Calculations of nuclei are often carried out in finite model spaces. Thus, finite-size corrections enter, and it is necessary to extrapolate the computed observables to infinite model spaces. In this work, we employ extrapolation methods based on artificial neural networks for observables such as the ground-state energy and the point-proton radius. We extrapolate results from no-core shell model and coupled-cluster calculations to very large model spaces and estimate uncertainties. Training the network on different data typically yields extrapolation results that cluster around distinct values. We show that a preprocessing of input data, and the inclusion of correlations among the input data, reduces the problem of multiple solutions and yields more stable extrapolated results and consistent uncertainty estimates. We perform extrapolations for ground-state energies and radii in ${}^4\mathrm{He}, {}^6\mathrm{Li}$, and ${}^{16}\mathrm{O}$, and compare the predictions from neural networks with results from infrared extrapolations.

Background: Level structure of the most neutron-deficient nucleon-bound carbon isotope, ${}^9\mathrm{C}$, is not well known. Definitive spin-parity assignments are only available for two excited states. No positive-parity states have been conclusively identified so far and the location of the $sd$ shell in the $A=9, T=3/2$ isospin quadruplet is not known.

Purpose: We have studied the level structure of exotic nucleus ${}^9\mathrm{C}$ at excitation energies below 6.4 MeV.

Methods: Excited states in ${}^9\mathrm{C}$ were populated in ${}^8\mathrm{B}+p$ resonance elastic scattering and excitation functions were measured using the active target approach.

Results: Two excited states in ${}^9\mathrm{C}$ were conclusively observed, and $R$-matrix analysis of the excitation functions was performed to make the spin-parity assignments. The first positive-parity state in the $A=9, T=3/2$ nuclear system, the $5/2^{+}$ resonance at 4.3 MeV, has been identified.

Conclusions: The new $5/2^{+}$ state at 4.3 MeV in ${}^9\mathrm{C}$ is a single-particle $\ell =0$ broad resonance and it determines the energy of the $2s$ shell. The $2s$ shell in this exotic nucleus appears well within the region dominated by the $p$-shell states.

High-precision data of the $\gamma p\to {\pi }^{0}p$ reaction from its threshold up to $W=1.9\mathrm{GeV}$ have been used in order to perform a single-energy partial-wave analysis with minimal model dependence. Continuity in energy was achieved by imposing constraints from fixed-$t$ analyticity in an iterative procedure. Reaction models were only used as starting point in the very first iteration. We demonstrate that, with this procedure, partial-wave amplitudes can be obtained which show only a minimal dependence on the initial model assumptions.

We describe here microscopic calculations performed on the dominant forbidden transitions in reactor antineutrino spectra above 4 MeV using the nuclear shell model. By taking into account Coulomb corrections in the most complete way, we calculate the shape factor with the highest fidelity and show strong deviations from allowed approximations and previously published results. Despite small differences in the ab initio electron cumulative spectra, large differences on the order of several percent are found in the antineutrino spectra. Based on the behavior of the numerically calculated shape factors we propose a parametrization of forbidden spectra. Using Monte Carlo techniques we derive an estimated spectral correction and uncertainty due to forbidden transitions. We establish the dominance and importance of forbidden transitions in both the reactor anomaly and spectral shoulder analysis with their respective uncertainties. Based on these results, we conclude that a correct treatment of forbidden transitions is indispensable in both the normalization anomaly and spectral shoulder.

Gamow-Teller (GT) and spin-dipole (SD) strength distributions of four doubly magic nuclei, ${}^{48}\mathrm{Ca}, {}^{90}\mathrm{Zr}, {}^{132}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$, are studied by the self-consistent Hartree-Fock plus random phase approximation (RPA) method. The Skyrme forces SAMi and SAMi-T without/with tensor interactions are adopted in our calculations. The calculated strengths are compared with available experimental data. The RPA results of GT and SD strengths of all four nuclei show fine agreement with observed GT and SD resonances in energy. A small GT peak below the main GT resonance is better described by the Skyrme interaction SAMi-T with the tensor terms. The quenching factors for GT and SD are extracted from the comparisons between RPA results and experimental strengths. It is pointed out that the quenching effect on experimental SD peaks is somewhat modest compared with that on GT peaks in the four nuclei.

The production of backward nucleons, $N\left({180}^{\circ }\right)$, at ${180}^{\circ }$ in the nuclear target rest frame in proton-nucleus ($p+A$) collisions is studied. The backward nucleons appearing outside of the kinematically allowed range of proton-nucleon ($p+N$) reactions are shown to be due to secondary reactions of heavy baryonic resonances produced inside the nucleus. Baryonic resonances $R$ created in primary $p+N$ reactions can change their masses and momenta due to successive collisions $R+N\to R+N$ with other nuclear nucleons. Two distinct mechanisms and kinematic restrictions are studied: the reaction $R+N\to N\left({180}^{\circ }\right)+N$ and the resonance decay $R\to N\left({180}^{\circ }\right)+\pi$. Simulations of $p+A$ collisions using the Ultrarelativistic Quantum Molecular Dynamics model support these mechanisms and are consistent with available data on proton backward production.

Elastic and inelastic alpha scatterings on ${}^{10}\mathrm{C}$ were measured using a 68-MeV/u radioactive ${}^{10}\mathrm{C}$ beam incident on the recently developed MAIKo active target system. The phenomenological effective $\alpha \text{−}N$ interaction and the point-nucleon density distribution in the ground state were determined from the elastic scattering data. The cross sections of the inelastic alpha scattering were calculated using this interaction and density distribution and were compared with the experiment to determine the neutron quadrupole transition matrix element $M_n$ between the ground state and the $2_1^{+}$ state at $E_x=3.35$ MeV in ${}^{10}\mathrm{C}$. The deduced neutron transition matrix element is $M_n=6.9\pm 0.7\left(\mathrm{fit}\right)\pm 1.2\left(\mathrm{sys}\right){\mathrm{fm}}^2$. The ratio of the neutron transition strength to proton transition strength was determined as $M_n/M_p=1.05\pm 0.11\left(\mathrm{fit}\right)\pm 0.17\left(\mathrm{sys}\right)$, which indicates that the quadrupole transition between the ground state and the $2_1^{+}$ state in ${}^{10}\mathrm{C}$ is less neutron dominant compared to that in ${}^{16}\mathrm{C}$.

Colliding heavy nuclear systems in the deep-inelastic regime may undergo partitioning into multiple fragments when fusion can not be achieved. While multiple breakups are common at Fermi energy, they are rather exotic in the deep-inelastic regime, where density, excitation, and, in general, transport conditions, are expected to be different. Abundant ternary and quaternary splits have been observed in recent experiments, for instance in symmetric semicentral and semiperipheral collisions with heavy systems, such as ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ at 15 MeV per nucleon. In these conditions, we undertook a microscopic description of the reaction dynamics. Relying on the full solution of the Boltzmann-Langevin equation implemented in the Boltzmann-Langevin one-body model approach, we could follow in time the development of instabilities along deformation.

Effects of dynamical deformation on the potential energy surface and the mass distribution in multinucleon transfer (MNT) reactions ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$, ${}^{136}\mathrm{Xe}+{}^{198}\mathrm{Pt}$ are studied in the framework of the dinuclear system concept. Considering the dynamical deformation rather than the ground-state deformation of the two interacting nuclei, the products distribution could be estimated in agreement with experimental data, especially in the region far from the incident channel. On this basis, the orientation effect on the final isotopic production is discussed. The present calculation supports the tendency of the MNT reaction to maintain a larger production of neutron-rich isotones around $N=126$, compared with the fragmentation reaction.

Background: The study of low-energy neutrinos and their interactions with atomic nuclei is crucial to several open problems in physics, including the neutrino mass hierarchy, $CP$ violation, candidates of physics beyond the standard model, and supernova dynamics. Examples of experiments include CAPTAIN at the Spallation Neutrino Source (SNS) as well as DUNE's planned detection program of supernova neutrinos.

Purpose: We present cross section calculations for charged current and neutral current neutrino-nucleus scattering at low energies, with a focus on ${}^{40}\mathrm{Ar}$. We also take a close look at pion decay-at-rest neutrino spectra, which are used in e.g. the SNS experiment at Oakridge.

Methods: We employ a Hartree-Fock $+$ continuum random phase approximation ($\mathrm{HF}+\mathrm{CRPA}$) framework, which allows us to model the responses and include the effects of long-range correlations. It is expected to provide a good framework to calculate forbidden transitions, whose contribution we show to be non-negligible.

Results: Our results for a ${}^{56}\mathrm{Fe}$ nucleus compare favorably to others models. Calculations performed for a ${}^{40}\mathrm{Ar}$ target shows that the cross section contributions by $1^{-}$ and $2^{-}$ transitions in the continuum channels are nontrivial for the energies considered.

Conclusions: Forbidden transitions can be expected to contribute sizeably to the reaction strength at typical low-energy kinematics. Modeling and Monte Carlo simulations need to take all due care to account for the influence of their contributions.

Lifetimes of the excited states in the neutron-rich ${}^{52,54}\mathrm{Ti}$ nuclei, produced in a multinucleon-transfer reaction, were measured by employing the Cologne plunger device and the recoil-distance Doppler-shift method. The experiment was performed at the Grand Accélérateur National d'Ions Lourds facility by using the Advanced Gamma Tracking Array for the $\gamma$-ray detection, coupled to the large-acceptance variable mode spectrometer for an event-by-event particle identification. A comparison between the transition probabilities obtained from the measured lifetimes of the $2_1^{+}$ to $8_1^{+}$ yrast states in ${}^{52,54}\mathrm{Ti}$ and that from the shell-model calculations based on the well-established GXPF1A, GXPF1B, and KB3G $fp$ shell interactions support the $N=32$ subshell closure. The $B\left(E2\right)$ values for ${}^{52}\mathrm{Ti}$ determined in this work are in disagreement with the known data, but are consistent with the predictions of the shell-model calculations and reduce the previously observed pronounced staggering across the even-even titanium isotopes.

Strengths of $M1$ transitions depopulating high-lying $1^{+}$ states and of subsequent transitions in cascades populating the first excited state were determined on the basis of large-scale shell-model calculations for the nuclide ${}^{54}\mathrm{Fe}$. The results reveal that the spectra of primary $M1$ transitions from $1^{+}$ states as well as the subsequent cascades of $M1$ transitions show an enhancement of strength toward low energy, which is similar to that found for a huge number of transitions between states of a wide spin range as observed in light-ion induced reactions. This allows, in principle, the study of low-energy $M1$ strength using photon scattering. Based on these results, intensities of $M1$ transitions under experimental conditions are estimated.

Background: The region around neutron number $N=60$ in the neutron-rich Sr and Zr nuclei is one of the most dramatic examples of a ground-state shape transition from (near) spherical below $N=60$ to strongly deformed shapes in the heavier isotopes.

Purpose: The single-particle structure of ${}^{95–97}\mathrm{Sr}$ approaching the ground-state shape transition at ${}^{98}\mathrm{Sr}$ has been investigated via single-neutron transfer reactions using the $(d,p)$ reaction in inverse kinematics. These reactions selectively populate states with a large overlap of the projectile ground state coupled to a neutron in a single-particle orbital.

Method: Radioactive ${}^{94,95,96}\mathrm{Sr}$ nuclei with energies of 5.5 $A\mathrm{MeV}$ were used to bombard a ${\mathrm{CD}}_2$, where D denotes ${}^2\mathrm{H}$, target. Recoiling light charged particles and $\gamma$ rays were detected using a quasi-$4\pi$ silicon strip detector array and a 12-element Ge array. The excitation energy of states populated was reconstructed employing the missing mass method combined with $\gamma$-ray tagging and differential cross sections for final states were extracted.

Results: A reaction model analysis of the angular distributions allowed for firm spin assignments to be made for the low-lying 352, 556, and 681 keV excited states in ${}^{95}\mathrm{Sr}$ and a constraint has been placed on the spin of the higher-lying 1666 keV state. Angular distributions have been extracted for ten states populated in the ${}^2\mathrm{H}({}^{95}\mathrm{Sr},p){}^{96}\mathrm{Sr}$ reaction, and constraints have been provided for the spins and parities of several final states. Additionally, the 0, 167, and 522 keV states in ${}^{97}\mathrm{Sr}$ were populated through the ${}^2\mathrm{H}({}^{96}\mathrm{Sr},p)$ reaction. Spectroscopic factors for all three reactions were extracted.

Conclusions: Results are compared to shell-model calculations in several model spaces and the structure of low-lying states in ${}^{94}\mathrm{Sr}$ and ${}^{95}\mathrm{Sr}$ is well described. The spectroscopic strength of the $0^{+}$ and $2^{+}$ states in ${}^{96}\mathrm{Sr}$ is significantly more fragmented than predicted. The spectroscopic factors for the ${}^2\mathrm{H}({}^{96}\mathrm{Sr},p){}^{97}\mathrm{Sr}$ reaction suggest that the two lowest-lying excited states have significant overlap with the weakly deformed ground state of ${}^{96}\mathrm{Sr}$, but the ground state of ${}^{97}\mathrm{Sr}$ has a different structure.

Background: While the tensor interaction has been shown to significantly affect the nuclear structure of exotic nuclei, its influence on nuclear reactions has only recently been investigated. The primary reason for this neglect is the fact that most studies of nuclear dynamics do not include the tensor force at all in their models. Indeed, only a few Skyrme parametrizations consider the tensor interaction in parameter determination. With modern research facilities extending our ability to probe exotic nuclei, a correct description of nuclear dynamics and heavy-ion fusion is vital to both supporting and leading experimental efforts.

Purpose: To investigate the effect of the tensor interaction on fusion cross sections for a variety of nuclear reactions spanning light and heavy nuclei.

Method: Fusion cross sections are calculated using ion-ion potentials generated by the fully microscopic density-constrained time-dependent Hartree-Fock method with the complete Skyrme tensor interaction.

Results: For light nuclei, the tensor force only slightly changes the sub-barrier fusion cross sections at very low energies. Heavier nuclei, however, begin to exhibit a substantial hindrance effect in the sub-barrier region. This effect is strongest in spin-unsaturated systems, though can manifest in other configurations as well. Static, ground state deformation effects of the tensor force can also affect cross sections by shifting the fusion barrier.

Conclusions: The tensor interaction has a measurable effect on the fusion cross sections of nuclei spanning the nuclear chart. The effect comes from both static effects present in the ground state and dynamic processes arising from the time evolution of the system. This motivates the development of a modern Skyrme parameter set that includes all time-odd and tensor terms and that studies moving forward should include the tensor force to ensure a more robust and complete description of nuclei.

The ${}^{54}\mathrm{Mn}^{*}$ (surrogate of $n+{}^{53}\mathrm{Mn}$) and ${}^{61}\mathrm{Ni}^{*}$ (surrogate of $n+{}^{60}\mathrm{Ni}$) compound systems have been populated at overlapping excitation energies by transfer reactions ${}^{52}\mathrm{Cr}({}^6\mathrm{Li},\alpha ){}^{54}\mathrm{Mn}^{*}$ at $E_{\mathrm{lab}}=33.0\mathrm{MeV}$ and ${}^{59}\mathrm{Co}({}^6\mathrm{Li},\alpha ){}^{61}\mathrm{Ni}^{*}$ at $E_{\mathrm{lab}}=40.5\mathrm{MeV}$, respectively. The proton decay probabilities of the compound systems have been determined by measuring evaporated protons at backward angles in coincidence with projectilelike fragments detected around the grazing angle. The ${}^{53}\mathrm{Mn}(n,xp)$ cross sections in the equivalent neutron energy range of 8.2–16.4 MeV have been determined within the framework of the surrogate reaction ratio method using ${}^{60}\mathrm{Ni}(n,xp)$ cross-section values from the literature as a reference. The measured ${}^{53}\mathrm{Mn}(n,xp)$ cross-section values are found to be consistent with the predictions of the talys-1.8 statistical model code using microscopic level densities and results of various evaluated nuclear data libraries: eaf-2010, rosfond-2010, and jeff-3.3 within the experimental uncertainties.

Background: A recent coupled-reaction-channel (CRC) study shows that the enhanced oscillation of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ section at backward angles is due mainly to the elastic $\alpha$ transfer or the core exchange. Such a process gives rise to a parity-dependent term in the total elastic $S$ matrix, an indication of the parity dependence of the ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ optical potential (OP).

Purpose: To explicitly determine the core exchange potential (CEP) induced by the symmetric exchange of the two ${}^{12}\mathrm{C}$ cores in the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering at $E_{\mathrm{lab}}=132$ and 300 MeV and explore its parity dependence.

Method: $S$ matrix generated by CRC description of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering is used as the input for the inversion calculation to obtain the effective local OP that contains both the Wigner and Majorana terms.

Results: The high-precision inversion results show a strong contribution by the complex Majorana term in the total OP of the ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ system and thus provide for the first time a direct estimation of the parity-dependent CEP.

Conclusions: The elastic $\alpha$ transfer or exchange of the two ${}^{12}\mathrm{C}$ cores in the ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ system gives rise to a complex parity dependence of the total OP. This should be a general feature of the OP for the light heavy-ion systems that contain two identical cores.

A novel technique has been developed, making use of the continuous wavelet transform to identify $\alpha$-clustered states from resonant scattering measurements in regions of high nuclear state density. This technique expedites the investigation of $\alpha$ clustering in medium mass and heavy nuclei where the role that $\alpha$ clustering plays in the structure of the nucleus is poorly understood. Here, we report the application of this technique to measurements of the ${}^4\mathrm{He}({}^{40,44,48}\mathrm{Ca},\alpha )$ resonant reactions, leading to an assessment of the $\alpha$-cluster structure of ${}^{44,48,52}\mathrm{Ti}$. Clustering involving α particles was identified in ${}^{44}\mathrm{Ti}$ and ${}^{52}\mathrm{Ti}$ but was observed to break down in ${}^{48}\mathrm{Ti}$. The implications of these results are discussed.

We demonstrate that the multiplicity distribution of a system located in the vicinity of a first-order phase transition can be successfully measured in terms of its factorial cumulants with a surprisingly small number of events. This finding has direct implications for the experimental search of a QCD phase transition conjectured to be located in the high baryon density region of the QCD phase diagram.

Three new highly-deformed (HD) bands are identified in ${}^{136}\mathrm{Nd}$ and the highly deformed band of ${}^{137}\mathrm{Nd}$ is extended at higher spin by four transitions, revealing a band crossing associated with the occupation of the second $\nu i_{13/2}$ intruder orbital. Extended cranked Nilsson-Strutinsky calculations are performed for all HD bands observed in ${}^{134}\mathrm{Nd}$, ${}^{136}\mathrm{Nd}$, and ${}^{137}\mathrm{Nd}$, achieving for the first time a consistent interpretation of all HD bands in the Nd nuclei. The new interpretation has significant consequences, like the change of parity of the yrast HD bands of ${}^{134}\mathrm{Nd}$ and ${}^{136}\mathrm{Nd}$, and the involvement of two negative-parity neutron intruder orbitals in the configurations of most HD bands. The present experimental results and their theoretical interpretation represent an important step forward in the understanding of the second-minimum excitations in the Nd nuclei.

We propose a novel method to extract the prompt neutron multiplicity distribution, $P\left(\nu \right)$, in fission reactions based on correlations between prompt neutrons, $\gamma$ rays, and fragment kinetic energy arising from energy conservation. In this approach, only event-by-event measurements of the total $\gamma$-ray energy released as a function of the total kinetic energy (TKE) of the fission fragments are performed, and no neutron detection is required. Using the cgmf fission event generator, we illustrate the method and explore the accuracy of extracting the neutron multiplicity distribution when taking into account the energy resolution and calibration of the energy measurements. We find that a TKE resolution of under 2 MeV produces reasonably accurate results, independent of typical $\gamma$-ray energy measurement resolution.