Phase transitions in hot, dense matter in the collapsing cores of massive stars have an important impact on the core-collapse supernova mechanism as they absorb heat, disrupt homology, and so weaken the developing shock. We perform a three-dimensional, finite temperature Skyrme-Hartree-Fock (SHF) study of inhomogeneous nuclear matter to determine the critical density and temperature for the phase transition between the pasta phase and homogeneous matter and its properties. We employ four different parametrizations of the Skyrme nuclear energy-density functional, ${\mathrm{SkM}}^{*}$, SLy4, NRAPR, and SQMC700, which span a range of saturation-density symmetry energy behaviors constrained by a variety of nuclear experimental probes. For each of these interactions we calculate free energy, pressure, entropy, and chemical potentials in the range of particle number densities where the nuclear pasta phases are expected to exist, 0.02–0.$12{\mathrm{fm}}^{-3}$, temperatures 2–8 MeV, and a proton fraction of 0.3. We find unambiguous evidence for a first-order phase transition to uniform matter, unsoftened by the presence of the pasta phases. No conclusive signs of a first-order phase transition between the pasta phases is observed, and it is argued that the thermodynamic quantities vary continuously right up to the first-order phase transition to uniform matter. We compare our results with thermodynamic spinodals calculated using the same Skyrme parametrizations, finding that the effect of short-range Coulomb correlations and quantum shell effects included in our model leads to the pasta phases existing at densities up to 0.$01{\mathrm{fm}}^{-3}$ above the spinodal boundaries, thus increasing the transition density to uniform matter by the same amount. The transition density is otherwise shown to be insensitive to the symmetry energy at saturation density within the range constrained by the concordance of a variety of experimental constraints, and can be taken to be a well determined quantity.

We present lattice Monte Carlo calculations of fermion-dimer scattering in the limit of zero-range interactions using the adiabatic projection method. The adiabatic projection method uses a set of initial cluster states and Euclidean time projection to give a systematically improvable description of the low-lying scattering cluster states in a finite volume. We use Lüscher's finite-volume relations to determine the $s$-wave, $p$-wave, and $d$-wave phase shifts. For comparison, we also compute exact lattice results using Lanczos iteration and continuum results using the Skorniakov-Ter-Martirosian equation. For our Monte Carlo calculations we use a new lattice algorithm called impurity lattice Monte Carlo. This algorithm can be viewed as a hybrid technique which incorporates elements of both worldline and auxiliary-field Monte Carlo simulations.

The ground state (g.s.) and low-lying continuum states of ${}^6\mathrm{He}$ are found within a shell model scheme, in a basis of two-particle states built out of continuum $p$ states of the unbound ${}^5\mathrm{He}$ nucleus, using a simple pairing contact-delta interaction. This accounts for the Borromean character of the bound ground state, revealing its composition. We investigate the quadrupole response of the system and we put our calculations into perspective with the latest experimental results. The calculated quadrupole strength distribution reproduces the narrow $2^{+}$ resonance, while a second wider peak is found at about 3.9 MeV above the g.s. energy.

We propose a novel method for low-lying states of hypernuclei based on the particle-rotor model, in which hypernuclear states are constructed by coupling the hyperon to low-lying states of the core nucleus. In contrast to the conventional particle-rotor model, we employ a microscopic approach for the core states; that is, the generator coordinate method (GCM) with the particle number and angular momentum projections. We apply this microscopic particle-rotor model to ${}_{\Lambda }^9\mathrm{Be}$ as an example employing a point-coupling version of the relativistic mean-field Lagrangian. A reasonable agreement with the experimental data for the low-spin spectrum is achieved using the $\Lambda N$ coupling strengths determined to reproduce the binding energy of the $\Lambda$ particle.

In this paper we investigate the possible $I^4$ dependence [$I=(N-Z)/A$] in “experimental” symmetry energy extracted from nuclear masses. Our results show that the inclusion of the $I^4$ term in mass formulas leads to sizable changes for symmetry energy coefficients of the $I^2$ terms.

In this paper we show that double differences of separation energies for four neighboring nuclei cancel out with remarkable accuracy. The well-known Garvey-Kelson relations (GKs) and their generalizations are reduced to special cases of our reconstituted relations. Some of the new relations given in this paper are found to be in competitive or even better agreement with experimental data than the GKs.

Coupling two $sd$-shell neutrons to a pure $p$-shell ${}^{12}\mathrm{Be}$ ground state (g.s.), rather than to the physical g.s., removes difficulties in applying a previous simple model to ${}^{14}\mathrm{Be}$. I have calculated the g.s. wave function in this simple model, and have estimated the $2s_{1/2}$ single-particle energy.

Based on reaction theory, we suggest a useful method for extracting total and partial reaction and capture (complete fusion) cross sections from the experimental elastic and quasi-elastic backscattering excitation functions taken at a single angle. We also propose a method to predict the differential reaction cross section from the observed elastic-scattering angular distribution.

The “compositeness” or “elementarity” is investigated for $s$-wave composite states dynamically generated by energy-dependent and independent interactions. The bare mass of the corresponding fictitious elementary particle in an equivalent Yukawa model is shown to be infinite, indicating that the wave function renormalization constant $Z$ is equal to zero. The idea can be equally applied to both resonant and bound states. In a special case of zero-energy bound states, the condition $Z=0$ does not necessarily mean that the elementary particle has the infinite bare mass. We also emphasize arbitrariness in the “elementarity” leading to multiple interpretations of a physical state, which can be either a pure composite state with $Z=0$ or an elementary particle with $Z\ne 0$. The arbitrariness is unavoidable because the renormalization constant $Z$ is not a physical observable.

The $(n,\gamma )$ cross sections of the most neutron-rich stable isotopes of Yb, Os, Pt, and Hg have been determined in a series of activation measurements at the Karlsruhe $3.7$ MV Van de Graaff accelerator, using the quasistellar neutron spectrum for $kT=25$ keV that can be produced with the ${}^7\mathrm{Li}(p,n){}^7\mathrm{Be}$ reaction. In this way, Maxwellian averaged cross sections could be directly obtained with only minor corrections. After irradiation the induced activities were counted with a HPGe detector via the strongest $\gamma$-ray lines. The stellar neutron capture cross sections of ${}^{174,176}\mathrm{Yb}$, ${}^{190,192}\mathrm{Os}$, ${}^{196,198}\mathrm{Pt}$, and ${}^{202,204}\mathrm{Hg}$, extrapolated to $kT=30$ keV, were found to be $157\pm 6$ mb, $114\pm 8$ mb, $278\pm 11$ mb, $160\pm 7$ mb, $171\pm 19$ mb, $94\pm 4$ mb, $62\pm 2$ mb, and $32\pm 15$ mb, respectively. In the case of ${}^{196}\mathrm{Pt}$ the partial cross section to the isomeric state at 399.5 keV could be determined as well. With these results the cross section data for long isotopic chains could be completed for a discussion of the predictive power of statistical model calculations towards the neutron-rich and proton-rich sides of the stability valley.

A smooth onset of collectivity in ${}^{88,92,94,96}\mathrm{Kr}$ has been determined from reported $B(E2;2_1^{+}\to 0_1^{+})$ and $E\left(2_1^{+}\right)$ values. This is in contrast to the sudden onset in even-even Zr, Mo, and Sr isotopes. Our objective was to complete the systematics by determining the $B(E2;2_1^{+}\to 0_1^{+})$ value in ${}^{90}\mathrm{Kr}$, which was produced by cold-neutron-induced fission of ${}^{235}\mathrm{U}$. The lifetime of the $2_1^{+}$ state in ${}^{90}\mathrm{Kr}$ was measured via the electronic $\gamma -\gamma$ timing technique using the EXILL and FATIMA spectrometers. Based on the measured mean lifetime of $\tau$ = 15(10) ps, the $B(E2;2_1^{+}\to 0_1^{+})$ value of $13{}_{-5}^{+26}$ W.u. in ${}^{90}\mathrm{Kr}$ is determined for the first time and the smooth onset of deformation in the even-even Kr isotopes beyond neutron number $N=50$ is confirmed.

A new shell-model calculation for ${}^{17}\mathrm{C}$ provides spectroscopic factors for use in a computation of mirror energy differences between ${}^{17}\mathrm{C}$ and ${}^{17}\mathrm{Na}$. Results are compared with previous predictions.

In the model calculations of heavy element nucleosynthesis processes the nuclear reaction rates are taken from statistical model calculations which utilize various nuclear input parameters. It is found that in the case of reactions involving $\alpha$ particles the calculations bear a high uncertainty owing to the largely unknown low-energy $\alpha$-nucleus optical potential. Experiments are typically restricted to higher energies and therefore no direct astrophysical consequences can be drawn. In the present work a ($p,\alpha$) reaction is used for the first time to study the $\alpha$-nucleus optical potential. The measured ${}^{64}\mathrm{Zn}(p,\alpha ){}^{61}\mathrm{Cu}$ cross section is uniquely sensitive to the $\alpha$-nucleus potential and the measurement covers the whole astrophysically relevant energy range. By the comparison to model calculations, direct evidence is provided for the incorrectness of global optical potentials used in astrophysical models.

The Gamow-Teller (GT) strength distributions and isobaric analog resonance (IAR) states of several $N=Z+2$ nuclei with mass number $A=42–58$ are studied by using a self-consistent Skyrme Hartree-Fock-Bogoliubov method plus quasiparticle random phase approximation (HFB+QRPA) formalism. The isoscalar spin-triplet pairing interaction is included in QRPA on top of the isovector spin-singlet one in the HFB method. It is found that the isoscalar pairing correlations mix largely the $(\nu j_{>}\to \pi j_{<})$ configurations into the low-energy states, and this mixing plays an important role in the formation and in the collectivity of these low-energy states. Furthermore, the observed excitation energy of the low-energy GT state with respect to the IAR can be well reproduced when the strength of isoscalar pairing is about $1.0–1.05$ times that of the isovector pairing, irrespective of the adopted Skyrme interactions. In $N=Z+2$ nuclei in the middle of the $pf$-shell, a mutual cooperative effect of isoscalar pairing and tensor interaction is found; namely, the tensor force reduces the spin-orbit splittings and enhances the effect of the isoscalar pairing.

We use a modified DKLMT model (M-DKLMT) to study the cold nuclear matter (CNM) effects on the color singlet $J/\psi$ production in $d\text{Au}$ collisions at RHIC. The cold nuclear effect of dipole-nucleus interactions has been investigated by introducing a nuclear geometric effect function $f\left(\xi \right)$ to study the nuclear geometry distribution effect in relativistic heavy-ion collisions. The dependencies of nuclear modification factors ($R_{dA}$) on rapidity and centrality are studied and compared to experimental data. It is found that the M-DKLMT model can well describe the experimental results at both forward- and midrapidity regions in $d\text{Au}$ collisions at RHIC.

There is now a large and increasing body of experimental data and theoretical analyses for reactions that remove a single nucleon from an intermediate-energy beam of neutron- or proton-rich nuclei. In each such measurement, one obtains the inclusive cross section for the population of all bound final states of the mass $A-1$ reaction residue. These data, from different regions of the nuclear chart, and that involve weakly and strongly bound nucleons, are compared with theoretical expectations. These calculations include an approximate treatment of the reaction dynamics and shell-model descriptions of the projectile initial state, the bound final states of the residues, and the single-particle strengths computed from their overlap functions. The results are discussed in the light of recent data, more exclusive tests of the eikonal dynamical description, and calculations that take input from more microscopic nuclear structure models.

Two-photon-exchange (TPE) contributions to elastic electron-proton scattering in the forward regime in leading logarithmic $\sim tln\left|t\right|$ approximation in the momentum transfer $t$ are considered. The imaginary part of the TPE amplitude in the forward kinematics is related to the total photoabsorption cross section. The real part of the TPE amplitude is obtained from an unsubtracted fixed-$t$ dispersion relation. This allows a clean prediction of the real part of the TPE amplitude at forward angles with the leading term $\sim tln\left|t\right|$. Numerical estimates are comparable with or exceed the experimental precision in extracting the charge radius from the experimental data.

In this paper the nucleon-pair approximation is studied for two typical cases of $N=Z$ nuclei, by using both schematic and effective interactions. The first case is given by four nucleons in a single-$j$ shell, for which we study the relevance of the seniority scheme, the spin-aligned isoscalar pair approximation, and the pair approximation of isoscalar pairs with spin 1, under different interactions. The nonorthogonality between wave functions with the lowest seniority quantum number and those of the spin-aligned pair approximation are studied with examples. In the second case we study low-lying states of two realistic nuclei, ${}^{20}\mathrm{Ne}$ and ${}^{24}\mathrm{Mg}$. In this case we find that, interestingly, the ground band states of these two nuclei are well described by both isovector and isoscalar pair approximations.

The methods of Bayesian statistics are used to extract the value of the proton radius from the elastic $ep$ scattering data in a model-independent way. To achieve that goal a large number of parametrizations (equivalent to neural network schemes) are considered and ranked by their conditional probability $P\left(\mathrm{parametrization}\right|\mathrm{data})$ instead of using the minimal error criterion. As a result the most probable proton radii values $(r_E^p=0.899\pm 0.003$ fm, $r_M^p=0.879\pm 0.007$ fm) are obtained and systematic error due to freedom in the choice of parametrization is estimated. Correcting the data for the two-photon-exchange effect leads to smaller differences between the extracted values of $r_E^p$ and $r_M^p$. The results disagree with recent muonic atom measurements.