The E12-14-012 experiment, performed in Jefferson Lab Hall A, has collected exclusive electron-scattering data $(e,e^{\prime }p)$ in parallel kinematics using natural argon and natural titanium targets. Here we report the first results of the analysis of the data set corresponding to beam energy 2222 GeV, electron scattering angle $21.5^{\circ }$, and proton emission angle $-{50}^{\circ }$. The differential cross sections, measured with $\approx 4\%$ uncertainty, have been studied as a function of missing energy and missing momentum, and compared to the results of Monte Carlo simulations, obtained from a model based on the distorted-wave impulse approximation.

The $\beta$ decays of ${}^{103,104m}\mathrm{Nb}$ were studied with the Summing NaI(Tl) (SuN) detector at the National Superconducting Cyclotron Laboratory. The $\beta$-decay feeding intensity distribution $I_{\beta }\left(E\right)$ for each isotope was extracted by measuring $\gamma$ rays in coincidence with an emitted electron. The $I_{\beta }\left(E\right)$ was extracted via the total absorption spectroscopy technique. The $I_{\beta }\left(E\right)$ for each nucleus was compared to predictions made by the quasiparticle random-phase approximation (QRPA) model which is commonly used to calculate $\beta$-decay properties for astrophysical applications. The main goal was to provide experimental data for neutron-rich nuclei, relevant to the astrophysical $r$ process. In addition, the extracted $\beta$-decay feeding intensity distributions can lead to a better understanding of nuclear structure in a region of rapid structure changes around $A=100$. Finally, experimental data for ${}^{104m}\mathrm{Nb}$ are also of interest to antineutrino studies of nuclear reactors.

New transitions in neutron-rich ${}^{100}\mathrm{Y}$ have been identified in a ${}^9\mathrm{Be}+{}^{238}\mathrm{U}$ experiment with mass and $Z$ gates to provide full fragment identification. These transitions and high spin levels of ${}^{100}\mathrm{Y}$ have been investigated by analyzing the high statistics $\gamma \text{−}\gamma \text{−}\gamma$ and $\gamma \text{−}\gamma \text{−}\gamma \text{−}\gamma$ coincidence data from the spontaneous fission of ${}^{252}\mathrm{Cf}$ at the Gammasphere detector array. Two new bands, 14 new levels, and 23 new transitions have been identified. The $K^{\pi }=4^{+}$ new band decaying to a $1s$ isomeric state is assigned to be the high-$K$ Gallagher-Moszkowski (GM) partner of the known $K^{\pi }=1^{+}$ band, with the $\pi 5/2\left[522\right]\otimes \nu 3/2\left[411\right]$ configuration. This $4^{+}$ band is also proposed to be the pseudospin partner of the new $K^{\pi }=5^{+}$ band with a $5^{+}\pi 5/2\left[422\right]\otimes \nu 5/2\left[413\right]$ configuration, to form a $\pi 5/2\left[422\right]\otimes \nu [3125/2,3/2]$ neutron pseudospin doublet. Constrained triaxial covariant density-functional theory and quantal particle rotor model calculations have been applied to interpret the band structure and available electromagnetic transition probabilities and are found to be in good agreement with experimental values.

The incomplete fusion dynamics in the ${}^{18}\mathrm{O}+{}^{93}\mathrm{Nb}$ system at energies above the Coulomb barrier has been investigated. The experimentally measured cross sections have been compared with the theoretical predictions of the statistical model code pace4. To examine the effect of entrance channel parameters on the onset and strength of incomplete fusion, relative contributions of complete and incomplete fusion have been deduced from the analysis of measured excitation functions. The contribution of incomplete fusion deduced from the analysis of excitation functions has been studied in terms of various entrance channel parameters, namely, entrance channel mass asymmetry (${\mu }_A$) of interacting projectile and target combination, Coulomb factor ($Z_P{Z}_T$), ground state $\alpha \text{−}Q$ value of the reaction, and neutron skin thickness of target nuclei. It has been found that the probability of incomplete fusion depends strongly on entrance channel parameters. Further, the incomplete fusion contribution for the ${}^{18}\mathrm{O}$ projectile with two excess neutrons is noticed to be relatively larger as compared to ${}^{16}\mathrm{O}$. This may be due to the larger probability of breakup for the ${}^{18}\mathrm{O}$ projectile resulting in rather weak binding forces as compared to ${}^{16}\mathrm{O}$. The existence of incomplete fusion below critical angular momentum (${\ell }_{\mathrm{crit}}$), i.e., $\ell ⩽{\ell }_{\mathrm{crit}}$, has also been observed for the studied system.

Background: The ${}^8\mathrm{Li}(n,\gamma ){}^9\mathrm{Li}$ reaction plays an important role in several astrophysics scenarios. It cannot be measured directly and indirect experiments have so far provided only cross section limits. Theoretical predictions differ by an order of magnitude.

Purpose: In this work we study the properties of ${}^9\mathrm{Li}$ bound states and low-lying resonances and calculate the ${}^8\mathrm{Li}(n,\gamma ){}^9\mathrm{Li}$ cross section within the no-core shell model with continuum (NCSMC) with chiral nucleon-nucleon and three-nucleon interactions as input.

Methods: The NCSMC is an ab initio method applicable to light nuclei that provides a unified description of bound and scattering states well suited to calculate low-energy nuclear scattering and reactions. For the capture cross section calculation, we adjust calculated thresholds to experimental values.

Results: Our calculations reproduce the experimentally known bound states as well as the lowest $5/2^{-}$ resonance of ${}^9\mathrm{Li}$. We predict a $3/2^{-}$ spin-parity assignment for the resonance observed at 5.38 MeV. In addition to the very narrow $7/2^{-}$ resonance corresponding presumably to the experimental 6.43 MeV state, we find several other broad low-lying resonances.

Conclusions: Our calculated ${}^8\mathrm{Li}(n,\gamma ){}^9\mathrm{Li}$ cross section is within the limits derived from the 1998 National Superconducting Cyclotron Laboratory Coulomb-dissociation experiment [Phys. Rev. C 57, 959 (1998)]. However, it is higher than cross sections obtained in recent phenomenological studies. It is dominated by a direct E1 capture to the ground state with a resonant contribution at $\approx 0.2$ MeV due to E2/M1 radiation enhanced by the $5/2^{-}$ resonance.

Background: The remarkable progress in recent multimessenger observations of both isolated neutron stars (NSs) and their mergers has provided some of the much needed data to improve our understanding about the equation of state (EOS) of dense neutron-rich matter. Various EOSs with or without some kinds of phase transitions from hadronic to quark matter (QM) have been widely used in many forward modelings of NS properties. Direct comparisons of these predictions with observational data sometimes also using ${\chi }^2$ minimizations have provided very useful constraints on the model EOSs. However, it is normally difficult to perform uncertain quantifications and analyze correlations of the EOS model parameters involved in forward modelings especially when the available data are still very limited.

Purpose: We infer the posterior probability distribution functions (PDFs) and correlations of nine parameters characterizing the EOS of dense neutron-rich matter encapsulating a first-order hadron-quark phase transition from the radius data of canonical NSs reported by LIGO/VIRGO, NICER, and Chandra Collaborations. We also infer the QM mass fraction and its radius in a $1.4{\mathrm{M}}_{\odot }$ NS and predict their values in more massive NSs.

Method: Metamodelings are used to generate both hadronic and QM EOSs in the Markov-Chain Monte Carlo sampling process within the Bayesian statistical framework. An explicitly isospin-dependent parametric EOS for the $npe\mu$ matter in NSs at $\beta$ equilibrium is connected through the Maxwell construction to the QM EOS described by the constant speed of sound (CSS) model of Alford, Han, and Prakash with and without using the Seidov stability condition for first-order phase transitions.

Results: In the default calculation with the Seidov stability condition, we find that (i) The most probable values of the hadron-quark transition density ${\rho }_t/{\rho }_0$ and the relative energy density jump there $\mathrm{\Delta }\varepsilon /{\varepsilon }_t$ are ${\rho }_t/{\rho }_0=1.6_{-0.4}^{+1.2}$ and $\mathrm{\Delta }\varepsilon /{\varepsilon }_t=0.4_{-0.15}^{+0.20}$ at 68% confidence level, respectively. The corresponding probability distribution of QM fraction in a $1.4{\mathrm{M}}_{\odot }$ NS peaks around 0.9 in a 10 km sphere. Strongly correlated to the PDFs of ${\rho }_t$ and $\mathrm{\Delta }\varepsilon /{\varepsilon }_t$, the PDF of the QM speed of sound squared $c_{\mathrm{QM}}^2/c^2$ peaks at $0.{95}_{-0.35}^{+0.05}$, and the total probability of being less than 1/3 is very small. (ii) The correlations between PDFs of hadronic and QM EOS parameters are very weak. While the most probable values of parameters describing the EOS of symmetric nuclear matter remain almost unchanged, the high-density symmetry energy parameters of neutron-rich matter are significantly different with or without considering the hadron-quark phase transition. Removing the Seidov condition, while there are appreciable and interesting changes in the PDFs of quark matter EOS parameters, the qualitative conclusions remain the same.

Conclusions: The available astrophysical data considered together with all known EOS constraints from theories and terrestrial nuclear experiments prefer the formation of a large volume of QM even in canonical NSs.

Background: A number of accelerator-based isotope production facilities utilize 100- to 200-MeV proton beams due to the high production rates enabled by high-intensity beam capabilities and the greater diversity of isotope production brought on by the long range of high-energy protons. However, nuclear reaction modeling at these energies can be challenging because of the interplay between different reaction modes and a lack of existing guiding cross-section data.

Purpose: A Tri-lab collaboration has been formed among the Lawrence Berkeley, Los Alamos, and Brookhaven National Laboratories to address these complexities by characterizing charged-particle nuclear reactions relevant to the production of established and novel radioisotopes.

Method: In the inaugural collaboration experiments, stacked-targets of niobium foils were irradiated at the Brookhaven Linac Isotope Producer ($E_p=200\mathrm{MeV}$) and the Los Alamos Isotope Production Facility ($E_p=100\mathrm{MeV}$) to measure ${}^{93}\mathrm{Nb}(p,x)$ cross sections between 50 and 200 MeV. First measurements of the ${}^{93}\mathrm{Nb}(p,4n){}^{90}\mathrm{Mo}$ beam monitor reaction beyond 100 MeV are reported in this work, as part of the broadest energy-spanning dataset for the reaction to date. ${}^{93}\mathrm{Nb}(p,x)$ production cross sections are additionally reported for 22 other measured residual products. The measured cross-section results were compared with literature data as well as the default calculations of the nuclear model codes TALYS, CoH, EMPIRE, and ALICE.

Results: The default code predictions largely failed to reproduce the measurements, with consistent underestimation of the preequilibrium emission. Therefore, we developed a standardized procedure that determines the reaction model parameters that best reproduce the most prominent reaction channels in a physically justifiable manner. The primary focus of the procedure was to determine the best parametrization for the preequilibrium two-component exciton model via a comparison to the energy-dependent ${}^{93}\mathrm{Nb}(p,x)$ data, as well as previously published ${}^{139}\mathrm{La}(p,x)$ cross sections.

Conclusions: This modeling study revealed a trend toward a relative decrease for internal transition rates at intermediate proton energies ($E_p=20$–60 MeV) in the current exciton model as compared to the default values. The results of this work are instrumental for the planning, execution, and analysis essential to isotope production.

Low- and medium-spin negative-parity bands of ${}^{187}\mathrm{Os}$ have been studied using the AFRican Omnipurpose Detector for Innovative Techniques and Experiments (AFRODITE) array, following the ${}^{186}\mathrm{W}({}^4\mathrm{He},3n){}^{187}\mathrm{Os}$ reaction at a beam energy of 37 MeV. In the current work, all the previously known bands have been significantly extended and three new bands have been added to the level scheme. The angular distribution ratio ($R_{\mathrm{AD}}$) and polarization measurements have been used to assign spin and parity to the observed new levels. The configurations of some of the bands have been modified. The observed bands are interpreted within the cranked shell model (CSM) and cranked Nilsson-Strutinsky-Bogoliubov (CNSB) formalism. Comparison with experimental data shows good agreements. Systematic comparison with the neighboring ${}^{185}\mathrm{Os}$ isotope is also discussed.

We link complex many-body correlations, which play a decisive role in the structural properties of atomic nuclei, to the electron capture occurring during star evolution. The recently developed finite-temperature response theory, taking into account the coupling between single-nucleon and collective degrees of freedom, is applied to spin-isospin transitions, which dominate the electron capture rates. Calculations are performed for ${}^{78}\mathrm{Ni}$ and for the surrounding even-even nuclei associated with a high-sensitivity region of the nuclear chart in the context of core-collapse supernova simulations. The obtained electron capture rates are compared to those of a simpler thermal quasiparticle random phase approximation (TQRPA), which is standardly used in such computations. The comparison indicates that correlations beyond TQRPA lead to significantly higher electron capture rates under the typical thermodynamical conditions.

The nonadiabatic quasiparticle approach is applied to study chiral doublet bands in ${}^{128}\mathrm{Cs}, {}^{130}\mathrm{Cs}$, and ${}^{130}\mathrm{La}$. The calculated energy spectra and electromagnetic transition probabilities reproduce quite well the experimental data. ${}^{130}\mathrm{Cs}$ turns out to be a better example for chiral symmetry breaking than ${}^{128}\mathrm{Cs}$, unlike it has been suggested in earlier studies. We present the first theoretical investigation of chiral geometry and its correlation with the single-particle configurations in ${}^{130}\mathrm{La}$ to understand the mode of chirality, i.e., static or vibrational.

Isotope harvesting is a method of collecting the long-lived radioisotopes that build up during the operation of ion-beam facilities in a way that is useful for subsequent research. As a demonstration of this method for the collection of a group IV metal at a fragmentation facility, the high-energy ${}^{88}\mathrm{Zr}$ secondary beam produced from a 140-MeV/u ${}^{92}\mathrm{Mo}$ primary beam at the National Superconducting Cyclotron Laboratory (NSCL) was stopped in a water target. The setup aimed to mimic the aqueous beam dump that will be implemented at the Facility for Rare Isotope Beams (FRIB). The collected ${}^{88}\mathrm{Zr}$ and accompanying ${}^{88}\mathrm{Y}$ decay daughter were radiochemically extracted from the solution and made into target samples suitable for neutron-capture cross-section measurements. These samples were then irradiated at two reactor facilities, and the ${}^{88}\mathrm{Zr}$ average thermal-neutron-capture cross section (${\sigma }_T$) and resonance integral ($I$) were determined to be ${\sigma }_T=(8.04\pm 0.63)\times {10}^5$ b and $I=(2.53\pm 0.28)\times {10}^6$ b. The ${\sigma }_T$ value agrees well with previous results and $I$, determined for the first time here, was found to be the largest measured resonance integral by two orders of magnitude. The ${}^{88}\mathrm{Y}$ thermal-neutron-capture cross section was determined to be less than $1.8\times {10}^4$ b. This work demonstrates the steps needed to make cross-section measurements with samples produced via aqueous isotope harvesting.

General formulas are presented for higher order cumulants of the conserved charge statistical fluctuations inside the mixed phase. As a particular example, the van der Waals model in the grand canonical ensemble is used. The higher order measures of the conserved charge fluctuations up to the hyperkurtosis are calculated in a vicinity of the critical point (CP). The analysis includes both the mixed phase region and the pure phases on the phase diagram. It is shown that even-order fluctuation measures, e.g., scaled variance, kurtosis, and hyperkurtosis, have only positive values in the mixed phase and go to infinity at the CP. For odd-order measures, such as skewness and hyperskewness, the regions of positive and negative values are found near the left and right binodals, respectively. The obtained results are discussed in a context of the event-by-event fluctuation measurements in heavy-ion collisions.

Multiparticle cumulants of azimuthal angle correlations have been compelling tools to probe the properties of the quark-gluon plasma (QGP) created in the ultrarelativistic heavy-ion collisions and the search for the QGP in small collision systems at BNL's Relativistic Heavy Ion Collider (RHIC) and at CERN's Large Hadron Collider (LHC). However, only very few of them are available and have been studied in theoretical calculations and experimental measurements, while the rest are generally very interesting, but their direct implementation was not feasible. In this paper, we present a generic recursive algorithm for multiparticle cumulants, which enables the calculation of arbitrary order single and mixed harmonic multiparticle cumulants. Among them, the new 10-, 12-, 14-, and 16-particle cumulants of a single harmonic, named $c_n\left\{10\right\}, c_n\left\{12\right\}, c_n\left\{14\right\}$, and $c_n\left\{16\right\}$, and the corresponding $v_n$ coefficients, will be discussed for the first time. Our Monte Carlos studies show that these new multiparticle cumulants can be readily used along with updates to the generic framework of multiparticle correlations to a very high order. Finally, we propose a particular series of mixed harmonic multiparticle cumulants, which measures the general correlations between any moments of different flow coefficients. The predictions of these new observables are shown based on an initial-state model MC-Glauber, a toy Monte Carlo model, and the HIJING transport model for future comparisons between experimental data and theoretical model calculations. The study of these new multiparticle cumulants in heavy-ion collisions will significantly improve the understanding of the joint probability density function which involves both different harmonics of flow and also the symmetry planes. This will pave the way for more stringent constraints on the initial state and help to extract more precisely information on how the created hot and dense matter evolves. Meanwhile the efforts applied to small systems could be very helpful in the understanding of the origin of the observed collectivity at RHIC and the LHC.

Whether quark- and gluon-initiated jets are modified differently by the quark-gluon plasma produced in heavy-ion collisions is a long-standing question that has thus far eluded a definitive experimental answer. A crucial complication for quark-gluon discrimination in both proton-proton and heavy-ion collisions is that all measurements necessarily average over the (unknown) quark-gluon composition of a jet sample. In the heavy-ion context, the simultaneous modification of both the fractions and substructure of quark and gluon jets by the quark-gluon plasma further obscures the interpretation. Here, we demonstrate a fully data-driven method for separating quark and gluon contributions to jet observables using a statistical technique called topic modeling. Assuming that jet distributions are a mixture of underlying “quark-like” and “gluon-like” distributions, we show how to extract quark- and gluon-jet fractions and constituent multiplicity distributions as a function of the jet transverse momentum. This proof-of-concept study is based on proton-proton and heavy-ion collision events from the Monte Carlo event generator Jewel with statistics accessible in Run 4 of the Large Hadron Collider. These results suggest the potential for an experimental determination of quark- and gluon-jet modifications.

This work presents further analysis of the three- and four-neutron systems in the low energy regime using adiabatic hyperspherical methods. In our previous article [M. D. Higgins et al., Phys. Rev. Lett. 125, 052501 (2020)], the low-energy behavior of these neutron systems was treated in the adiabatic approximation, neglecting the off-diagonal nonadiabatic couplings. A thorough analysis of the density of states through a multichannel treatment of the three-and four-neutron scattering near the scattering continuum threshold is performed, showing no evidence of a $4n$ resonance at low energy. A detailed analysis of the long-range behavior of the lowest few adiabatic hyperspherical potentials shows there is an attractive ${\rho }^{-3}$ universal behavior which dominates in the low-energy regime of the multichannel scattering. This long-range behavior leads to a divergent behavior of the density of state for $E\to 0$ that could account for the low-energy signal observed in the 2016 experiment by Kisamori et al. [Phys. Rev. Lett. 116, 052501 (2016)].

Lifetime measurements have been carried out for the levels of the negative parity yrast sequence in ${}^{103}\mathrm{Pd}$ nucleus using the Doppler shift attenuation method. The levels were populated via ${}^{94}\mathrm{Zr}({}^{13}\mathrm{C}, 4n\gamma ){}^{103}\mathrm{Pd}$ fusion-evaporation reaction at a beam energy of 55 MeV. De-exciting $\gamma$ rays were detected by utilizing the Indian National Gamma Array. The extracted transition probabilities and other auxiliary observations indicate that the sequence may be resulting from the antimagnetic rotational (AMR) motion of valence nucleons. The key characteristic feature of the AMR motion is the steady decrease of the $B\left(E2\right)$ transition probability with spin, which is seen in the present measured transitions for ${}^{103}\mathrm{Pd}$. The experimental results are compared with the theoretical predictions of tilted axis cranked approach based on the covariant density functional theory. It is noted that the properties of the AMR band structure for ${}^{103}\mathrm{Pd}$ predicted in this model analysis are in good agreement with the present experimental findings. Further, semi-classical particle-rotor model has been employed to substantiate the AMR interpretation of the observed band structure in ${}^{103}\mathrm{Pd}$ and it is shown that results are similar to the band structures observed in the neighboring isotopes, which have also been considered as candidates for AMR motion.

A family of analytically solvable potential models for the one- and two-channel problems is considered within the Jost matrix approach. The potentials are chosen to be constant in the interior region and to have different asymptotic behavior (tails) at large distances. The migration of the $S$-matrix poles on the Riemann surface of the energy, caused by variations of the potential strength, is studied. It is demonstrated that the long-range ($\sim 1/r^2$) tails and Coulomb potential ($\sim 1/r$) cause an unusual behavior of the $S$-matrix poles. It is found that in the two-channel problem with the long-range potentials the $S$-matrix poles may appear at complex energies on the physical Riemann sheet. The Coulomb tail not only changes the topology of the Riemann surface, but also breaks down the so-called mirror symmetry of the poles in both the single-channel and the two-channel problems.

The reaction systems ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ and ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$ are investigated within the improved dinuclear system model+GEMINI++. The theoretical results show that the distributions of isotopes in the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ reaction are well described with the model. For the ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$ reaction, the model partly describes well the experimental production cross sections. Experimental and theoretical data from multinucleon transfer reactions indicate that the isotopic distributions of the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ reaction system above Pb are shifted toward the neutron-rich side as compared to the ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ reaction except the isotopic distribution of Bi.

The photoproduction reaction of $\gamma p\to K^{+}\mathrm{\Lambda }\left(1405\right)$ is investigated based on an effective Lagrangian approach at the tree-level approximation with the purpose of understanding the reaction mechanism and extracting the resonance contents and the associated resonance parameters in this reaction. Apart from the $t$-channel $K$ and $K^{*}$ exchanges, $s$-channel nucleon ($N$) exchange, $u$-channel $\mathrm{\Sigma }, \mathrm{\Lambda }$, and $\mathrm{\Lambda }\left(1405\right)$ exchanges, and generalized contact term, the exchanges of a minimum number of $N$ resonances in the $s$ channel are taken into account in constructing the reaction amplitudes to describe the experimental data. It is found that by introducing the $N\left(2000\right){5/2}^{+}$ resonance exchange in the $s$ channel, one can reproduce the most recent differential cross-section data from the CLAS Collaboration quite well. Further analysis shows that the cross sections of $\gamma p\to K^{+}\mathrm{\Lambda }\left(1405\right)$ at high energies are dominated by the $t$-channel $K$ exchange, while the contributions from the $s$-channel $N$ and $N\left(2000\right){5/2}^{+}$ exchanges are rather significant to the cross sections in the near-threshold energy region. Predictions for the beam and target asymmetries for $\gamma p\to K^{+}\mathrm{\Lambda }\left(1405\right)$ are given.

The $\beta$ decay of ${}^{101,102}\mathrm{Zr}$ and ${}^{109}\mathrm{Tc}$ was studied using the technique of total absorption spectroscopy. The experiment was performed at the National Superconducting Cyclotron Laboratory using the Summing NaI(Tl) (SuN) detector in the first-ever application of total absorption spectroscopy with a fast beam produced via projectile fragmentation. The $\beta$-decay feeding intensity and Gamow-Teller transition strength distributions were extracted for these three decays. The extracted distributions were compared to three different quasiparticle random-phase approximation (QRPA) models based on different mean-field potentials. A comparison with calculations from one of the QRPA models was performed to learn about the ground-state shape of the parent nucleus. For ${}^{101}\mathrm{Zr}$ and ${}^{102}\mathrm{Zr}$, calculations assuming a pure shape configuration (oblate or prolate) were not able to reproduce the extracted distributions. These results may indicate that some type of mixture between oblate and prolate shapes is necessary to reproduce the extracted distributions. For ${}^{109}\mathrm{Tc}$, a comparison of the extracted distributions with QRPA calculations suggests a dominant oblate configuration. The other two QRPA models are commonly used to provide $\beta$-decay properties in $r$-process network calculations. This work shows the importance of making comparisons between the experimental and theoretical $\beta$-decay distributions, rather than just half-lives and $\beta$-delayed neutron emission probabilities, as close to the $r$-process path as possible.