The interpretation of experiments that search for neutrinoless double-$\beta$ decay relies on input from nuclear theory. Cirigliano et al. [Phys. Rev. Lett. 120, 202001 (2018)] recently showed that, for the light Majorana exchange formalism, effective field theory calculations require a $nn\to pp{e}^{-}{e}^{-}$ contact term at leading order. They estimated the size of this contribution by relating it to measured charge-independence-breaking (CIB) nucleon-nucleon interactions and making an assumption about the relative sizes of CIB operators. We show that the assumptions underlying this approximation are justified in the limit of the number of colors, $N_c$, being large. We also obtain a large-$N_c$ hierarchy among CIB nucleon-nucleon interactions that is in agreement with phenomenological results.

We investigate four-body nuclear reactions in stellar environments contributing to the creation of light nuclei, exemplified by ${}^9\mathrm{Be}$ and ${}^{12}\mathrm{C}$. The originally assumed process is radiative capture, where nuclear clusters combine into the excited final nucleus and photon emission populates the stable nuclear ground states. Instead, we consider nuclear four-body recombination reactions where a spectator nuclear particle replaces the photon. We first develop the elaborate formalism for both direct and sequential capture processes, where the decaying three-body resonance is formed without and with population of an intermediate two-body resonance, respectively. To facilitate both calculations and practical applications we parametrize the involved cross sections as done successfully in previous computations of reaction rates. We consider the lowest-lying nuclear states with their dominant contributions at low stellar temperatures. We calculate and compare reaction and production rates for different processes. The direct reaction mechanism dominates by many orders of magnitude at low temperature, where the sequential stepping stones are energetically too expensive to use. At somewhat higher temperatures these two different nuclear four-body mechanisms become comparable. Comparison to radiative three-body capture reveals already formally, but also numerically, that four-body nuclear recombination must dominate for sufficiently high nuclear densities. Numerical values are given for all these rates as a function of temperature and density. The relative importance is exhibited.

The rotating neutron-star properties are studied to investigate a phase transition to quark matter. The density-dependent relativistic mean-field model (DD-RMF) is employed to study the hadron matter, while the vector-enhanced bag (vBag) model is used to study the quark matter. The star-matter properties such as mass, radius, the moment of inertia, rotational frequency, Kerr parameter, and other important quantities are studied to see their effect on quark matter. The maximum mass of a rotating neutron star with the DD-LZ1 and DD-MEX parameter sets is found to be around $3M_{\odot }$ for pure hadronic phase and decreases to around $2.6M_{\odot }$ upon phase transitioning to quark matter, which satisfies the recent GW190814 possible maximum mass constraint, implying that the secondary component of GW190814 could be a fast-rotating hybrid star. For DDV, DDVT, and DDVTD parameter sets, the maximum mass decreases to satisfy $2M_{\odot }$. The moment of inertia calculated for various DD-RMF parameter sets decreases with the increasing mass satisfying constraints from various measurements. Other important quantities calculated also vary with the bag constant and hence show that the presence of quarks inside neutron stars can also allow us to constraint these quantities to determine a proper equation of state. Also, the theoretical study along with the accurate measurement of uniformly rotating neutron-star properties may offer some valuable information concerning the high-density part of the equation of state.

Background: Radionuclides in the Mo-Tc region play an important role in modern medical diagnostics. These applications require a $\gamma$-emitting radioisotope that is injected into the patient. Various production methods of those radionuclides have been investigated in the past; among them are ($p,x$) reactions on natural or enriched molybdenum. Reliable estimations for the produced activity of the radionuclides and radioactive byproducts are required. Therefore, either precise theoretical calculations or a firm experimental database for the nuclear production reactions are needed. In addition, experimental cross-section data of proton-induced reactions on heavy nuclei are very valuable to test nuclear models that enter theoretical calculations of reaction rates relevant for nuclear astrophysics.

Purpose: The present paper reports on experimental cross sections of the ${}^{96}\mathrm{Mo}(p,n){}^{96m+g}\mathrm{Tc}$ reaction. The contribution of the ground-state population as well as for the population of the metastable state in ${}^{96}\mathrm{Tc}$ are determined individually. The obtained results are very valuable to test existing models that enter statistical model calculations. In addition, the present work aims at remeasuring the branching ratio of the decay of the metastable state ${}^{96m}\mathrm{Tc}$.

Method: Highly enriched ${}^{96}\mathrm{Mo}$ targets were irradiated with protons at energies between $E_p=3.9\mathrm{MeV}$ and $E_p=5.4\mathrm{MeV}$, which are slightly above the ($p,n$) threshold ($E_{th}=3.8\mathrm{MeV}$). By employing an offline analysis, the $\gamma$-ray decay of the reaction product was investigated and reaction cross sections were calculated by means of the activation technique.

Results: Individual reaction cross sections for the production channel of the metastable state ${\sigma }_m$ and the ground state ${\sigma }_{gs}$ as well as the branching of the ${}^{96m}\mathrm{Tc}\to {}^{96}\mathrm{Tc}$ decay were determined.

Conclusion: The measured cross sections are in good agreement with previously measured cross sections as well as with recent Hauser-Feshbach calculations. The new branching ratio for the direct decay of ${}^{96m}\mathrm{Tc}$ into ${}^{96}\mathrm{Mo}$ amounts to $4.1{}_{-0.34}^{+0.39}\%$ compared to previously reported $2\pm 0.5\%$.

We evaluated CLAS Collaboration measurements for the ${90}^{\circ }$ meson photoproduction off the nucleon using a tagged photon beam spanning the energy interval $s=3–11{\mathrm{GeV}}^2$. The results are compared with the “quark counting rules” predictions.

Ground state properties of ${}^{19}\mathrm{B}$ are studied by using the deformed relativistic Hartree-Bogoliubov theory in continuum. The calculations with the density functional PK1 show that ${}^{19}\mathrm{B}$ is a deformed two-neutron ($2n$) halo nucleus. By examining the evolution of single neutron levels, it is found that the valence levels, which are weakly bound or embedded in the continuum due to pairing, contain considerable $s$-wave components with the probability amplitude of 0.359 and lead to the formation of the halo. Strong quadrupole correlations mix $sd$ orbitals and drive ${}^{19}\mathrm{B}$ to be prolate. The calculated density of the neutron core presents a prolate shape while the neutron halo is oblate, meaning ${}^{19}\mathrm{B}$ is a $2n$ halo candidate with shape decoupling effects.

Two separate analyses of $E2$ strengths among the first two bands in ${}^{154}\mathrm{Sm}$ are consistent. They indicate that mixing is small and decreases with increasing $J$.

We present a theoretical formalism for scattering of twisted neutrons by nuclei in a kinematic regime where interference between the Coulomb interaction and the strong interaction is essential. Twisted neutrons have definite quantized values of an angular momentum projection along the direction of propagation, and we show that this results in novel observable effects for the scattering cross section, spin asymmetries, and polarization of the scattered neutrons. We demonstrate that additional capabilities provided by a beam's orbital angular momentum enable new techniques for measuring both real and imaginary parts of the scattering amplitude. Several possible observables are considered, for which the targets may be either well localized with respect to the spatial beam profile or the scattering occurs incoherently on nuclei in a bulk target. The developed approach can be applied to other nuclear reactions with strongly interacting twisted particles.

We introduce a model for heavy ion collisions named trajectum, which includes an expanded initial stage with a variable free streaming velocity $v_{\mathrm{fs}}$ and a hydrodynamic stage with three varying second order transport coefficients. We describe how to obtain a Gaussian emulator for this 20-parameter model and show results for key observables. This emulator can be used to obtain Bayesian posterior estimates on the parameters, which we test by an elaborate closure test as well as a convergence study. Lastly, we employ the optimal values of the parameters found in Nijs et al. [G. Nijs, W. van der Schee, U. Gürsoy, and R. Snellings, Phys. Rev. Lett. 126, 202301 (2021)] to perform a detailed comparison to experimental data from PbPb and $p\mathrm{Pb}$ collisions. This includes both observables that have been used to obtain these values as well as wider transverse momentum ranges and new observables such as correlations of event-plane angles.

Mean-field calculations in multidimensional deformation spaces are performed and the shape coexistence and isomers generated by exotic nuclear configurations and toroidal and superdeformed ones are addressed. We use a phenomenological mean-field Hamiltonian of Woods-Saxon type with its universal parametrization involving eight parameters fixed once for all for the full periodic table. Original parametric correlations existing in this type of Hamiltonians are removed using methods of inverse problem theory of applied mathematics. Stochastic analysis of uncertainties of the final nuclear energy predictions with the obtained correlation-free parametrization is performed and the viability tests are illustrated and discussed. Prediction capacities of resulting model related to the description of the nuclear shape properties are cross-checked using the experimental information available, revealing full coherence. Presented results encourage experimental verification of predicted exotic structures; suggestions related to identification possibilities are formulated and discussed.

The $\beta \text{−}\gamma$ spectroscopy of ${}^{195}\mathrm{Os}$ nucleus was performed at the KEK isotope separation system (KISS). The radioactive isotope of ${}^{195}\mathrm{Os}$ was produced by the multinucleon transfer reactions of ${}^{136}\mathrm{Xe}$ beams and ${}^{198}\mathrm{Pt}$ target. The isotope of interest was separated and extracted by using KISS, which is an argon-gas-cell based laser ion source with a mass separator. Those extracted isotopes are implanted into an aluminized mylar tape, which is surrounded by the multisegmented proportional gas counter (MSPGC) and four clover-type high-purity germanium (HPGe) detectors for the $\beta \text{−}\gamma$ spectroscopy. 27 $\gamma$-ray peaks were observed in coincidence with internal conversion electrons and x rays detected by the MSPGC. 21 of them were identified as $\beta$-delayed $\gamma$ rays of the ${}^{195}\mathrm{Os}$ ground state, where the energies of 19 $\gamma$-ray peaks agree with the literature values of transitions observed in ${}^{195}\mathrm{Ir}(n,\gamma )$ reactions and two $\gamma$-ray peaks were newly found. The $\beta$-decay branching ratios of the ${}^{195}\mathrm{Os}$ ground state were deduced. The obtained log-$ft$ values range from $5.99\left(4\right)$ to $7.56\left(22\right)$, indicating all $\beta$-decay channels are the first forbidden transitions. It suggests that the spin-parity of the ${}^{195}\mathrm{Os}$ ground state is $3/2^{-}$, which is consistent with the systematical expectation. The $\beta$-decay half-life of the ${}^{195}\mathrm{Os}$ ground state was evaluated to be 6.5(4) min, which agrees well to the previously known value 6.5(11) min.

Background: Recently, Bijker et al. [Phys. Rev. Lett. 122, 162501 (2019)] explained the rotation-vibration spectrum of ${}^{13}\mathrm{C}$ by assuming a triangular nuclear shape with $D_{3h}^{\prime }$ symmetry.

Purpose: The purpose of this work is to test the shape and symmetry of ${}^{13}\mathrm{C}$ based on a microscopic nuclear model without assumption of nuclear shape.

Method: We have applied the real-time evolution method to ${}^{13}\mathrm{C}$. By using the equation-of-motion of clusters, the model describes the $3\alpha +n$ system without any assumption of symmetry.

Results: REM described the low-lying states more accurately than the previous cluster model studies. The analysis of the wave functions showed that the ground band has approximate triangular symmetry, while the excited bands deviate from it.

Conclusion: This work confirmed that the ground band has the intrinsic structure with the triangular arrangement of three $\alpha$ particles.

Background: Effective interactions for elastic nucleon-nucleus scattering from first principles require the use of the same nucleon-nucleon interaction in the structure and reaction calculations, as well as a consistent treatment of the relevant operators at each order.

Purpose: Previous work using these interactions has shown good agreement with available data. Here, we study the physical relevance of one of these operators, which involves the spin of the struck nucleon, and examine the interpretation of this quantity in a nuclear structure context.

Methods: Using the framework of the spectator expansion and the underlying framework of the no-core shell model, we calculate and examine spin-projected, one-body momentum distributions required for effective nucleon-nucleus interactions in $J=0$ nuclear states.

Results: The calculated spin-projected, one-body momentum distributions for ${}^4\mathrm{He}$, ${}^6\mathrm{He}$, and ${}^8\mathrm{He}$ display characteristic behavior based on the occupation of protons and neutrons in single-particle levels, with more nucleons of one type yielding momentum distributions with larger values. Additionally, we find this quantity is strongly correlated to the magnetic moment of the $2^{+}$ excited state in the ground state rotational band for each nucleus considered.

Conclusions: We find that spin-projected, one-body momentum distributions can probe the spin content of a $J=0$ wave function. This feature may allow future ab initio nucleon-nucleus scattering studies to inform spin properties of the underlying nucleon-nucleon interactions. The observed correlation to the magnetic moment of excited states illustrates a previously unknown connection between reaction observables such as the analyzing power and structure observables like the magnetic moment.

The body of experimental measurements of intermediate-energy reactions that remove a single nucleon from a secondary beam of neutron- or proton-rich nuclei continues to grow. These data have been analyzed consistently using an approximate, eikonal-model treatment of the reaction dynamics combined with appropriate shell-model descriptions of the projectile initial state, the bound final states spectrum of the reaction residue, and single-particle removal strengths computed from their wave-function overlaps. The systematics of the ratio $R_s$ of the measured inclusive cross section to all bound final states and the calculated cross section to bound shell-model states—in different regions of the nuclear chart and involving both very weakly bound and strongly bound valence nucleons—is important in relating the empirically deduced orbital occupancies to those from the best available shell-model predictions. Importantly, several new higher-energy measurements, for which the sudden-approximation aspect of the dynamical description is placed on an even stronger footing, now supplement the previously analyzed measurements. These additional data sets are discussed. Their $R_s$ values are shown to conform to and reinforce the earlier-observed systematics, with no indication that the approximately linear reduction in $R_s$ with increasing nucleon separation energy is a consequence of a breakdown of the sudden approximation.

Nuclear symmetry energy $E_{\text{sym}}\left(\rho \right)$ at density $\rho$ is normally expanded or simply parameterized as a function of $\chi =(\rho -{\rho }_0)/3{\rho }_0$ in the form of $E_{\text{sym}}\left(\rho \right)\approx S+L\chi +2^{-1}{K}_{\text{sym}}{\chi }^2+6^{-1}{J}_{\text{sym}}{\chi }^3+\cdots$ using its magnitude $S$, slope $L$, curvature $K_{\text{sym}}$, and skewness $J_{\text{sym}}$ at the saturation density ${\rho }_0$ of nuclear matter. Much progress has been made in recent years in constraining especially the $S$ and $L$ parameters using various terrestrial experiments and astrophysical observations. However, such expansions/parametrizations do not converge at suprasaturation densities where $\chi$ is not small enough, hindering an accurate determination of high-density $E_{\text{sym}}\left(\rho \right)$ even if its characteristic parameters at ${\rho }_0$ are all well determined by experiments/observations. By expanding the $E_{\text{sym}}\left(\rho \right)$ in terms of a properly chosen auxiliary function ${\mathrm{\Pi }}_{\text{sym}}(\chi ,{\mathrm{\Theta }}_{\text{sym}})$ with a parameter ${\mathrm{\Theta }}_{\text{sym}}$ fixed accurately by an experimental $E_{\text{sym}}\left({\rho }_{\text{r}}\right)$ value at a reference density ${\rho }_{\text{r}}$, we show that the shortcomings of the $\chi$ expansion can be completely removed or significantly reduced in determining the high-density behavior of $E_{\text{sym}}\left(\rho \right)$. In particular, using two significantly different auxiliary functions, we show that the new approach effectively incorporates higher $\chi$-order contributions and converges to the same $E_{\text{sym}}\left(\rho \right)$ much faster than the conventional $\chi$ expansion at densities $\lesssim 3{\rho }_0$. Moreover, the still poorly constrained skewness $J_{\text{sym}}$ plays a small role in determining the $E_{\text{sym}}\left(\rho \right)$ at these densities in the auxiliary function approach. The new approach thus provides a nearly model-independent constraint on the $E_{\text{sym}}\left(\rho \right)$ at densities $\lesssim 3{\rho }_0$. Several quantitative demonstrations using Monte Carlo simulations are given.

Electromagnetic transition strengths in the even-even neutron-rich sulfur isotopes ${}^{38,40,42,44}\mathrm{S}$ were measured using intermediate-energy Coulomb excitation at the National Superconducting Cyclotron Laboratory. By utilizing the sensitivity of the experimental technique to $E2$ excitations from the ground state, the evolution of the pattern of $B\left(E2\right)$ strengths to several low-lying $2^{+}$ states was investigated at $Z=16$ from near stability to the $N=28$ island of inversion. The experimental results allowed a detailed comparison with predictions from shell-model calculations using the SDPF-MU Hamiltonian, which was designed to describe collectivity in this region of the nuclear chart. While the shell-model calculations succeeded in modeling transition strengths at $N=22,24,26$, the experimental $B(E2;0_1^{+}\to 2_1^{+})$ at $N=28$ was smaller than the predicted value by about a factor of 2, similar to previous observations for chlorine and argon isotopes around $N=28$. The dependence of this overprediction by theory on the choice of effective charges was explored.

Background: Precise measurements of atomic transitions affected by electron-nucleus hyperfine interactions offer sensitivity to explore basic properties of the atomic nucleus and study fundamental symmetries, including the search for new physics beyond the standard model of particle physics. In particular, such measurements, augmented by atomic and nuclear calculations, will enable extraction of the higher-order radial moments of the charge-density distribution in spherical and deformed nuclei. The new data impose higher precision requirements on a theoretical description.

Purpose: The nuclear charge density is composed of the proton point distribution folded with the nucleonic charge distributions. The latter induce subtle relativistic corrections due to the coupling of nucleon magnetic moments with the nuclear spin-orbit density. Additional corrections come from the effect of center-of-mass projection. We assess the precision of nuclear charge density calculations by studying the behavior of relativistic and center-of-mass motion corrections to the second and fourth charge radial moments. Special attention has been paid to the magnetic spin-orbit density associated with the local variations of the spin-orbit current.

Methods: The calculations for semimagic and open-shell nuclei are performed in the framework of self-consistent mean-field theory using quantified energy density functionals and density-dependent pairing forces. We used the general expression for the spin-orbit form factor that is valid for spherical and deformed nuclei.

Results: We studied the impact of various correction terms on the charge radii, fourth radial moments, diffraction radii, and surface thickness of spherical and deformed nuclei. The spin-orbit corrections to charge radial moments and surface thickness show strong shell fluctuations which can make an appreciable effect when aiming at high-precision predictions of isotopic shifts. The inclusion of relativistic and center-of-mass corrections impacts the quality of energy density functionals optimized to charge radii data.

Conclusions: To establish reliable constraints on the existence of new forces from isotope shift measurements, precise calculations of nuclear charge densities of deformed nuclei are needed. The proper inclusion of the spin-orbit charge density and other correction terms is essential when aiming at extraction of subtle effects which become particularly visible in isotopic trends. It is also important when developing high-quality nuclear energy density functionals optimized using heterogeneous datasets involving absolute charge radii, differential charge radii, and charge form factor properties deduced from electron-scattering data.

A new measurement of the ${}^{239}\mathrm{Pu}(n,2n)$ ${}^{238}\mathrm{Pu}$ cross section was performed at 7.1, 7.7, and 9.3-MeV incident neutron energy using an activation technique to help resolve inconsistencies in the existing database above the threshold of the reaction. The method is based on the collection of ${}^{238}\mathrm{Pu}$ nuclei produced in the $(n,2n)$ reaction. Although never used before to obtain a neutron cross section, this recoil technics overcomes the difficulty of having deposits of ${}^{239}\mathrm{Pu}$ of extremely high purity. The collection efficiency must be determined using previously published data at higher energy, and our measurements are relative to these points. The neutrons were produced via the ${}^2\mathrm{H}(d,n)$ ${}^3\mathrm{He}$ reaction. The incident neutron flux was determined via the ${}^{27}\mathrm{Al}$($n$,α) ${}^{24}\mathrm{Na}$ standard reaction. The present measurements are consistent with the previous data and disagree with the jeff3.3 evaluation.

We investigate the effects of prehydrodynamic evolution on final-state observables in heavy-ion collisions using state-of-the art event simulations coupled to different prehydrodynamic scenarios, which include the recently developed effective kinetic transport theory evolution model KøMPøST. Differential flow observables are found to be mostly insensitive to the details of prehydrodynamic evolution. The main effect we observe is in the $p_T$ spectra, particularly the mean transverse momentum. However, at least part of this effect is a consequence of the underlying conformal invariance assumption currently present in such approaches, which is known to be violated in the temperature regime probed in heavy-ion collisions. This assumption of early time conformal invariance leads to an artificially large out-of-equilibrium bulk pressure when switching from (conformal) prehydrodynamic evolution to hydrodynamics (using the nonconformal QCD equation of state), which in turn increases the transverse momentum. Our study indicates that a consistent treatment of prehydrodynamic evolution in heavy-ion collisions requires the use of nonconformal models of early time dynamics.