Background: Obtaining reaction rates for nuclear astrophysics applications is often limited by the availability of radioactive beams. Indirect techniques to establish reaction rates often rely heavily on the properties of excited states inferred from mirror symmetry arguments. Mirror energy differences can depend sensitively on nuclear structure effects.

Purpose: The present work sets out to establish a detailed comparison of mirror symmetry in the $A=23$, $T=1/2$ mirror nuclei ${}^{23}$Na and ${}^{23}$Mg both to high spin, and high excitation energy, including beyond the proton threshold. These data can be used to benchmark state-of-the-art shell-model calculations of these nuclei.

Methods: Excited states in ${}^{23}$Na and ${}^{23}$Mg were populated using the ${}^{12}$C(${}^{12}$C,$p$) and ${}^{12}$C(${}^{12}$C,$n$) reactions at beam energies of 16 and 22 MeV, and their resulting $\gamma$ decay was measured with Gammasphere.

Results: Level schemes for ${}^{23}$Na and ${}^{23}$Mg have been considerably extended; highly excited structures have been found in ${}^{23}$Na, as well as their counterparts in ${}^{23}$Mg for previously known rotational structures in ${}^{23}$Na. Mirror symmetry has been investigated up to an excitation energy of 8 MeV and spin-parity of 13/2${}^{+}$. Excited states in the region above the proton threshold have been studied in both nuclei.

Conclusions: A detailed exploration of mirror symmetry has been performed which heavily constrains expectations as to how mirror energy differences should evolve for different structures. Agreement with shell-model calculations provides confidence in using such estimations where real data are absent.

An analysis of six different sets of experimental data indicates that infinite, neutron-proton symmetric, neutral nuclear matter has a critical temperature of $T_c=17.9\pm 0.4$ MeV, a critical density of ${\rho }_c=0.06\pm 0.01$ nucleons/fm${}^3$, and a critical pressure of $p_c=0.31\pm 0.07$ MeV/fm${}^3$. These values have been obtained by analyzing data from six different reactions studied in three experiments: two “compound nuclear” reactions, ${}^{58}\mathrm{Ni}{+}^{12}\mathrm{C}{\to }^{70}$Se and ${}^{64}\mathrm{Ni}{+}^{12}\mathrm{C}{\to }^{76}$Se (both performed at the LBNL 88-in. cyclotron); and four “multifragmentation” reactions, 1 GeV/$c$ $\pi {+}^{197}$Au (performed by the Indiana Silicon Sphere Collaboration), 1 GeV/nucleon ${}^{197}\mathrm{Au}{+}^{12}$C, 1 GeV/nucleon ${}^{139}\mathrm{La}{+}^{12}$C, and 1 GeV/nucleon ${}^{84}\mathrm{Kr}{+}^{12}$C (all performed by the Equation of State Collaboration). The charge yields of all reactions as a function of the excitation energy were fit with a version of Fisher's droplet model modified to account for the dual components of the fluid (i.e., protons and neutrons), Coulomb effects, finite-size effects, and angular momentum arising from the nuclear collisions.

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.

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.

We study the equation of state and composition of hypernuclear matter within a relativistic density functional theory with density-dependent couplings. The parameter space of hyperon–scalar-meson couplings is explored by allowing for mixing and breaking of SU(6) symmetry, while keeping the nucleonic coupling constants fixed. The subset of equations of state, which corresponds to small values of hyperon–scalar-meson couplings, allows for massive $M\le 2.25M_{\odot }$ compact stars; the radii of hypernuclear stars are within the range 12–14 km. We also study the equation of state of hot neutrino-rich and neutrinoless hypernuclear matter and confirm that neutrinos stiffen the equation of state and dramatically change the composition of matter by keeping the fractions of charged leptons nearly independent of the density prior to the onset of neutrino transparency. We provide piecewise polytropic fits to six representative equations of state of hypernuclear matter, which are suitable for applications in numerical astrophysics.

The controlled transfer of nuclear state population using two x-ray laser pulses is investigated theoretically. The laser pulses drive two nuclear transitions in a nuclear three-level system facilitating coherent population transfer via the quantum optics technique of stimulated Raman adiabatic passage. To overcome present limitations of the x-ray laser frequency, we envisage accelerated nuclei interacting with two copropagating or crossed x-ray laser pulses in a three-beam setup. We present a systematic study of this setup providing both pulse temporal sequence and laser pulse intensity for optimized control of the nuclear state population. The tolerance for geometrical parameters such as laser beam divergence of the three-beam setup as well as for the velocity spread of the nuclear beam are studied and a two-photon resonance condition to account for experimental uncertainties is deduced. This additional condition gives a less strict requirement for the experimental implementation of the three-beam setup. Present experimental state of the art and future prospects are discussed.

Excited states of ${}^{76}$Ge have been populated in above-barrier Coulomb excitation and inelastic scattering of a 530-MeV ${}^{76}$Ge beam on a ${}^{238}$U target and studied using in-beam $\gamma$-ray spectroscopy with the Gammasphere array. The $\gamma$ band was extended considerably and one new band was identified. Comparisons of the $\gamma$ band with collective- and shell-model calculations suggest that ${}^{76}$Ge may be a rare example of a nucleus exhibiting rigid triaxial deformation in the low-lying states.

Background: The calculation of the hyperon binding energy in hypernuclei is crucial to understanding the interaction between hyperons and nucleons.

Purpose: We assess the relative importance of two- and three-body hyperon-nucleon force by studying the effect of the hyperon-nucleon-nucleon interaction in closed shell $\Lambda$ hypernuclei from A = 5 to 91.

Methods: The $\Lambda$ binding energy has been calculated using the auxiliary field diffusion Monte Carlo method for the first time, to study light and heavy hypernuclei within the same model.

Results: Our results show that including a three-body component in the hyperon-nucleon interaction leads to a saturation of the $\Lambda$ binding energy remarkably close to the experimental data. In contrast, the two-body force alone gives an unphysical limit for the binding energy.

Conclusions: The repulsive contribution of the three-body hyperon-nucleon-nucleon force is essential to reproduce, even qualitatively, the binding energy of hypernuclei in the mass range considered.

We find the height of the third fission barrier $B_{\mathrm{III}}$ and energy of the third minimum $E_{\mathrm{III}}$ in ${}^{232}$Th using the macroscopic-microscopic model, which is very well tested in this region of nuclei. For the first time it is done on an eight-dimensional deformation hypercube. The dipole distortion is included among the shape variables to ensure that no important shapes are missed. The saddle point is found on a lattice containing more than $50\times {10}^6$ points by the immersion water flow method. The shallow third minimum, $B_{\mathrm{III}}-E_{\mathrm{III}}\approx 0.36$ MeV, agrees with the experimental data of Blons et al. [Phys. Rev. Lett. 35, 1749 (1975)]. This is in sharp contrast with the status of the third minima in ${}^{232-236}$U: their experimental depth of $\ge 3$ MeV contradicts all realistic theoretical predictions. We emphasize the importance of repeating the experiment on ${}^{232}$Th, by a technique similar to that used in the uranium nuclei, for settling the puzzle of the third minima in actinides.

We introduce a unified approach to nuclear bound and continuum states based on the coupling of the no-core shell model (NCSM), a bound-state technique, with the no-core shell model/resonating group method (NCSM/RGM), a nuclear scattering technique. This new ab initio method, no-core shell model with continuum (NCSMC), leads to convergence properties superior to either NCSM or NCSM/RGM while providing a balanced approach to different classes of states. In the NCSMC, the ansatz for the many-nucleon wave function includes (i) a square-integrable $A$-nucleon component expanded in a complete harmonic oscillator basis and (ii) a binary-cluster component with asymptotic boundary conditions that can properly describe weakly bound states, resonances, and scattering. The Schrödinger equation is transformed into a system of coupled-channel integral-differential equations that we solve using a modified microscopic $R$-matrix formalism within a Lagrange mesh basis. We demonstrate the usefulness of the approach by investigating the unbound ${}^7$He nucleus.

Quantum Monte Carlo calculations of electromagnetic moments and transitions are reported for $A\le 9$ nuclei. The realistic Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon potentials are used to generate the nuclear wave functions. Contributions of two-body meson-exchange current (MEC) operators are included for magnetic moments and $M1$ transitions. The MEC operators have been derived in both a standard nuclear physics approach and a chiral effective field theory formulation with pions and nucleons including up to one-loop corrections. The two-body MEC contributions provide significant corrections and lead to very good agreement with experiment. Their effect is particularly pronounced in the $A=9$, $T=3/2$ systems, in which they provide up to $\sim 20\%$ ($\sim 40\%$) of the total predicted value for the ${}^9$Li (${}^9$C) magnetic moment.

We have performed shell-model calculations for the two one-valence-neutron isotones ${}^{135}$Te and ${}^{137}$Xe and the two one-valence-proton isotopes ${}^{135,137}$Sb. The main aim of our study has been to investigate the evolution of single-particle states with increasing nucleon number. To this end, we have focused attention on the spectroscopic factors and the effective single-particle energies. In our calculations, we have employed a realistic low-momentum two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential that has already proved quite successful in describing the spectroscopic properties of nuclei in the ${}^{132}$Sn region. Comparison shows that our results reproduce very well the available experimental data. This gives confidence in the evolution of the single-particle states predicted by the present study.

Problems of production and study of new neutron-enriched heavy nuclei are discussed. Low-energy multinucleon transfer reactions are shown to be quite appropriate for this purpose. Reactions with actinide beams and targets are of special interest for synthesis of new neutron-enriched transfermium nuclei and not-yet-known nuclei with closed neutron shell $N=126$ having the largest impact on the astrophysical r-process. The estimated cross sections for the production of these nuclei look very promising for planning such experiments at currently available accelerators. These experiments, however, are rather expensive and difficult to perform because of low intensities of the massive projectile beams and problems of separating and detecting the heavy reaction products. Thus, realistic predictions of the corresponding cross sections for different projectile-target combinations are definitely required. Some uncertainty still remains in the values of several parameters used for describing the low-energy nuclear dynamics. This uncertainty does not allow one to perform very accurate predictions for the productions of new heavier-than-target (trans-target) nuclei in multinucleon transfer reactions. Most of these parameters (nucleon transfer rate, nuclear viscosity, and fission barriers) are fundamental characteristics of low-energy nuclear dynamics. Determination of the values of these parameters (as well as their temperature dependence) is of significance in its own right. The available experimental data on the production of heavy nuclei in low-energy multinucleon transfer reactions are still insufficient and fragmentary. Several new experiments are proposed, these include those in which the role of shell effects in reaction dynamics can be better clarified.

Our earlier Faddeev three-body study in the $K^{-}$-deuteron scattering length, $A_{K^{-}d}$, is revisited here in light of the recent developments on two fronts: (i) the improved chiral unitary approach to the theoretical description of the coupled $\overline{K}N$ related channels at low energies, and (ii) the new and improved measurement from SIDDHARTA Collaboration of the strong interaction energy shift and width in the lowest $K^{-}$-hydrogen atomic level. Those two, in combination, have allowed us to produce a reliable two-body input to the three-body calculation. All available low-energy $K^{-}p$ observables are well reproduced and predictions for the $\overline{K}N$ scattering lengths and amplitudes, ${\left(\pi \Sigma \right)}^{\circ }$ invariant-mass spectra, as well as for $A_{K^{-}d}$ are put forward and compared with results from other sources. The findings of the present work are expected to be useful in interpreting the forthcoming data from CLAS, HADES, LEPS, and SIDDHARTA Collaborations.

We present the first ab initio coupled-cluster calculations of medium-mass nuclei with explicit chiral three-nucleon (3$N$) interactions. Using a spherical formulation of coupled cluster with singles and doubles excitations including explicit 3$N$ contributions, we study ground states of ${}^{16,24}\text{O}$, ${}^{40,48}\text{Ca,}$ and ${}^{56}\text{Ni}$. We employ chiral nucleon-nucleon ($\mathit{\text{NN}}$) plus 3$N$ interactions softened through a similarity renormalization group (SRG) transformation at the three-body level. We investigate the impact of all truncations and quantify the resulting uncertainties—this includes the contributions from triple excitations, the truncation of the set of three-body matrix elements, and the omission of SRG-induced four-body interactions. Furthermore, we assess the quality of a normal-ordering approximation of the 3$N$ interaction beyond light nuclei. Our study points towards the predictive power of chiral Hamiltonians in the medium-mass regime.

The ground state of neutron-rich unbound ${}^{13}$Li was observed for the first time in a one-proton removal reaction from ${}^{14}$Be at a beam energy of 53.6 MeV/u. The ${}^{13}$Li ground state was reconstructed from ${}^{11}$Li and two neutrons giving a resonance energy of 120${}_{-80}^{+60}$ keV. All events involving single- and double-neutron interactions in the Modular Neutron Array (MoNA) were analyzed, simulated, and fitted self-consistently. The three-body (${}^{11}\text{Li}+n+n$) correlations within Jacobi coordinates showed strong dineutron characteristics. The decay energy spectrum of the intermediate ${}^{12}$Li system (${}^{11}\text{Li}+n$) was described with an $s$-wave scattering length of greater than $-4$ fm, which is a smaller absolute value than reported in a previous measurement.

We present a microscopic calculation of the complete quasiparticle interaction, including central as well as noncentral components, in neutron matter from high-precision two- and three-body forces derived within the framework of chiral effective-field theory. The contributions from two-nucleon forces are computed in many-body perturbation theory to first and second order (without any simplifying approximations). In addition we include the leading-order one-loop diagrams from the next-to next-to leading order (N${}^2$LO) chiral three-nucleon force, which contribute to all Fermi liquid parameters except those associated with the center-of-mass tensor interaction. The relative-momentum dependence of the quasiparticle interaction is expanded in Legendre polynomials up to $L=2$. Second-order Pauli blocking and medium polarization effects act coherently in specific channels; namely, for the Landau parameters $f_1$, $h_0$, and $g_0$, which results in a dramatic increase in the quasiparticle effective mass as well as a decrease in both the effective tensor force and the neutron matter spin susceptibility. For densities greater than about half the nuclear matter saturation density ${\rho }_0$, the contributions to the Fermi liquid parameters from the leading-order chiral three-nucleon force scale in all cases approximately linearly with the nucleon density. The largest effect of the three-nucleon force is to generate a strongly repulsive effective interaction in the isotropic spin-independent channel. We show that the leading-order chiral three-nucleon force leads to an increase in the spin susceptibility of neutron matter, but we observe no evidence for a ferromagnetic spin instability in the vicinity of the saturation density ${\rho }_0$. This work sets the foundation for future studies of neutron matter response to weak and electromagnetic probes with applications to neutron star structure and evolution.

The prompt neutron and $\gamma$ emission from primary fission fragments are calculated for thermal neutron induced fission of ${}^{235}$U and ${}^{239}$Pu and for spontaneous fission of ${}^{252}$Cf using a Monte Carlo Hauser-Feshbach approach for the evaporation of the excited fission fragments. Remaining free model parameters, such as excitation energy sharing and initial spin distribution, are determined by comparison of the neutron emission characteristics with experimental data. Using the obtained parameters the $\gamma$-ray characteristics, e.g., $\gamma$ spectrum, multiplicity distribution, average multiplicity and energy, and multiplicity distribution, are calculated and compared with available experimental data.

This paper details the solar neutrino analysis of the 385.17-day phase-III data set acquired by the Sudbury Neutrino Observatory (SNO). An array of ${}^3$He proportional counters was installed in the heavy-water target to measure precisely the rate of neutrino-deuteron neutral-current interactions. This technique to determine the total active ${}^8$B solar neutrino flux was largely independent of the methods employed in previous phases. The total flux of active neutrinos was measured to be $5.{54}_{-0.31}^{+0.33}{\text{(stat.)}}_{-0.34}^{+0.36}\text{(syst.)}\times {10}^6$ cm${}^{-2}$ s${}^{-1}$, consistent with previous measurements and standard solar models. A global analysis of solar and reactor neutrino mixing parameters yielded the best-fit values of $\Delta m^2=7.{59}_{-0.21}^{+0.19}\times {10}^{-5}{\text{eV}}^2$ and $\theta =34.4_{-1.2}^{+1.3}\text{degrees}$.

The single-neutron properties of $N$ $=$ 51 nuclei have been studied with the ($d$,$p$) and ($\alpha$,${}^3$He) reactions, at beam energies of 15 and 50 MeV respectively, on ${}^{88}$Sr, ${}^{90}$Zr, and ${}^{92}$Mo targets. The light reaction products were momentum analyzed using a conventional magnetic spectrometer. Additionally, the ${}^2{\mathrm{H}(}^{86}\mathrm{Kr},p$) reaction was measured at a beam energy of 10 MeV/u, where outgoing light ions were analyzed using a helical-orbit spectrometer. Absolute cross sections and angular distributions corresponding to the population of different final states in the heavy product were obtained for each reaction. Spectroscopic factors were extracted and centroids of the single-particle strength were deduced. The observations appear consistent with calculations based on an evolution of single-particle structure driven by the nucleon-nucleon forces acting between valence protons and neutrons.