Background: An electron localization measure was originally introduced to characterize chemical bond structures in molecules. Recently, a nucleon localization based on Hartree-Fock densities has been introduced to investigate $\alpha$-cluster structures in light nuclei. Compared to the local nucleonic densities, the nucleon localization function has been shown to be an excellent indicator of shell effects and cluster correlations.

Purpose: Using the spatial nucleon localization measure, we investigate the emergence of fragments in fissioning heavy nuclei.

Methods: To illustrate basic concepts of nucleon localization, we employ the self-consistent energy density functional method with a quantified energy density functional optimized for fission studies.

Results: We study the particle densities and spatial nucleon localization distributions along the fission pathways of ${}^{264}\mathrm{Fm}$, ${}^{232}\mathrm{Th}$, and ${}^{240}\mathrm{Pu}$. We demonstrate that the fission fragments are formed fairly early in the evolution, well before scission. We illustrate the usefulness of the localization measure by showing how the hyperdeformed state of ${}^{232}\mathrm{Th}$ can be understood in terms of a quasimolecular state made of ${}^{132}\mathrm{Sn}$ and ${}^{100}\mathrm{Zr}$ fragments.

Conclusions: Compared to nucleonic distributions, the nucleon localization function more effectively quantifies nucleonic clustering: its characteristic oscillating pattern, traced back to shell effects, is a clear fingerprint of cluster/fragment configurations. This is of particular interest for studies of fragment formation and fragment identification in fissioning nuclei.

Consistent description of ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ has been a long-standing problem of microscopic $\alpha$ cluster models, where the wave function is fully antisymmetrized and the effective interaction is applied not between $\alpha$ clusters but between nucleons. When the effective interaction is designed to reproduce the binding energy of ${}^{16}\mathrm{O}$ (four $\alpha$), the binding energy of ${}^{12}\mathrm{C}$ (three $\alpha$) becomes underbound by about 10 MeV. In the present study, by taking into account the coupling with the $jj$-coupling shell model components and utilizing the Tohsaki interaction, which is phenomenological but has finite-range three-body interaction terms, it is shown that consistent understanding of these nuclei can be achieved. The original Tohsaki interaction gives a small overbound value of about 3 MeV for ${}^{16}\mathrm{O}$, and this is improved by slightly modifying the three-body Majorana exchange parameter. Also, the coupling with the $jj$-coupling shell model wave function strongly contributes to the increase of the binding energy of ${}^{12}\mathrm{C}$. So far the application of the Tohsaki interaction has been limited to $4N$ nuclei; here, Bartlet and Heisenberg exchange terms are added in the two-body interaction part for the purpose of applying it to neutron-rich systems, and it is applied to ${}^6\mathrm{He}$.

We study the sum rules of double Gamow-Teller (DGT) excitations through double spin-isospin operator ${\left(\sigma t_{-}\right)}^2$. In general, $2^{+}$ states in the grand-daughter nuclei have dominant transition strength in DGT excitations and $0^{+}$ states are weak, except in $T=1$ mother nuclei in which $0^{+}$ strength is competitive with $2^{+}$ strength. The isospin selection of DGT is also discussed among five possible isospin states in grand-daughter nuclei. A possibility to extract the unit cross section for the DGT transition strength is pointed out in the ${\left(\sigma t_{-}\right)}^2$ excitation of double isobaric analog state (DIAS) in $T=1$ nuclei.

Using the improved scission-point model, the isotopic trends of the charge distribution of fission fragments are studied in induced fission of even-even Th isotopes. The calculated results are in good agreement with available experimental data. With increasing neutron number the transition from symmetric to asymmetric fission mode is shown to be related to the change of the potential energy surface. The change of the shape of mass distribution with increasing excitation energy is discussed for fissioning ${}^A\mathrm{Th}$ nuclei. At high excitation energies, there are unexpected large asymmetric modes in the fission of neutron-deficient Th isotopes considered.

Background: Since more than 40 years of theoretical and experimental studies of true ternary fission, one is still quite far from its understanding. The true ternary fission channel, being strongly suppressed by the macroscopic properties of the potential energy, may, however, be present with a significant probability due to shell effects.

Purpose: Development of a model for the multidimensional potential energy suitable for analysis of the nucleus-nucleus collisions with the possibility of ternary exit channel. Study of the potential possibility of fission of actinides into three heavy fragments.

Method: The asymmetric three-center shell model of deformed nucleus is developed in this paper. The model can be applied for analysis of ternary as well as binary fission processes.

Results: The potential energy surfaces for few ternary combinations in the fission channel are calculated for the ${}^{252}\mathrm{Cf}$ nucleus. Their properties are discussed.

Conclusions: The potential energy structures are compared with the experimental observations. It was found that the potential energy has pronounced valleys favorable for ternary fission with formation of doubly magic tin as one of the fragments and two other lighter fragments. The positions of the found fission valleys are in a good agreement with the experimental data.

We study the production of $\mathrm{\Lambda }\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }n}$ exotic states in central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s_{\mathit{NN}}}=2.76$ TeV at the CERN Large Hadron Collider (LHC) via both hadron and quark coalescence within a covariant coalescence model with a blast-wave-like parametrization for the phase-space configurations of constituent particles at freeze-out. In the hadron coalescence, the two states are considered as molecular states while they are considered as six-quark states in the quark coalescence. For $\overline{\mathrm{\Lambda }n}$, we find that the yields of both molecular and six-quark states are much larger than the experimental upper-limits. For $\mathrm{\Lambda }\mathrm{\Lambda }$, while the molecule-state yield is much larger than the experimental upper limits, the six-quark-state yield could be lower than the upper limits. The higher molecule-state yields are mainly due to the large contribution of short-lived strong resonance decays into (anti-)nucleons and (anti-)$\mathrm{\Lambda }$ which can significantly enhance the molecule-state yields of $\mathrm{\Lambda }\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }n}$ via hadron coalescence. Our results suggest that the current experimental measurement at the LHC cannot exclude the existence of the $\mathrm{\Lambda }\mathrm{\Lambda }$ as an exotic six-quark state, and if $\mathrm{\Lambda }\mathrm{\Lambda }$ is a six-quark state, it is then on the brink of being discovered.

This is the first study of ${}^{27}\mathrm{P}$ to measure both the $\beta$-delayed proton and $\beta$-delayed $\gamma$ decays. While no new proton groups in the astrophysically interesting energy region of 300–400 keV were observed, a new upper limit on the proton branching of 0.16% was estimated. Several new $\gamma$-ray lines were observed, mainly coming from the isobaric analog state in ${}^{27}\mathrm{Si}$, which has been assigned a more accurate energy value of 6638(1) keV.

The WASA-at-COSY experiment has collected $3\times {10}^7$ events with $\eta$ mesons produced via the reaction $pd\to {}^3\mathrm{He}\eta$ at $\mathrm{T}=1.0\mathrm{GeV}$. Using this data set, we evaluate the branching ratios of the decays $\eta \to {\pi }^{+}{\pi }^{-}\gamma$, $\eta \to e^{+}{e}^{-}\gamma$, $\eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$, and $\eta \to e^{+}{e}^{-}{e}^{+}{e}^{-}$. The branching ratios are normalized to the $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ decay. In addition an upper limit on a $CP$-violating asymmetry in $\eta \to {\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$ is extracted.

The electromagnetic responses of carbon obtained from the Green's function Monte Carlo and spectral function approaches using the same dynamical input are compared in the kinematical region corresponding to momentum transfer in the range 300–570 MeV. The results of our analysis, aimed at pinning down the limits of applicability of the approximations involved in the two schemes, indicate that the factorization ansatz underlying the spectral function formalism provides remarkably accurate results down to momentum transfer as low as 300 MeV. On the other hand, it appears that at 570 MeV relativistic corrections to the electromagnetic current not included in the Monte Carlo calculations may play a significant role in the transverse channel.

The emission of prompt fission $\gamma$ rays within a few nanoseconds to a few microseconds following the scission point is studied in the Hauser-Feshbach formalism applied to the deexcitation of primary excited fission fragments. Neutron and $\gamma$-ray evaporations from fully accelerated fission fragments are calculated in competition at each stage of the decay, and the role of isomers in the fission products, before $\beta$ decay, is analyzed. The time evolution of the average total $\gamma$-ray energy, the average total $\gamma$-ray multiplicity, and the fragment-specific $\gamma$-ray spectra is presented in the case of neutron-induced fission reactions of ${}^{235}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$, as well as spontaneous fission of ${}^{252}\mathrm{Cf}$. The production of specific isomeric states is calculated and compared to available experimental data. About 7% of all prompt fission $\gamma$ rays are predicted to be emitted between 10 ns and 5 $\mu \mathrm{s}$ following fission, in the case of ${}^{235}\mathrm{U}$ and ${}^{239}\mathrm{Pu}(n_{\mathrm{th}},f)$ reactions, and up to 3% in the case of ${}^{252}\mathrm{Cf}$ spontaneous fission. The cumulative average total $\gamma$-ray energy increases by 2% to 5% in the same time interval. Finally, those results are shown to be robust against significant changes in the model input parameters.

Electromagnetic resonance properties are uniquely defined at the pole and do not depend on the separation of the resonance from background or the decay channel. Photon-nucleon branching ratios are nowadays often quoted at the pole, and we generalize the considerations to the case of virtual photons. We derive and compare relations for nucleon to baryon transition form factors both for the Breit-Wigner and the pole positions. Using the MAID2007 and SAID SM08 partial wave analyses of pion electroproduction data, we compare the $G_M, G_E$, and $G_C$ form factors for the $\mathrm{\Delta }\left(1232\right)$ resonance excitation at the Breit-Wigner resonance and pole positions up to $Q^2=5{\mathrm{GeV}}^2$. We also explore the $E/M$ and $S/M$ ratios as functions of $Q^2$. For pole and residue extraction, we apply the Laurent + Pietarinen method.

A model for the $\overline{K}d\to \pi YN$ reactions with $Y=\mathrm{\Lambda },\mathrm{\Sigma }$ is developed, aiming at establishing the low-lying $\mathrm{\Lambda }$ and $\mathrm{\Sigma }$ hyperon resonances through analyzing the forthcoming data from the J-PARC E31 experiment. The off-shell amplitudes generated from the dynamical coupled-channels (DCC) model, which was developed in Kamano et al. [Phys. Rev. C 90, 065204 (2014)], are used as input to the calculations of the elementary $\overline{K}N\to \overline{K}N$ and $\overline{K}N\to \pi Y$ subprocesses in the $\overline{K}d\to \pi YN$ reactions. It is shown that the cross sections for the J-PARC E31 experiment with a rather high incoming-$\overline{K}$ momentum, $|{\vec{p}}_{\overline{K}}|=1$ GeV, can be predicted reliably only when the input $\overline{K}N\to \overline{K}N$ amplitudes are generated from a $\overline{K}N$ model, such as the DCC model used in this investigation, which describes the data of the $\overline{K}N$ reactions at energies far beyond the $\overline{K}N$ threshold. We find that the data of the threefold differential cross section $d\sigma /\left(d{M}_{\pi \mathrm{\Sigma }}d{\mathrm{\Omega }}_{p_n}\right)$ for the $K^{-}d\to \pi \mathrm{\Sigma }n$ reaction below the $\overline{K}N$ threshold can be used to test the predictions of the resonance poles associated with $\mathrm{\Lambda }\left(1405\right)$. We also find that the momentum dependence of the threefold differential cross sections for the $K^{-}d\to {\pi }^{-}\mathrm{\Lambda }p$ reaction can be used to examine the existence of a low-lying $J^P=1/2^{+} \mathrm{\Sigma }$ resonance with a pole mass $M_R=1457-i39$ MeV, which was found from analyzing the $K^{-}p$ reaction data within the employed DCC model.

Motivated by the recently observed hypernucleus (Kiso event) ${}_{\mathrm{\Xi }}{}^{15}\mathrm{C}$ (${}^{14}\mathrm{N}+{\mathrm{\Xi }}^{-}$), we identify the state of this system theoretically within the framework of the relativistic-mean-field and Skyrme–Hartree–Fock models. The $\mathrm{\Xi }N$ interactions are constructed to reproduce the two possibly observed ${\mathrm{\Xi }}^{-}$ removal energies, $4.38\pm 0.25$ MeV or $1.11\pm 0.25$ MeV. The present result is preferable to be ${}^{14}\mathrm{N}(\mathrm{g}.\mathrm{s}.)+{\mathrm{\Xi }}^{-}\left(1p\right)$, corresponding to the latter value.

We suggest a method for calculating scattering phase shifts and energies and widths of resonances which utilizes only eigenenergies obtained in variational calculations with oscillator basis and their dependence on oscillator basis spacing $\hslash \mathrm{\Omega }$. We make use of simple expressions for the $S$ matrix at eigenstates of a finite (truncated) Hamiltonian matrix in the oscillator basis obtained in the HORSE ($J$-matrix) formalism of quantum scattering theory. The validity of the suggested approach is verified in calculations with model Woods-Saxon potentials and applied to calculations of $n\alpha$ resonances and nonresonant scattering using the no-core shell model.

Microscopic optical potential of ${}^4\mathrm{He}$ interaction with nuclei is constructed by means of the single-folding model using the nucleon-nucleus optical potentials, which earlier were successfully applied to describing the neutron and proton scattering and are obtained from approximate calculations of the mass operator of the one-particle Green's function with the effective Skyrme nucleon-nucleon forces. The ${}^4\mathrm{He}$ scattering processes are described in a self-consistent approach based on the standard and extended Skyrme forces, which simultaneously provide a satisfactory description of nuclear structure and nucleon-nucleus scattering. The performed calculations reasonably describe experimental data on differential cross sections of the elastic and inelastic $\alpha$-particle scattering on different target nuclei in the mass-number range from ${}^{28}\mathrm{Si}$ to ${}^{208}\mathrm{Pb}$ at different projectile energies below or about 100 MeV, as well as the energy dependences of $\alpha$-particle reaction cross sections on nuclei in a wide energy range.

By use of the variational methods and differential geometry in the framework of the liquid drop model we formulate appropriate equilibrium equations for pasta phases with imposed periodicity. The extension of the Young-Laplace equation in the case of charged fluid is obtained. The $\beta$ equilibrium and virial theorem are also generalized. All equations are shown in gauge invariant form. For the first time, the pasta shape stability analysis is carried out. The proper stability condition in the form of the generalized Jacobi equation is derived. The presented formalism is tested on some particular cases.

We present a coupled quasiparticle random phase approximation and Hauser-Feshbach (QRPA+HF) model for calculating delayed particle emission. This approach uses microscopic nuclear structure information, which starts with Gamow-Teller strength distributions in the daughter nucleus and then follows the statistical decay until the initial available excitation energy is exhausted. Explicitly included at each particle emission stage is $\gamma$-ray competition. We explore this model in the context of neutron emission of neutron-rich nuclei and find that neutron-$\gamma$ competition can lead to both increases and decreases in neutron emission probabilities, depending on the system considered. A second consequence of this formalism is a prediction of more neutrons on average being emitted after $\beta$ decay for nuclei near the neutron drip line compared to models that do not consider the statistical decay.

We develop a theoretical approach for nuclear spectral functions at high missing momenta and removal energies based on the multinucleon short-range correlation (SRC) model. The approach is based on the effective Feynman diagrammatic method which allows us to account for the relativistic effects important in the SRC domain. In addition to two-nucleon (2N) SRC with center of mass motion we also derive the contribution of three-nucleon SRCs to the nuclear spectral functions. The latter is modeled based on the assumption that 3N SRCs are a product of two sequential short-range nucleon-nucleon (NN) interactions. This approach allows us to express the 3N SRC part of the nuclear spectral function as a convolution of two NN SRCs. Thus the knowledge of 2N SRCs allows us to model both two- and three-nucleon SRC contributions to the spectral function. The derivations of the spectral functions are based on two theoretical frameworks for evaluating covariant Feynman diagrams: In the first, referred to as virtual nucleon approximation, we reduce Feynman diagrams to the time ordered noncovariant diagrams by evaluating nucleon spectators in the SRC at their positive energy poles, neglecting explicitly the contribution from vacuum diagrams. In the second approach, referred to as light-front approximation, we formulate the boost invariant nuclear spectral function in the light-front reference frame in which case the vacuum diagrams are generally suppressed and the bound nucleon is described by its light-front variables such as momentum fraction, transverse momentum, and invariant mass.