The Gamow-Teller (GT) strength distribution has been investigated in a high-resolution (${}^3$He,$t$) charge-exchange experiment on the double-beta ($\beta \beta$) decaying nucleus ${}^{96}$Zr. The experiment was carried out at the Osaka University Research Center for Nuclear Physics (RCNP) with a 420 MeV incident ${}^3$He beam and the Grand Raiden magnetic spectrometer. A final-state energy resolution of 32 keV was achieved. A large fraction of the low-energy GT${}^{-}$ strength is identified in a single state at 694 keV. A similar observation has been made in a ${}^{96}$Mo($d$,${}^2$He)${}^{96}$Nb experiment at 120 keV resolution for the GT${}^{+}$ strength. It is found that this single state makes up nearly 100$\%$ of the nuclear matrix element for the ${}^{96}$Zr two-neutrino double-beta ($2\nu \beta \beta$) decay.

The binding energies of the light, the moderate and the heavy closed shell nuclei, that is, ${}^4\mathrm{He}$, ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, ${}^{28}\mathrm{Si}$, ${}^{32}\mathrm{S}$, ${}^{40}\mathrm{Ca}$, ${}^{56}\mathrm{Ni}$, ${}^{48}\mathrm{Ca}$, ${}^{90}\mathrm{Zr}$, ${}^{120}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$ are calculated, using all of the channels-dependent effective two-body interactions (CDEI) matrix elements, which are generated through our lowest order constrained variational (LOCV) nuclear matter calculations with the $A{v}_{18}$ $(J_{\max }=2$ and $5)$ phenomenological nucleon-nucleon potential. The $\mathcal{J}$-coupling scheme is applied to construct the interaction Hamiltonian matrix elements in the spherical harmonics oscillator shell model basis. In the channels with $J>J_{\max }$, the CDEI are replaced by the average effective two-body interactions. It is shown that the nondiagonal matrix elements with the $A{v}_{18,J_{\max }=2}$ interaction increase the binding energies of nuclei; that is, the maximum magnitude of them is about 1.49 MeV for the ${}^{56}\mathrm{Ni}$ nucleus. However, for the similar calculations with the $A{v}_{18,J_{\max }=5}$ potential, they increase the binding energies of the symmetric nuclei more than the asymmetric ones; that is, the maximum magnitude of them is about 2.74 MeV for the ${}^{56}\mathrm{Ni}$ nucleus. Owing to the huge computational time that is obviously needed for the calculation of the matrix elements of the heavy closed shell nuclei, their binding energies are evaluated only at their saturation points, which are available from our previous works.

Background: Temperature ($T$) in heavy-ion collisions is an important parameter. Previously, many works have focused on the temperature of the hot emitting source. But there are few systematic studies of the temperature among heavy fragments in peripheral collisions with incident energies near the Fermi energy to a few $A$ GeV, though it is very important to study the property of neutron-rich nucleus in heavy-ion collisions.

Purpose: This work focuses on the study of temperature associated with the final heavy fragments in reactions induced by both the neutron-proton symmetric and the neutron-rich projectiles, and with incident energy ranges from 60$A$ MeV to 1$A$ GeV.

Methods: Isobaric yield ratio (IYR) is used to determine the temperature of heavy fragments. Cross sections of measured fragments in reactions are analyzed, and a modified statistical abrasion-ablation (SAA) model is used to calculate the yield of fragment in 140$A$ MeV ${}^{64}$Ni+${}^9$Be and 1$A$ GeV ${}^{136}$Xe+${}^{208}$Pb reactions.

Results: Relatively low $T$ of heavy fragments are obtained in different reactions ($T$ ranges from 1 to 3 MeV). $T$ is also found to depend on the neutron richness of the projectile. The incident energy affects $T$ very little. $\Delta \mu /T$ (the ratio of the difference between the chemical potential of neutron and proton to temperature) is found to increase linearly as $N/Z$ of projectile increases. It is found that $T$ of the ${}^{48}$Ca reaction, for which IYRs are $A<50$ isobars, is affected greatly by the temperature-corrected $\Delta B\left(T\right)$. But $T$ of reactions using IYRs of heavier fragments are only slightly affected by the temperature-corrected $\Delta B\left(T\right)$. The SAA model analysis gives a consistent overview of the results extracted in this work.

Conclusions: $T$ from IYR, which is for secondary fragments, is different from that of the hot emitting source. $T$ and $\Delta \mu$ are essentially governed by the sequential decay process.

In the context of a ${}^3{P}_0$ quark-pair creation model for the process $\rho \to \pi \pi$, a method is developed for taking relativity into account in the calculation of hadron decays. Following a brief review of relativistic quantum mechanics, an expression is derived for the general relation between a momentum-space, two-particle, instant form wave function in an arbitrary frame and the wave function associated with the c.m. frame. This relation is used to develop relativistic wave functions for the $\pi$ and $\rho$ mesons. Second quantized state vectors for $\pi \pi$ and $\rho$ states are constructed with the help of these relativistic wave functions. The $\rho \to \pi \pi$ transition amplitude is obtained by using these state vectors to calculate matrix elements of a second quantized ${}^3{P}_0$ quark-pair creation operator derived from a scalar Lagrangian density. The amplitude differs from the one obtained using nonrelativistic wave functions in the appearance of Wigner rotations. In spite of the complications arising from these rotations the calculation of the relativistic amplitude is reduced to carrying out a two-dimensional integral. The amplitude is of the same form as one derived from an effective $\rho \pi \pi$ Lagrangian except for the presence of a form factor that depends on the magnitude of the three-momentum of a final-state pion. The shape of the form factor is determined by the relativistic $\pi$ and $\rho$ wave functions. Using the $\rho \to \pi \pi$ transition amplitude as a vertex interaction in a relativistic model of $\pi \pi$ scattering, the $p$-wave, $\pi \pi$ scattering amplitude is calculated and fit to data by adjusting the interaction strength and the $\rho$ bare mass. This leads to a mass shift and decay width for the $\rho$ meson. Using nonrelativistic wave functions to calculate the form factor leads to a negligible mass shift, whereas using the relativistic wave functions leads to a bare $\rho$ mass of 855.7 MeV, corresponding to a physical $\rho$ mass of 775.5 MeV. The quark-pair creation operator strength parameter for the relativistic case is roughly a factor of 2 larger than that for the nonrelativistic case.

We address the behavior of the Dirac equation with scalar ($S$), vector ($V$), and tensor ($U$) interactions under the ${\gamma }^5$ discrete chiral transformation. By using this transformation, in a simple way, we can obtain solutions for the Dirac equation with spin ($\Delta =V-S=0$) and pseudospin ($\Sigma =V+S=0$) symmetries, which includes a tensor interaction. As an application, the Dirac equation with scalar, vector, and tensor Cornell radial potentials is considered, and the correct solution to this problem is obtained.

A study of neutron-rich isotopes in the $A=185$ region of the nuclear chart has uncovered long-lived ($>$1 s) isomers in several isotopes of hafnium, tantalum, tungsten, rhenium, and osmium. The region was accessed via the use of projectile fragmentation with the UNILAC-SIS accelerators at GSI. Fragmentation products of ${}^{197}$Au were passed through the fragment separator (FRS) and injected into the experimental storage ring (ESR), where single-ion identifications could be made. Evidence is presented for isomers in ${}^{183,184,186}$Hf, ${}^{186,187}$Ta,${}^{186}$W, ${}^{190,192,194}$Re, and ${}^{195}$Os with excitation energies in the range of 0.1–3.0 MeV. The lightest of these nuclides have well deformed prolate shapes, while the heaviest are transitional and susceptible to shape changes. Their properties are interpreted with the help of multi-quasiparticle and potential-energy-surface calculations.

New high-spin microsecond isomers, with $J^{\pi }=\left({31}^{+}\right)$ and $J^{\pi }=\left({28}^{-}\right)$, have been identified in ${}^{206}$Bi at 10 170 and 9233 keV, respectively, using $\gamma$-ray coincidence spectroscopy following deep-inelastic reactions with the ${}^{76}\mathrm{Ge}+{}^{208}\mathrm{Pb}$ system. Yrast and near-yrast levels populated in the decay of these isomers have been located and interpreted with the help of shell-model calculations. The states identified at energies up to approximately 7 MeV can be described well in terms of one-proton-particle, three-neutron-hole couplings.

The nuclear structure dependence of direct reactions that remove a pair of like or unlike nucleons from a fast ${}^{12}$C projectile beam are considered. Specifically, we study the differences in the two-nucleon correlations present and the predicted removal cross sections when using $p$-shell shell-model and multi-$\hslash \omega$ no-core shell-model (NCSM) descriptions of the two-nucleon overlaps for the transitions to the mass $A=10$ projectile residues. The NCSM calculations use modern chiral two-nucleon and three-nucleon (NN+3N) interactions. The $np$-removal cross sections to low-lying $T=0$, ${}^{10}$B final states are enhanced when using the NCSM two-nucleon amplitudes. The calculated absolute and relative partial cross sections to the low-energy ${}^{10}$B final states show a significant sensitivity to the interactions used, suggesting that assessments of the overlap functions for these transitions and confirmations of their structure could be made using final-state-exclusive measurements of the $np$-removal cross sections and the associated momentum distributions of the forward traveling projectile-like residues.

Comparing the capture cross sections calculated without the breakup effect and experimental complete fusion cross sections, the breakup was analyzed in reactions with weakly bound projectiles ${}^{6,7,9}$Li, ${}^{9,11}$Be, and ${}^{6,8}$He. A trend of systematic behavior for the complete fusion suppression as a function of the target charge and bombarding energy is not achieved. The quasielastic backscattering is suggested as a useful tool to study the behavior of the breakup probability in reactions with weakly bound projectiles.

Background: Quantum chromodynamics is expected to have a phase transition in the same static universality class as the 3D Ising model and the liquid-gas phase transition. The properties of the equation of state, the transport coefficients, and especially the location of the critical point are under intense theoretical investigation. Some experiments are underway, and many more are planned, at high-energy heavy ion accelerators.

Purpose: Develop a model of the thermal conductivity, which diverges at the critical point, and use it to study the impact of hydrodynamic fluctuations on observables in high-energy heavy ion collisions.

Methods: We apply mode-coupling theory, together with a previously developed model of the free energy that incorporates the critical exponents and amplitudes, to construct a model of the thermal conductivity in the vicinity of the critical point. The effect of the thermal conductivity on correlation functions in heavy ion collisions is studied in a boost-invariant hydrodynamic model via fluctuations, or noise.

Results: We find that the closer a thermodynamic trajectory comes to the critical point the greater is the magnitude of the fluctuations in thermodynamic variables and in the 2-particle correlation functions in momentum space.

Conclusions: It may be possible to discern the existence of a critical point, its location, and thermodynamic and transport properties near to it in heavy ion collisions using the methods developed here.

We present results of a new multichannel partial-wave analysis for $\pi N$ scattering in the c.m. energy range 1080 to 2100 MeV. This work explicitly includes $\eta N$ and $K\Lambda$ channels and the single pion photoproduction channel. Resonance parameters were extracted by fitting partial-wave amplitudes from all considered channels using a multichannel parametrization that is consistent with $S$-matrix unitarity. The resonance parameters so obtained are compared to predictions of quark models.

We consider two-photon exchange (TPE) in the elastic electron-proton scattering and study the contribution arising from the production of $\Delta \left(1232\right)$ resonance in the intermediate state. We calculate all three TPE amplitudes (generalized form factors), and find that the $\Delta$ contribution mainly influences the generalized electric form factor (contrary to the elastic contribution, which affects the magnetic form factor), and the effect grows with $Q^2$. If the corresponding correction is applied to the recent polarization transfer measurements of proton form factors, their results will change markedly. Thus we suggest that TPE corrections due to inelastic intermediate states are important to polarization experiments at high $Q^2$, and should not be neglected.

Neutron star crusts are studied using a classical molecular dynamics model developed for heavy-ion reactions. After the model is shown to produce a plethora of the so-called pasta shapes, a series of techniques borrowed from nuclear physics, condensed matter physics, and topology is used to craft a method that can be used to characterize the shape of the pasta structures in an unequivocal way.

Precise electromagnetic transition matrix elements in ${}^{10}$Be and ${}^{10}$C have provided surprisingly stringent tests of modern ab initio calculations using realistic nuclear forces. The analog transition in ${}^{10}$B can further constrain these new calculations and probe the symmetry of the wave functions across the $A=10$ multiplet. We report on a careful measurement of the $\gamma$-ray intensities from states populated in the ${}^{10}$B($p$,$p^{\prime }$) reaction at 10 MeV, including a determination of the key $E$2 branch from the $J=2$ $T=1$ state at 5164 keV to the $J=0$ $T=1$ state at 1740 keV of 0.16(4)$\%$.

A new methodology is presented to analyze the threshold anomaly and to compare different kinds of reaction systems together. In this methodology, the experimental and theoretical values of the quarter-point angle are compared directly for different reaction systems. A suitable reduction method is employed to minimize the system effects. This new method can be used to evaluate and study the dynamic effects in the reaction systems.

This Brief Report presents a phenomenological formula of total reaction cross sections for different reaction systems at low energies, taking into account the case of weakly bound nuclei as projectiles. To get this phenomenological formula, a large set of experimental data were collected and compared. Based on the experimental total reaction cross sections, three parameters were used to modify Wong's formula. The total reaction cross sections of different systems at low energies including weakly bound projectiles were reproduced using the modified formula.

The newly developed multichannel cluster model (MCCM) based on the coupled-channel Schrödinger equation with outgoing wave boundary conditions is extended to study the $\alpha$-decay fine structure in heavy odd-$A$ nuclei. More decay channels are considered for convergence in solving the coupled equations. Calculations are performed for 32 deformed nuclei with atomic numbers $Z=93$–102. The branching ratios for various daughter states are well reproduced without any additional free parameters, and the calculated $\alpha$-decay half-lives show good agreement with the experimental data. This indicates that the MCCM has universal applicability and equal validity regardless of even-even or odd-$A$ $\alpha$ emitters.

The giant halos predicted in neutron-rich Zr isotopes with $A=124–138$ are investigated by using the self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov approach, in which the asymptotic behavior of continuum quasiparticle states is properly treated by the Green's function method. We study in detail the neutron pair correlation involved in the giant halo by analyzing the asymptotic exponential tail of the neutron pair condensate (pair density) in addition to that of the neutron particle density. The neutron quasiparticle spectra associated with these giant halo nuclei are examined. It is found that the asymptotic exponential tail of the neutron pair condensate is dominated by nonresonant continuum quasiparticle states corresponding to the scattering states with low asymptotic kinetic energy. This is in contrast to the asymptotic tail of the neutron density, whose main contributions arise from the resonant quasiparticle states corresponding to the weakly bound single-particle orbits and resonance orbits in the Hartree-Fock potential.

A search for isomeric γ decays among fission fragments from 345 MeV/nucleon ${}^{238}$U has been performed at the RIKEN Nishina Center RI Beam Factory. Fission fragments were selected and identified using the superconducting in-flight separator BigRIPS and were implanted in an aluminum stopper. Delayed γ rays were detected using three clover-type high-purity germanium detectors located at the focal plane within a time window of 20 μs following the implantation. We identified a total of 54 microsecond isomers with half-lives of ∼0.1–10 μs, including the discovery of 18 new isomers in very neutron-rich nuclei: ${}^{59}$Ti${}^m$, ${}^{90}{\mathrm{As}}^m$, ${}^{92}$Se${}^m$, ${}^{93}$Se${}^m$, ${}^{94}$Br${}^m$, ${}^{95}$Br${}^m$, ${}^{96}$Br${}^m$, ${}^{97}$Rb${}^m$, ${}^{108}$Nb${}^m$, ${}^{109}$Mo${}^m$, ${}^{117}$Ru${}^m$, ${}^{119}$Ru${}^m$, ${}^{120}$Rh${}^m$, ${}^{122}$Rh${}^m$, ${}^{121}$Pd${}^m$, ${}^{124}$Pd${}^m$, ${}^{124}$Ag${}^m$, and ${}^{126}$Ag${}^m$, and obtained a wealth of spectroscopic information such as half-lives, γ-ray energies, γ-ray relative intensities, and γγ coincidences over a wide range of neutron-rich exotic nuclei. Proposed level schemes are presented for ${}^{59}$Ti${}^m$, ${}^{82}$Ga${}^m$, ${}^{92}$Br${}^m$, ${}^{94}$Br${}^m$, ${}^{95}$Br${}^m$, ${}^{97}$Rb${}^m$, ${}^{98}$Rb${}^m$, ${}^{108}$Nb${}^m$, ${}^{108}$Zr${}^m$, ${}^{109}$Mo${}^m$, ${}^{117}$Ru${}^m$, ${}^{119}$Ru${}^m$, ${}^{120}$Rh${}^m$, ${}^{122}$Rh${}^m$, ${}^{121}$Pd${}^m$, ${}^{124}$Ag${}^m$, and ${}^{125}$Ag${}^m$, based on the obtained spectroscopic information and the systematics in neighboring nuclei. The nature of the nuclear isomerism is discussed in relation to the evolution of nuclear structure.

High-spin states of ${}^{40}$K have been populated in the fusion-evaporation reaction ${}^{12}$C(${}^{30}$Si,$np$)${}^{40}$K and studied by means of $\gamma$-ray spectroscopy techniques using one triple-cluster detector of the Advanced Gamma Tracking Array at the Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro. Several states with excitation energy up to 8 MeV and spin up to ${10}^{-}$ have been discovered. These states are discussed in terms of $J=3$ and $T=0$ neutron-proton hole pairs. Shell-model calculations in a large model space have shown good agreement with the experimental data for most of the energy levels. The evolution of the structure of this nucleus is here studied as a function of excitation energy and angular momentum.