We perform large-scale shell-model calculations of $\beta$-decay properties for neutron-rich nuclei with $13\le Z\le 18$ and $22\le N\le 34$, taking the first-forbidden transitions into account. The natural-parity and unnatural-parity states are calculated in the $0\hslash \omega$ and $1\hslash \omega$ model spaces, respectively, within the full $sd+pf+sdg$ valence shell. The calculated $\beta$-decay half-lives and $\beta$-delayed neutron emission probabilities show good agreement with the experimental data. The first-forbidden transitions make a non-negligible contribution to the half-lives of $N\gtrsim 28$ nuclei. The low-lying Gamow-Teller strengths of even-even nuclei are considerably larger than those of the neighboring odd-$A$ and odd-odd nuclei, strongly affecting the half-lives and neutron emission probabilities. It is shown that this even-odd effect is caused by the $J^{\pi }=1^{+}$ proton-neutron pairing interaction. We derive a formula to represent the positions of the Gamow-Teller giant resonances from the calculated strength distributions.

The nuclear surface provides useful information on nuclear radius, nuclear structure, as well as properties of nuclear matter. We discuss the relationship between the nuclear surface diffuseness and elastic scattering differential cross section at the first diffraction peak of high-energy nucleon-nucleus scattering as an efficient tool in order to extract the nuclear surface information from limited experimental data involving short-lived unstable nuclei. The high-energy reaction is described by a reliable microscopic reaction theory, the Glauber model. Extending the idea of the black sphere model, we find one-to-one correspondence between the nuclear bulk structure information and proton-nucleus elastic scattering diffraction peak. This implies that we can extract both the nuclear radius and diffuseness simultaneously, using the position of the first diffraction peak and its magnitude of the elastic scattering differential cross section. We confirm the reliability of this approach by using realistic density distributions obtained by a mean-field model.

The elastic scattering angular distribution of the ${}^{16}\mathrm{O}+{}^{60}\mathrm{Ni}$ system at 260 MeV was measured in the range of the Rutherford cross section down to seven orders of magnitude. The cross sections of the lowest $2^{+}$ and $3^{-}$ inelastic states of the target were also measured over several orders of magnitude. Coupled-channel (CC) calculations were performed and are shown to be compatible with the whole set of data only when including the excitation of the projectile and when the deformations of the imaginary part of the nuclear optical potential are taken into account. Similar results were obtained when the procedure is applied to the existing data on ${}^{16}\mathrm{O}+{}^{27}\mathrm{Al}$ elastic and inelastic scattering at 100 and 280 MeV. An analysis in terms of dynamical polarization potentials (DPP) indicates the major role of coupled-channel effects in the overlapping surface region of the colliding nuclei.

Background: The semimagic Sn ($Z=50$) isotopes have been subject to many nuclear-structure studies. Signatures of shape coexistence have been observed and attributed to two-proton–two-hole (2p-2h) excitations across the $Z=50$ shell closure. In addition, many low-lying nuclear-structure features have been observed which have effectively constrained theoretical models in the past. One example are so-called quadrupole-octupole coupled states (QOC) caused by the coupling of the collective quadrupole and octupole phonons.

Purpose: Proton-scattering experiments followed by the coincident spectroscopy of $\gamma$ rays have been performed at the Institute for Nuclear Physics of the University of Cologne to excite low-spin states in ${}^{112}\mathrm{Sn}$ and ${}^{114}\mathrm{Sn}$ to determine their lifetimes and extract reduced transition strengths $B\left(\mathrm{\Pi }L\right)$.

Methods: The combined spectroscopy setup SONIC@HORUS has been used to detect the scattered protons and the emitted $\gamma$ rays of excited states in coincidence. The novel $(p,p^{\prime }\gamma )$ Doppler-shift attenuation (DSA) coincidence technique was employed to measure sub-ps nuclear level lifetimes.

Results: Seventy-four (74) level lifetimes $\tau$ of states with $J=0–6$ were determined. In addition, branching ratios were deduced which allowed the investigation of the intruder configuration in both nuclei. Here, $sd$ IBM-2 mixing calculations were added which support the coexistence of the two configurations. Furthermore, members of the expected QOC quintuplet are proposed in ${}^{114}\mathrm{Sn}$ for the first time. The $1^{-}$ candidate in ${}^{114}\mathrm{Sn}$ fits perfectly into the systematics observed for the other stable Sn isotopes.

Conclusions: The $E2$ transition strengths observed for the low-spin members of the so-called intruder band support the existence of shape coexistence in ${}^{112,114}\mathrm{Sn}$. The collectivity in this configuration is comparable to the one observed in the Pd nuclei, i.e., the 0p-4h nuclei. Strong mixing between the $0^{+}$ states of the normal and intruder configuration might be observed in ${}^{114}\mathrm{Sn}$. The general existence of QOC states in ${}^{112,114}\mathrm{Sn}$ is supported by the observation of QOC candidates with $J\ne 1$.

An empirical model with independent variable moments of inertia for triaxial nuclei is devised and applied to ${}^{76}\mathrm{Ge}$ and ${}^{192}\mathrm{Os}$. Three intrinsic moments of inertia, $J_1$, $J_2$, and $J_3$, are varied independently as a particular function of spin $I$ within a revised version of the triaxial rotor model so as to reproduce the energy levels of the ground-state, $\gamma$, and (in the case of ${}^{192}\mathrm{Os}$) $K^{\pi }=4^{+}$ bands. The staggering in the $\gamma$ band is well reproduced in both phase and amplitude. Effective $\gamma$ values are extracted as a function of spin $I$ from the ratios of the three moments of inertia. The eigenfunctions and the effective $\gamma$ values are subsequently used to calculate the ratios of $B\left(E2\right)$ values associated with these bands. Good agreement between the model calculation and the experimental data is obtained for both ${}^{76}\mathrm{Ge}$ and ${}^{192}\mathrm{Os}$.

Large longitudinal spin alignment of $E/A=24\mathrm{MeV}{}^7\mathrm{Li}$ projectiles inelastically excited by Be, C, and Al targets was observed when the latter remain in their ground state. This alignment is a consequence of an angular-momentum-excitation-energy mismatch, which is well described by a DWBA cluster-model ($\alpha +t$). The longitudinal alignment of several other systems is also well described by DWBA calculations, including one where a cluster model is inappropriate, demonstrating that the alignment mechanism is a more general phenomenon. Predictions are made for inelastic excitation of ${}^{12}\mathrm{C}$ for beam energies above and below the mismatch threshold.

We studied multinucleon transfer reactions in the ${}^{197}\mathrm{Au}+{}^{130}\mathrm{Te}$ system at $E_{\mathrm{lab}}=1.07$ GeV by employing the PRISMA magnetic spectrometer coupled to a coincident detector. For each light fragment we constructed, in coincidence, the distribution in mass of the heavy partner of the reaction. With a Monte Carlo method, starting from the binary character of the reaction, we simulated the de-excitation process of the produced heavy fragments to be able to understand their final mass distribution. The total cross sections for pure neutron transfer channels have also been extracted and compared with calculations performed with the grazing code.

In an unconventional presentation of the data on the transverse momentum spectra of baryons produced in heavy-ion collisions, regularities are found that make possible the discovery of a universal formula valid for $p,\mathrm{\Lambda },\mathrm{\Xi }$, and $\mathrm{\Omega }$. The formula describes the baryon distributions over wide ranges of $p_T(0.5\lesssim p_T\lesssim 5$ GeV/$c)$ for $0.06\lesssim \sqrt{s_{NN}}\lesssim 3$ TeV, except for very peripheral collisions. Some aspects of their empirical properties are derived in the recombination model, resulting in a revelation of some features of the light and strange quark distributions before hadronization. Interpretation of the inverse slopes of their exponential behavior leads to an implication that cannot accommodate the conventional description of fluid flow. This is mainly a study of phenomenology without detailed model input.

Charge symmetry breaking (CSB) effects associated with the $u$ and $d$ quark mass difference are investigated in the quark distribution functions and spacelike electromagnetic form factors of the pion and kaon. We use a confining version of the Nambu–Jona-Lasinio model, where CSB effects at the infrared scale associated with the model are driven by the dressed $u$ and $d$ quark mass ratio, which because of dynamical chiral symmetry breaking is much closer to unity than the associated current quark mass ratio. The pion and kaon are given as bound states of a dressed quark and a dressed antiquark governed by the Bethe-Salpeter equation, and exhibit the properties of Goldstone bosons, with a pion mass difference given by $m_{{\pi }^{+}}^2-m_{{\pi }^0}^2\propto {(m_u-m_d)}^2$ as demanded by dynamical chiral symmetry breaking. We find significant CSB effects for realistic current quark mass ratios ($m_u/m_d\sim 0.5$) in the quark flavor-sector electromagnetic form factors of both the pion and kaon. For example, the difference between the $u$ and $d$ quark contributions to the ${\pi }^{+}$ electromagnetic form factors is about 8% at a momentum transfer of $Q^2\simeq 10{\mathrm{GeV}}^2$, while the analogous effect for the light quark sector form factors in the $K^{+}$ and $K^0$ is about twice as large. For the parton distribution functions we find CSB effects which are considerably smaller than those found in the electromagnetic form factors.

Background: $\alpha$-nucleus optical potentials are basic ingredients of statistical model calculations used in nucleosynthesis simulations. While the nucleon+nucleus optical potential is fairly well known, for the $\alpha$+nucleus optical potential several different parameter sets exist and large deviations, reaching sometimes even an order of magnitude, are found between the cross section predictions calculated using different parameter sets.

Purpose: A measurement of the radiative $\alpha$-capture and the $\alpha$-induced reaction cross sections on the nucleus ${}^{115}\mathrm{In}$ at low energies allows a stringent test of statistical model predictions. Since experimental data are scarce in this mass region, this measurement can be an important input to test the global applicability of $\alpha$+nucleus optical model potentials and further ingredients of the statistical model.

Methods: The reaction cross sections were measured by means of the activation method. The produced activities were determined by off-line detection of the $\gamma$ rays and characteristic x rays emitted during the electron capture decay of the produced Sb isotopes. The ${}^{115}\mathrm{In}(\alpha ,\gamma ){}^{119}\mathrm{Sb}$ and ${}^{115}\mathrm{In}(\alpha ,n){}^{118}\mathrm{Sb}^m$ reaction cross sections were measured between $E_{\mathrm{c}.\mathrm{m}.}=8.83$ and 15.58 MeV, and the ${}^{115}\mathrm{In}(\alpha ,n){}^{118}\mathrm{Sb}^g$ reaction was studied between $E_{\mathrm{c}.\mathrm{m}.}=11.10$ and 15.58 MeV. The theoretical analysis was performed within the statistical model.

Results: The simultaneous measurement of the ($\alpha ,\gamma$) and ($\alpha ,n$) cross sections allowed us to determine a best-fit combination of all parameters for the statistical model. The $\alpha$+nucleus optical potential is identified as the most important input for the statistical model. The best fit is obtained for the new Atomki-V1 potential, and good reproduction of the experimental data is also achieved for the first version of the Demetriou potentials and the simple McFadden-Satchler potential. The nucleon optical potential, the $\gamma$-ray strength function, and the level density parametrization are also constrained by the data although there is no unique best-fit combination.

Conclusions: The best-fit calculations allow us to extrapolate the low-energy ($\alpha ,\gamma$) cross section of ${}^{115}\mathrm{In}$ to the astrophysical Gamow window with reasonable uncertainties. However, still further improvements of the $\alpha$-nucleus potential are required for a global description of elastic ($\alpha ,\alpha$) scattering and $\alpha$-induced reactions in a wide range of masses and energies.

The sequential two-proton decay of the second excited state in ${}^{17}\mathrm{Ne}$, produced by inelastic excitation at intermediate energy, is studied. This state is found to be highly spin aligned, providing another example of a recently discovered alignment mechanism. The fortuitous condition that the second decay step is slightly more energetic than the first, permits the lifetime of the one-proton daughter, the ground state of ${}^{16}\mathrm{F}$, to be determined from the magnitude of the final-state interactions between the protons. This new method gave a result [$\mathrm{\Gamma }=20.6\left(57\right)$ keV] consistent with that obtained by directly measuring the width of the state [$\mathrm{\Gamma }=21.3\left(51\right)$ keV]. This width allows one to determine the continuum coupling constant in this mass region. Real-energy continuum-shell-model studies yield a satisfactory description of both spectra and widths of low-energy resonances in ${}^{16}\mathrm{F}$ and suggest an unusual large ratio of proton-proton to proton-neutron continuum couplings in the vicinity of the proton drip line.

The photon transverse momentum spectrum and its anisotropy from Pb+Pb collisions at the CERN Large Hadron Collider energy $\sqrt{s_{NN}}=2.76$ TeV are investigated within the integrated hydrokinetic model (iHKM). Photon production is accumulated from the different processes at the various stages of relativistic heavy ion collisions: from the primary hard photons of very early stage of parton collisions to the thermal photons from equilibrated quark-gluon and hadron gas stages. Along the way a hadronic medium evolution is treated in two distinct, in a sense opposite, approaches: chemically equilibrated and chemically frozen system expansion. Studying the centrality dependence of the results obtained allows us to conclude that a relatively strong transverse momentum anisotropy of thermal radiation is suppressed by prompt photon emission which is an isotropic. We find out that this effect is getting stronger as centrality increases because of the simultaneous increase in the relative contribution of prompt photons in the soft part of the spectra. The substantial results obtained in iHKM with nonzero viscosity ($\eta /s=0.08$) for photon spectra and $v_2$ coefficients are mostly within the error bars of experimental data, but there is some systematic underestimation of both observables for the near central events. We claim that a situation could be significantly improved if an additional photon radiation that accompanies the presence of a deconfined environment is included. Since a matter of a space-time layer where hadronization takes place is actively involved in anisotropic transverse flow, both positive contributions to the spectra and $v_2$ are considerable, albeit such an argument needs further research and elaboration.

We report on new or more precise half-lives, $\beta$-decay endpoint energies, and $\beta$-delayed proton emission branching ratios of ${}^{91}\mathrm{Pd}$, ${}^{95}\mathrm{Cd}$, ${}^{97}\mathrm{In}$, and ${}^{99}\mathrm{Sn}$. The measured values are consistent with known mirror transitions in lighter $T_z=-1/2$ nuclei, shell-model calculations, and various mass models. In addition to the $\beta$-decaying $(9/2^{+})$ ground state, circumstantial evidence for a short-lived, proton-emitting isomer with spin $(1/2^{-})$ was found in ${}^{97}\mathrm{In}$. Based on the experimental data, a semiempirical theory on proton emission, and shell-model calculations, the proton separation energy of the ${}^{97}\mathrm{In}$ ground state was determined to be $-0.10\pm 0.19$ MeV. The existence of the short-lived, proton-unstable $(1/2^{-})$ isomer in ${}^{97}\mathrm{In}$ establishes ${}^{96}\mathrm{Cd}$ as an $rp$-process waiting point.

The $\alpha$-decay half-lives of even-even nuclei from Sm to Th are systematically studied based on the transfer matrix method. For the nuclear potential, a type of cosh-parametrized form is applied to calculate the penetration probability. Through a least-squares fit to experimental half-lives, we optimize the parameters in the potential and the $\alpha$ preformation factor $P_0$. During this process, $P_0$ is treated as a constant for each parent nucleus. Eventually, the calculated half-lives are found to agree well with the experimental data, which verifies the accuracy of the present approach. Furthermore, in recent studies, $P_0$ is regulated by the shell and paring effects plus the nuclear deformation. To this end, $P_0$ is here associated with the structural quantity, i.e., the microscopic correction of nuclear mass ($E_{\mathrm{mic}}$). In this way, the agreement between theory and experiment is greatly improved by more than 20%, validating the appropriate treatment of $P_0$ in the scheme of $E_{\mathrm{mic}}$.

Decay of ${}^{85}\mathrm{Ga}$ was studied by means of $\beta$-neutron-$\gamma$ spectroscopy. A pure beam of ${}^{85}\mathrm{Ga}$ was produced at the Holifield Radioactive Ion Beam Facility using a resonance ionization laser ion source and a high-resolution electromagnetic separator. The $\beta$-delayed neutron emission probability was measured for the first time, yielding 70(5)%. An upper limit of 0.1% for $\beta$-delayed two-neutron emission was also experimentally established for the first time. A detailed decay scheme including absolute $\gamma$-ray intensities was obtained. Results are compared with theoretical $\beta$-delayed emission models.

The linear-chain states of ${}^{16}\mathrm{C}$ and their decay modes are theoretically investigated by using the antisymmetrized molecular dynamics. It is found that the positive-parity linear-chain states have the ${(3/2_{\pi }^{-})}^2{(1/2_{\sigma }^{-})}^2$ configuration and primary decay to ${}^{12}\mathrm{Be}\left(2_1^{+}\right)$ as well as to ${}^{12}\mathrm{Be}$(g.s.) by $\alpha$-particle emission. Moreover, we show that they also decay via the ${}^6\mathrm{He}+{}^{10}\mathrm{Be}$ channel. In the negative-parity states, it is found that two types of linear chains exist. One has the valence neutrons occupying the molecular orbits ${(3/2_{\pi }^{-})}^2(1/2_{\sigma }^{-})(3/2_{\pi }^{+})$, while the other's configuration cannot be explained in terms of the molecular orbits because of the strong parity mixing. Both configurations constitute the rotational bands with a large moment of inertia and intraband $E2$ transitions. Their $\alpha$ and ${}^6\mathrm{He}$ reduced widths are sufficiently large to be distinguished from other noncluster states although they are smaller than those of the positive-parity linear chain.

Background: Special attention has been paid to study the shell effect and odd-even staggering (OES) in the nuclear spallation.

Purpose: In this paper, we investigate the influence of the nuclear level density on the OES in the ${}^{56}\mathrm{Fe}+p$ spallations at energies from 300 to 1500 MeV/nucleon.

Method: The isospin-dependent quantum molecular dynamics (IQMD) model is applied to produce the highly excited and equilibrium remnants, which is then de-excited using the statistical model gemini. The excitation energy of the heaviest hot fragments is applied to match the IQMD model with the gemini model. In the gemini model, the statistical description of the evaporation are based on the Hauser-Feshbach formalism, in which level density prescriptions are applied.

Results: By investigating the OES of the excited pre-fragments, it is found that the OES originates at the end of the decay process when the excitation energy is close to the nucleon-emission threshold energy, i.e., the smaller value of the neutron separation energy and proton separation energy. The strong influence of level density on the OES is noticed. Two types of the nuclear level densities, the discrepancy of which is only about 7% near the nucleon emission threshold energy, are used in the model. However, the calculated values of the OES differ by the factor of 3 for the relevant nuclei.

Conclusions: It is suggested that, although the particle-separation energies play a key role in determining the OES, the level density at excitation energy lower than the particle-separation energies should be taken into consideration

The second-order Israel-Stewart-$\mathrm{M}\ddot{\mathrm{u}}\mathrm{ller}$ relativistic hydrodynamics was applied to study the effects of causality on the acoustic oscillation in relativistic fluid. Causal dispersion relations have been derived with nonvanishing shear viscosity, bulk viscosity, and thermal conductivity at nonzero temperature and baryonic chemical potential. These relations have been used to investigate the fluidity of quark-gluon plasma (QGP) at finite temperature ($T$). Results of the first-order dissipative hydrodynamics have been obtained as a limiting case of the second-order theory. The effects of the causality on the fluidity near the transition point and on the viscous horizon are found to be significant. We observe that the inclusion of causality increases the value of fluidity measure of QGP near $T_c$ and hence makes the flow strenuous. It was also shown that the inclusion of the large magnetic field in the causal hydrodynamics alters the fluidity of QGP.

A quantitative study of the astrophysically important subbarrier fusion of ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ is presented. Low-energy collisions are described in the body-fixed reference frame using wave-packet dynamics within a nuclear molecular picture. A collective Hamiltonian drives the time propagation of the wave packet through the collective potential-energy landscape. The fusion imaginary potential for specific dinuclear configurations is crucial for understanding the appearance of resonances in the fusion cross section. The theoretical subbarrier fusion cross sections explain some observed resonant structures in the astrophysical $S$ factor. These cross sections monotonically decline towards stellar energies. The structures in the data that are not explained are possibly due to cluster effects in the nuclear molecule, which need to be included in the present approach.