Trace formulas for the contributions of degenerate periodic-orbit families to the semiclassical level density in truncated spherical hard-wall potentials are derived. In addition to the portion of the continuous periodic-orbit family contribution which persists after truncation, end-point corrections to the truncated family should be taken into account. I propose a formula to evaluate these end-point corrections as separate contributions of what I call marginal orbits. Applications to the two-dimensional billiard and three-dimensional cavity systems with the three-quadratic-surfaces shape parametrization, initiated to describe the nuclear fission processes, reveal unexpectedly large effects of the marginal orbits.

Making use of the semiclassical periodic orbit theory (POT), we propose, for the first time, a method to exclusively evaluate the shell effects associated with each of the nascent fragments (prefragments) generated by the neck formation in nuclear fission processes. In spite of the strong indication of such shell effects in asymmetric fragment mass distributions, they could not have been accessed by any previous theoretical approach since most of the single-particle wave functions are delocalized. In the POT, we have found that the prefragment shell effects can be naturally and unambiguously identified as the contributions of the classical periodic orbits localized in each of the prefragments. For a numerical test, simple cavity potential models are employed with the shape described by the three-quadratic-surface shape parametrization. Deformed shell energies are studied with the trace formula for degenerate orbits in a truncated spherical cavity which was recently derived [K. Arita, preceding paper, Phys. Rev. C 98, 064310 (2018)]. In this simple model, it is shown that the prefragment shell effect dominates the total shell energy shortly after the neck formation, and the magicity of the heavier prefragment plays a significant role in establishing the fission saddle with asymmetric shape which leads to an asymmetric scission.

A low-energy enhancement of radiative strength functions was observed in experiment in several mass regions of nuclei, and it is believed to impact considerably the calculated neutron-capture rates. In the shell-model framework it was demonstrated to be possibly due to the magnetic dipole radiation. Up to now, the $M1$ deexcitation strength function was described within this framework in the mid-mass nuclei from the $pf$ and $pfg$ shells (e.g., ${}^{44}\mathrm{Sc},{}^{50}\mathrm{Cr},{}^{56,57,60,66,68}\mathrm{Fe},{}^{59,60,70}\mathrm{Ni},{}^{94–96}\mathrm{Mo},{}^{90}\mathrm{Zr})$, indicating systematically the presence of an up-bend at low energy. Therefore, the enhancement was accepted as a robust feature of the radiative decay. However, its exact magnitude and regions of emergence in the nuclear chart are still to be characterized in microscopic calculations. In this work, for the first time, the low-energy behavior of the radiative $M1$ strength in heavier nuclei, which can be described in the $g_{7/2}{d}_{5/2,3/2}{s}_{1/2}{h}_{11/2}$ shell, is investigated. The enhancement of the $M1$ deexcitation strength around $N=80$ is confirmed, and is similar to that found previously in lighter nuclei. In contrast, no such up-bend is present on the proton drip line, in the deformed $N=Z=54{}^{108}\mathrm{Xe}$ nucleus. From analysis of calculated magnetic dipole strengths the orbital nature of the observed enhancement is suggested. Photoemission and photoabsorption distributions on selected states are compared and the impact of different uncertainties in the theoretical treatment on the magnitude of $M1$ strengths at low photon energies is discussed.

The nuclear mean-field potential built up by the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ interaction at energies relevant for the carbon burning process is calculated in the double-folding model (DFM) using the realistic ground-state density of ${}^{12}\mathrm{C}$ and the CDM3Y3 density dependent nucleon-nucleon (NN) interaction, with the rearrangement term properly included. To validate the use of a density dependent NN interaction in the DFM calculation in the low-energy regime, an adiabatic approximation is suggested for the nucleus-nucleus overlap density. The reliability of the nuclear mean-field potential predicted by this low-energy version of the DFM is tested in a detailed optical model analysis of the elastic ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ scattering data at energies below 10 MeV/nucleon. The folded mean-field potential is then used to study the astrophysical $S$ factor of ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion in the barrier penetration model. Without any adjustment of the potential strength, our results reproduce very well the nonresonant behavior of the $S$ factor of ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion over a wide range of energies.

We have studied the $\alpha$-decay properties of superheavy nuclei $Z=121$ in the range $265\le A\le 316$. A detailed study of competition between $\alpha$ decay and fission enables us to identify the possible isotopes for superheavy element $Z=121$. The nuclei ${}^{299–304}121$ were found to have long half-lives and hence they could be detected if synthesized in a laboratory. After identifying the possible isotopes, we have identified the most probable projectile-target combinations by studying the fusion cross section, evaporation residue cross section, compound nucleus formation probability ($P_{\mathrm{CN}}$), and survival probability ($P_{\mathrm{Surv}}$) of different projectile-target combinations to synthesize the superheavy element $Z=121$. The most probable projectile-target combinations to synthesize the superheavy nuclei ${}^{299–305}121$ is $\mathrm{V}+\mathrm{Cf}$. The predicted $\alpha$-decay half-lives and projectile-target combinations play a vital role in the synthesis of the superheavy element $Z=121$.

Experiments searching for neutrinoless double $\beta$ decay ($0\nu \beta \beta$) require precise energy calibration and extremely low backgrounds. One of the most popular isotopes for $0\nu \beta \beta$ experiments is ${}^{136}\mathrm{Xe}$. In support of these experiments, the neutron inelastic scattering properties of this isotope have been measured at the GErmanium Array for Neutron Induced Excitations (GEANIE) at the Los Alamos Neutron Science Center. Time-of-flight techniques are utilized with high-purity germanium detectors to search for inelastic scattering $\gamma$ rays for neutron energies between 0.7 and 100 MeV. Limits are set on production of yet-unobserved $\gamma$ rays in the energy range critical for $0\nu \beta \beta$ studies, and measurements are made of multiple $\gamma$-ray production cross sections. In particular, we have measured the production of the 1313 keV $\gamma$ ray, which comes from the transition of the first-excited to ground state of ${}^{136}\mathrm{Xe}$. This neutron-induced $\gamma$ line may be useful for a novel energy calibration technique, described in this paper.

Effects of strong longitudinal color fields (SLCF) on the identified (anti)particle transverse momentum ($p_T$) distributions in $pp$ collision at $\sqrt{s}=7\mathrm{TeV}$ are investigated within the framework of the HIJING/$B\overline{B}$ v2.0 model. The comparison with the experiment is performed in terms of the correlation between mean transverse momentum ($\langle p_T\rangle$) and multiplicity ($N_{\mathrm{ch}}^{*}$) of charged particles at central rapidity, as well as the ratios of the $p_T$ distributions to the one corresponding to the minimum bias (MB) $pp$ collisions at the same energy, each of them normalized to the corresponding charged particle density, for high multiplicity (HM, $N_{\mathrm{ch}}>100$) and low multiplicity (LM, $N_{\mathrm{ch}}<100$) class of events. The theoretical calculations show that an increase of the strength of color fields (as characterized by the effective values of the string tension $\kappa$), from $\kappa =2$ to $\kappa =5\mathrm{GeV}/\mathrm{fm}$, from LM to HM class of events, respectively, led to a ratio at low and intermediate $p_T$ (i.e., 1 GeV/$c <p_T<6$ GeV/$c$), consistent with recent data obtained at the Large Hadron Collider by the ALICE Collaboration. These results point out the necessity of introducing a multiplicity (or energy density) dependence for the effective value of the string tension. Moreover, the string tension $\kappa =5\mathrm{GeV}/\mathrm{fm}$, describing the $p_T$ spectra of identified particles (anti)particle in $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$ for high charged particle (HM) multiplicity event classes, has the same value as the one used in describing the $p_T$ spectra in central Pb-Pb collisions at $\sqrt{s_{NN}}=2.76\mathrm{TeV}$. Therefore, we can conclude that at the LHC energies the global features of the interactions could be mostly determined by the properties of the initial chromoelectric flux tubes, while the system size may play a minor role.

Xe+Xe collision at relativistic energies may provide us with a partonic system whose size is approximately in between those produced by $p+p$ and Pb+Pb collisions. The experimental results on anisotropic flow in Xe+Xe and Pb+Pb collisions should provide us with an opportunity to study the system size dependence of $v_2$. In the present work, we have used a multiphase transport model to calculate charged particles' $v_2$ for Xe+Xe collisions at $\sqrt{s_{NN}}=5.44\mathrm{TeV}$. We have also tried to demonstrate the number of constituent quark, $N_q$, and $m_T$ scaling of the elliptic flow. We find that $n_q$ scaling of $v_2$ is not observed for the identified hadrons. The $v_2$ results from Xe+Xe collisions have also been compared to Pb+Pb collisions at $\sqrt{s_{NN}}=5.02\mathrm{TeV}$. We find that flow of charged particles in (50–60)% central collisions for xenon nuclei is almost 30% less than particle flow developed in lead ion collisions, implying the important role the system size plays in the development of particle collective motion in relativistic heavy ion collisions.

Effective Hamiltonians and effective electroweak operators are calculated with the Okubo-Lee-Suzuki formalism for two-nucleon systems. Working within a harmonic oscillator basis, first without and then with a confining harmonic oscillator trap, we demonstrate the effects of renormalization on observables calculated for truncated basis spaces. We illustrate the renormalization effects for the root-mean-square point-proton radius, electric quadrupole moment, magnetic dipole moment, Gamow-Teller transition, and neutrinoless double-$\beta$ decay operator using nucleon-nucleon interactions from chiral effective field theory. Renormalization effects tend to be larger in the weaker traps and smaller basis spaces, suggesting applications to heavier nuclei with transitions dominated by weakly bound nucleons would be subject to more significant renormalization effects within achievable basis spaces.

Background: The ${}^{51}\mathrm{Fe}(p,\gamma ){}^{52}\mathrm{Co}$ reaction lies along the main rp-process path leading up to the ${}^{56}\mathrm{Ni}$ waiting point. The uncertainty in the reaction $Q$ value, which determines the equilibrium between the forward proton-capture and reverse photodisintegration ${}^{52}\mathrm{Co}(\gamma ,p){}^{51}\mathrm{Fe}$ reaction, contributes to considerable uncertainty in the reaction rate in the temperature range of interest for Type I x-ray bursts and thus to an $\approx 10\%$ uncertainty in burst ashes lighter than $A=56$.

Purpose: With a recent Penning trap mass measurement of ${}^{52}\mathrm{Co}$ reducing the uncertainty on its mass to 6.6 keV [Nesterenko et al., J. Phys. G 44, 065103 (2017)], the dominant source of uncertainty in the reaction $Q$ value is now the mass of ${}^{51}\mathrm{Fe}$, reported in the 2016 atomic mass evaluation to a precision of 9 keV [Wang et al., Chin. Phys. C 41, 030003 (2017)]. A new, high-precision Penning trap mass measurement of ${}^{51}\mathrm{Fe}$ was performed to allow the determination of an improved precision $Q$ value and thus new reaction rates.

Method: ${}^{51}\mathrm{Fe}$ was produced using projectile fragmentation at the Coupled Cyclotron Facility at the National Superconducting Cyclotron Laboratory, and separated using the A1900 fragment separator. The resulting secondary beam was then thermalized in the beam stopping area before a mass measurement was performed using the LEBIT 9.4T Penning trap mass spectrometer.

Results: The new mass excess, $\mathrm{ME}=-40189.2\left(1.6\right)$ keV, is sixfold more precise than the current AME value, and $1.6\sigma$ less negative. This value was used to calculate a new proton separation energy for ${}^{52}\mathrm{Co}$ of 1431(7) keV. New excitation levels were then calculated for ${}^{52}\mathrm{Co}$ using the nushellx code with the GXPF1A interaction, and a new reaction rate and burst ash composition was calculated.

Conclusions: With a new measured $Q$ value, the uncertainty on the ${}^{51}\mathrm{Fe}(p,\gamma )$ reaction rate is dominated by the poorly measured ${}^{52}\mathrm{Co}$ level structure. Reducing this uncertainty would allow a more precise rate calculation and a better determination of the mass abundances in the burst ashes.

The proton-unbound argon and chlorine isotopes have been studied by measuring trajectories of their decay-in-flight products by using a tracking technique with microstrip detectors. The proton ($1p$) and two-proton ($2p$) emission processes have been detected in the measured angular correlations “heavy-fragment”+$p$ and “heavy-fragment”+$p+p$, respectively. The ground states of the previously unknown isotopes ${}^{30}\mathrm{Cl}$ and ${}^{28}\mathrm{Cl}$ have been observed for the first time, providing the $1p$-separation energies $S_p$ of $-0.48\left(2\right)$ and $-1.60\left(8\right)$, MeV, respectively. The relevant systematics of $1p$- and $2p$-separation energies have been studied theoretically in the $\mathrm{core}+p$ and $\mathrm{core}+p+p$ cluster models. The first-time observed excited states of ${}^{31}\mathrm{Ar}$ allow one to infer the $2p$-separation energy $S_{2p}$ of 6(34) keV for its ground state. The first-time observed state in ${}^{29}\mathrm{Ar}$ with $S_{2p}=-5.50\left(18\right)$ MeV can be identified as either a ground state or an excited state according to different systematics.

Prospects of experimental studies of argon and chlorine isotopes located far beyond the proton dripline are studied by using systematics and cluster models. The deviations from the widespread systematics observed in ${}^{28,29}\mathrm{Cl}$ and ${}^{29,30}\mathrm{Ar}$ have been theoretically substantiated, and analogous deviations have been predicted for the lighter chlorine and argon isotopes. The limits of nuclear structure existence are predicted for Ar and Cl isotopic chains, with ${}^{26}\mathrm{Ar}$ and ${}^{25}\mathrm{Cl}$ found to be the lightest sufficiently long-living nuclear systems. By simultaneous measurements of protons and $\gamma$ rays following decays of such systems as well as their $\beta$-delayed emission, an interesting synergy effect may be achieved, which is demonstrated by the example of ${}^{30}\mathrm{Cl}$ and ${}^{31}\mathrm{Ar}$ ground-state studies. Such a synergy effect may be provided by the new EXPERT setup (EXotic Particle Emission and Radioactivity by Tracking) being operated inside the fragment separator and spectrometer facility at GSI, Darmstadt.

The uncertainty quantifications of theoretical results are of great importance in making meaningful comparisons of those results with experimental data and making predictions in experimentally unknown regions. By quantifying uncertainties, one can make more solid statements about, e.g., origins of discrepancy in some quantities between theory and experiment. We propose a novel method for uncertainty quantification for the effective interactions of nuclear shell-model calculations as an example. The effective interaction is specified by a set of parameters, and its probability distribution in the multidimensional parameter space is considered. This enables us to quantify the agreement with experimental data in a statistical manner and the resulting confidence intervals show unexpectedly large variations. Moreover, we point out that a large deviation of the confidence interval for the energy in shell-model calculations from the corresponding experimental data can be used as an indicator of some exotic property, e.g., $\alpha$ clustering. Other possible applications and impacts are also discussed.

For the first time the excitation cross section of ${}^{115}\mathrm{In}$ to its first excited state at 336.24 keV has been measured with monoenergetic photon beams at 15 energies between 1.8 and 3.7 MeV. The measurements were performed at the High-Intensity Gamma-ray Source ($\mathrm{HI}\gamma \mathrm{S}$) facility with natural In targets and incident photon fluxes ranging from $0.7\times {10}^7\gamma /\left({\mathrm{cm}}^2\text{s}\right)$ to $3.2\times {10}^7\gamma /\left({\mathrm{cm}}^2\text{s}\right)$. The inelastic scattering cross section was obtained from the yield of the 336.24 keV deexcitation $\gamma$ rays. The cross-section values varied between $<0.05$ and 28.7 $\mu \mathrm{b}$ at 1.8 and 3.7 MeV, respectively. Compared to standard photon inelastic scattering cross-section data in this energy range of medium-mass nuclei, these extremely small values are not completely unexpected, given the nature of the low-lying nuclear levels of ${}^{115}\mathrm{In}$. Model calculations, however, overestimate the measured cross-section data by approximately one order of magnitude. Using different choices for the $E1 \gamma$-ray strength function, the data can be well described. The data are important for improving our knowledge of the level scheme of ${}^{115}\mathrm{In}$, especially spin and parity assignments of already known states.

Recently, a microscopically motivated nuclear energy density functional was derived by applying the density-matrix expansion to the Hartree-Fock (HF) energy obtained from long-range chiral effective-field theory two- and three-nucleon interactions. However, the HF approach cannot account for all many-body correlations. One class of correlations is included by Brueckner-Hartree-Fock (BHF) theory, which gives an improved definition of the one-body HF potential by replacing the interaction by a reaction matrix $G$. In this paper, we find that the difference between the $G$ matrix and the similarity renormalization group evolved nucleon-nucleon potential $V_{\mathrm{SRG}}$ can be well accounted for by a truncated series of contact terms. This is consistent with renormalization-group decoupling generating a series of counterterms as short-distance physics is integrated out. The coefficients $C_n$ of the power series expansion $\sum C_n{q}^n$ for the counterterms are examined for two potentials at different renormalization-group resolutions and at a range of densities. The success of this expansion for $G-V_{\mathrm{SRG}}$ means we can apply the density-matrix expansion at the HF level with low-momentum interactions and density-dependent zero-range interactions to model BHF correlations.

To study whether long-lived superheavy nuclei could really exist around $Z=120$ and $N=184$, the competition between $\alpha$ decay and spontaneous fission in the region $104\le Z\le 124$ are systemically studied. The $\alpha$-decay half-lives are investigated by employing a generalized liquid drop model and the analytical universal decay law formula. The calculation of spontaneous fission half-lives are carried out based on generalized Swiatecki's formula. The competition between $\alpha$ decay and spontaneous fission is analyzed in detail and the decay modes are predicted for the unknown nuclei.

High-energy nuclear reactions enable us to produce a large variety of hypernuclei through the capture of hyperons by nuclear residues. We explore the statistical disintegration of such hypernuclear systems and the connection of fragment production to the binding energies of hyperons. It has been demonstrated that the hyperon binding energies can be effectively evaluated from the yields of different isotopes of hypernuclei by using the double ratio method. The advantages of this procedure are its universality and the possibility to involve many different isotopes. This method can also be applied for multistrange nuclei, for which binding energies were very difficult to measure in previous hypernuclear experiments. Corrections caused by secondary deexcitation processes are also discussed.

We consider alternative modes of two-neutrino and neutrinoless double-$\beta$ decays in which one $\beta$ electron goes over to a continuous spectrum and the other occupies a vacant bound level of the daughter ion. We calculate the corresponding phase-space factors of the final states, estimate the partial decay rates, and derive the one- and two-electron energy spectra using relativistic many-electron wave functions of atoms provided by the multiconfiguration Dirac-Hartree-Fock package Grasp2K. While the bound-state neutrinoless double-$\beta$ decays are strongly suppressed, their two-neutrino counterparts can be observed in the next-generation double-$\beta$-decay experiments, most notably SuperNEMO.

I have systematically investigated the equations of state (EOSs) in nuclear statistical equilibrium under thermodynamic conditions relevant for core collapse of massive stars by varying the bulk properties of nuclear matter, the mass data for neutron-rich nuclei, and the finite-temperature modifications of the nuclear model. It is found that the temperature dependence of the nuclear free energies has a significant impact on the entropy and nuclear composition, which affect the dynamics of core-collapse supernovae. There is a little influence from the bulk properties and the mass data. For all models, common nuclei that are likely to contribute to core-deleptonization are those near $Z\approx 30$ and $N\approx 50$. A model with a semi-empirical expression for internal degrees of freedom, however, overestimates the number densities of magic nuclei with $N\approx 50$ and 82, while a model in which nuclear shell effects are not considered underestimates the number densities of heavy nuclei, and especially of the magic nuclei. Other models, which include the temperature dependence of shell effects in the internal degrees of freedom and/or in the nuclear internal free energy, indicate that the difference in population between magic nuclei and non-magic nuclei disappears as the temperature increases. The construction of complete statistical EOS will require further theoretical and experimental studies of medium-mass, neutron-rich nuclei with proton numbers 25–45 and neutron numbers 40–85.

We introduce the formalism to describe heavy-ion double-charge-exchange (DCE) processes in the eikonal approximation. We focus on the low-momentum-transfer limit, corresponding to the differential cross section at $\theta =0^{\circ }$, and for the first time, we show that it is possible to factorize the DCE cross section in terms of reaction and nuclear parts. Whereas in the $\theta \ne 0^{\circ }$ case the nuclear part is a convolution of the beam and target nuclear matrix elements (NMEs), for $\theta =0^{\circ }$ we demonstrate for the first time that the transition matrix elements can be written as the sum of double Gamow-Teller (DGT) and double Fermi (DF) type parts, and that they can both be further factorized in terms of target and projectile NMEs. By making use of the interacting boson model (IBM) formalism, we also show that the DGT and total parts of the neutrinoless double-$\beta$-decay NMEs are in linear correlation with DCE-DGT NMEs. This confirms the hypothesis of a linear correlation between them, as introduced earlier [N. Shimizu et al., Phys. Rev. Lett. 120, 142502 (2018)]. The possibility of a two-step factorization (TSF) of the very forward differential DCE cross section and the emergence of DGT and DF types for the DCE nuclear matrix elements, combined with a linear correlation between DCE-DGT and $0\nu \beta \beta$ NMEs, opens the possibility of placing an upper limit on neutrinoless double-$\beta$-decay NMEs in terms of the DCE experimental data at $\theta =0^{\circ }$.