We discuss the most effective energy range for charged-particle-induced reactions in a plasma environment at a given plasma temperature. The correspondence between the plasma temperature and the most effective energy should be modified from the one given by the Gamow peak energy, in the presence of a significant incident-energy dependence in the astrophysical $S$ factor as in the case of resonant reactions. The suggested modification of the effective energy range is important not only in thermonuclear reactions at high temperature in the stellar environment, e.g., in advanced burning stages of massive stars and in explosive stellar environments, as has been already claimed, but also in the application of nuclear reactions driven by ultra-intense laser-pulse irradiation.

In this paper we present results from measurements of prompt $\gamma$ rays from the thermal neutron induced fission of ${}^{235}$U. Photons were measured in coincidence with fission fragments with cerium-doped LaCl${}_3$ and LaBr${}_3$ as well as CeBr${}_3$ scintillation detectors, which offer an intriguing combination of excellent timing resolution and good resolving power. The spectra measured with all employed detectors are in excellent agreement with respect to their shapes. Characteristic parameters were extracted for a $\gamma$-energy range from 0.1 to 6.0 MeV and the results obtained with several detectors were averaged. From that, the average emission yield of prompt-fission $\gamma$ rays was determined to be ${\overline{\nu }}_{\gamma }=(8.19\pm 0.11)$ per fission, the average energy per photon to be ${\epsilon }_{\gamma }=(0.85\pm 0.02)$ MeV, and the total energy to be $E_{\gamma ,\mathrm{tot}}=(6.92\pm 0.09)$ MeV. The uncertainties are much lower than the 7.5$\%$ requested for the modeling of advanced nuclear reactor cores. Estimating the influence of $\gamma$ rays with energies between 6 and 10 MeV on the values determined in this work revealed a negligible deviation of the order of the found uncertainties.

Background: Well-developed third minima, corresponding to strongly elongated and reflection-asymmetric shapes associated with dimolecular configurations, have been predicted in some non-self-consistent models to impact fission pathways of thorium and uranium isotopes. These predictions have guided the interpretation of resonances seen experimentally. On the other hand, self-consistent calculations consistently predict very shallow potential-energy surfaces in the third minimum region.

Purpose: We investigate the interpretation of third-minimum configurations in terms of dimolecular (cluster) states. We study the isentropic potential-energy surfaces of selected even-even thorium and uranium isotopes at several excitation energies. In order to understand the driving effects behind the presence of third minima, we study the interplay between pairing and shell effects.

Methods: We use the finite-temperature superfluid nuclear density functional theory. We consider two Skyrme energy density functionals: a traditional functional SkM${}^{*}$ and a recent functional UNEDF1 optimized for fission studies.

Results: We predict very shallow or no third minima in the potential-energy surfaces of ${}^{232}$Th and ${}^{232}$U. In the lighter Th and U isotopes with $N=136$ and 138, the third minima are better developed. We show that the reflection-asymmetric configurations around the third minimum can be associated with dimolecular states involving the spherical doubly magic ${}^{132}$Sn and a lighter deformed Zr or Mo fragment. The potential-energy surfaces for ${}^{228,232}$Th and ${}^{232}$U at several excitation energies are presented. We also study isotopic chains to demonstrate the evolution of the depth of the third minimum with neutron number.

Conclusions: We show that the neutron shell effect that governs the existence of the dimolecular states around the third minimum is consistent with the spherical-to-deformed shape transition in the Zr and Mo isotopes around $N=58$. We demonstrate that the depth of the third minimum is sensitive to the excitation energy of the nucleus. In particular, the thermal reduction of pairing, and related enhancement of shell effects, at small excitation energies help to develop deeper third minima. At large excitation energies, shell effects are washed out and third minima disappear altogether.

$\alpha$ decay of ${}^{249}$Bk has been investigated by measuring its $\alpha$ and $\gamma$-ray spectra, both in singles and in coincidence modes. The $\alpha$ spectrum of a freshly purified ${}^{249}$Bk sample was measured with a high-resolution, double-focusing magnetic spectrometer. $\gamma$ singles, $\gamma$-$\gamma$ coincidence, and $\gamma$-$\alpha$ coincidence spectra were also recorded. The absolute intensity of the 327.45-keV $\gamma$ ray has been determined to be ($1.44\pm 0.08)\times {10}^{-5}$% per ${}^{249}$Bk decay. Assignments of previously known single-particle states were confirmed. A new rotational band was identified in the $\alpha$ singles spectrum and Am K x rays have been observed in its decay. This single-particle state, with an energy of 154 keV, has been assigned to the 3/2${}^{-}$[521] Nilsson state. This is the lowest excitation energy for this orbital in any Am nucleus. More precise energies and intensities of the ${}^{249}$Bk $\alpha$ groups and $\gamma$-ray transitions are provided.

Dissipative ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reactions at 95 MeV are fully detected in charge with the GARFIELD and RCo apparatuses at Laboratori Nazionali di Legnaro. A comparison to a dedicated Hauser-Feshbach calculation allows us to select events which correspond, to a large extent, to the statistical evaporation of highly excited ${}^{24}$Mg, as well as to extract information on the isotopic distribution of the evaporation residues in coincidence with their complete evaporation chain. Residual deviations from statistical behavior are observed in $\alpha$ yields and attributed to the persistence of cluster correlations well above the ${}^{24}$Mg threshold for six-$\alpha$ decay.

Background: The triple-$\alpha$ reaction is the key to our understanding about the nucleosynthesis and the observed abundance of ${}^{12}$C in stars. The theory of this process is well established at high temperatures but rather ambiguous in the low temperature regime where measurements are impossible.

Purpose: Develop a new three-body method, which tackles properly the scattering boundary condition for three charged particles and takes into account both the resonant and the nonresonant reaction mechanisms on the same footing, to compute the triple-$\alpha$ reaction rate at low temperatures.

Methods: We combine the $R$-matrix expansion, the $R$-matrix propagation method, and the screening technique in the hyperspherical harmonics basis.

Results: Both the $2_1{}^{+}$ bound state and the $0_2{}^{+}$ resonant state in ${}^{12}$C are well reproduced. We also study the cluster structure of these states. We calculate the triple-$\alpha$ reaction rate for $T=0.01–0.1$ GK.

Conclusions: We obtain the same rate as NACRE for temperatures above $0.07$ GK, but the new rate is largely enhanced at lower temperatures ($\approx$${10}^{12}$ at $0.02$ GK). The differences are caused by the direct capture contribution to the reaction when three $\alpha$ particles cannot reach the resonant energies.

The condensation of neutrons into a ${}^3{P}_2$ superfluid phase occurs at densities relevant for the interior of neutron stars. The triplet pairing breaks rotational symmetry spontaneously and leads to the existence of gapless modes (angulons) that are relevant for many transport coefficients and to the star's cooling properties. We derive the leading terms of the low-energy effective field theory, including the leading coupling to electroweak currents, valid for a variety of possible ${}^3{P}_2$ phases.

The hyperfine structure and isotope shifts of Sr isotopes, both even-even and odd-even nuclei, are studied in the covariant density functional theory with the new parameter set DD-PC1. Pairing correlation is treated using the Bogoliubov model with a separable form of the pairing interaction. Spin parity, charge radii, two-neutron separation energies, and pairing energies of ground states are calculated and compared with experimental data. We find a shape transition at $N\approx 60$ in charge radii and spin parity, which are consistent with each other and generally agree with experiments. Although the nuclear masses are not very sensitive to these shape changes, odd-even mass differences and pairing effects are very important for study of the shape transition and shape coexistence phenomena in Sr isotopes.

Starting from the Boltzmann equation with the relaxation time approximation for the collision term and using a Chapman-Enskog-like expansion for the distribution function close to equilibrium, we derive hydrodynamic evolution equations for the dissipative quantities directly from their definition. Although the form of the equations is identical to those obtained in traditional Israel-Stewart approaches employing Grad's 14-moment approximation and the second moment of the Boltzmann equation, the coefficients obtained are different. In the case of a one-dimensional scaling expansion, we demonstrate that our results are in better agreement with a numerical solution of the Boltzmann equation as compared to Israel-Stewart results. We also show that including approximate higher-order corrections in viscous evolution significantly improves this agreement, thus justifying the relaxation time approximation for the collision term.

The double-humped structure of many actinide fission barriers is well established both experimentally and theoretically. There is also evidence, both experimental and theoretical, that some actinide nuclei have barriers with a third minimum, outside the second, fission-isomeric minimum. We perform a large-scale, systematic calculation of actinide fission barriers to identify which actinide nuclei exhibit third minima. We find that only a relatively few nuclei accessible to experiment exhibit third minima in their barriers: approximately nuclei with proton number $Z$ in the range $88\le Z\le 94$ and nucleon number $A$ in the range $230\le A\le 236$. We find that the third minimum is less than 1 MeV deep for light Th and U isotopes. This is consistent with some previous experimental and theoretical results, but it differs from some others. We discuss possible origins of these incompatible results and what are the most realistic predictions of where third minima are observable.

Background: The most significant source of background in direct dark matter searches are neutrons that scatter elastically from nuclei in the detector's sensitive volume. Experimental data for the elastic scattering cross section of neutrons from argon and neon, which are target materials of interest to the dark matter community, were previously unavailable.

Purpose: Measure the differential cross section for elastic scattering of neutrons from argon and neon in the energy range relevant to backgrounds from ($\alpha ,n$) reactions in direct dark matter searches.

Method: Cross-section data were taken at the Triangle Universities Nuclear Laboratory (TUNL) using the neutron time-of-flight technique. These data were fit using the spherical optical model.

Results: The differential cross section for elastic scatting of neutrons from neon at 5.0 and 8.0 MeV and argon at 6.0 MeV was measured. Optical-model parameters for the elastic scattering reactions were determined from the best fit to these data. The total elastic scattering cross section for neon was found to differ by 6$\%$ at 5.0 MeV and 13$\%$ at 8.0 MeV from global optical-model predictions. Compared to a local optical model for ${}^{40}$Ar, the elastic scattering cross section was found to differ from the data by 8$\%$ at 6.0 MeV.

Conclusions: These new data are important for improving Monte Carlo simulations and background estimates for direct dark matter searches and for benchmarking optical models of neutron elastic scattering from these nuclei.

Background: Theoretical calculations of the four-particle scattering above the four-cluster breakup threshold are technically very difficult due to nontrivial singularities or boundary conditions. Further complications arise when the long-range Coulomb force is present.

Purpose: We aim at calculating proton-${}^3$He elastic scattering observables above three- and four-cluster breakup threshold.

Methods: We employ Alt, Grassberger, and Sandhas (AGS) equations for the four-nucleon transition operators and solve them in the momentum-space framework using the complex-energy method whose accuracy and practical applicability is improved by a special integration method.

Results: Using realistic nuclear interaction models we obtain fully converged results for the proton-${}^3$He elastic scattering. The differential cross section, proton and ${}^3$He analyzing powers, spin correlation and spin transfer coefficients are calculated at proton energies ranging from 7 to 35 MeV. Effective three- and four-nucleon forces are included via the explicit excitation of a nucleon to a $\Delta$ isobar.

Conclusions: Realistic proton-${}^3$He scattering calculations above the four-nucleon breakup threshold are feasible. There is quite good agreement between the theoretical predictions and experimental data for the proton-${}^3$He scattering in the considered energy regime. The most remarkable disagreements are the peak of the proton analyzing power at lower energies and the minimum of the differential cross section at higher energies. Inclusion of the $\Delta$ isobar reduces the latter discrepancy.

Elastic $\overline{p}d$ scattering is studied within the Glauber theory based on the single- and double $\overline{p}N$ scattering mechanisms. The full spin dependence of the elementary $\overline{p}N$ scattering amplitudes is taken into account and both the $S$- and $D$-wave components of the deuteron are considered. The treatment of the spin dependence is done in a (properly modified) formalism developed recently by Platonova and Kukulin for the $pd\to pd$ scattering process. Predictions for differential cross sections and the spin observables $A_y^d$, $A_y^{\overline{p}}$, $A_{xx}$, $A_{yy}$ are presented for antiproton beam energies between 50 and 300 MeV, using amplitudes generated from the $\overline{N}N$ interaction model developed by the Jülich group. Total polarized cross sections are calculated utilizing the optical theorem. The efficiency of the polarization buildup for antiprotons in a storage ring is investigated.

The production of ${\eta }^{\prime }$ mesons in photon- and hadron-induced reactions has been revisited in view of the recent additions of high-precision data to the world data base. Based on an effective Lagrangian approach, we performed a combined analysis of the free and quasifree $\gamma N\to {\eta }^{\prime }N$, $NN\to NN{\eta }^{\prime }$, and $\pi N\to {\eta }^{\prime }N$ reactions. Considering spin-$\frac{1}{2}$ and -$\frac{3}{2}$ resonances, we found that a set of above-threshold resonances $\{S_{11}$, $P_{11}$, $P_{13}\}$, with fitted mass values of about $M_R=1925$, 2130, and 2050 MeV, respectively, and the four-star subthreshold $P_{13}\left(1720\right)$ resonance reproduce best all existing data for the ${\eta }^{\prime }$ production processes in the resonance-energy region considered in this work. All three above-threshold resonances found in the present analysis are essential and indispensable for the good quality of the present fits.

Pairing rotations and pairing vibrations are collective modes associated with a field, the pair field, which changes the number of particles by two. Consequently, they can be studied at profit with the help of two-particle transfer reactions in superfluid and in normal nuclei, respectively. The advent of exotic beams has opened, for the first time, the possibility to carry out such studies in medium heavy nuclei, within the same isotopic chain. The case studied in the present paper is that of the Sn isotopes [essentially from closed ($Z=N=50$) to closed ($Z=50$, $N=82$) shells]. The static and dynamic off-diagonal, long-range order phase coherence in gauge space displayed by pairing rotations and vibrations, respectively, leads to coherent states which behave almost classically. Consequently, these modes are amenable to an accurate nuclear structure description in terms of simple models containing the right physics, in particular, BCS plus quasiparticle random-phase approximation and Hartree-Fock mean field plus random-phase approximation, respectively. The associated two-nucleon transfer spectroscopic amplitudes predicted by such model calculations can thus be viewed as essentially “exact.” This fact, together with the availability of optical potentials for the different real and virtual channels involved in the reactions considered, namely ${}^{A+2}\text{Sn}+p$, ${}^{A+1}\text{Sn}+d$, and ${}^A\text{Sn}+t$, allows for the calculation of the associated absolute cross sections without, arguably, free parameters. The numerical predictions of the absolute differential cross sections, obtained making use of the above-mentioned nuclear structure and optical potential inputs, within the framework of second-order distorted-wave Born approximation, taking into account simultaneous, successive, and nonorthogonality contributions, provide, within experimental errors in general, and below $10\%$ uncertainty in particular, an overall account of the experimental findings for all of the measured ${}^{A+2}\text{Sn}(p,t){}^A\text{Sn}\left(\text{gs}\right)$ reactions, for which absolute cross sections have been reported to date.

Neutron-rich chlorine isotopes were populated in the ${}^{40}$Ar+${}^{208}$Pb multiple transfer reaction via the $-1p$ channels in a fragment-$\gamma$ coincident measurement employing the Prisma-Clara setup. New $\gamma$ transitions have been identified and, together with already available data, level schemes have been revised and compared with the results of large-scale $sd-pf$ shell-model calculations. The evolution of the energy splitting between the $s_{1/2}$ and $d_{3/2}$ orbitals and the increased mixing of different proton configurations in the populated Cl isotopic chain have been deduced by inspecting the shell-model wave functions.

We deduce the rms nuclear charge radii for ground states of light and medium-mass nuclei from experimental data of cluster radioactivity and proton emission in a unified framework. On the basis of the density-dependent cluster model, the calculated decay half-lives are obtained within the modified two-potential approach. The charge distribution of emitted clusters in the cluster decay and that of daughter nuclei in the proton emission are determined to correspondingly reproduce the experimental half-lives within the folding model. The obtained charge distribution is then employed to give the rms charge radius of the studied nuclei. Satisfactory agreement between theory and experiment is achieved for available experimental data, and the present results are found to be consistent with theoretical estimations. This study is expected to be helpful in the future detection of nuclear sizes, especially for these exotic nuclei near the proton dripline.

The structural evolution of heavy nuclei, with $Z>82$, is investigated by looking at the differential variation of the two-neutron separation energies. It indicates, by nonmonotonous behavior at certain neutron numbers, structure phenomena such as major shell ($N=126$) and deformed subshell ($N=152$) closures. Another interesting effect is observed at $N\sim 142$, which is very well correlated with a previously observed, intriguing behavior of quantities measured in $\alpha$ decay, such as relative branching ratios and hindrance factors of excited states from the ground-state band of deformed nuclei in this region. Corroboration of the existing experimental data indicates another possible deformed subshell closure.

The $g$ factors of the first-excited states of stable ${}^{124}$Sn and radioactive ${}^{126,128}$Sn were measured by the recoil-in-vacuum method with comparatively high precision. The experiments were performed at the Holifield Radioactive Ion Beam Facility by Coulomb exciting $\sim 3$ MeV/u beams in inverse kinematics on carbon and titanium targets. The results for ${}^{124}$Sn and ${}^{126}$Sn are in excellent agreement with recent shell-model calculations. For ${}^{128}$Sn the experiment suggests an increase in the magnitude of $g\left(2_1^{+}\right)$, as predicted by some models. The present results provide a sensitive probe of the valence orbitals that contribute to the $2_1^{+}$ wave functions as the double-shell closure at ${}^{132}$Sn is approached.

Production cross sections for neutron-rich nuclei from the fragmentation of a ${}^{82}$Se beam at 139 MeV/u were measured. The longitudinal momentum distributions of 126 neutron-rich isotopes of elements $11\le Z\le 32$ were scanned using an experimental approach of varying the target thickness. Production cross sections with beryllium and tungsten targets were determined for a large number of nuclei including several isotopes first observed in this work. These are the most neutron-rich nuclides of the elements $22\le Z\le 25$ (${}^{64}$Ti, ${}^{67}$V, ${}^{69}$Cr, and ${}^{72}$Mn). One event was registered consistent with ${}^{70}$Cr and another one with ${}^{75}$Fe. The production cross sections are correlated with $Q_g$ systematics to reveal trends in the data. The results presented here confirm our previous results from a similar measurement using a ${}^{76}$Ge beam and can be explained with a shell model that predicts a subshell closure at $N=34$ around $Z=20$. This is demonstrated by systematic trends and calculations with the abrasion-ablation model that are sensitive to separation energies.