Background: Over the past two decades high energy-resolution inelastic proton scattering studies were used to gain an understanding of the origin of fine structure observed in the isoscalar giant quadrupole resonance (ISGQR) and the isovector giant dipole resonance (IVGDR). Recently, the isoscalar giant monopole resonance (ISGMR) in ${}^{58}\mathrm{Ni}, {}^{90}\mathrm{Zr}, {}^{120}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$ was studied at the iThemba Laboratory for Accelerator Based Sciences (iThemba LABS) by means of inelastic $\alpha$-particle scattering at very forward scattering angles (including $0^{\circ }$). The good energy resolution of the measurement revealed significant fine structure of the ISGMR.

Objective: To extract scales by means of wavelet analysis characterizing the observed fine structure of the ISGMR in order to investigate the role of different mechanisms contributing to its decay width.

Methods: Characteristic energy scales are extracted from the fine structure using continuous wavelet transforms. The experimental energy scales are compared to different theoretical approaches performed in the framework of quasiparticle random phase approximation (QRPA) and beyond-QRPA including complex configurations using both non-relativistic and relativistic density functional theory.

Results: All models highlight the role of Landau fragmentation for the damping of the ISGMR especially in the medium-mass region. Models which include the coupling between one-particle–one-hole (1p-1h) and two-particle–two-hole (2p-2h) configurations modify the strength distributions and wavelet scales indicating the importance of the spreading width. The effect becomes more pronounced with increasing mass number.

Conclusions: Wavelet scales remain a sensitive measure of the interplay between Landau fragmentation and the spreading width in the description of the fine structure of giant resonances. The case of the ISGMR is intermediate between the IVGDR, where Landau damping dominates, and the ISGQR, where fine structure originates from coupling to low-lying surface vibrations.

The radon radioactivity is an unavoidable background in present and future underground experiments attempting to detect the neutrinoless double $\beta$ decay, WIMP-nucleus interactions in direct dark-matter searches, etc. In particular, the ${}^{220,222}\mathrm{Rn}$ radioactive chains lead to ${\beta }^{-}$ decays of ${}^{212,214}\mathrm{Pb}$ and ${}^{212,214}\mathrm{Bi}$, notorious backgrounds in the mentioned experiments. In this paper, we compute the total $\beta$-electron spectral shapes of these decays by including next-to-leading-order terms and other correction factors in the $\beta$ spectral shape. The studied ${\beta }^{-}$ decays involve strong allowed and first-forbidden $\beta$ transitions, the nonunique first-forbidden transitions being nuclear-structure dependent through the numerous involved nuclear matrix elements (NMEs). We compute these NMEs by using the nuclear shell model with the khpe Hamiltonian. This Hamiltonian renders a very nice description of the level energies of the daughter nuclei ${}^{212,214}\mathrm{Bi}$ and ${}^{212,214}\mathrm{Po}$ of the mentioned mother nuclei. We adopt experimental endpoint energies and engage the small relativistic NMEs (sNME), to accurately describe the measured branching ratios, a necessary prerequisite for a precise description of the total $\beta$ spectra. We also discuss the uncertainties of our computed spectra and hope that these computations will be of help for present and future rare-decays and dark-matter experiments.

Lying between ${}^{16}\mathrm{O}$ and ${}^{40}\mathrm{Ca}$, the $sd$ shell is well described by robust phenomenological and ab initio nuclear theories. In this work, however, we highlight an unexplained reduction in electric-quadrupole strength in the rare isotope ${}^{32}\mathrm{Si}$, studied through sub-barrier Coulomb excitation. It is found that the oblate nature of the deformation is well reproduced, while the absolute scale of quadrupole deformation, however, is inhibited by approximately a factor of 2 compared to theoretical predictions. Through comparison with shell-model and ab initio calculations, we present a number of possible explanations for this inhibited $E2$ strength. By comparing the results of these calculations to multiple observables, we conclude that there is a reduced role for out-of-space excitations in ${}^{32}\mathrm{Si}$, resulting in a reduction in the corrections normally applied to both models.

Within the framework of the dinuclear system model, the experimentally accessible projectile-target combinations are predicted for the production of new superheavy elements with $Z=119$ and $Z=120$. The entrance channel effect and the isotopic dependence of targets and projectiles on the capture, fusion, and survival stages of the fusion reaction are discussed. The reactions ${}^{45}\mathrm{Sc}+{}^{249}\mathrm{Cf}$ and ${}^{50}\mathrm{V} + {}^{246}\mathrm{Cm}$ are found to be promising candidates for the synthesis of the element with $Z=119$, achieving the maximal evaporation residue cross sections of 0.288 pb at an incident energy of 211.2 MeV and 0.237 pb at an incident energy of 226.2 MeV, respectively. Meanwhile, the element with $Z=120$ can be synthesized through the reaction ${}^{46}\mathrm{Ti} + {}^{249}\mathrm{Cf}$ with a maximal evaporation residue cross section of 0.040 pb at 221.8 MeV.

An approach is proposed to link the charge symmetry breaking (CSB) nuclear interaction and the low-energy constants in quantum chromodynamics (QCD) by matching the CSB effect in nuclear matter. The resulting CSB interaction is applied to study the Okamoto-Nolen-Schiffer anomaly, still lacking a satisfactory microscopic understanding, on the energy differences of mirror nuclei by taking ${}^{17}\mathrm{F}\text{−}{}^{17}\mathrm{O}, {}^{15}\mathrm{O}\text{−}{}^{15}\mathrm{N}, {}^{41}\mathrm{Sc}\text{−}{}^{41}\mathrm{Ca}$, and ${}^{39}\mathrm{Ca}\text{−}{}^{39}\mathrm{K}$ as typical examples. The magnitude and sign of the QCD-based CSB interactions are found to resolve the anomaly successfully within theoretical uncertainties.

We propose a new basis state, which satisfies the Pauli principle in the nuclear cluster model. The basis state is defined as the generalized coherent state of the harmonic oscillator wave function using a pair of the creation operators and is orthogonal to the Pauli-forbidden states having smaller quanta. In the coherent basis state, the range parameter is changeable and controls the radial dilation. This property is utilized for the precise description of the relative motion between nuclear clusters. We show the reliability of this framework for the $2\alpha$ system of ${}^8\mathrm{Be}$ in the semimicroscopic orthogonality condition model. We obtain the resonances and nonresonant continuum states of $2\alpha$ with complex scaling. The resonance solutions and the phase shifts of the $\alpha \text{−}\alpha$ scattering agree with those using the conventional projection operator method to remove the Pauli-forbidden states. We further discuss the extension of the present framework to the multi-$\alpha$ cluster systems using the SU(3) wave functions.

Root mean square (rms) radii of light-heavy nuclei ${}^{6–9,11}\mathrm{Li}, {}^{9–12}\mathrm{Be}, {}^{10–15}\mathrm{B}, {}^{11,12,14–18}\mathrm{C}, {}^{14,16–19}\mathrm{N}$, and ${}^{15,17,19–21}\mathrm{O}$ are studied by analyzing the total reaction cross section data on a ${}^{\mathrm{nat}}\mathrm{Cu}$ target at intermediate energies within the range of $25–65$ MeV/nucleon with the eikonal model. For calculations at such low and intermediate incident energies, the turning point corrections to the eikonal model, which effectively account for the distortions of the projectile trajectory caused by the Coulomb and/or nuclear forces, are examined with the elastic scattering angular distributions and total reaction cross sections of ${}^{16}\mathrm{O}$ on ${}^{12}\mathrm{C}, {}^{63}\mathrm{Cu}$, and ${}^{208}\mathrm{Pb}$ targets at incident energies from 12.5 to 200 MeV/nucleon. Effects of the corrections taking into account the turning points calculated with the Coulomb potential only, with both Coulomb and the real parts of the optical model potentials (OMPs), and with both the Coulomb and the complex OMPs, are evaluated by comparing with the exact results of partial wave Schrödinger equations. Complex turning point corrections are found to be important for light and intermediate-mass targets. With the complex turning point corrections, the rms radii obtained in this work differ, on average, from the results obtained from high-energy total interaction cross section measurements at around $650–1020$ MeV/nucleon by 1.4%, which is much smaller than the averaged differences of 8% when no corrections to the eikonal model were made, and smaller than the averaged differences of 7.7% found in literature.

The excited states of ${}^{209}\mathrm{Rn}$ ($Z=86, N=123$) have been populated by the heavy-ion induced fusion evaporation reaction ${}^{198}\mathrm{Pt}({}^{16}\mathrm{O},5n){}^{209}\mathrm{Rn}$ at a beam energy of 102 MeV. The de-excited $\gamma$ rays were detected with the Compton suppressed clover HPGe detectors of the Indian National Gamma Array (INGA) set-up. The high spin spectroscopic study of ${}^{209}\mathrm{Rn}$ has been carried out up to an excitation energy of 7.9 MeV and spin (55/2)$\hslash$. Spin-parity assignments of the excited levels have been determined and are confirmed on the basis of the ratio of directional correlation and polarization asymmetry measurement. The possible presence of new isomeric states has been observed and the half-lives have been estimated. A negative parity sequence of $M1$ transitions has been observed which exhibits the property of magnetic rotation and is interpreted in the framework of semiclassical model calculation. The large basis shell-model calculation has been performed for all the nuclear levels and is found to be in well agreement with the experimental results.

Spin and pseudospin symmetries play vital roles in nuclear physics and have been studied extensively in spherical nuclei. However, there are much fewer studies in deformed systems and there remain many open questions. In this work, for the first time, we examine the possible spin and pseudospin symmetries (SS and PSS) in deformed nuclei by solving a coupled-channels Dirac equation with the Green's function method, which provides a novel way to exactly determine the single-particle levels and properly describe the spacial density distributions. Taking axially deformed nucleus ${}^{154}\mathrm{Dy}$ as an example, the spin doublets with a combination of Nilsson levels $\mathrm{\Lambda }\pm 1/2[\mathcal{N},n_z,\mathrm{\Lambda }]$ and pseudospin doublets with a combination of $\tilde{\mathrm{\Lambda }}\pm 1/2\left[\widetilde{\mathcal{N},n_z,\mathrm{\Lambda }}\right]$ are determined. Different behaviors are displayed for the spin and pseudospin doublets. For the spin partners, those with smaller angular momentum $l$ and the third component $\mathrm{\Lambda }$ owns better symmetry such as the $1p$ doublet while good pseudospin symmetry appears in partners locating close to the continuum threshold. By examining the single-particle Nilsson levels $\mathrm{\Omega }[\mathcal{N},n_z,\mathrm{\Lambda }]$ and the energy splittings between the partners, the conservation and breaking of SS and PSS are examined at different deformations. In the prolate side, the Nilsson levels for the spin and pseudospin doublets are almost parallel and the energy splittings are stable against varying deformations. By examining the density distributions, great similarities have been observed in the upper components for the spin doublets while great similarities in the lower component for the pseudospin doublets. Besides, these similarities maintain well at different deformations.

Neutrino scattering and absorption rates of relevance to supernovae and neutron star mergers are obtained from nuclear matter dynamical structure functions that encode many-body effects from nuclear mean fields and correlations. We employ nuclear interactions from chiral effective field theory to calculate the density, spin, isospin, and spin-isospin response functions of warm $\beta$-equilibrium nuclear matter. We include corrections to the single-particle energies in the mean field approximation as well as vertex corrections resummed in the random phase approximation (RPA), including both direct and exchange diagrams. We find that correlations included through the RPA redistribute the strength of the response to higher energy for neutrino absorption and lower energy for antineutrino absorption. This tends to suppress the absorption rate of electron neutrinos across all relevant energy scales. In contrast, the inclusion of RPA correlations enhances the electron antineutrino absorption rate at low energy and suppresses the rate at high energy. These effects are especially important at high-density and in the vicinity of the neutrino decoupling region. Implications for heavy element nucleosynthesis, electromagnetic signatures of compact object mergers, supernova dynamics, and neutrino detection from galactic supernovae are discussed briefly.

The magnetic dipole $\left(M1\right)$ resonances of even-even ${}^{112–120,124}\mathrm{Sn}$ isotopes are investigated in the framework of the self-consistent Skyrme Hartree-Fock + Bardeen-Cooper-Schrieffer (HF+BCS) and quasiparticle random phase approximation (QRPA). The Skyrme energy density functionals SLy5 and T11 with and without tensor terms are adopted in our calculations. The mixed type pairing interaction is used to take care of the pairing effect for open-shell nuclei both in the ground and excited states calculations. The calculated magnetic dipole strengths are compared with available experimental data. The QRPA results calculated by SLy5 and T11 with tensor force show a better agreement with the experimental data than those without the tensor force. By analyzing the HF and QRPA strength distributions of ${}^{112}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}$, we discuss the effect of tensor force on the $M1$ resonances in detail. It is found that the $M1$ resonance is sensitive to the tensor interaction, and favors especially a negative triplet-odd tensor one. Depending on the nucleus, a quenching factor of the $M1$ operator of about 0.71–0.95 is needed to reproduce the total observed transition strength. In our calculations, we also find some low-lying, pygmy-type magnetic dipole states distributed below 6.0 MeV, and they are formed mainly from the neutron configuration $\nu 2d_{5/2}\to \nu 2d_{3/2}$.

Understanding of $\gamma$-ray production via neutron interactions on oxygen is essential for the study of neutrino neutral-current quasielastic interactions in water Cherenkov detectors. A measurement of $\gamma$-ray production from such reactions was performed using a 77 MeV quasimonoenergetic neutron beam. Several $\gamma$-ray peaks, which are expected to come from neutron-${}^{16}\mathrm{O}$ reactions, are observed and production cross sections are measured for nine $\gamma$-ray components of energies between 2 and 8 MeV. These are the first measurements at this neutron energy using a nearly monoenergetic beam.

We calibrate a ($3+1$)-dimensional multistage hybrid framework using the measured pseudorapidity distribution of charged particles and rapidity distribution of net protons for central Au $+$ Au collisions at $\sqrt{s_{NN}}=7.7,19.6,62.4,200$ GeV. We then study the thermodynamic properties of the nuclear matter along the beam direction, and the phase diagram regions probed by the hadronization process near the chemical freeze-out. Using the rapidity-dependent thermal yields of identified particles with full rapidity coverage from the hybrid framework, we apply different scenarios of the statistical thermal model to extract the thermodynamic parameters at the freeze-out, with the known system properties from the hybrid model as a closure test. We find significant theoretical uncertainties in the thermal models when applied to regions away from midrapidity. We also propose a thermal model inspired by the hybrid approach that includes thermal smearing and longitudinal flow for the nuclear matter created at low beam energies.

We calculate the density fluctuations of net baryon number up to sixth order induced by the interactions of nuclear matter, and explore their relationship with the nuclear liquid-gas phase transition (LGPT), including the stable and metastable phases as well as the region far from the phase transition. The results show that dramatic density fluctuations exist in the vicinity of LGPT, and the higher order density fluctuations are more sensitive than the lower order ones to the interactions and structural properties of nuclear matter. The study also indicates that, even far away from the critical region of LGPT, the hadronic interactions can still lead to larger fifth- and sixth-order density fluctuations. In combination with the chemical freeze-out line fitted from the experimental data, the derived results can be used to investigate the chiral phase transition and nuclear LGPT, as well as to analyze related experimental signals.

This work aims at determining the composition of certain $N^{*}$ and $\mathrm{\Delta }$ resonances, i.e., whether they are compact states formed directly by quarks and gluons, or hadronic molecules generated from the meson-baryon interaction. The information of the resonance poles is provided by a comprehensive coupled-channels approach, the Jülich-Bonn model. Thirteen states that are significant in this approach are studied. Two criteria for each state are adopted in this paper, the comparison thereof roughly indicates the model uncertainties. It is found that the conclusions for eight resonances are relatively certain: $N\left(1535\right){\frac{1}{2}}^{-}, N\left(1440\right){\frac{1}{2}}^{+}, N\left(1710\right){\frac{1}{2}}^{+}$, and $N\left(1520\right){\frac{3}{2}}^{-}$ tend to be composite, whereas $N\left(1650\right){\frac{1}{2}}^{-}, N\left(1900\right){\frac{3}{2}}^{+}, N\left(1680\right){\frac{5}{2}}^{+}$, and $\mathrm{\Delta }\left(1600\right){\frac{3}{2}}^{+}$ tend to be compact.

We study the $\mathrm{\Xi }\left(1620\right)$ resonance near the $\overline{K}\mathrm{\Lambda }$ threshold in the light of recent experimental constraints. The Belle Collaboration have found a resonance peak of $\mathrm{\Xi }\left(1620\right)$ slightly below the ${\overline{K}}^0\mathrm{\Lambda }$ threshold in the ${\pi }^{+}{\mathrm{\Xi }}^{-}$ invariant mass spectrum, and the ALICE Collaboration have determined the $K^{-}\mathrm{\Lambda }$ scattering length from the measurement of the momentum correlation functions in heavy ion collisions. Using the effective range expansion, we classify the nature of the pole of the near-threshold eigenstate in terms of the scattering length, in the presence of the decay channel. It is shown that the quasibound state below the threshold can be described by only the scattering length, while the description of the resonance above the threshold requires the contribution from the effective range. Based on the chiral unitary approach, we construct a theoretical model which generates the pole of $\mathrm{\Xi }\left(1620\right)$ below the $\overline{K}\mathrm{\Lambda }$ threshold with relatively narrow width, as reported by the Belle Collaboration. It is quantitatively demonstrated that the spectrum of the $\mathrm{\Xi }\left(1620\right)$ quasibound state is distorted by the effect of the nearby $\overline{K}\mathrm{\Lambda }$ threshold. We then construct another model which reproduces the $K^{-}\mathrm{\Lambda }$ scattering length by the ALICE Collaboration. In this case, the eigenstate pole does not appear in the physically relevant Riemann sheet, and the spectrum shows a cusp structure at the $\overline{K}\mathrm{\Lambda }$ threshold. We finally examine the compatibility of the value of the $\overline{K}\mathrm{\Lambda }$ scattering length and the subthreshold pole of $\mathrm{\Xi }\left(1620\right)$ including the experimental uncertainties.

Background: Resonances with binary and few-body decay modes, such as the excited and ground states of neutron- and proton-rich nuclei, are important objects in nuclear physics. However, a description of three- and few-body states in the continuum and their decays, especially in case of the Coulomb interaction, remains a hardly solvable problem.

Purpose: We aim to develop an effective technique for finding the parameters of multichannel resonances based on the analysis of discretized spectra without explicitly taking into account boundary conditions.

Methods: We introduce a new method for analyzing discretized spectra using spectral and integrated densities of states. For multichannel two-body scattering problems, this approach allows to one calculate a sum of the eigen phase shifts as well as the resonance parameters via solving an eigenvalue problem for the total and asymptotic Hamiltonian matrices in some $L^2$ basis. The generalization of the method to the three-body continuum is used to find the positions and widths of the resonances.

Results: We test the presented approach for several multichannel problems and for the three-particle $\alpha NN$ model for light nuclei with $A=6$. In particular, the width of the ${}^6\mathrm{Be}$ ground state and the parameters of the $3^{+}0$ resonance for the ${}^6\mathrm{Li}$ nucleus are found from a diagonalization of the matrix Hamiltonian with realistic interactions on the Gaussian basis.

Conclusions: The proposed method can be employed to study three-body decays in nonbinary channels, such as the decay that accompanies two-proton radioactivity.

We have calculated the cross sections (CS), differential cross sections (DCS), and astrophysical $S$ factors for the reactions ${}^{11}\mathrm{B}\left(p,{\alpha }_1\right){}^8\mathrm{Be}^{*}$, ${}^{11}\mathrm{B}\left(p,{\alpha }_0\right){}^8\mathrm{Be}$, ${}^{11}\mathrm{B}\left(p,p_0\right){}^{11}\mathrm{B}$, ${}^{11}\mathrm{B}{\left(p,p_1\right)}^{11}{\mathrm{B}}^{*}$, ${}^{11}\mathrm{B}\left(p,{\gamma }_0\right){}^{12}\mathrm{C}$, ${}^{11}\mathrm{B}{\left(p,{\gamma }_1\right)}^{12}{\mathrm{C}}^{*}$, and ${}^{11}\mathrm{B}\left(\mathrm{p},{\mathrm{n}}_0\right){}^{11}\mathrm{C}$ through a multichannel-multilevel $R$-matrix analysis. We have performed calculations for the energy range 100 keV–3.5 MeV and compared the calculated values with the experimental values. As a result, we have obtained the energy value, spin, and parity of some ${}^{12}\mathrm{C}$ excited levels within this energy interval. Additionally, we have determined the channel spins and angular momentum of the ${\alpha }_1-{}^8\mathrm{Be}^{*}$, ${\alpha }_0-{}^8\mathrm{Be}$, $p_0-{}^{11}\mathrm{B}$, $p_1-{}^{11}\mathrm{B}^{*}$, and $n_0-{}^{11}\mathrm{C}$ pairs, as well as the electric and magnetic multipoles of the ${}^{11}\mathrm{B}\left(p,{\gamma }_0\right){}^{12}\mathrm{C}$ and ${}^{11}\mathrm{B}{\left(p,{\gamma }_1\right)}^{12}{\mathrm{C}}^{*}$ channels. Although the analysis results and experimental data mostly agree, we have found some inconsistencies in the $S$-factor values for the ${}^{11}\mathrm{B}{\left(p,p_1\right)}^{11}{\mathrm{B}}^{*}$ channel at the 19.2–19.5 MeV energy interval. For the ${}^{11}\mathrm{B}\left(p,{\alpha }_1\right){}^8\mathrm{Be}^{*}$ decay channel of the 16.57 MeV $\left(2^{-}\right)$ resonance, the literature discusses which orbital angular momentum quantum value ($l=1$ or $l=3$) is true. We used both values in our analysis, and although no significant difference in the results were observed in the region of the 16.57 MeV $\left(2^{-}\right)$ resonance, we obtained a better fit with $l=3$ values in the high energy region affected by the tail of this resonance.

Fission barrier heights of short-lived nuclei away from line of $\beta$ stability are not known reliably. Low-energy fission of ${}^{210}\mathrm{Fr}$ and ${}^{210}\mathrm{Ra}$, produced by ($d,p$) and ($d,n$) transfer reaction on the re-accelerated unstable beam ${}^{209}\mathrm{Fr}$ was investigated at HIE-ISOLDE. Four Timepix3 pixel detectors were installed on the body of the ACTAR TPC demonstrator chamber. Polyethylene converters were used for the detection of fast neutrons. Since no significant background was observed, it was possible to measure the spatial distribution of emitted neutrons reflecting the fission excitation function. Subsequent simulations employing the results of the talys code and available data on fission fragment distributions allowed to estimate directly the value of the fission barrier height for the neutron-deficient nucleus ${}^{210}\mathrm{Fr}$. This first direct measurement confirmed the reduction of the fission barrier compared to available theoretical calculations by 15–30%.