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The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. This white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS., Comment: White paper prepared for the 2023 Long Range Plan. v3: Updated version as published in Progress in Particle and Nuclear Physics. Note: the published version does not include the executive summary; in the updated arXiv version, the executive summary is included as an appendix. v4: Corrected list of authors

Nuclear fission produces fragments whose spins are coupled to the relative angular motion via angular momentum conservation. It is shown how ensembles of such spins can readily be obtained by either direct microcanonical sampling or by sampling of the associated normal modes of rotation. The resulting distribution of the spin-spin opening angle is illustrated in various three- and two- dimensional scenarios and it is demonstrated how recent mutually conflicting model calculations can be well reproduced with different assumptions about the scission geometry., Comment: 5 pages, 5 figures

We study $\gamma$-ray emission following $^{239}\mathrm{Pu}(n,\mathrm{f})$ over an incident neutron energy range of $2 < E_i < 40$ MeV. We present the first experimental evidence for positive correlations between the total angular momentum generated in fission and the excitation energy of the compound nucleus prior to fission. The $\gamma$-ray multiplicity increases linearly with incident energy below the 2\textsuperscript{nd}-chance fission threshold with a slope of $0.085 \pm 0.010$ MeV$^{-1}$. This linear trend appears to hold for the average excitation energy of the compound nucleus between $9 < \langle E_x \rangle < 19$ MeV. Most of the multiplicity increase comes from an enhancement around a $\gamma$-ray energy of 0.7 MeV, which we interpret as stretched quadrupole $\gamma$ rays that indicate an increase in total fission-fragment angular momentum with excitation energy., Comment: 9 pages, 5 figures

We differentiate the event-by-event n-$\gamma$ multiplicity data from \ce{^{252}Cf}(sf) with respect to the energies of the emitted particles as well as their relative angles of emission. We determine that neutron emission enhances $\gamma$-ray emission around $0.7$ and $1.2$ MeV, but the only directional alignment was observed for $E_\gamma \leq 0.7$ MeV and tended to be parallel and antiparallel to neutrons emitted in the same event. The emission of $\gamma$ rays at other energies was determined to be nearly isotropic. The presence of the emission and alignment enhancements is explained by positive correlations between neutron emission and quadrupole $\gamma$-ray emission along rotational bands in the de-exciting fragments. This observation corroborates the hypothesis of positive correlations between the angular momentum of a fragment and its intrinsic excitation energy. The results of this work are especially relevant in view of the recent theoretical and experimental interest in the generation of angular momentum in fission. Specifically, we have determined an alignment of the fragments angular momenta in a direction perpendicular to the direction of motion. We interpret the lack of $n$-$\gamma$ angular correlations for fission fragments near closed shells as a weakening of the alignment process for spherical nuclei. Lastly, we have observed that statistical $\gamma$ rays are emitted isotropically, indicating that the average angular momentum removed by this radiation is small. These results, and the analysis tools presented in this work, represent a stepping stone for future analysis of $n$-$\gamma$ emission correlations and their connection to angular momentum properties., Comment: 17 pages, 3 figures, no table

The emission of neutrons and gamma rays by fission fragments reveal important information about the properties of fragments immediately following scission. The initial fragment properties, correlations between fragments, and emission competition give rise to correlations in neutron-gamma emission. Neutron-gamma correlations are important in nonproliferation applications because the characterization of fissionable samples relies on the identification of signatures in the measured radiation. Furthermore, recent theoretical and experimental advances have proposed to explain the mechanism of angular momentum generation in fission. In this paper, we present a novel analysis method of neutrons and gamma rays emitted by fission fragments that allows us to discern structure in the observed correlations. We have analyzed data collected on \ce{^{252}Cf}(sf) at the Chi-Nu array at the Los Alamos Neutron Science Center. Through our analysis of the energy-differential neutron-gamma multiplicity covariance, we have observed enhanced neutron-gamma correlations, corresponding to rotational band gamma-ray transitions, at gamma-ray energies of $0.7$ and $1.2$ MeV. To shed light on the origin of this structure, we compare the experimental data with the predictions of three model calculations. The origin of the observed correlation structure is understood in terms of a positive spin-energy correlation in the generation of angular momentum in fission., Comment: 21 pages, 4 figures, 1 table

During nuclear fission, a heavy nucleus splits into two rotating fragments. The associated angular momentum is large, yet the mechanism of its generation and its dependence on the mass of fragments remain poorly understood. In this Letter, we provide the first microscopic calculations of angular momentum distributions in fission fragments for a wide range of fragment masses. For the benchmark case of $^{239}$Pu($n_{\text{th}}$,f), we find that the angular momentum of the fragments is largely determined by the nuclear shell structure and deformation, and that the heavy fragments therefore typically carry less angular momentum than their light partners. We use the fission model $\tt{FREYA}$ to simulate the emission of neutrons and photons from the fragments. The dependence of the angular momenta on fragment mass after the emission of neutrons and statistical photons is linear for the heavy fragments and either constant or weakly linear for the light fragments, consistent with the universal sawtooth pattern suggested by recent experimental data. Finally, we observe that using microscopic angular momentum distributions modifies the number of emitted photons significantly., Comment: 7 pages, 2 figures

Neutron star mergers (NSMs) are the first verified sites of rapid neutron capture (r-process) nucleosynthesis, and could emit gamma rays from the radioactive isotopes synthesized in the neutron-rich ejecta. These MeV gamma rays may provide a unique and direct probe of the NSM environment as well as insight into the nature of the r process, just as observed gammas from the 56Ni radioactive decay chain provide a window into supernova nucleosynthesis. In this work, we include the photons from fission processes for the first time in estimates of the MeV gamma-ray signal expected from an NSM event. We consider NSM ejecta compositions with a range of neutron richness and find a dramatic difference in the predicted signal depending on whether or not fissioning nuclei are produced. The difference is most striking at photon energies above ~3.5 MeV and at a relatively late time, several days after the merger event, when the ejecta is optically thin. We estimate that a Galactic NSM could be detectable by a next generation gamma-ray detector such as AMEGO in the MeV range, up to ~10^4 days after the merger, if fissioning nuclei are robustly produced in the event., Comment: 9 pages, 5 figures, v2 matches version to appear in ApJL

There has been much recent interest in nuclear fission, due in part to a new appreciation of its relevance to astrophysics, stability of superheavy elements, and fundamental theory of neutrino interactions. At the same time, there have been important developments on a conceptual and computational level for the theory. The promising new theoretical avenues were the subject of a workshop held at the University of York in October 2019; this report summarises its findings and recommendations., Comment: 86 LaTeX pages, 3 figures, 331 references, version published as Topical Review in Journal of Physics G

The coordinate and momentum space configurations of the net baryon number in heavy ion collisions that undergo spinodal decomposition, due to a first-order phase transition, are investigated using state-of-the-art machine-learning methods. Coordinate space clumping, which appears in the spinodal decomposition, leaves strong characteristic imprints on the spatial net density distribution in nearly every event which can be detected by modern machine learning techniques. On the other hand, the corresponding features in the momentum distributions cannot clearly be detected, by the same machine learning methods, in individual events. Only a small subset of events can be systematically differentiated if only the momentum space information is available. This is due to the strong similarity of the two event classes, with and without spinodal decomposition. In such scenarios, conventional event-averaged observables like the baryon number cumulants signal a spinodal non-equilibrium phase transition. Indeed the third-order cumulant, the skewness, does exhibit a peak at the beam energy ($\mathrm{E}_{\mathrm{lab}}= 3-4$ A GeV), where the transient hot and dense system created in the heavy ion collision reaches the first-order phase transition., Comment: 24 pages, 14 figures, accepted for publication by JHEP

We evaluate the impact of using sets of fission yields given by the GEF code for spontaneous (sf), neutron-induced ((n,f)), and beta-delayed (betadf) fission processes which take into account the approximate initial excitation energy of the fissioning compound nucleus. We further explore energy-dependent fission dynamics in the r process by considering the sensitivity of our results to the treatment of the energy sharing and de-excitation of the fission fragments using the FREYA code. We show that the asymmetric-to-symmetric yield trends predicted by GEF can reproduce the high-mass edge of the second r-process peak seen in solar data and examine the sensitivity of this result to the mass model and astrophysical conditions applied. We consider the effect of fission yields and barrier heights on the nuclear heating rates used to predict kilonova light curves. We find that fission barriers influence the contribution of 254Cf spontaneous fission to the heating at ~100 days, such that a light curve observation consistent with such late-time heating would both confirm that actinides were produced in the event and imply the fission barriers are relatively high along the 254Cf beta-feeding path. We lastly determine the key nuclei responsible for setting the r-process abundance pattern by averaging over thirty trajectories from a 1.2--1.4 M_odot neutron star merger simulation. We show it is largely the odd-N nuclei undergoing (Z,N)(n,f) and (Z,N)betadf that control the relative abundances near the second peak. We find the "hot spots" for beta-delayed and neutron-induced fission given all mass models considered and show most of these nuclei lie between the predicted N=184 shell closure and the location of currently available experimental decay data.

The dependence of correlations of neutron multiplicity {\nu} and gamma-ray multiplicity Mg in spontaneous fission of 252Cf on fragment mass A* and total kinetic energy TKE has been investigated employing the ratio of Mg/{\nu} and the form of Mg({\nu}). We show for the first time that Mg and {\nu} have a complex correlation for heavy fragment masses, while there is a positive dependence of Mg({\nu}) for light fragment masses and for near-symmetric mass splits. The ratio Mg/{\nu} exhibits strong shell effects for the neutron magic number N = 50 and near the doubly magic number shell closure at Z = 50 and N = 82. The gamma-ray multiplicity Mg has a maximum for TKE = 165-170 MeV. Above 170 MeV Mg(TKE) is approximately linear, while it deviates significantly from a linear dependence at lower TKE. The correlation between the average neutron and gamma-ray multiplicities can be partly reproduced by model calculations., Comment: 14 pages,8 figures

Within the context of relativistic nuclear collisions aimed at exploring hot and baryon-dense matter, we investigate how the general features of the expansion dynamics, as well as a number of specific observables, depend on the equation of state used in dynamical simulations of the non-equilibrium confinement phase transition., Comment: 13 pages, 10 figures, version accepted by PRC

We recently introduced a fluid-dynamical model for simulating relativistic nuclear collisions in the presence of a first-order phase transition and made explorative studies of head-on lead-lead collisions. We give here a more detailed account of this novel theoretical tool and carry out more exhaustive studies of the phase-separation dynamics. Extracting the density enhancement caused by the spinodal instabilities, the associated clump size distribution, and the resulting transverse flow velocity, we examine the sensitivity of these quantities to the strength of the gradient term that promotes the phase separation, to the details of the initial density fluctuations that form the seeds for the subsequent amplification, and to the equation of state., Comment: 11 pages, 14 figures, version accepted by PRC

Extending a previously developed two-phase equation of state, we simulate head-on relativistic lead-lead collisions with fluid dynamics, augmented with a finite-range term, and study the effects of the phase structure on the evolution of the baryon density. For collision energies that bring the bulk of the system into the mechanically unstable spinodal region of the phase diagram, the density irregularities are being amplified significantly. The resulting density clumping may be exploited as a signal of the phase transition, possibly through an enhanced production of composite particles., Comment: 4 pages 4 figures, version accepted by PRL

The surface tension of quark matter plays a crucial role for the possibility of quark matter nucleation during the formation of compact stellar objects, because it determines the nucleation rate and the associated critical size. However, this quantity is not well known and the theoretical estimates fall within a wide range, $\gamma_0 \approx 5-300 MeV/fm^2$. We show here that once the equation of state is available one may use a geometrical approach to obtain a numerical value for the surface tension that is consistent with the model approximations adopted. We illustrate this method within the two-flavor linear \sigma model and the Nambu--Jona-Lasinio model with two and three flavors. Treating these models in the mean-field approximation, we find $\gamma_0 \approx 7-30 MeV/fm^2$. Such a relatively small surface tension would favor the formation of quark stars and may thus have significant astrophysical implications. We also investigate how the surface tension decreases towards zero as the temperature is raised from zero to its critical value.

Although nuclear fission can be understood qualitatively as an evolution of the nuclear shape, a quantitative description has proven to be very elusive. In particular, until now, there exists no model with demonstrated predictive power for the fission fragment mass yields. Exploiting the expected strongly damped character of nuclear dynamics, we treat the nuclear shape evolution in analogy with Brownian motion and perform random walks on five-dimensional fission potential-energy surfaces which were calculated previously and are the most comprehensive available. Test applications give good reproduction of highly variable experimental mass yields. This novel general approach requires only a single new global parameter, namely the critical neck size at which the mass split is frozen in, and the results are remarkably insensitive to its specific value., Comment: 4 pages, 2 ps figures

The spinodal amplification of density fluctuations is treated perturbatively within dissipative fluid dynamics for the purpose of elucidating the prospects for this mechanism to cause a phase separation to occur during a relativistic nuclear collision. The present study includes not only viscosity but also heat conduction (whose effect on the growth rates is of comparable magnitude but opposite), as well as a gradient term in the local pressure, and the corresponding dispersion relation for collective modes in bulk matter is derived from relativistic fluid dynamics. A suitable two-phase equation of state is obtained by interpolation between a hadronic gas and a quark-gluon plasma, while the transport coefficients are approximated by simple parametrizations that are suitable at any degree of net baryon density. We calculate the degree of spinodal amplification occurring along specific dynamical phase trajectories characteristic of nuclear collision at various energies. The results bring out the important fact that the prospects for spinodal phase separation to occur can be greatly enhanced by careful tuning of the collision energy to ensure that the thermodynamic conditions associated with the maximum compression lie inside the region of spinodal instability., Comment: 14 pages, 12 figures

We construct a simple two-phase equation of state intended to resemble that of compressed baryon-rich matter and then introduce a gradient term in the compressional energy density to take account of fintie-range effects in non-uniform configurations. With this model we study the interface between the two coexisting phases and obtain estimates for the associated interface tension. Subsequently, we incorporate the finite-range equation of state into ideal or viscous fluid dynamics and derive the collective dispersion relation for the mechanically unstable modes of bulk matter in the spinodal region of the thermodynamic phase diagram. Combining these results with time scales extracted from existing dynamical transport simulations, we discuss the prospects for spinodal phase separation to occur in nuclear collisions. We argue that these can be optimized by a careful tuning of the collision energy to maximize the time spent by the bulk of the system inside the mechanically unstable spinodal region of the phase diagram. Our specific numerical estimates suggest cautious optimism that this phenomenon may in fact occur, though a full dynamical simulation is needed for a detailed assessment., Comment: 13 pages, 11 eps files

Using simple parametrizations of the thermodynamic freeze-out parameters extracted from the data over a wide beam-energy range, we reexpress the hadronic freeze-out line in terms of the underlying dynamical quantities, the net baryon density rhoB and the energy density epsilon, which are subject to local conservation laws. This analysis makes it apparent that rhoB exhibits a maximum as the collision energy is decreased. This maximum freeze-out density has muB=400-500 MeV, which is above the critical value, and it is reached for a fixed-target bombarding energy of 20-30 GeV/A., Comment: 3 pages, 1 eps figure

If the deconfinement phase transformation of strongly interacting matter is of first-order and the expanding chromodynamic matter created in a high-energy nuclear collision enters the corresponding region of phase coexistence, a spinodal phase separation might occur. The matter would then condense into a number of separate blobs, each having a particular net strangeness that would remain approximately conserved during the further evolution. We investigate the effect that such `strangeness trapping' may have on strangeness-related hadronic observables. The kaon multiplicity fluctuations are significantly enhanced and thus provide a possible tool for probing the nature of the phase transition experimentally., Comment: 15 pages, 11 eps figures

High-energy nuclear collisions produce quark-gluon plasmas that expand and hadronize. If the associated phase transition is of first order then the hadronization should proceed through a spinodal phase separation. We explore here the possibility of identifying the associated clumping by analysis of suitable N-particle momentum correlations., Comment: 7 pages, incl 4 ps figures

We investigate the effects of strong color fields and of the associated enhanced intrinsic transverse momenta on the phi-meson production in ultrarelativistic heavy ion collisions at RHIC. The observed consequences include a change of the spectral slopes, varying particle ratios, and also modified mean transverse momenta. In particular, the composition of the production processes of phi mesons, that is, direct production vs. coalescence-like production, depends strongly on the strength of the color fields and intrinsic transverse momenta and thus represents a sensitive probe for their measurement., Comment: 4 pages, 3 figures

The expansion of strongly interacting matter formed in high-energy nuclear collisions drives the system through the region of phase coexistence. The present study examines the associated spinodal instability and finds that the degree of amplification may be sufficient to raise the prospect of using the spinodal pattern formation as a diagnostic tool for probing the hadronization phase transition., Comment: 4 pages, 4 eps figures

Recent experimental data appear to confirm the existence of the exotic Theta+ (uudd\bar{s}) baryon. Simple statistical considerations, which have generally proven rather successful, suggest that this particle should be produced in observable abundance in relativistic nuclear collisions at RHIC, where it may be identifed through the p-K0_s invariant mass spectrum. The observation would not only add new evidence for its existence, but would also provide an additional means for probing the collision system, especially with regard to strangeness., Comment: 4 pages, RevTeX, no figures

Employing a previously derived formulation, and extending the treatment from purely transverse modes to wave vectors having a longitudinal component, we discuss the prospects for the occurrence of Weibel-type color-current filamentation in high-energy nuclear collisions. Numerical solutions of the dispersion equation for a number of scenarios relevant to RHIC and LHC suggest that modes with (predominantly transverse) wave numbers of several hundred MeV may become moderately agitated during the early collision stage. The emergence of filamentation helps to speed up the equilibration of the parton plasma and it may lead to non-statistical azimuthal patterns in the hadron final state., Comment: 11 pages, RevTex, 13 (e)ps files (revised for PRC)

We calculate the antibaryon-to-baryon ratios, anti-p/p, anti-Lambda/Lambda, anti-Xi/Xi, and anti-Omega/Omega for Au+Au collisions at RHIC (sqrt{s}_{NN}=200 GeV). The effects of strong color fields associated with an enhanced strangeness and diquark production probability and with an effective decrease of formation times are investigated. Antibaryon-to-baryon ratios increase with the color field strength. The ratios also increase with the strangeness content |S|. The netbaryon number at midrapidity considerably increases with the color field strength while the netproton number remains roughly the same. This shows that the enhanced baryon transport involves a conversion into the hyperon sector (hyperonization) which can be observed in the (Lambda - anti-Lambda)/(p - anti-p) ratio., Comment: 5 pages, 2 figures, 1 table

The environment generated in the mid-rapidity region of a high-energy nuclear collision endows the pionic degrees of freedom with a time-dependent effective mass. Its specific evolution provides a mechanism for the production of back-to-back charge-conjugate pairs of soft pions which may present an observable signal of the non-equilibrium dynamics of the chiral order parameter., Comment: revtex body and 3 eps figures (4 pages total)

A practical quantum-field treatment is developed for systems endowed with an effective mass function depending on both space and time and a schematic application illustrates the quantitative importance of quantum fluctuations in the dynamics of disoriented chiral condensates., Comment: revtex body and 4 eps figures (4 pages total)

Using a semi-classical treatment of the linear sigma model, we simulate the dynamical evolution of an initially hot cylindrical rod endowed with a longitudinal Bjorken scaling expansion (a ``Bjorken rod''). The field equation is propagated until full decoupling has occurred and the asymptotic many-body state of free pions is then obtained by a suitable Fourier decomposition of the field and a subsequent stochastic determination of the number of quanta in each elementary mode. The resulting transverse pion spectrum exhibits visible enhancements below 200 MeV due to the parametric amplification caused by the oscillatory relaxation of the chiral order parameter. Ensembles of such final states are subjected to various event-by-event analyses. The factorial moments of the multiplicity distribution suggest that the soft pions are non-statistical. Furthermore, their emission patterns exhibit azimuthal correlations that have a bearing on the domain size in the source. Finally, the distribution of the neutral pion fraction shows a significant broadening for the soft pions which grows steadily as the number of azimuthal segments is increased. All of these features are indicative of disoriented chiral condensates and it may be interesting to apply similar analyses to actual data from high-energy nuclear collision experiments., Comment: 38 pages total, incl 26 ps figures (Randrup@LBL.gov)

In order to elucidate the enhancement of pion production that may occur during dynamical scenarios of interest in connection with disoriented chiral condensates, we study the evolution of boson modes whose frequencies have a given arbitrary time dependence. The quantum-field treatment yields expressions for the time dependence of observables that depend only on the initial state and specific state-independent enhancement coefficients which can be obtained from the given evolution of the frequency. It is shown how these coefficients also can be obtained within an entirely classical framework by judicious usage of the dependence of the resulting enhancement on the phase of the initial state. Illustrative application is made for frequency evolutions obtained from idealized simulations of high-energy heavy-ion collisions and it is shown how the non-equilibrium evolution of the order parameter may lead to significant enhancements in the final pion spectra., Comment: 28 pages total, incl 8 ps figures (Randrup@LBL.gov)

Wavelet-type methods are employed for the analysis of pion field configurations that have been obtained by dynamical simulations in idealized scenarios relevant to the formation of disoriented chiral condensates. It is illustrated how the measurement of the isospin domain structure depends on the ability to zoom in on limited parts of the phase space, due to the interplay between the pion correlation length and the effective source geometry. The need for advanced analysis methods is underscored by the fact that the extracted neutral-fraction distribution would differ significantly from the ideal form, even under perfect experimental conditions, and, moreover, by the circumstance that thermal sources with suitably adjusted temperatures can lead to distributions that may be practically indistinguishable from those arising from DCC-type non-equilibrium evolutions., Comment: 18 pages, Latex, 7 Figures included as .ps files

Approximate mean-field equations of motion for the classical chiral field are developed within the linear sigma model by means of a Hartree factorization. Both the approximate and the unapproximated equations of motion are augmented with a Rayleigh cooling term to emulate a uniform expansion, thereby allowing the extraction of observables relevant to the detection of disoriented chiral condensates, specifically the pion power spectrum, the pion correlation function, and the distribution of the neutral pion fraction. While the mean-field dynamics appears to be sufficiently accurate to be practically useful, the results also illustrate some difficulties associated with identifying the phenomenon experimentally., Comment: 25 pages total, incl 4 ps figures (Randrup@LBL.gov)