Two-proton scattering at sub-Coulomb energies has been measured indirectly via the Trojan horse method applied to the $p\hspace{0.5em}+\hspace{0.5em}d\to p\hspace{0.5em}+\hspace{0.5em}p\hspace{0.5em}+\hspace{0.5em}n$ reaction to investigate off-energy shell effects for scattering processes. The three-body experiment was performed at 5 and 4.7 MeV corresponding to a $p\text{−}p$ relative energy ranging from 80 to 670 keV. The free $p\text{−}p$ cross section exhibits a deep minimum right within this relative energy region due to Coulomb plus nuclear destructive interference. No minimum occurs instead in the Trojan horse $p\text{−}p$ cross section, which was extracted by employing a simple plane-wave impulse approximation. A detailed formalism was developed to build up the expression of the theoretical half-off-shell $p\text{−}p$ cross section. Its behavior agrees with the Trojan horse data and in turn formally fits the $n\text{−}n$, $n\text{−}p$, and nuclear $p\text{−}p$ cross sections given the fact that in its expression the Coulomb amplitude is negligible with respect to the nuclear one. These results confirm the Trojan horse suppression of the Coulomb amplitude for scattering due to the off-shell character of the process.

We study the effects of the isospin-symmetry breaking on the superallowed Fermi $\beta$ decay of the ground state of ${}^{82}\mathrm{Nb}$ to ${}^{82}\mathrm{Zr}$. Results on the analog as well as nonanalog $\beta$-decay branches are self-consistently obtained within the complex excited VAMPIR approach. The ${}^{82}\mathrm{Nb}$ $\to$ ${}^{82}\mathrm{Zr}$ $\beta$ decay to the first two excited $0^{+}$ states with significant strength is predicted to coexist with the superallowed decay. The structure and electromagnetic properties of the analog and nonanalog low- and high-spin states in ${}^{82}\mathrm{Nb}$ and ${}^{82}\mathrm{Zr}$ are compared with the available experimental data.

We compute the energy functional of a three-level Lipkin model via a Legrendre transform and compare exact numerical results with analytical solutions obtained from the random phase approximation (RPA). Except for the region of the phase transition, the RPA solutions perform very well. We also study the case of three nondegenerate levels and again find that the RPA solution agrees well with the exact numerical result. For this case, the analytical results give us insight into the form of the energy functional in the presence of symmetry-breaking one-body potentials.

Background: The strength of electron capture for medium mass nuclei has a significant effect on the evolution of supernovae. There is insufficient knowledge of these strengths and very little data for important radioactive nuclei. Purpose: Determine whether it is feasible to obtain EC strength from studies of $T_o+1$ excitations in ($p$, $n$) reactions, and whether this might yield information for radioactive nuclei. Methods: Cross sections for the ${}^{58,60,62,64}\mathrm{Ni}$($p$, $n$)${}^{58,60,62,64}\mathrm{Cu}$ reactions were measured over the angular range of $0.3{}^{\circ }$ to $11.6{}^{\circ }$ at 134.3 MeV using the IUCF neutron time-of-flight facility. Results: The $T_o+1$ excitations in ${}^{60,62}\mathrm{Ni}$ were identified by comparison with inelastic proton scattering spectra, their $B$(GT) were extracted, and the corresponding electron capture rates in supernovae were calculated. Data from the TRIUMF ($n$, $p$) experiments at 198 MeV were reanalyzed; the electron capture rates for the reanalyzed data are in moderately good agreement with the higher resolution ($p$, $n$) results, but differ in detail. The possibility of future measurements with radioactive nuclei was considered. Conclusions: It may be possible to obtain low-lying electron capture strength for radioactive nuclei by studying ($p$, $n$) reactions in inverse kinematics.

The coordinate-space formulation of the Hartree-Fock-Bogoliubov (HFB) method enables the self-consistent treatment of mean field and pairing in weakly bound systems whose properties are affected by the particle continuum space. Of particular interest are neutron-rich, deformed drip-line nuclei, which can exhibit novel properties associated with neutron skin. To describe such systems theoretically, we developed an accurate two-dimensional lattice Skyrme-HFB solver HFB-AX based on basis (or B)-splines. Compared to previous implementations, ours incorporated a number of improvements aimed at boosting the solver's performance. These include the explicit imposition of axiality and space inversion, use of the modified Broyden method to solve self-consistent equations, and a partial parallelization of the code. HFB-AX has been compared with other HFB codes, both spherical and deformed, and the accuracy of the B-spline expansion was tested by employing the multiresolution wavelet method. Illustrative calculations are carried out for stable and weakly bound nuclei at spherical and very deformed shapes, including constrained fission pathways. In addition to providing new physics insights, HFB-AX can serve as a useful tool to assess the reliability and applicability of coordinate-space and configuration-space HFB frameworks, both existing and in development.

New developments have been brought to our energy-, spin-, and parity-dependent nuclear level densities based on the microscopic combinatorial model. As in our previous study, a detailed calculation of the intrinsic state density and of the rotational enhancement factor is included, but this time the vibrational contributions explicitly take the phonon excitations into account. The present model predicts the experimental $s$- and $p$-wave neutron resonance spacings with a degree of accuracy comparable to that of the best global models available. It is also shown that the model gives a reliable extrapolation at low energies where experimental data on the cumulative number of levels can be extracted. The predictions are also in good agreement with the experimental data extracted from the analysis of particle-$\gamma$ coincidence in the (${}^3\mathrm{He}$, $\alpha \gamma$) and (${}^3\mathrm{He}$, ${}^3\mathrm{He}$${}^{\text{'}}\gamma$) reactions. Total as well as partial level densities for more than 8500 nuclei are made available in a table format for practical applications. For the nuclei for which experimental $s$-wave spacings and enough low-lying states exist, renormalization factors are provided to reproduce simultaneously both observables. The same combinatorial method is used to estimate the nuclear level densities at the fission saddle points of actinides and at the shape isomer deformation. Finally, the new nuclear level densities are applied to the calculation of radiative neutron capture cross sections.

Estimates of the neutrino-nucleus cross section, for the charged-current process $\nu +$${}^{208}\mathrm{Pb}$ $\to e^{-}+$${}^{208}\mathrm{Bi}$${}^{*}$, are presented. The nuclear structure calculations were performed by considering bound, resonant, and continuum states in the single-particle basis used to construct correlated proton-particle neutron-hole configurations. The observed features of the spectrum of ${}^{208}\mathrm{Bi}$ were reproduced, as accurately as possible, by diagonalizing a phenomenological multipole-multipole interaction. Calculations of the cross section, for values of $q⩽200$ MeV, were performed, and the dependence of the results on the choice of the residual proton-neutron interaction was investigated. It is found that the inclusion of resonant states in the calculation of the nuclear wave functions increases the neutrino-nucleus cross section and that the contribution of the continuum is negligible.

It is shown that in the Bohr Hamiltonian the use of three different mass coefficients for the two vibrational and the rotational modes is very important for the correct description of the properties of the well deformed axially symmetric nuclei. Four parameters per nucleus are needed to describe the relative values of energies and $B(E2)$'s.

Cross-section angular distributions of 38 ($p$, $t$) transitions to final states of ${}^{118}\mathrm{Sn}$ up to an excitation energy of 3.597 MeV have been measured in a high-resolution experiment at an incident proton energy of 21 MeV. A distorted-wave Born approximation (DWBA) analysis of the 38 experimental differential cross sections, carried out by using conventional Woods-Saxon potentials, allowed us either 18 confirmations of previous spin and parity values or new assignments of spin and parity to 14 states of ${}^{118}\mathrm{Sn}$. A shell-model calculation has been performed by using a realistic two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential. The doubly-magic nucleus ${}^{132}\mathrm{Sn}$ is assumed as a closed core, with 14 valence neutron holes occupying the five levels of the 50–82 shell. Within this model space the calculations are performed by employing the seniority scheme including states with seniority up to 4. The energy spectrum of ${}^{118}\mathrm{Sn}$ has been calculated and compared with the experimental one. The theoretical two-neutron spectroscopic amplitudes are used in the microscopic DWBA calculations of some cross-section angular distributions.

A new hybrid surrogate ratio approach has been employed to determine neutron-induced fission cross sections of ${}^{233}\mathrm{Pa}$ in the energy range of 11.5 to 16.5 MeV for the first time. The fission probability of ${}^{234}\mathrm{Pa}$ and ${}^{236}\mathrm{U}$ compound nuclei produced in ${}^{232}\mathrm{Th}$(${}^6\mathrm{Li}$, $\alpha$)${}^{234}\mathrm{Pa}$ and ${}^{232}\mathrm{Th}$(${}^6\mathrm{Li}$, $d$)${}^{236}\mathrm{U}$ transfer reaction channels has been measured at $E_{\mathrm{lab}}=38.0$ MeV in the excitation energy range of 17.0 to 22.0 MeV within the framework of the absolute surrogate method. The ${}^{233}\mathrm{Pa}$$(n,f)$ cross sections are then deduced from the measured fission decay probability ratios of ${}^{234}\mathrm{Pa}$ and ${}^{236}\mathrm{U}$ compound nuclei using the surrogate ratio method. The ${}^{233}\mathrm{Pa}$$(n,f)$ cross section data from the present experiment along with the data from the literature, covering the neutron energy range of 1.0 to 16.5 MeV have been compared with the predictions of statistical model code EMPIRE-2.19. While the present data are consistent with the model predictions, there is a discrepancy between the earlier experimental data and EMPIRE-2.19 predictions in the neutron energy range of 7.0 to 10.0 MeV.

We review the properties of nuclear halos and nuclear skins in drip line nuclei in the framework of the spherical Hartree-Fock-Bogoliubov (HFB) theory with continuum effects and projection on a good particle number with the Gogny force. We first establish the position of the unprojected HFB drip lines for the two most employed parametrizations of the Gogny force and show that the use of finite-range interactions leads almost always to small-sized halos, even in the least bound nuclei, which is in agreement with most mean-field predictions. We also discuss the size of the neutron skin at the drip line and its relation to neutron asymmetry. The impact of particle-number projection and its conceptual consequences near the drip line are analyzed in detail. In particular, we discuss the role of chemical potential in a projected theory and the criteria required to define the drip line. We show that including particle-number projection can shift the latter, in particular near closed shells. We notice that, as a result, the size of the halo can be increased due to larger pairing correlations. However, combining the most realistic pairing interaction, a proper treatment of the continuum, and particle-number projection does not permit us to reproduce the very large halos observed in very light nuclei.

In the momentum kick model, a near-side jet emerges near the surface, kicks medium partons, loses energy, and fragments into the trigger particle and fragmentation products. The kicked medium partons subsequently materialize as the observed ridge particles, which carry direct information on the magnitude of the momentum kick and the initial parton momentum distribution at the moment of jet–medium-parton collisions. The initial parton momentum distribution extracted from the STAR ridge data for central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV has a thermal-like transverse momentum distribution and a rapidity plateau structure with a relatively flat distribution at mid-rapidity and sharp kinematic boundaries at large rapidities. Such a rapidity plateau structure may arise from particle production in flux tubes, as color charges and anticolor charges separate at high energies. The centrality dependence of the ridge yield and the degree of jet quenching can be consistently described by the momentum kick model.

We have studied the production of the projectile-like fragments ${}^8\mathrm{Be}$ and ${}^9\mathrm{B}$ produced in interactions of 200 to 400 MeV/nucleon carbon ions with water, using emulsion detectors. In this Brief Report we present the first published production cross section of the projectile-like fragment ${}^9\mathrm{B}$ in the energy region above 100 MeV/nucleon. The measured production cross sections of these nuclides were compared to calculations using a semiempirical model. We found that the measured cross sections deviate from the calculated values by a factor up to about six. This information is of importance for benchmarking and improving heavy ion nuclear reaction models.

A self-consistent quasiparticle random-phase approximation (QRPA) model that employs the canonical Hartree-Fock-Bogoliubov (HFB) basis and an energy-density functional with a Skyrme mean-field part and a density-dependent pairing is used to study the monopole collective excitations of spherical even-even nuclei. The influence of the spurious state on the strength function of the isoscalar monopole excitations is clearly assessed. We compare the effect of different kinds of pairing forces (volume pairing, surface pairing, and mixed pairing) on the monopole excitation strength function. The energy of the isoscalar giant monopole resonance (ISGMR), which is related to the nuclear incompressibility $K_{\infty }$, is calculated for tin isotopes and the results are discussed.

Using recently derived relations between spin-dependent nuclear and nucleon $g_1$ and $g_2$ structure functions at finite $Q^2$, we study nuclear effects in ${}^3\mathrm{He}$ in the nucleon resonance and deep inelastic regions. Comparing the finite-$Q^2$ results with the standard convolution formulas obtained in the large-$Q^2$ limit, we find significant broadening of the effective nucleon momentum distribution functions, leading to additional suppression of the nuclear $g_1$ and $g_2$ structure functions around the resonance peaks.

The low-lying structure of ${}_{40}^{94}\mathrm{Zr}$ was studied with the ($n,n^{\text{'}}\gamma$) reaction, and a level scheme was established based on excitation function and $\gamma \gamma$ coincidence measurements. Branching ratios, multipole mixing ratios, and spin assignments were determined from angular distribution measurements. Lifetimes of levels up to 3.4 MeV were measured by the Doppler-shift attenuation method, and for many transitions the reduced transition probabilities were determined. In addition to the anomalous $2_2^{+}$ state, which has a larger $B(E2;2_2^{+}\to 0_1^{+})$ value than the $B(E2;2_1^{+}\to 0_1^{+})$, the experimental results revealed interesting and unusual properties of the low-lying states in ${}^{94}\mathrm{Zr}$. In a simple interpretation, the excited states are classified in two distinct categories, i.e., those populating the $2_2^{+}$ state and those decaying to the $2_1^{+}$ state.

Energy distributions of emitted neutrons were measured for 110 MeV ${}^{19}\mathrm{F}$ ions incident on a thick ${}^{27}\mathrm{Al}$ target. Measurements were done at $0^{°}$, ${30}^{°}$, ${60}^{°}$, ${90}^{°}$, and ${120}^{°}$ with respect to the projectile direction employing the time-of-flight technique using a proton recoil scintillation detector. Comparison with calculated results from equilibrium nuclear reaction model codes like PACE-2 and EMPIRE 2.18 using various level-density options was carried out. It is observed that the dynamic level-density approach in EMPIRE 2.18 gives the closest approximation to the measured data. In the Fermi-gas level-density approach the best approximation of the level-density parameter is $a=A/12.0$, where $A$ is the mass number of the composite system. The trend in the angular distribution of emitted neutrons is well reproduced by the projection of the angular momentum on the recoil axis as done in the PACE-2 code.

We consider single gluon production in the dipole model and reproduce the result of Kovchegov and Tuchin for the adjoint (gluonic) dipole structure of the inclusive cross section. We show the validity of the adjoint dipole structure to any order of evolution by deriving and solving the nonlinear evolution for the nondiagonal cross section of a dipole scattering off the target. The form of the solution to this equation restores the dipole interpretation for nondiagonal cross sections that appear in gluon production. Using this formalism, we analyze the single inclusive production cross section in terms of the contributions of different multiplicities, and we derive the Abramovskii-Gribov-Kancheli (AGK) cutting rules for two-Pomeron exchange. The cutting rules, which were found in this formalism, fully reproduce the original AGK rules for the total cross section. However, for the case of gluon production, the AGK rules are violated already for one-gluon emission from the vertex.

Green's function Monte Carlo calculations of magnetic moments and $M1$ transitions including two-body meson-exchange current (MEC) contributions are reported for $A⩽7$ nuclei. The realistic Argonne $v_{18}$ two-nucleon and Illinois-2 three-nucleon potentials are used to generate the nuclear wave functions. The two-body meson-exchange operators are constructed to satisfy the continuity equation with the Argonne $v_{18}$ potential. The MEC contributions increase the $A=3,7$ isovector magnetic moments by $16\%$ and the $A=6,7$ $M1$ transition rates by $17–34\%$, bringing them into very good agreement with the experimental data.