In high-energy heavy-ion collisions, the initial condition of the produced quark-gluon plasma (QGP) and its evolution are sensitive to collective nuclear structure parameters describing the shape and radial profiles of the nuclei. We find a general scaling relation between these parameters and many experimental observables such as elliptic flow, triangular flow, and particle multiplicity distribution. In particular, the ratios of observables between two isobar systems depend only on the differences of these parameters, but not on the details of the final state interactions, hence offering a new way to constrain the QGP initial condition. Using this scaling relation, we show how the structure parameters of ${}_{44}^{96}\mathrm{Ru}$ and ${}_{40}^{96}\mathrm{Zr}$ conspire to produce the rich centrality dependences of these ratios, as measured by the STAR Collaboration. Our scaling approach demonstrates that isobar collisions are a precision tool to probe the initial condition of heavy-ion collisions, as well as the collective nuclear structures, including the neutron skin, of the atomic nuclei across energy scales.

The magnetic hyperfine structure constants have been calculated for low-lying levels in aneutral potassium atoms taking into account the Bohr-Weisskopf (BW) and Breit–Rosenthal (BR) effects. According to our results the $4p_{1/2}$ state of K I is free from both BR and BW corrections on the level of the current theoretical uncertainties. Using this finding and the measured values of the $A\left(4p_{1/2}\right)$ constants, we corrected the nuclear magnetic moments for several short-lived potassium isotopes. The BW correction is represented as a product of atomic and nuclear factors. We calculated the atomic factor for the ground state of K I, which allowed us to extract nuclear factors for potassium $I^{\pi }=3/2^{+}$ isotopes from the experimental data. In this way the application range of the single-particle nuclear model for nuclear-factor calculation in these isotopes has been clarified.

Background: Single-charge-exchange reactions are appropriate tools to study the nuclear response to one-particle/one-hole isospin probes, gaining additional interest from the connection to beta decay. This analogy has been recently extended to second order, connecting double-charge-exchange reactions and double beta decays. Nowadays, the availability of powerful experimental setups and advanced nuclear theories and models allows one to access precious information on key nuclear structure aspects embedded in the widely sought neutrinoless double beta decay.

Purpose: We intend to bring to light the main nuclear structure and reaction features involved in the ${}^{18}\mathrm{O}+{}^{12}\mathrm{C}$ collision at 275 MeV incident energy. In this paper, the main focus is on the role of the initial- and final-state interactions in the overall reaction dynamics and on the single-particle nuclear structure properties accessed via the study of single-nucleon transfer reactions. Forthcoming articles will be devoted to go into the details of the response to one- and two-particle/hole isospin probes.

Methods: Cross-section energy spectra and angular distributions were measured in a unique experimental setup for the ${}^{12}\mathrm{C}({}^{18}\mathrm{O},{}^{18}\mathrm{O}){}^{12}\mathrm{C}$ elastic and inelastic scattering, the ${}^{12}\mathrm{C}({}^{18}\mathrm{O},{}^{17}\mathrm{O}){}^{13}\mathrm{C}$ one-neutron stripping, the ${}^{12}\mathrm{C}({}^{18}\mathrm{O},{}^{19}\mathrm{F}){}^{11}\mathrm{B}$ one-proton pickup, and the ${}^{12}\mathrm{C}({}^{18}\mathrm{O},{}^{18}\mathrm{F}){}^{12}\mathrm{B}$ single-charge-exchange nuclear reactions. A unique comprehensive and coherent theoretical calculation, able to describe the whole network of direct reactions using state-of-the-art nuclear structure and reaction theories, was performed, and it is presented for the first time in this article. This holistic approach, applied both to the experimental and theoretical analysis, is the main feature and worth of the work here presented.

Results: The energy and angular resolutions achieved in each reaction channel allowed us to isolate specific transitions and to map the diffraction patterns in the angular distributions. The cross-section calculations describe well the experimental data, both in terms of the absolute values and diffraction patterns. Although the distorted wave Born approximation (DWBA) calculations prove to be accurate in describing all the studied channels, better results are achieved when the couplings to inelastic transitions in both the incoming and outgoing partitions are introduced, as done in the coupled channels Born approximation (CCBA) calculations. Otherwise, no real improvement is found when the coupling effects among different partitions are explicitly taken into account in the coupled reaction channels (CRC) calculations.

Conclusions: The multichannel approach proposed in this paper is a promising method for accurate investigations of direct reactions originating in heavy-ion collisions. This is quite appealing for the precise spectroscopy of heavy nuclei proposed in many areas of nuclear physics. An example is the NUMEN project with its challenging commitment to provide valuable information on neutrinoless double beta decay nuclear matrix elements from single- and double-charge-exchange cross-section measurements.

The neutron-induced fission cross section of ${}^{239}\mathrm{Pu}$ was measured relative to ${}^{235}\mathrm{U}(n,f)$ at the back-streaming white neutron beam line (Back-n) of the China Spallation Neutron Source (CSNS). A multicell fast fission ionization chamber was used to perform the measurement. The reliability of the measurement was verified by the high consistency of ${}^{235}\mathrm{U}$'s resonances between the measurement and the evaluation data. The ${}^{239}\mathrm{Pu}$ fission cross sections from $4\mathrm{keV}$ to $100\mathrm{MeV}$ are obtained with 1.7–5.8 % uncertainty when unfolding uncertainties are excluded. The total uncertainties including the unfolding errors, which reflect the effect of the double-bunch unfolding method, are 2.6–15 % from $10\mathrm{keV}$ to $100\mathrm{MeV}$.

We apply an equal-velocity quark combination model to systematically study the transverse momentum ($p_T$) spectra of identified hadrons $K_S^0, \varphi , \mathrm{\Lambda }, {\mathrm{\Xi }}^{-}, {\mathrm{\Omega }}^{-}, \overline{\mathrm{\Lambda }}, {\overline{\mathrm{\Xi }}}^{+}, {\overline{\mathrm{\Omega }}}^{+}, p, \overline{p}, {\pi }^{+}$, and ${\pi }^{-}$ at midrapidity in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 54.4 GeV. The relative deviation between model calculations and experimental data of these 12 hadrons is generally about 10% in central collisions even at low collision energies and is weakly increased in peripheral collisions. We systematically explain the dependence of two baryon-to-meson ratios $\overline{\mathrm{\Lambda }}/K_S^0$ and $\mathrm{\Omega }/\varphi$ on $p_T$, collision centrality, and collision energy by the property of quark $p_T$ spectra at hadronization. We derive the analytic relations between $R_{CP}$ of hadrons and those of quarks, and we use them to naturally explain the species and $p_T$ dependence of $R_{CP}$ of those strange hadrons.

We investigate the exchange effect between the final atom's bound electrons and those emitted in the allowed $\beta$ decay of the initial nucleus. The electron wave functions are obtained with the Dirac-Hartree-Fock-Slater self-consistent method, and we ensure the orthogonality between the continuum and bound electron states, in the potential of the final atom, by modifying the last iteration of the self-consistent method. We show that orthogonality plays an essential role in calculating the exchange correction. After imposing the orthogonality, we found considerable differences in magnitude and energy dependence compared to previous results. We argue that our findings can solve the mismatch between the previous predictions and experimental measurements in the low-energy region of the $\beta$ spectrum. First, we calculate the exchange effect for the low-energy $\beta$ transitions in ${}^{14}\mathrm{C}$, ${}^{45}\mathrm{Ca}$, ${}^{63}\mathrm{Ni}$, and ${}^{241}\mathrm{Pu}$, recently investigated in the literature. Next, we compute the total exchange correction for a large number of $\beta$ emitters with $Z$ from 1 to 102. From the systematic study, we found that for ultralow energy, i.e., 5 eV, the $Z$ dependence of the total exchange effect is affected by $s_{1/2}$ and $p_{1/2}$ orbitals closure. We also show that the contributions from orbitals higher than the $2s_{1/2}$ orbital are essential for correctly calculating the total effect, especially for low energies and heavy $\beta$ emitters. Finally, we provide an analytical expression of the total exchange correction for each atomic number for easy implementation in experimental investigations.

Nuclear fission is still one of the most complex physical processes we can observe in nature due to the interplay of macroscopic and microscopic nuclear properties that decide the result. An example of this coupling is the presence of nuclear dissipation as an important ingredient that contributes to drive the dynamics and has a clear impact on the time of the process. However, different theoretical interpretations, and scarce experimental data make it poorly understood. In this Letter, we present the first experimental determination of the dissipation energy in fission as a function of the fragment split, for three different fissioning systems. The amount of dissipation was obtained through the measurement of the relative production of fragments with even and odd atomic numbers with respect to different initial fission energies. The results reveal a clear effect of particular nuclear shells on the dissipation and fission dynamics. In addition, the relative production of fragments with even and odd atomic numbers appears as a potential contributor to the long-standing problem of the time scale in fission.

Based on the reflection-asymmetric Nilsson potential, the parity-doublet rotational bands in odd-$A$ isotones ${}^{237}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$ have been investigated by using the particle-number-conserving (PNC) method in the framework of the cranked shell model (CSM). The experimental kinematic moments of inertia (MOIs) and angular momentum alignments are reproduced very well by the PNC-CSM calculations. The significant differences of rotational properties between ${}^{237}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$ are explained with the contribution of nucleons occupying proton octupole-correlation pairs of ${\pi }^2{i}_{13/2}{f}_{7/2}$. The upbendings of MOIs of the parity-doublet bands in ${}^{237}\mathrm{U}$ are due to the interference terms of alignments of protons occupying $\pi f_{7/2}$ ($\mathrm{\Omega }=1/2$) and the high-$j$ intruder $\pi i_{13/2}(\mathrm{\Omega }=1/2,3/2)$ orbitals. The splittings between the simplex partner bands of the parity-doublet bands in both ${}^{237}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$ result from the contribution of alignment of neutron occupying the $\nu d_{5/2}$ ($\mathrm{\Omega }=1/2$) orbital.

The ground-state magnetic dipole moment of the neutron-rich ${}^{21}\mathrm{O}$ isotope has been measured via $\beta$-ray-detected nuclear magnetic resonance ($\beta \text{−}\mathrm{NMR}$) spectroscopy by using a spin-polarized secondary beam of ${}^{21}\mathrm{O}$ produced from the ${}^{22}\mathrm{Ne}$ primary beam. From the present measurement, the $g$ factor $|g_{\exp }\left({}^{21}\mathrm{O}_{\mathrm{g}.\mathrm{s}.}\right)|=0.6036\left(14\right)$ has been determined. Based on the comparison of this value with Schmidt values, we unambiguously confirm the $\nu d_{5/2}$ configuration with spin and parity assignments $I^{\pi }=5/2^{+}$ for the ${}^{21}\mathrm{O}$ ground state, suggested by previously reported studies. Consequently, the magnetic moment has been determined as ${\mu }_{\exp }\left({}^{21}\mathrm{O}_{\mathrm{g}.\mathrm{s}.}\right)=(-)1.5090\left(35\right){\mu }_N$. The obtained experimental magnetic moment is in good agreement with the predictions of the shell-model calculations using the USD, YSOX, and SDPF-M interactions as well as random phase approximation (RPA) calculations. This observation indicates that the ${}^{21}\mathrm{O}$ nucleus in its ground state does not manifest any anomalous structure and is not influenced by the proximity of the drip line.

The multinucleon transfer reactions ${}^{197}\mathrm{Au}+{}^{232}\mathrm{Th}, {}^{186}\mathrm{W}+{}^{232}\mathrm{Th}$, and ${}^{238}\mathrm{U}+{}^{232}\mathrm{Th}$ are investigated within the framework of dinuclear system (DNS) model with a decay model gemini$++$. The calculated isotopic production cross sections in the ${}^{136}\mathrm{Xe}+{}^{249}\mathrm{Cf}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}=567\mathrm{MeV}$ can reproduce the experimental data well. Due to the subshell closures, the behavior of “inverse” quasifission process is found in the collisions of ${}^{186}\mathrm{W}+{}^{232}\mathrm{Th}$ and ${}^{197}\mathrm{Au}+{}^{232}\mathrm{Th}$. The reaction ${}^{197}\mathrm{Au}+{}^{232}\mathrm{Th}$ is more advantageous to produce neutron-rich isotopes with $Z=92–106$ than ${}^{186}\mathrm{W}+{}^{232}\mathrm{Th}$ and ${}^{238}\mathrm{U}+{}^{232}\mathrm{Th}$, because it has the lowest value of the potential energy that needed to overcome in the nucleon transfer process. Furthermore, the incident energy dependence of isotopic production cross sections in the reaction ${}^{197}\mathrm{Au}+{}^{232}\mathrm{Th}$ is studied. It is found that $E_{\mathrm{c}.\mathrm{m}.}=756.47$ MeV is more suitable for producing new isotopes with $Z=92–98$, while $E_{\mathrm{c}.\mathrm{m}.}=690.69$ MeV is the optimal incident energy for $Z=99–106$. The effect of incident energy on the interaction time is also investigated. The production cross sections of 88 unknown neutron-rich transuranium nuclei are predicted with the cross sections at the order of ${10}^{-6}$ to $10\mu \mathrm{b}$.

Ab initio approaches to the nuclear many-body problem have seen their reach considerably extended over the past decade. However, collective excitations have been scarcely addressed so far due to the prohibitive cost of solving the corresponding equations of motion. Here, a numerically efficient method to compute electromagnetic response functions at zero- and finite-temperature in superfluid and deformed nuclei from an ab initio standpoint is presented and applied to ${}^{16}\mathrm{O}, {}^{28}\mathrm{Si}, {}^{46}\mathrm{Ti}$, and ${}^{56}\mathrm{Fe}$. This work opens the path to systematic ab initio calculations of nuclear responses to electroweak probes across a significant portion of the nuclear chart.

A minimal set of five low energy constants (LECs) for time-reversal and parity violating $\left(\cancel{T}\cancel{P}\right)$ nucleon-nucleon $\left(NN\right)$ interactions at low energies $(E<m_{\pi }^2/M_N)$ is given. Using a large-$N_C$ (number of colors in quantum chromodynamics) analysis we show that one linear combination of LECs is $\mathcal{O}\left(N_C\right)$, three LECs are $\mathcal{O}\left(N_C^0\right)$, and one linear combination of LECs is $\mathcal{O}\left(N_C^{-1}\right)$. We also calculate the $\cancel{T}\cancel{P}$ observables of neutron spin rotation through a polarized deuteron target and a spin correlation coefficient in nucleon-deuteron scattering using pionless effective field theory. Using the large-$N_C$ analysis we show that the spin correlation coefficient and the neutron spin rotation are predominantly determined by the same two LECs in the large-$N_C$ basis.

Within the improved scission-point fission model, it is shown that the average neutron number per proton is not the same in fission fragments and is not equal to that in a fissioning nucleus. For the induced fission of ${}^{238}\mathrm{U}$, ${}^{240}\mathrm{Pu}$, ${}^{244}\mathrm{Cm}$, and ${}^{250}\mathrm{Cf}$, the dependencies of the fission-fragment neutron-excess ratio on the shell structure and excitation energy of fragment are studied.

Recently, the PHENIX Collaboration has published second- and third-harmonic Fourier coefficients $v_2$ and $v_3$ for midrapidity $(\left|\eta \right|<0.35)$ charged hadrons in 0%–5% central $p+\mathrm{Au}$, $d+\mathrm{Au}$, and ${}^3\mathrm{He}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV, utilizing three sets of two-particle correlations for two detector combinations with different pseudorapidity acceptance [Acharya et al., Phys. Rev. C 105, 024901 (2022)]. This paper extends these measurements of $v_2$ to all centralities in $p+\mathrm{Au}$, $d+\mathrm{Au}$, and ${}^3\mathrm{He}+\mathrm{Au}$ collisions, as well as $p+p$ collisions, as a function of transverse momentum ($p_T$) and event multiplicity. The kinematic dependence of $v_2$ is quantified as the ratio $R$ of $v_2$ between the two detector combinations as a function of event multiplicity for $0.5<p_T<1$ and $2<p_T<2.5\mathrm{GeV}/c$. A multiphase-transport (AMPT) model can reproduce the observed $v_2$ in most-central to midcentral $d+\mathrm{Au}$ and ${}^3\mathrm{He}+\mathrm{Au}$ collisions. However, the AMPT model systematically overestimates the measurements in $p+p$, $p+\mathrm{Au}$, and peripheral $d+\mathrm{Au}$ and ${}^3\mathrm{He}+\mathrm{Au}$ collisions, indicating a higher nonflow contribution in the AMPT model than in the experimental data. The AMPT model fails to describe the observed $R$ for $0.5<p_T<1\mathrm{GeV}/c$, but there is qualitative agreement with the measurements for $2<p_T<2.5\mathrm{GeV}/c$.

In this work, we perform a study of the ${\pi }^{-}p\to a_0^{-}\eta p$ reaction within an effective Lagrangian approach and isobar model. In our model, we consider the excitation of the $N^{*}$ and ${\mathrm{\Delta }}^{*}$ resonances in the intermediate states and background terms. Based on our model, it is found that this reaction is dominated by the production of the $N\left(1535\right)$ in the near threshold region. And the contributions from other well-established $N^{*}$ or ${\mathrm{\Delta }}^{*}$ resonances only play minor roles. Besides, we discuss the possibility of verifying the existence of a narrow nucleon resonance $N\left(1685\right)$/$N\left(1700\right)$ proposed by some recent works in the present reaction. With adopting different quantum numbers, we find that it may contribute significantly in this reaction. Thus this reaction may provide a good platform to study the properties of nucleon resonances, e.g., $N\left(1535\right)$ and $N\left(1685\right)$/$N\left(1700\right)$, which couple strongly with the $\eta N$ channel. To compare with future experiments, the predictions of the total cross sections, the angular distributions, and invariant mass spectrums of final particles are also presented. Furthermore, the off-shell effects due to high-spin states are also discussed.

Background: The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. Recently, it has attracted increasing interest as it can be exploited to extend ab initio methods to the collective excitations of medium-mass and heavy deformed nuclei, as well as the nuclear matrix elements (NME) of candidates for neutrinoless double-beta ($0\nu \beta \beta$) decay.

Purpose: The computational complexity of the GCM increases rapidly with the number of collective coordinates. It imposes a strong restriction on the applicability of the method. We aim to exploit statistical machine-learning (ML) algorithms to speed up GCM calculations and ultimately provide a more efficient description of nuclear energy spectra and other observables such as the NME of $0\nu \beta \beta$ decay without loss of accuracy.

Method: In this work, we propose a subspace-reduction algorithm that employs optimal statistical ML models as surrogates for exact quantum-number projection calculations for norm and Hamiltonian kernels. The model space of the original GCM is reduced to a subspace relevant for nuclear low energy spectra and the NME of ground state to ground state $0\nu \beta \beta$ decay based on the orthogonality condition (OC) and the energy-transition-orthogonality procedure (ENTROP), respectively. Nuclear energy spectra are determined by the GCM through the configuration mixing within this subspace. For simplicity, the polynomial ridge regression (RR) algorithm is used to learn the norm and Hamiltonian kernels of axially deformed configurations. The efficiency and accuracy of this algorithm are illustrated for ${}^{76}\mathrm{Ge}$ and ${}^{76}\mathrm{Se}$ by comparing results obtained using the optimal RR models to direct GCM calculations. The nonrelativistic Gogny force D1S and relativistic energy density functional PC-PK1, a valence-space shell-model Hamiltonian, and a modern nuclear interaction derived from chiral effective field theory are employed.

Results: The low-lying energy spectra of ${}^{76}\mathrm{Ge}$ and ${}^{76}\mathrm{Se}$, as well as the $0\nu \beta \beta$-decay NME between their ground states, are computed. The results show that the performance of the $\mathrm{GCM}+\text{OC/ENTROP}+\mathrm{RR}$ is more robust than that of the $\mathrm{GCM}+\mathrm{RR}$ alone, and the former can reproduce the results of the original GCM calculation accurately with a significantly reduced computational cost.

Conclusions: Statistical ML algorithms, when implemented properly, can accelerate GCM calculations without loss of accuracy. In applications with axially deformed states, the computation time can be reduced by a factor of three to nine for energy spectra and NMEs, respectively. This factor is expected to increase significantly with the number of employed generator coordinates.