angular correlations were performed to establish a number of transition multipolarities and mixing ratios, thus helping in the spin assignment of the states. The experimental findings are discussed along with microscopic, self-consistent beyond-mean-field calculations performed with the hybrid configuration mixing model, based on a Skyrme SkX Hamiltonian. The latter suggests that a fraction of the low-spin states of the ${}^{41}\mathrm{Ca}, {}^{49}\mathrm{Ca}$, and ${}^{47}\mathrm{Ca}$ nuclei is characterized by the coexistence of either 2p-1h (two-particle–one-hole) and 1p-2h excitations, or couplings between single-particle or single-hole degrees of freedom and collective vibrations (phonons) of the doubly-magic “core.”

The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While various options for the computational basis are available, perturbatively constructed natural orbitals recently have been shown to lead to significant improvement in many-body applications yielding faster model-space convergence and lower sensitivity to basis set parameters in large-scale no-core shell model diagonalizations. This work provides a detailed comparison of single-particle basis sets and a systematic benchmark of natural orbitals in nonperturbative many-body calculations using the in-medium similarity renormalization group approach. As a key outcome we find that the construction of natural orbitals in a large single-particle basis enables for performing the many-body calculation in a reduced space of much lower dimension, thus offering significant computational savings in practice that help extend the reach of ab initio methods towards heavier masses and higher accuracy.

Background: $\beta$-decay spectroscopy provides valuable information on exotic nuclei and a stringent test for nuclear theories beyond the stability line.

Purpose: To search for new $\beta$-delayed protons and $\gamma$ rays of ${}^{25}\mathrm{Si}$ to investigate the properties of ${}^{25}\mathrm{Al}$ excited states.

Method: ${}^{25}\mathrm{Si}\beta$ decays were measured by using the Gaseous Detector with Germanium Tagging system at the National Superconducting Cyclotron Laboratory. The protons and $\gamma$ rays emitted in the decay were detected simultaneously. A Monte Carlo method was used to model the Doppler broadening of ${}^{24}\mathrm{Mg}\gamma$-ray lines caused by nuclear recoil from proton emission. Shell-model calculations using two newly developed universal sd-shell Hamiltonians were performed.

Results: The most precise ${}^{25}\mathrm{Si}$ half-life to date has been determined. A new proton branch at 724(4) keV and new proton-$\gamma$-ray coincidences have been identified. Three ${}^{24}\mathrm{Mg}\gamma$-ray lines and eight ${}^{25}\mathrm{Al}\gamma$-ray lines are observed for the first time in ${}^{25}\mathrm{Si}$ decay. The first measurement of the ${}^{25}\mathrm{Si}\beta$-delayed $\gamma$-ray intensities through the ${}^{25}\mathrm{Al}$ unbound states is reported. All the bound states of ${}^{25}\mathrm{Al}$ are observed to be populated in the $\beta$ decay of ${}^{25}\mathrm{Si}$. Several inconsistencies between the previous measurements have been resolved, and new information on the ${}^{25}\mathrm{Al}$ level scheme is provided. An enhanced decay scheme has been constructed and compared to the mirror decay of ${}^{25}\mathrm{Na}$ and the shell-model calculations.

Conclusions: The measured excitation energies, $\gamma$-ray and proton branchings, log $ft$ values, and Gamow-Teller transition strengths for the states of ${}^{25}\mathrm{Al}$ populated in the $\beta$ decay of ${}^{25}\mathrm{Si}$ are in good agreement with the shell-model calculations, offering gratifyingly consistent insights into the fine nuclear structure of ${}^{25}\mathrm{Al}$.