We investigate the structure of neutron star crusts, including the crust-core boundary, based on new Skyrme mean field models constrained by the bulk-matter equation of state from chiral effective field theory and the ground-state energies of doubly-magic nuclei. Nuclear pasta phases are studied using both the liquid drop model as well as the Thomas-Fermi approximation. We compare the energy per nucleon for each geometry (spherical nuclei, cylindrical nuclei, nuclear slabs, cylindrical holes, and spherical holes) to obtain the ground state phase as a function of density. We find that the size of the Wigner-Seitz cell depends strongly on the model parameters, especially the coefficients of the density gradient interaction terms. We employ also the thermodynamic instability method to check the validity of the numerical solutions based on energy comparisons.

Background: The path towards the production of $r$-process seed nuclei follows a course where the neutron rich light and medium mass nuclei play a crucial role. The neutron capture rates for these exotic nuclei could dominate over their $\alpha$-capture rates, thereby enhancing their abundances at or near the drip line. Sodium isotopes especially should have a strong neutron capture flow to gain abundance at the drip line. In this context, study of ${}^{33}\mathrm{Na}(n,\gamma ){}^{34}\mathrm{Na}$ and ${}^{33}\mathrm{Na}(\alpha ,n){}^{36}\mathrm{Al}$ reactions becomes indispensable.

Purpose: In this paper, we calculate the radiative neutron capture cross section for the ${}^{33}\mathrm{Na}(n,\gamma ){}^{34}\mathrm{Na}$ reaction involving deformation effects. Subsequently, the rate for this reaction is found and compared with that of the $\alpha$-capture for the ${}^{33}\mathrm{Na}(\alpha ,n){}^{36}\mathrm{Al}$ reaction to determine the possible path flow for the abundances of sodium isotopes.

Method: We use the entirely quantum mechanical theory of finite-range distorted-wave Born approximation upgraded to incorporate deformation effects, and calculate the Coulomb dissociation of ${}^{34}\mathrm{Na}$ as it undergoes elastic breakup on ${}^{208}\mathrm{Pb}$ when directed at a beam energy of 100 MeV/u. Using the principle of detailed balance to study the reverse photodisintegration reaction, we find the radiative neutron capture cross section with variation in one-neutron binding energy and quadrupole deformation of ${}^{34}\mathrm{Na}$. The rate of this ${}^{33}\mathrm{Na}(n,\gamma ){}^{34}\mathrm{Na}$ reaction is then compared with that of the $\alpha$-capture by ${}^{33}\mathrm{Na}$ deduced from the Hauser-Feshbach theory.

Results: The nonresonant one-neutron radiative capture cross section for ${}^{33}\mathrm{Na}(n,\gamma ){}^{34}\mathrm{Na}$ is calculated and is found to increase with increasing deformation of ${}^{34}\mathrm{Na}$. An analytic scrutiny of the capture cross section with neutron separation energy as a parameter is also done at different energy ranges. The calculated reaction rate is compared with the rate of the ${}^{33}\mathrm{Na}(\alpha ,n){}^{36}\mathrm{Al}$ reaction, and is found to be significantly higher below a temperature of $T_9=2$.

Conclusion: At the equilibrium temperature of $T_9=0.62$, the rate for the neutron capture had a small but non-negligible dependence on the structural parameters of ${}^{34}\mathrm{Na}$. In addition, this neutron capture rate exceeded that of the $\alpha$-capture reaction by orders of magnitude, indicating that the $\alpha$-process should not break the $(n,\gamma )$ r-process path at the ${}^{33}\mathrm{Na}$ isotope, thus effectively pushing the abundance of sodium isotopes towards the neutron drip line.

The $\beta$ decay of the odd-odd nucleus ${}^{70}\mathrm{Br}$ has been investigated with the BigRIPS and EURICA setups at the Radioactive Ion Beam Factory (RIBF) of the RIKEN Nishina Center. The $T=0\left(J^{\pi }=9^{+}\right)$ and $T=1\left(J^{\pi }=0^{+}\right)$ isomers have both been produced in in-flight fragmentation of ${}^{78}\mathrm{Kr}$ with ratios of 41.6(8)% and 58.4(8)%, respectively. A half-life of $t_{1/2}={2157}_{-49}^{+53}$ ms has been measured for the $J^{\pi }=9^{+}$ isomer from $\gamma$-ray time decay analysis. Based on this result, we provide a new value of the half-life for the $J^{\pi }=0^{+}$ ground state of ${}^{70}\mathrm{Br},t_{1/2}=78.42\pm 0.51$ ms, which is slightly more precise, and in excellent agreement, with the best measurement reported hitherto in the literature. For this decay, we provide the first estimate of the total branching fraction decaying through the $2_1^{+}$ state in the daughter nucleus ${}^{70}\mathrm{Se},R\left(2_1^{+}\right)=1.3\pm 1.1\%$. We also report four new low-intensity $\gamma$-ray transitions at 661, 1103, 1561, and 1749 keV following the $\beta$ decay of the $J^{\pi }=9^{+}$ isomer. Based on their coincidence relationships, we tentatively propose two new excited states at 3945 and 4752 keV in ${}^{70}\mathrm{Se}$ with most probable spins and parities of $J^{\pi }=\left(6^{+}\right)$ and $\left(8^{+}\right)$, respectively. The observed structure is interpreted with the help of shell-model calculations, which predict a complex interplay between oblate and prolate configurations at low excitation energies.

Background: Binding energies and charge radii are fundamental properties of atomic nuclei. When inspecting their particle-number dependence, both quantities exhibit pronounced odd-even staggering. While the odd-even effect in binding energy can be attributed to nucleonic pairing, the origin of staggering in charge radii is less straightforward to ascertain.

Purpose: In this work, we study the odd-even effect in binding energies and charge radii, and systematic behavior of differential radii, to identify the underlying components of the effective nuclear interaction.

Method: We apply nuclear density functional theory using a family of Fayans and Skyrme energy density functionals fitted to similar data sets but using different optimization protocols. We inspect various correlations between differential charge radii, odd-even staggering in energies and radii, and nuclear matter properties. The Fayans functional is assumed to be in the local ${\mathrm{FaNDF}}^0$ form. Detailed analysis is carried out for medium-mass and heavy semimagic nuclei with a particular focus on the Ca chain.

Results: By making the surface and pairing terms dependent on density gradients, the Fayans functional offers the superb simultaneous description of odd-even staggering effects in energies and charge radii. Conversely, when the data on differential radii are added to the pool of fit observables, the coupling constants determining the strengths of the gradient terms of Fayans functional are increased by orders of magnitude. The Skyrme functional optimized in this work with the generalized Fayans pairing term offers results of similar quality. We quantify these findings by performing correlation analysis based on the statistical linear regression technique. The nuclear matter parameters characterizing Fayans and Skyrme functionals optimized to similar data sets are fairly close.

Conclusion: The Fayans paring functional, with its generalized density dependence, significantly improves the description of charge radii in odd and even nuclei. Adding differential charge radii to the set of fit observables in the optimization protocol is helpful for both description of radii and for improving the pairing functional. In particular, the Fayans functional ${\mathrm{FaNDF}}^0$ constrained in this way is capable of explaining charge radii in the even-even Ca isotopes. However, in order to obtain good description of differential radii data in both medium-mass and heavy nuclei, an $A$-dependent scaling of the Fayans pairing functional is still needed. Various extensions of the current model are envisioned that carry out a promise for the global description.

Experimental angular distributions for the ${}^7\mathrm{Li}+{}^{120}\mathrm{Sn}$ elastic and inelastic (projectile and target excitations) scattering, and for the neutron stripping reaction, have been obtained at $E_{\mathrm{LAB}}=20$, 22, 24, and 26 MeV, covering an energy range around the Coulomb barrier $(V_B^{\left(\mathrm{LAB}\right)}\approx 21.4$ MeV). Coupled channel and coupled reaction channel calculations were performed and both describe satisfactorily the experimental data sets. The ${\frac{1}{2}}^{-}$ state ${}^7\mathrm{Li}$ inelastic excitation (using a rotational model), as well as the projectile coupling to the continuum $(\alpha$ plus a tritium particle) play a fundamental role on the proper description of elastic, inelastic, and transfer channels. Couplings to the one-neutron stripping channel do not significantly affect the theoretical elastic scattering angular distributions. The spectroscopic amplitudes of the transfer channel were obtained through a shell model calculation. The theoretical angular distributions for the one-neutron stripping reaction agreed with the experimental data.

Two-particle pseudorapidity correlations are measured in $\sqrt{s_{\mathrm{NN}}}=2.76\mathrm{TeV}\mathrm{Pb}+\mathrm{Pb}$, $\sqrt{s_{\mathrm{NN}}}=5.02\mathrm{TeV}p$+Pb, and $\sqrt{s}=13\mathrm{TeV}pp$ collisions at the Large Hadron Collider (LHC), with total integrated luminosities of approximately $7\mu {\mathrm{b}}^{-1}$, 28 ${\mathrm{nb}}^{-1}$, and 65 ${\mathrm{nb}}^{-1}$, respectively. The correlation function $C_{\mathrm{N}}({\eta }_1,{\eta }_2)$ is measured as a function of event multiplicity using charged particles in the pseudorapidity range $\left|\eta \right|<2.4$. The correlation function contains a significant short-range component, which is estimated and subtracted. After removal of the short-range component, the shape of the correlation function is described approximately by $1+{\langle a_1^2\rangle }^{1/2}{\eta }_1{\eta }_2$ in all collision systems over the full multiplicity range. The values of $\langle a_1^2\rangle {}^{1/2}$ are consistent for the opposite-charge pairs and same-charge pairs, and for the three collision systems at similar multiplicity. The values of $\langle a_1^2\rangle {}^{1/2}$ and the magnitude of the short-range component both follow a power-law dependence on the event multiplicity. The short-range component in $p$ + Pb collisions, after symmetrizing the proton and lead directions, is found to be smaller at a given $\eta$ than in $pp$ collisions with comparable multiplicity.

Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes of the matrices that need to be solved. Various approximation schemes have been invoked, for example by truncating the spaces, imposing seniority limits, or appealing to various symmetry schemes such as pseudo-SU(3). This paper proposes a new symmetry scheme also based on SU(3). This proxy-SU(3) can be applied to well-deformed nuclei, is simple to use, and can yield analytic predictions.

Purpose: To present the new scheme and its microscopic motivation, and to test it using a Nilsson model calculation with the original shell model orbits and with the new proxy set.

Method: We invoke an approximate, analytic, treatment of the Nilsson model, that allows the above vetting and yet is also transparent in understanding the approximations involved in the new proxy-SU(3).

Results: It is found that the new scheme yields a Nilsson diagram for well-deformed nuclei that is very close to the original Nilsson diagram. The specific levels of approximation in the new scheme are also shown, for each major shell.

Conclusions: The new proxy-SU(3) scheme is a good approximation to the full set of orbits in a major shell. Being able to replace a complex shell model calculation with a symmetry-based description now opens up the possibility to predict many properties of nuclei analytically and often in a parameter-free way. The new scheme works best for heavier nuclei, precisely where full microscopic calculations are most challenged. Some cases in which the new scheme can be used, often analytically, to make specific predictions, are shown in a subsequent paper.

Using a new approximate analytic parameter-free proxy-SU(3) scheme, we make simple predictions of shape observables for deformed nuclei, namely $\gamma$ and $\beta$ deformation variables, the global feature of prolate dominance, and the locus of the prolate-oblate shape transition. The predictions are compared with empirical results.

In the present work, the critical temperature, critical pressure, and critical density, known as the critical parameters related to the liquid-gas phase transition are calculated for 34 relativistic mean-field models, which were shown to satisfy nuclear matter constraints in a comprehensive study involving 263 models. The compressibility factor was calculated and all 34 models present values lower than the one obtained with the van der Waals equation of state. The critical temperatures were compared with experimental data and just two classes of models can reach values close to them. A correlation between the critical parameters and the incompressibility was obtained.

We derive formulas for the efficiency correction of cumulants with many efficiency bins. The derivation of the formulas is simpler than the previously suggested method, but the numerical cost is drastically reduced from the naïve method. From analytical and numerical analyses in simple toy models, we show that use of the averaged efficiency in the efficiency correction might cause large deviations in some cases and should not be used, especially for high order cumulants. These analyses show the importance of carrying out the efficiency correction without taking the average.

Background: There have been measurements on roughly 230 nuclei that are $\beta$-delayed neutron emitters. They range from ${}^8\mathrm{He}$ up to ${}^{150}\mathrm{La}$. Apart from ${}^{210}\mathrm{Tl}$, with a branching ratio of only 0.007%, no other neutron emitter has been measured beyond $A=150$. Therefore, new data are needed, particularly in the region of heavy nuclei around $N=126$, in order to guide theoretical models and help understand the formation of the third $r$-process peak at $A\sim 195$.

Purpose: To measure both $\beta$-decay half-lives and neutron branching ratios of several neutron-rich Au, Hg, Tl, Pb, and Bi isotopes beyond $N=126$.

Method: Ions of interest were produced by fragmentation of a ${}^{238}\mathrm{U}$ beam, selected and identified via the GSI-FRS fragment separator. A stack of segmented silicon detectors (SIMBA) was used to measure ion implants and $\beta$ decays. An array of 30 ${}^3\mathrm{He}$ tubes embedded in a polyethylene matrix (BELEN) was used to detect neutrons with high efficiency and selectivity. A self-triggered digital system is employed to acquire data and to enable time correlations. The latter were analyzed with an analytical model and results for the half-lives and neutron-branching ratios were derived by using the binned maximum-likelihood method.

Results: Twenty new $\beta$-decay half-lives are reported for ${}^{204-206}\mathrm{Au}, {}^{208–211}\mathrm{Hg},{}^{211–216}\mathrm{Tl},{}^{215–218}\mathrm{Pb}$, and ${}^{218–220}\mathrm{Bi}$, nine of them for the first time. Neutron emission probabilities are reported for ${}^{210,211}\mathrm{Hg}$ and ${}^{211–216}\mathrm{Tl}$.

Conclusions: The new $\beta$-decay half-lives are in good agreement with previous measurements on nuclei in this region. The measured neutron emission probabilities are comparable to or smaller than values predicted by global models such as relativistic Hartree Bogoliubov plus the relativistic quasi-particle random phase approximation (RHB + RQRPA).

We report the results of a $\gamma$-ray spectroscopic study of ${}^{211}\mathrm{Po}$ via the ${}^{208}\mathrm{Pb}(\alpha ,n$) reaction at 24-MeV incident energy using a thick target. We observe 26 new $\gamma$ rays, allowing us to identify 18 states that were not observed in previous $\gamma$-ray studies. In total, we observe 45 states below 2.0 MeV. A shell model calculation using the modified Kuo-Herling interaction developed by Warburton and Brown predicts 46 states below 2.0 MeV having spins of 21/2 and below, demonstrating the power of this calculation to provide detailed nuclear structure information on nuclei in the vicinity of ${}^{208}\mathrm{Pb}$.

Yield ratios of identified hadrons observed in high multiplicity $p+p$ and $p+\text{Pb}$ collisions at the CERN Large Hadron Collider show remarkable similarity with those in $\text{Pb}+\text{Pb}$ collisions, indicating some important and universal underlying dynamics in hadron production for different quark gluon final states. We use the quark combination model to explain the data of yield ratios in these three collision systems. The observed $p/\pi$ and $\mathrm{\Lambda }/K_s^0$ can be reproduced simultaneously by quark combination, and these two ratios reflect the probability of baryon production at hadronization which is the same in the light sector and strange sector and is roughly constant in $p+p, p+\text{Pb}$, and $\text{Pb}+\text{Pb}$ collision systems over three orders of magnitude in charged particle multiplicity. The data of $K_s^0/\pi , \mathrm{\Lambda }/\pi , \mathrm{\Xi }/\pi$, and $\mathrm{\Omega }/\pi$ show a hierarchy behavior relating to the strangeness content and are naturally explained by quark combination both in the saturate stage at high multiplicity and in the increase stage at moderate multiplicity. Our results suggest that the characteristic of quark combination is necessary in describing the production of hadrons in small systems created in $p+p$ and $p+\text{Pb}$ collisions.

We show the important role played by the $\pi \mathrm{\Delta }\left(1232\right)$ channel in the build up of the $N\left(1700\right)(3/2^{-})$ resonance due to the nontrivial enhancement produced by a singularity of a triangular loop. The $N\left(1700\right)$ is one of the dynamically generated resonances produced by the coupled-channel vector-baryon interaction. The $\pi \mathrm{\Delta }$ channel was neglected in previous works but we show that it has to be incorporated into the coupled-channel formalism due to an enhancement produced by a singularity in the triangular loop with $\rho$, nucleon, and $\pi$ as internal loop lines and $\pi$ and $\mathrm{\Delta }$ as external ones. The enhancement is of nonresonant origin but it contributes to the dynamical generation of the $N\left(1700\right)$ resonance due to the nonlinear dynamics involved in the coupled-channel mechanisms. We obtain an important increase of the total width of the $N\left(1700\right)$ resonance when the $\pi \mathrm{\Delta }$ channel is included and provide predictions for the partial widths of the $N\left(1700\right)$ decays into $VB$ and $\pi \mathrm{\Delta }$.

We calculate for the first time the electric dipole moment (EDM) of ${}^{13}\mathrm{C}$ generated by the isovector charge conjugation-parity (CP)-odd pion exchange nuclear force in the $\alpha$-cluster model, which describes well the structures of low-lying states of the ${}^{13}\mathrm{C}$ nucleus. The linear dependence of the EDM of ${}^{13}\mathrm{C}$ on the neutron EDM and the isovector CP-odd nuclear coupling is found to be $d_{{}^{13}\mathrm{C}}=-0.33d_n-0.0020{\overline{G}}_{\pi }^{\left(1\right)}$. The linear enhancement factor of the CP-odd nuclear coupling is smaller than that of the deuteron, due to the difference of the structure between the $1/2_1^{-}$ state and the opposite-parity ($1/2^{+}$) states. We clarify the role of the structure played in the enhancement of the EDM. This result provides good guiding principles to search for other nuclei with large enhancement factor. We also mention the role of the EDM of ${}^{13}\mathrm{C}$ in determining the new physics beyond the standard model.

The decay properties of the linear-chain states in ${}^{14}\mathrm{C}$ are investigated by using antisymmetrized molecular dynamics. The calculation predicts two rotational bands with linear-chain configurations having the $\pi$-bond and $\sigma$-bond valence neutrons. For the $\pi$-bond linear-chain, the calculated excitation energies and the widths of $\alpha$-decay to the ground state of ${}^{10}\mathrm{Be}$ reasonably agree with the experimental candidates observed by the $\alpha +{}^{10}\mathrm{Be}$ resonant scattering. On the other hand, the $\sigma$-bond linear-chain is the candidate of the higher-lying resonant states reported by the breakup reaction. As the evidence of the $\sigma$-bond linear chain, we discuss its decay pattern. It is found that the $\sigma$-bond linear chain not only decays to the excited band of ${}^{10}\mathrm{Be}$ but also decays to the three-body channel of ${}^6\mathrm{He}+\alpha +\alpha$, and the branching ratio of these decays are comparable. Hence, we suggest that this characteristic decay pattern is a strong signature of the linear-chain formation and a key observable to distinguish two different linear chains.