We propose a microscopic calculation of fusion reactions for $\alpha +{}^{197}\mathrm{Au},\alpha +{}^{208}\mathrm{Pb},\alpha +{}^{209}\mathrm{Bi}$, and $\alpha +{}^{238}\mathrm{U}$ systems. Inspired by recent studies of $\alpha$-cluster decay in radioactive nuclei [Phys. Rev. C 95, 061306(R) (2017)], a Pauli blocking term depending on the density overlap of projectile and target nuclei is introduced in addition to the strong and electromagnetic interactions between them. As compared to the $\alpha$-core potential obtained from the double-folding potential with standard Michigan-3-Yukawa-Reid effective nucleon-nucleon interaction, the one including the Pauli blocking interaction results in a shallow “pocket” in the inner part. On account of highlighting the density dependence of Pauli blocking potential, we make a comparison of fusion cross sections between two extreme neutron density distributions of target nuclei, namely, (i) “skin type” with same diffuseness but different half-density radii in density distributions of proton and neutron, and (ii) “halo type” with same half-density radii but different diffuseness. The fusion cross sections resulting from the potential considering Pauli blocking effects are also compared with the experimental data in detail.

The nuclide ${}^{35}\mathrm{Cl}$ can act as a minor “neutron poison” in the stellar slow neutron capture process. Neutron activation combined with accelerator mass spectrometry (AMS) was applied to measure the $(n,\gamma )$ cross section of ${}^{35}\mathrm{Cl}$ for neutron spectra simulating Maxwell-Boltzmann distributions of $kT\approx 30$ and 40 keV. The neutron activations were performed at the Karlsruhe Van de Graaff accelerator and at the superconducting linear accelerator of the Soreq Applied Research Accelerator Facility utilizing the ${}^7\mathrm{Li}(p,n){}^7\mathrm{Be}$ reaction. AMS measurements of the irradiated samples were performed at the 3 MV Vienna Environmental Research Accelerator, the 6 MV tandem accelerator at the Dresden AMS facility, and the 14 UD tandem accelerator of the Australian National University in Canberra. Our method is independent of previous measurements. For an energy of $kT=30\mathrm{keV}$, we report a Maxwellian averaged cross section of 8.33(32) mb. Using this new value in stellar isotopic abundance calculations, minor changes for the abundances of ${}^{35}\mathrm{Cl}$, ${}^{36}\mathrm{Cl}$, and ${}^{36}\mathrm{S}$ are derived.

Low-lying states of neutron-rich ${}^{32}\mathrm{Ne}$ were populated by means of one- and two-proton knockout reactions at the RIKEN Radioactive Isotope Beam Factory. A new transition is observed at 1410(15) keV and assigned to the $4_1^{+}\to 2_1^{+}$ decay. With this energy the $R_{4/2}$ ratio is calculated to be 2.99(6), lying close to the rigid rotor limit and suggests a high degree of collectivity and strongest deformation among neutron-rich neon isotopes. Comparisons of experimental inclusive and exclusive reaction cross sections with shell-model and eikonal reaction dynamical calculations reveals considerable quenching for this highly asymmetric system and contributes to systematic trends.

We apply the convection stability criterion to a fluid in global thermodynamic equilibrium with a rigid rotation or with a constant acceleration along the streamlines. Different equations of state describing strongly interacting matter are considered, and for each of them the analyzed system is found to be stable with respect to convection. This finding brings new evidence for physical relevance of nonstatic global equilibrium states. Our results can be directly used for other similar media to check their convective stability.

Valuable theoretical predictions of nuclear dipole excitations in the whole chart are of great interest for different nuclear applications, including, in particular, nuclear astrophysics. Here on the basis of experimental and theoretical information on the $E1$ and $M1$ strength functions, inspired both from axially deformed quasiparticle random-phase approximation and shell-model calculations, we derive simple expressions to determine systematically the dipole strength in order to update former prescriptions with a special emphasis on new expressions for the $M1$ spin-flip and scissors modes. We compare our final prediction of the $E1$ and $M1$ strengths with available experimental data at low energies and show that a relatively good agreement is obtained. Its impact on the total radiative width as well as radiative neutron capture cross sections is also discussed. The new expressions are believed to represent an improvement with respect to the analytical systematics proposed in the past and used traditionally in reaction codes, such as the recommended ripl-3 prescriptions.

I have compared new experimental information on resonances in ${}^{13}\mathrm{Be}$ with results of theoretical calculations. For the $1/2^{+}$ resonance at 0.86 MeV, the reported width of 1.70(15) MeV is considerably larger than the single-particle limit of 1.3 MeV. For the first $5/2^{+}$, the calculated width and $2^{+}$ branching ratio for neutron decay are both in rough agreement with the data. I discuss the possibility that events from decay of the second $5/2^{+}$ to ${}^{12}\mathrm{Be}\left(2^{+}\right)$ could contribute to the 0.86-MeV peak. If the 4.0-MeV resonance is indeed $3/2^{+}$, then its width should be considerably larger than reported.

Ranges for heavy atoms of evaporation residues (ERs) produced in nuclear fusion-evaporation reactions induced by accelerated heavy ions have been systematically considered. New range data obtained for $\alpha$-emitting short-lived Rn nuclei produced in the ${}^{16}\mathrm{O}+{}^{194}\mathrm{Pt}$ fusion-evaporation reaction have been obtained. These data were derived by the comparison of mean $\alpha$-particle energies of Rn-isotopes detected in experiments with the Monte Carlo simulations of these energies for the same isotopes stopped in the rotating Al catcher foil. As the result of this procedure applied to the production of ${}^{206}\mathrm{Rn}$ to ${}^{203}\mathrm{Rn}$ in the reaction, the ranges obtained in our experiments are 1.65 times larger than those expected from SRIM/TRIM calculations/simulations. To obtain an agreement of the predictions with the experimental data for such heavy atoms at low energies their electronic and/or nuclear stopping power components should be reduced.

Measured charge- and mass-changing cross sections for the systems ${}^4\mathrm{He}+{}^{12}C$, ${}^4\mathrm{He}+{}^{16}O$, ${}^4\mathrm{He}+{}^{28}\mathrm{Si}$, and ${}^4\mathrm{He}+{}^1\mathrm{H}$ in the energy range $70–220\mathrm{MeV}/\mathrm{u}$ are presented. The cross sections were obtained via the attenuation method where a $\mathrm{\Delta }E\text{−}E$ scintillator telescope was used for particle identification. These new data have particular relevance for future applications of ${}^4\mathrm{He}$ ions in ion-beam radiotherapy because this technique relies on precise heavy ion transport models for an accurate dose calculation. The radiation transport codes applied for this purpose typically make use of parametrizations of the total reaction cross section ${\sigma }_R$. The widely used parametrization for nucleus-nucleus reaction cross sections by Tripathi et al. is shown to underpredict the new experimental cross sections for ${}^4\mathrm{He}$ ions in the therapeutic energy range by up to $30\%$, which can lead to considerable dose calculation uncertainties. Therefore, modifications of the parameters in the Tripathi model are proposed to optimize it for applications related to ${}^4\mathrm{He}$ ion-beam therapy.

Background: The population and decay of two-nucleon resonances offer exciting new opportunities to explore dripline phenomena. A proper understanding of these systems requires a solid description of the three-body ($\text{core}+N+N$) continuum. The identification of a state with resonant character from the background of nonresonant continuum states in the same energy range poses a theoretical challenge.

Purpose: Establish a robust theoretical framework to identify and characterize three-body resonances in a discrete basis, and apply the method to the two-neutron unbound system ${}^{16}\mathrm{Be}$.

Method: A resonance operator is proposed, which describes the sensitivity to changes in the potential. Resonances, understood as normalizable states describing localized continuum structures, are identified from the eigenstates of the resonance operator with large negative eigenvalues. For this purpose, the resonance operator is diagonalized in a basis of Hamiltonian pseudostates, which in the present work are built within the hyperspherical harmonics formalism using the analytical transformed harmonic oscillator basis. The energy and width of the resonance are determined from its time dependence.

Results: The method is applied to ${}^{16}\mathrm{Be}$ in a ${}^{14}\mathrm{Be}+n+n$ model. An effective $\text{core}+n$ potential, fitted to the available experimental information on the binary subsystem ${}^{15}\mathrm{Be}$, is employed. The $0^{+}$ ground state resonance of ${}^{16}\mathrm{Be}$ presents a strong dineutron configuration. This favors the picture of a correlated two-neutron emission. Fitting the three body interaction to the experimental two-neutron separation energy $|S_{2n}|=1.35\left(10\right)$ MeV, the computed width is $\mathrm{\Gamma }\left(0^{+}\right)=0.16$ MeV. From the same Hamiltonian, a $2^{+}$ resonance is also predicted with ${\varepsilon }_r\left(2^{+}\right)=2.42$ MeV and $\mathrm{\Gamma }\left(2^{+}\right)=0.40$ MeV.

Conclusions: The dineutron configuration and the computed $0^{+}$ width are consistent with previous $R$-matrix calculations for the true three-body continuum. The extracted values of the resonance energy and width converge with the size of the pseudostate basis and are robust under changes in the basis parameters. This supports the reliability of the method in describing the properties of unbound $\text{core}+N+N$ systems in a discrete basis.

The emission of the 4.439-MeV $\gamma$ ray in proton inelastic scattering off ${}^{12}\mathrm{C}$ has been investigated in detail. For this, two independent descriptions of the correlated scattering and emission process have been used: one for the direct reaction mechanism and the other for the compound-nucleus (CN) component. Direct reactions were calculated in the framework of the coupled-channels formalism, while the CN component was described as a superposition of separate resonances with definite spin and parity, treated with the angular momentum coupling theory. Both components were incoherently added and compared to a comprehensive data set on measured $\gamma$-ray line shapes and angular distributions in the proton energy range $E_p=5.44–25.0$ MeV. In the range $E_p\approx 14–25$ MeV, good agreement with data was obtained with a dominating direct reaction component. At lower energy, an important CN component was required to describe line shape and angular distribution data. In general, a good description of the data could be found for a CN component with spin and parity corresponding to a known nearby resonance. The new calculation was found to improve significantly the agreement with line shape data in particular in the region of dominating CN resonances compared to previous calculations. Based on these results, predictions for $\gamma$-ray line shapes and angular distributions up to $E_p=100$ MeV were made and applied to $\gamma$-ray emissions in solar flares and proton radiotherapy.

The experimental excitation function for the $7\alpha$ de-excitation of ${}^{28}\mathrm{Si}$ nuclei excited to high excitation energies in the collisions of 35 MeV/nucleon ${}^{28}\mathrm{Si}$ with ${}^{12}\mathrm{C}$ reveals resonance structures. The possibility that these structures may indicate the population of toroidal high-spin isomers such as those predicted by a number of recent theoretical calculations is discussed and the need for further investigations is emphasized.

A large yield of $\alpha$ particles produced in the ${}^{120}\mathrm{Sn}({}^6\mathrm{He},\alpha )$ reaction was measured at 20.3-, 22.2-, 22.4-, and 24.5-MeV bombarding energies. The $\alpha$ particles are distributed over a broad energy range in the vicinity and below the elastic scattering ${}^6\mathrm{He}$ peak. Energy integrated $\alpha$-particle cross sections have been obtained at ${\theta }_{\text{lab}}={36}^{\circ },{40}^{\circ }$, and ${60}^{\circ }$. The $\alpha$ energy distributions have been analyzed at a fixed laboratory angle $\left(\approx {60}^{\circ }\right)$ in terms of the reaction $Q$ value, considering the $2n$-transfer reaction kinematics ${}^{120}\mathrm{Sn}({}^6\mathrm{He},\alpha ){}^{122}\mathrm{Sn}$. A kinematical analysis of the $Q$-value distribution shows that the recoil system ${}^{120}\mathrm{Sn}+2n$ is formed in highly excited states in the continuum, at increasing excitation energies as the bombarding energy increases. It is shown that by using Brink's formula, the excitation energy depends on the transferred angular momentum following a linear relation with the square of the angular momentum, indicating that some kind of dinuclear rotating system is formed after the reaction.

We report a new precision half-life measurement of ${}^{20}\mathrm{F}$, performed using the $\beta$-counting station of the University of Notre Dame's Nuclear Science Laboratory. The measured half-life of $11.0160{\left(41\right)}_{\text{stat}}{\left(155\right)}_{\text{sys}}$ s resulting from this work will help resolve the longstanding discrepancy between two earlier sets of high-precision half-life measurements.

I propose a new algorithm that applies the variational principle to a coherent-pair condensate. The result is equivalent to that of the so-called variation after particle-number projection in the BCS case, but now the particle number is always conserved and the time-consuming projection is avoided. I derive analytical expressions for the average energy and its gradient in terms of the coherent-pair structure. In addition, I give analytically the pair structure at the energy minimum, and discuss its asymptotic behavior away from the Fermi surface, which looks quite simple and allows easy physical interpretations. The new algorithm iterates these pair-structure expressions to minimize energy. I demonstrate the new algorithm in a semirealistic example using the realistic $V_{\mathrm{low}-k}$ interaction and large model spaces (up to 15 harmonic-oscillator major shells). The energy can be minimized to practically arbitrary precision. The result shows that the realistic $V_{\mathrm{low}-k}$ interaction does not cause divergences in the pairing channel, although tiny occupation numbers (for example smaller than ${10}^{-5}$) contribute to the energy (by a few tens of keV).

Excited states in the neutron-rich ${}^{70}\mathrm{Fe}$ nucleus were populated in a one-proton removal reaction from ${}^{71}\mathrm{Co}$ projectiles at 87 MeV/nucleon. A new transition was observed with the $\gamma$-ray tracking array GRETINA and shown to feed the previously assigned $4_1^{+}$ state. In comparison to reaction theory calculations with shell-model spectroscopic factors, it is argued that the new $\gamma$ ray possibly originates from the $6_1^{+}$ state. It is further shown that the Doppler-reconstructed $\gamma$-ray spectra are sensitive to the very different lifetimes of the $2^{+}$ and $4^{+}$ states, enabling their approximate measurement. The emerging structure of ${}^{70}\mathrm{Fe}$ is discussed in comparison to LNPS-new large-scale shell-model calculations.

The high-spin structures of ${}^{136}\mathrm{Ba}$ and ${}^{137}\mathrm{Ba}$ are investigated after multinucleon-transfer (MNT) and fusion-evaporation reactions. ${}^{136}\mathrm{Ba}$ is populated in a ${}^{136}\mathrm{Xe}+{}^{238}\mathrm{U}$ MNT reaction employing the high-resolution Advanced GAmma Tracking Array (AGATA) coupled to the magnetic spectrometer PRISMA at the Laboratori Nazionali di Legnaro, Italy, and in two ${}^9\mathrm{Be}+{}^{130}\mathrm{Te}$ fusion-evaporation reactions using the High-efficiency Observatory for $\gamma$-Ray Unique Spectroscopy (HORUS) at the FN tandem accelerator of the University of Cologne, Germany. Furthermore, both isotopes are populated in an elusive reaction channel in the ${}^{11}\mathrm{B}+{}^{130}\mathrm{Te}$ fusion-evaporation reaction utilizing the HORUS $\gamma$-ray array. The level scheme above the $J^{\pi }={10}^{+}$ isomer in ${}^{136}\mathrm{Ba}$ is revised and extended up to an excitation energy of approximately 5.5 MeV. From the results of angular-correlation measurements, the $E_x=3707$- and $E_x=4920$-keV states are identified as the bandheads of positive- and negative-parity cascades. While the high-spin regimes of both ${}^{132}\mathrm{Te}$ and ${}^{134}\mathrm{Xe}$ are characterized by high-energy ${12}^{+}\to {10}^{+}$ transitions, the ${}^{136}\mathrm{Ba}E2$ ground-state band is interrupted by negative-parity states only a few hundred keV above the $J^{\pi }={10}^{+}$ isomer. Furthermore, spins are established for several hitherto unassigned high-spin states in ${}^{137}\mathrm{Ba}$. The new results close a gap along the high-spin structure of $N<82$ Ba isotopes. Experimental results are compared to large-scale shell-model calculations employing the GCN50:82, Realistic SM, PQM130, and SN100PN interactions. The calculations suggest that the bandheads of the positive-parity bands in both isotopes are predominantly of proton character.

Background: Shell evolution can impact the structure of the nuclei and lead to effects such as shape coexistence. The nuclei around ${}^{68}\mathrm{Ni}$ represent an excellent study case, however, spectroscopic information of the neutron-rich, $Z<28$ nuclei is limited.

Purpose: The goal is to measure $\gamma$-ray transitions in ${}^{66}\mathrm{Fe},{}^{66}\mathrm{Co}$, and ${}^{66}\mathrm{Ni}$ populated in the ${\beta }^{-}$ decay of ${}^{66}\mathrm{Mn}$ to determine absolute $\beta$ feedings and relative $\gamma$-decay probabilities and to compare the results with Monte Carlo shell model calculations in order to study the influence of the relevant single neutron and proton orbital occupancies around $Z=28$ and $N=40$.

Method: The low-energy structures of ${}^{65,66}\mathrm{Fe},{}^{66}\mathrm{Co}$, and ${}^{66}\mathrm{Ni}$ were studied in the ${\beta }^{-}$ decay of ${}^{66}\mathrm{Mn}$ produced at ISOLDE, CERN. The beam was purified by means of laser resonance ionization and mass separation. The $\beta$ and $\gamma$ events detected by three plastic scintillators and two MiniBall cluster germanium detectors, respectively, were correlated in time to build the low-energy excitation schemes and to determine the $\beta$-decay half-lives of the nuclei.

Results: The relative small $\beta$-decay ground state feeding of ${}^{66}\mathrm{Fe}$ obtained in this work is at variant to the earlier studies. Spin and parity $1^{+}$ was assigned to the ${}^{66}\mathrm{Co}$ ground state based on the strong ground-state feeding in the decay of ${}^{66}\mathrm{Fe}$ as well as in the decay of ${}^{66}\mathrm{Co}$. Experimental log($ft$) values, $\gamma$-ray de-excitation patterns, and energies of excited states were compared to Monte Carlo shell model calculations. Based on this comparison, spin and parity assignments for the selected number of low-lying states in the ${}^{66}\mathrm{Mn}$ to ${}^{66}\mathrm{Ni}$ chain were proposed.

Conclusions: The $\beta$-decay chain starting ${}^{66}\mathrm{Mn}$ toward ${}^{66}\mathrm{Ni}$, crossing $N=40$, evolves from deformed nuclei to sphericity. The $\beta$-decay population of a selected number of $0^{+}$ and $2^{+}$ states in ${}^{66}\mathrm{Ni}$, which is understood within shape coexistence framework of Monte Carlo shell model calculations, reveals the crucial role of the neutron $0g_{9/2}$ shell and proton excitations across the $Z=28$ gap.

For a description of large-amplitude collective motion associated with nuclear pairing, requantization of time-dependent mean-field dynamics is performed using the stationary-phase approximation (SPA) to the path integral. We overcome the difficulty of the SPA, which is known to be applicable to integrable systems only, by developing a requantization approach combining the SPA with the adiabatic self-consistent collective coordinate method (ASCC+SPA). We apply the ASCC+SPA to multilevel pairing models, which are nonintegrable systems, to study the nuclear pairing dynamics. The ASCC+SPA gives a reasonable description of low-lying excited $0^{+}$ states in nonintegrable pairing systems.

The mechanism involved in compound nucleus formation through heavy ion induced fusion reactions at near- and sub-barrier energies has been stimulating the interest of both experimentalists and theoreticians. The study of fusion reactions is important not only for the production of superheavy elements but also to unfold the mysteries involved in the evolution of neutron stars and nucleosynthesis of elements in astrophysical scenarios. The detection of gravitational waves originating from the merging of two black holes, and the possibility of observing similar events originating from black-hole–neutron-star mergers, highlighted the necessity of understanding the behavior of neutron-rich nuclear matter. One of the potential methods to understand the character of neutron-rich matter is through the study of fusion of an isotopic chain of reactions. Recently, the first experimental evidence of fusion enhancement at near-barrier energies for neutron-rich nuclei was reported for the light and mid-mass regime. To understand the dynamics involved in such reactions, the investigation of K-induced reactions has been performed using the quantum mechanical fragmentation based dynamical cluster-decay model (DCM). The experimental fusion cross sections of ${}^{39,47}\mathrm{K}+{}^{28}\mathrm{Si}$ are reproduced using DCM and, further, the fusion cross sections are predicted for other isotopes of K beam on ${}^{28}\mathrm{Si}$ to investigate the fusion enhancement as a function of neutron number. It has been observed that fusion enhancement is significant at near-barrier energies for neutron-rich nuclei. The fusion enhancement observed is larger for odd neutron number nuclei as compared to adjacent neutron nuclei. This indicates the influence of unpaired neutrons on fusion cross sections. Also, the fusion cross sections predicted in the present work will act as input for planning more experimental measurements.

We show that the commonly used criterion for $\beta$ equilibrium in neutrino-transparent dense nuclear matter becomes invalid as temperatures rise above 1 MeV. Such temperatures are attained in neutron-star mergers. By numerically computing the relevant weak-interaction rates we find that the correct criterion for $\beta$ equilibrium requires an isospin chemical potential that can be as large as 10–20 MeV, depending on the temperature at which neutrinos become trapped.