This document summarizes the discussions and outcomes of the Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program "The path to Superheavy Isotopes" held in June 2024 at FRIB. Its content is non-exhaustive, reflecting topics chosen and discussed by the participants. The program aimed to assess the current status of theory in superheavy nuclei (SHN) research and identify necessary theoretical developments to guide experimental programs and determine fruitful production mechanisms. This report details the intersection of SHN research with other fields, provides an overview of production mechanisms and theoretical models, discusses future needs in theory and experiment, explores other potential avenues for SHN synthesis, and highlights the importance of building a strong theory community in this area.

We investigate meson-exchange currents (MEC) in the one-particle emission transverse response of nuclear matter, incorporating short-range correlations via the Bethe-Goldstone equation with a realistic nucleon-nucleon interaction. The interference between one-body and two-body currents, strengthened by the high-momentum components of correlated pairs, produces a marked enhancement of the transverse response. We also indicate how the formalism extends to neutrino scattering, where similar effects are expected to impact oscillation experiments.

We derive the three-nucleon neutrinoless double beta decay potential in $\Delta$-full chiral effective field theory through next-to-next-to-next-to leading order in Weinberg's power counting. The matrix elements of the resulting operators are computed in light nuclei using Variational Monte Carlo with wave functions constructed from the Norfolk family of nuclear interactions. We find that three-nucleon corrections induce a modest quenching of the total nuclear matrix elements. We discuss model dependencies and the potential impact of these corrections on the sensitivity of experimental programs to probe lepton number violating parameters. These results provide a benchmark of many-body methods capable of reaching heavier nuclei of experimental interest.

We present an approach for including relativistic corrections in lepton-nucleus scattering calculations within the Short-Time Approximation (STA). Previous ab-initio studies employed electromagnetic currents expanded in powers of $q/m$, where $q$ is the momentum transfer and $m$ is the nucleon mass, restricting their validity to low-$q$ kinematics. We adopt an expansion scheme that treats the initial nucleon momentum perturbatively while allowing for arbitrary momentum transfer, thereby extending the applicability of the STA to high-$q$ regimes. Additionally, we incorporate a relativistic treatment of the two-nucleon final-state energies. Calculations for $^3$He and $^4$He inclusive electron scattering cross sections show a substantial improvement over previous results, achieving good agreement with experimental data in the quasi-elastic region for both low- and high-momentum transfer.

The Compton process with the initial states of photons and neutrons described by the density matrices of a general form is studied for low energies of photons. The coherent contribution to the inclusive probability to record a photon is investigated in detail. This contribution gives the hologram of the neutron one-particle density matrix. The evolution of the Stokes parameters of scattered photons is described. The susceptibility tensor of a neutron gas and a wave packet of a single neutron is obtained. The explicit expression for the photon polarization operator in the presence of free neutrons is derived. It turns out that this polarization operator possesses pole singularities in the short wavelength approximation. These singularities corresponding to the additional degrees of freedom are identified with plasmons and the respective plasmon-polaritons are described. There are eight independent plasmon-polariton modes in a neutron gas and on a single neutron wave packet. Some plasmon-polariton modes prove to be tachyonic and unstable manifesting a spontaneous generation of the magnetic field. The estimates of the parameters of the neutron gas when it becomes ferromagnetic are found. In the infrared limit, the neutron wave packet behaves in coherent Compton scattering as a point particle with dynamical magnetic moment, the additional degrees of freedom being reduced to the dynamical part of the magnetic moment.

Toward an improved understanding of the role of quantum information in nuclei and exotic matter, we examine the quantum magic (non-stabilizerness) in low-energy strong interaction processes. As stabilizer states can be prepared efficiently using classical computers, and include classes of entangled states, it is quantum magic and fluctuations in quantum magic, together with entanglement, that determine computational resource requirements. As a measure of fluctuations in quantum magic, and hence the severity of the exponentially-scaling classical computing resource requirements, induced by scattering, the "magic power" of the S-matrix is introduced. This provides indirect experimental constraints on quantum resources required to model nuclei and dense matter using fault-tolerant quantum computers. Using experimentally-determined scattering phase shifts and mixing parameters, the magic power in nucleon-nucleon and hyperon-nucleon scattering, along with the magic in the deuteron, are found to exhibit interesting and distinct features. The $\Sigma^-$-baryon is identified as a potential candidate catalyst for enhanced spreading of magic and entanglement in dense matter, depending on in-medium decoherence.

Ground state properties across the entire nuclear chart are described predominantly and rather accurately within the density functional theory (DFT). DFT however breaks many symmetries, among them the most important being the translational, rotational, and gauge symmetries. The translational symmetry breaking is special, since it is broken for all nuclei, unlike the rotational and gauge symmetries. The center-of-mass (CoM) correction most commonly used in the literature, see \textcite{Vautherin:1972} and \textcite{Bender:2003} leads to a gain of 15,...,19 MeV, which varies rather weakly for medium and heavy mass nuclei. A better approximation to the CoM correction was suggested by \textcite{Butler:1984} and its magnitude varies between 10 and 5 MeV from light to heavy nuclei, a correction which is also significantly larger than the RMS energy error in the Bethe-Weizsäcker mass formula, initially proposed by \textcite{Gamow:1930}, which is at most 3.5 MeV, and which for heavy nuclei corresponds to about 0.2\% of their mass. The CoM energy correction due Butler {\it et al.} is also significantly larger than the RMS energy deviation achieved in any DFT evaluations of the nuclear masses performed without any symmetry restoration or zero-point energy fluctuations, with an energy RMS typically between 2 and 3 MeV. Here we analyze the CoM projection method suggested by \textcite{Peierls:1957} (PY), which leads to a translationally invariant many-body wave function, in a procedure fully equivalent to those suggested for restoring rotational and gauge symmetries. This is the only approach for the evaluation of the CoM energy correction to the mean field binding energies, which is not contaminated by contributions from excited states.

In relativistic heavy-ion collisions, the quark-gluon plasma is created, and as the medium cools down, the system transitions into a hadronic phase. While such interactions are well established for large systems, such as Pb-Pb collisions, their relevance in smaller collision systems remains unclear. Consequently, hadronic interactions during the hadronic phase are studied in pp collisions at $\sqrt{s}=13$ TeV and p-Pb collisions at $\sqrt{s_{\rm{NN}}}=5.02$ TeV with the PYTHIA8 event generator. The interaction is studied via the yield ratios between resonances and stable particles with similar quark contents, which are obtained as a function of transverse momentum ($p_{\rm{T}}$) using $\mathrm{\rho(770)^0}$, $\mathrm{K^*(892)^0}$, and $\mathrm{\phi(1020)}$ mesons and their stable particles, $\mathrm{\pi^\pm}$ and $\mathrm{K^\pm}$ at midrapidity ($|\rm{y}|<0.5$). Yield ratios are calculated in five multiplicity classes for pp and six for p-Pb collisions, using the 60-100% multiplicity class in pp as a reference. Although rescattering leads to stronger suppression at low $p_{\rm{T}} < 2$ GeV/$c$, a visible suppression remains even when rescattering is turned off. To isolate the rescattering effect, double ratios between the rescattering on and off configurations are obtained. These are then integrated in the full $p_{\rm{T}}$ range ($0<p_{\rm{T}}<6.0$ GeV/$c$). The normalized double ratios show a decreasing trend with increasing multiplicity, independent of the collision system. The lower limit of the hadronic phase lifetimes extracted in the integrated-$p_{\rm{T}}$ region increases with multiplicity in both systems, but with a notable discrepancy between pp and p-Pb collisions.

The search for the chiral magnetic effect (CME) in relativistic heavy-ion collisions (HICs) is challenged by significant background contamination. We present a novel deep learning approach based on a U-Net architecture to time-reversely unfold the dynamics of CME-related charge separation, enabling the reconstruction of the physics signal across the entire evolution of HICs. Trained on the events simulated by a multi-phase transport model with different cases of CME settings, our model learns to recover the charge separation based on final-state transverse momentum distributions at either the quark-gloun plasma freeze-out or hadronic freeze-out. This devises a methodological tool for the study of CME and underscores the promise of deep learning approaches in retrieving physics signals in HICs.

In this work, we study the properties of single-flavor heavy baryons, $\Omega_{\rm ccc}$ and $\Omega_{\rm bbb}$, in a strong magnetic field. For that sake, we simply treat the baryons as quark-diquark two-body systems, and a systematic formalism is developed to deal with two-body Schr$\ddot{\text o}$dinger equations in a magnetic field. It is found that: 1. The orbital properties of $\Omega_{\rm bbb}$ are almost not affected by the magnetic field. 2. $\Omega_{\rm ccc}$ is more tightly bound in the presence of a magnetic field. 3. The magnetic-spin effect dominates over the magnetic-orbital effect. Applying to peripheral heavy ion collisions, $\Omega_{\rm ccc}$ is much better than $\Omega_{\rm bbb}$ to explore the magnetic effect, and the discovery of $\Omega_{\rm ccc}$ could be more promising.

The Drell-Levy-Yan relation is employed to obtain pion and kaon elementary fragmentation functions (EFFs) from the hadron-scale parton distribution functions (DFs) of these mesons. Two different DF sets are used: that calculated using a symmetry-preserving treatment of a vector $\times$ vector contact interaction (SCI) and the other expressing results obtained using continuum Schwinger function methods (CSMs). Thus determined, the EFFs serve as driving terms in a coupled set of hadron cascade equations, whose solution yields the complete array of hadron-scale fragmentation functions (FFs) for pion and kaon production in high energy reactions. After evolution to scales typical of experiments, the SCI and CSM FF predictions are seen to be in semiquantitative agreement. Importantly, they conform with a range of physical expectations for FF behaviour on the endpoint domains $z\simeq 0, 1$, e.g., nonsinglet FFs vanish at $z=0$ and singlet FFs diverge faster than $1/z$. Predictions for hadron multiplicities in jets are also delivered. They reveal SU$(3)$ symmetry breaking in the charged-kaon/neutral-kaon multiplicity ratio, whose size diminishes with increasing reaction energy, and show that, with increasing energy, the pion/kaon ratio in $e^+ e^- \to h X$ diminishes to a value that is independent of hadron masses.

Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of properly accounting for theoretical uncertainties. In this Letter, we present a Bayesian framework that explicitly quantifies these uncertainties by statistically modeling theory errors, guided by qualitative knowledge of a theory's varying reliability across the input domain. We demonstrate the effectiveness of this approach using two systems: a simple ball drop experiment and multi-stage heavy-ion simulations. In both cases incorporating model discrepancy leads to improved parameter estimates, with systematic improvements observed as additional experimental observables are integrated.

Experimental extraction of $\beta$-shape functions, C(W), is challenging. Comparing different experimental $\beta$-shapes to each other and to those predicted by theory in a consistent manner is difficult. This difficulty is compounded when different parameterizations of the $\beta$-shape function are used. Usually some form of a power polynomial of the total electron energy is chosen for this parametrization. This choice results in extracted coefficients that are highly correlated, with their physical meaning and numerical value dependent on the order of polynomial chosen. This is true for both theoretical and experimental coefficients, and leads to challenges when comparing coefficients from polynomials of different orders. Accurately representing the highly correlated uncertainties is difficult and subtle. These issues impact the underlying physical interpretation of shape function parameters. We suggest an alternative approach based on orthogonal polynomials. Orthogonal polynomials offer more stable coefficient extraction which is less dependent on the order of the polynomial, allow for easier comparison between theory and experimental coefficients from polynomials of different orders, and offer some observations on simple physical meaning and on the statistical limits of the extracted coefficients.

This work investigates the impact of mirror dark matter (DM) on the global properties of rotating neutron stars (NSs) across evolutionary stages, from hot, lepton-rich protoneutron stars (PNSs) to cold, catalyzed NSs along the Kelvin-Helmholtz timescale. The baryonic matter (BM) is modeled using a relativistic mean-field (RMF) approach with density-dependent couplings, while the dark sector mirrors the visible sector with analogous thermodynamic conditions. Using a two-fluid formalism with purely gravitational DM-BM interaction, we find that rotation enlarges the star, whereas DM admixture increases compactness and enhances gravitational stability. However, increased compactness due to DM lowers the threshold for rotational instabilities, making DM-admixed stars more susceptible. Rotation decreases {central temperature behavior} by redistributing thermal energy over a larger volume and reducing central density, while DM raises temperatures by deepening the gravitational potential and increasing thermal energy. Stars become more prone to collapse and rotational instabilities as frequency ($\nu$) rises and the polar-to-equatorial radius ratio ($r_p/r_e$) decreases, especially near the Keplerian limit ($\nu_K$). DM-admixed stars also show higher surface gravitational redshifts due to their compactness. Our results qualitatively agree with universal relations primarily derived for rotating cold stars. These findings highlight competing effects of rotation and DM on NS thermal evolution, structure, and observables, potentially offering indirect probes of DM within NSs.