By integrating the quantum Monte Carlo technique into the similarity renormalization group (SRG), we have developed a stochastic SRG framework (SRGQMC) capable of both free-space two-body and in-medium many-body evolutions. This approach circumvents the combinatorial tensor-space explosion of many-body flow equations by mapping continuous unitary transformations onto an ensemble of signed random walkers. We benchmark the SRGQMC against deterministic free-space SRG evolutions of realistic nucleon-nucleon (NN) interactions, as well as against in-medium SRG (IMSRG) many-body calculations with the Richardson pairing model at two- and three-body levels [IMSRG(2)/(3)]. While a deterministic extension to the four-body level [IMSRG(4)] remains unfeasible due to prohibitive computational costs, we have achieved the first IMSRG(4) calculation by using the stochastic technique, demonstrating a substantial improvement toward the full configuration-interaction limit. This stochastic framework provides a practical pathway to higher-order IMSRG calculations.

We study the static response of dense neutron-star matter to a prescribed magnetic-field strength within a deliberately minimal and internally consistent relativistic mean-field (RMF) baseline. The model includes neutrons, protons, electrons, and muons in beta equilibrium and charge neutrality, with a uniform external magnetic field incorporated through Landau quantisation of the charged species. The equation of state is evaluated self-consistently at zero temperature, while moderate finite-temperature effects are estimated through leading-order degenerate Sommerfeld corrections. Magnetic pressure anisotropy is included through the Maxwell contribution in the no-magnetisation approximation. The purpose of this baseline is to isolate the hierarchy of magnetic-field effects before introducing additional microphysics or dynamical magnetic-field evolution. We compare the linear QHD-I parameterisation, used as a stiff benchmark, with the nonlinear GM1 model as a more realistic reference. The results show that canonical magnetar-scale fields produce negligible changes in the bulk core equation of state, while visible Landau-quantisation and pressure-anisotropy effects emerge only as the field approaches the strongly quantising regime. The comparison between QHD-I and GM1 further shows that nuclear-model dependence dominates over static magnetic-field corrections up to the field strengths explored here. As an exploratory diagnostic, we use the isotropised equation of state to estimate the sensitivity of ordinary TOV mass--radius sequences to the prescribed magnetic field. This should not be interpreted as a fully anisotropic magnetised-star calculation. Anomalous magnetic moments, hyperons, quark degrees of freedom, and dynamical magnetic-field evolution are left for future extensions.

We present an ab initio calculation of the band-to-band internal-conversion rate of the $\hbar\omega_{\rm nuc} \approx 8.35$ eV isomeric transition in $^{229}$ThO$_2$. Because the nuclear transition energy exceeds the electronic band gap of ThO$_2$, the isomer can decay nonradiatively by resonantly promoting a valence electron into the conduction band. We formulate this process as a Brillouin-zone sum over vertical interband transitions weighted by local Th-centered hyperfine matrix elements, which are evaluated directly from all-electron full-potential linearized augmented-plane-wave Bloch spinors. A finite nuclear magnetization model is included to regularize the short-range hyperfine interaction and to account for the Bohr-Weisskopf effect. After applying scissor shifts to span the experimentally reported ThO$_2$ band gaps, we find calculated internal-conversion lifetimes in the range of $1-16~\mu{\rm s}$. The lifetime increases strongly as the band gap approaches $\omega_{\rm nuc}$ because the resonant interband phase space at the nuclear transition energy is reduced. For the larger reported ThO$_2$ gaps, the calculated lifetime is comparable to the measured conversion-electron Mössbauer lifetime [Nature 648, 300 (2025)]. Our analysis implies that choosing solid-state hosts with band-gap values slightly lower than $\omega_{\rm nuc}$ can optimize solid-state nuclear clock performance with internal-conversion electron readout.

The $^{8}$Li$(n,\gamma)^{9}$Li reaction is considered significant for the synthesis of nuclei beyond the $A=8$ stability gap in inhomogeneous big-bang nucleosynthesis models, as well as in $r$-process nucleosynthesis scenarios. However, direct measurement of this reaction is precluded by the short half-life of $^{8}$Li and the absence of a neutron target. Consequently, existing reaction rate estimates based on indirect experimental methods and theoretical calculations differ by orders of magnitude. In the present work, the $^{8}$Li(n,$\gamma$)$^{9}$Li neutron-capture cross section and the corresponding thermonuclear reaction rate are evaluated within a phenomenological $R$-matrix framework, including both non-resonant direct capture (DC) and resonant capture through the $5/2^{-}$ state at $E_{x} = 4.30$~MeV. The uncertainties associated with the $R$-matrix input parameters are propagated using Monte Carlo sampling, while the sensitivity to the channel radius is treated as an $R$-matrix model uncertainty. The effective total uncertainties in the calculated cross sections and reaction rates are obtained by adding these two uncertainty contributions in quadrature. We obtain a total capture rate of $983.9^{+410.9}_{-261.5}~\mathrm{cm^{3}\,mol^{-1}\,s^{-1}}$ at $T = 1$~GK, with DC dominating at low temperatures ($T=0.01-0.4$~GK) and the $5/2^{-}$ resonance at higher temperatures ($T=0.5-5$~GK). The present results are consistent with the upper limit of Kobayashi et al.~\cite{Kobayashi2003}, which previous theoretical predictions exceed by factors of 3-50.

The p-process is responsible for the production of the stable neutron-deficient nuclei heavier than iron observed in the solar system. However, important nuclear uncertainties still limit our understanding of this nucleosynthesis process. Among the most significant are the nuclear level densities (NLDs) and photon strength functions (PSFs) entering the calculation of photodisintegration rates under supernova conditions. We investigate both model (systematic) and parameter (statistical) uncertainties affecting NLDs and PSFs and quantify their impact on p-process nucleosynthesis in type-Ia and type-II supernovae. Correlated model uncertainties are estimated using several NLD and PSF models that reproduce available experimental observables. Uncorrelated parameter uncertainties are evaluated with a backward-forward Monte Carlo approach, in which parameter variations are constrained by measured reaction rates before being propagated to unknown cross sections of neutron-deficient nuclei. The resulting uncertainties are propagated through p-process calculations while preserving model correlations. To identify the reactions driving abundance uncertainties, we combine regularized linear-response modeling, stability analysis, and contribution and interaction decompositions. We find that photoneutron-emission uncertainties dominate the overall uncertainty budget. The leading source of uncertainty arises from local parameter variations still compatible with current experimental constraints, highlighting the lack of constraining nuclear data in the neutron-deficient region. For many p-nuclei, the dominant contribution originates either from the photoneutron emission of the p-nucleus itself or from a nearby $(\gamma,n)$ reaction along the same isotopic chain. While improved nuclear models remain important, many key reactions involve stable or near-stable nuclei and should be experimentally accessible.

We compute ground-state energies and charge radii of light- to medium-mass nuclei with up to $A=58$ nucleons, leveraging a variational Monte Carlo method based on Pfaffian-Jastrow neural quantum states. To further understand which elements of the nuclear Hamiltonian are "essential" to predict binding energies and charge radii across the nuclear chart with few-percent errors, we consider different interactions inspired by pionless effective field theory. Specifically, in addition to model "o" of [Phys. Rev. C 103, 054003 (2021)], we study the impact of charge-symmetry-breaking and charge-dependent terms in the nucleon-nucleon force, as well as $p$-wave contributions, which have been found to be critical for the stability of $p$-shell nuclei. In addition to its intrinsic interest, our work assesses the performance of neural quantum states in the medium-mass regime and examines the impact of these interaction modifications. Using the resulting ground-state simulations, we analyze the computational scaling of variational Monte Carlo with neural quantum states as a function of system size and computational resources, enabling projections for future large-scale calculations.

Charged-current (anti)neutrino interactions create $\Lambda$ and $\Sigma$ hyperons \emph{inside} the nucleus, making hyperon final-state interactions a terrestrial probe of the in-medium potentials that govern hyperon onset in neutron stars. In the StrangeMC simulation the trapped-$\Lambda$ fraction, escaping hyperon momenta, and a kaon-vetoed $\Sigma^+$ tag respond monotonically to $U_\Lambda$ and $U_\Sigma$ at SBND and DUNE. Marginalised over the low-density slope, a forecast gives $\delta U_\Lambda\approx6\MeV$ with systematics distinct from hypernuclear data; $U_\Sigma$ is limited by hyperon--nucleon cross sections.

Hyperon single-particle potentials $U_Y(\rho)$ control propagation in nuclei and hyperon onset in dense matter, where they soften the neutron-star equation of state and reduce the maximum mass -- the ``hyperon puzzle''. We show that charged-current accelerator (anti)neutrino interactions on $^{40}$Ar, producing $\Lambda$ and $\Sigma$ inside the nucleus, can constrain these potentials. At SBND and DUNE energies, the trapped-$\Lambda$ fraction and escaping-hyperon momenta vary monotonically with $U_\Lambda$ and $U_\Sigma$, with a kaon-vetoed FSI-$\Sigma^+$ tag adding sensitivity. Inserted in a GM1 relativistic mean-field equation of state at established hypernuclear/$\Sigma$-atom depths, the same potentials give $M_{\rm max} = 1.94\,M_\odot$ and $\Lambda_{1.4}=1034$, below the heaviest pulsars and above the GW170817 bound typical of GM1-class mean fields. A detector-level Fisher forecast yields $\delta U_\Lambda \simeq 0.3\,$MeV and $\delta U_\Sigma \simeq 3$-$4\,$MeV for fixed low-density exponent $\gamma$. Since hyperons are produced below saturation, $U_\Lambda(\rho_0)$ and $\gamma$ are 99.8\% anti-correlated; marginalising over $\gamma$ degrades the anchor to $\delta U_\Lambda \simeq 5.6\,$MeV ($1.3\,$MeV with a $\pm 0.2$ prior), while $\delta U_\Sigma$ is unchanged. For $U_\Lambda$, comparable systematics arise from hyperon-nucleon final-state cross sections ($-5/{+}2\,$MeV) and the exit-shift/gradient transport prescription ($-6\,$MeV). For $U_\Sigma$, the same $YN$ uncertainty biases the fit by $\mathcal{O}(150)\,$MeV; removing the $\Sigma^+$ tag does not cure this, because the $\Lambda$ momentum spectrum carries most $U_\Sigma$ information and is itself $YN$-sensitive. The low-density $U_\Lambda$ anchor is a robust handle, at several-MeV rather than sub-MeV precision. A joint fit with terrestrial and heavy-ion priors gives $M_{\rm max} = 2.21^{+0.04}_{-0.15}\,\,$Msun, set mainly by the external $c_\Lambda$ prior.

Quarkyonic matter resolves the neutron-star hyperon puzzle statistically: neutrons fill low-momentum $d$-quark phase space, shifting the $S=-1$ threshold from $\muB=M_Y$ to $2M_Y-M_N$ and suppressing residual softening by $1/\Nc^3$ in the Fujimoto--Kojo--McLerran (FKM) mechanism. We dress FKM's IdylliQ model with in-medium potentials, constrained by hypernuclear data and neutrino-induced hyperon FSI, and find: (i) the dressed onset, $\muB^{\rm onset}=(2M_Y{-}M_N)+2U_Y-\UN$, carries $U_Y$ at weight 2, with $dn_{\rm onset}/dU_Y\simeq0.3\,\nz$ per $10\MeV$, twice the leverage. (ii) A self-consistent neutron potential enters at weight $-2$, so protection needs $\UN(n_{\rm onset})\lesssim+96\MeV$. (iii) With leptons in $\beta$ equilibrium, the $\Sigma^-$ ($dds$) onset becomes $\mue\ge258\MeV+\US-\UN$, never reached inside a $2\,\Msun$ core: $\Sigma^-$ switches from first hyperon to forbidden and the $\Sigma$ ordering inverts. (iv) The $\kY\ge\kbu$ continuation gives TOV softening below $0.05\,\Msun$ in the FKM ansatz family and below $0.025\,\Msun$ for the realistic interacting star, $4$--$8$ below hadronic models. In the family this is a ceiling; generally it is a floor, since hyperons above $\kbu$ are omitted. (v) In an interacting low-density sector calibrated to $\Mmax=2.12\,\Msun$, core strangeness is controlled by $(\UL(\nz),c_\Lambda)$: at $\UL(\nz)=-28\MeV$, the maximum-mass star is hyperon-free once the supra-saturation $YNN$ turn-over exceeds a few-MeV threshold $c^*_\Lambda$. Projected SBND+DUNE FSI precision pins $\UL(\nz)$ but leaves $c_\Lambda$ -- to which neutrino data are blind -- decisive: with the heavy-ion prior, $P({\rm hyperon\mbox{-}free\ core})=0.90$, versus $0.89$ from priors alone, prior-dominated rather than measured. The sharpest observable is differential: $d\Mmax/dU_Y$ is an order of magnitude smaller than in mean-field models, discriminating the two resolutions.

The nonrelativistic theory of nuclear matter (NM) based on Brussels-Skyrme interactions is employed to develop models for dense and neutron-rich matter within a Bayesian framework. We employ the following set of constraints: the four best-known nuclear empirical parameters, density dependence of the energy per particle in pure neutron matter (PNM), density dependence of the Landau effective mass ($m_\mathrm{eff}$) of neutrons in PNM and symmetric NM, and a lower limit on the maximum gravitational mass that neutron stars (NSs) can sustain. In addition, a number of ``sanity checks'' are added: the values of the speed of sound, neutron and proton Landau effective masses and Fermi velocities are constrained up to the central density of the most massive NS configuration and for isospin asymmetries $\delta=(n_n-n_p)/(n_n+n_p)$ ranging from 0 to 1. Our ensemble of models \emph{fully} explores the capacity of non-relativistic Brussels-Skyrme effective interactions to describe NM at densities exceeding several times the nuclear saturation density. This is a necessary step toward a better understanding of the properties of dense matter and possible correlations between the parameters of NSs and the parameters of NM. Due to pronounced U-shaped density-dependencies of $m_\mathrm{eff}$, all our models exhibit a non-monotonic ``rise-and-fall'' behavior of the thermal pressure ($p_\mathrm{th}$) as a function of density, which in extreme cases leads to $p_\mathrm{th} < 0$. This work is a generalization of [Beznogov and Raduta, Phys. Rev. C 110, 035805 (2024)].

Electron-capture (EC) rates in medium-mass nuclei are governed by Gamow--Teller (GT) strength distributions and provide important input for stellar weak-interaction processes. In this work, we investigate the deformation dependence of the GT strengths and stellar EC rates in selected medium-mass nuclei in and near the $pf$ shell, namely $^{48}$Ti, $^{56}$Ni, $^{60}$Zn, and $^{64}$Ge. The GT$^{(+/-)}$ strength distributions are calculated in the deformed quasiparticle random-phase approximation (DQRPA) on a single-particle basis obtained by the Skyrme SGII interaction, while the stellar EC rates are evaluated from the resulting $B(\mathrm{GT}^+)$ strengths using the standard phase-space formalism. The potential-energy curves are used to identify shape softness and possible shape coexistence in the nuclei under consideration. We find that deformation strongly modifies the GT strength distributions by changing the centroid energies, resonance splitting, and fragmentation patterns. In particular, a pronounced shape dependence of the GT$^{(+/-)}$ strengths is found for $^{56}$Ni and $^{64}$Ge, whereas $^{60}$Zn is characterized by a favoured prolate minimum and $^{48}$Ti exhibits a soft near-spherical/prolate landscape. By contrast, the corresponding EC rates are generally much less sensitive to deformation than the differential GT response itself, except at low temperatures and low densities where the low-lying GT$^+$ strength becomes decisive because of the negative EC $Q$-value in the electron phase space. Available charge-exchange data for $^{48}$Ti and $^{56}$Ni are used as benchmarks of the model predictions. The present results provide microscopic constraints on the role of deformation and shape coexistence in stellar weak rates for selected medium-mass nuclei, including proton-rich isotopes near the $N = Z$ line.

The maximum mass of neutron stars provides a key constraint on the equation of state (EoS) of dense matter. Recent observations, including the ${\approx}2 M_{\odot}$ pulsar PSR~J0740+6620, have placed strong constraints on a large class of soft EoSs, while the possible existence of a compact object with a mass of $2.50$ - $2.67$ $M_{\odot}$ in GW 190814 further challenges our understanding of dense matter. Moreover, the inclusion of hyperonic degrees of freedom generally softens the EoS, making it difficult to support massive neutron stars even when the $2$ $M_{\odot}$ constraint is satisfied (a problem known as the hyperon puzzle). In this work, we investigate whether differential rotation can enhance the maximum mass of neutron stars constructed with an EoS including hyperons, thereby addressing the maximum-mass constraints imposed by current observations. We employ the Cook-Shapiro-Teukolsky (CST) approach, a numerically improved reformulation of the Komatsu-Eriguchi-Hachisu (KEH) scheme, to construct equilibrium configurations of differentially rotating neutron stars. For the nuclear matter EoS, we adopt a relativistic mean-field (RMF) model incorporating hyperonic degrees of freedom through an SU(6) symmetric coupling scheme. We find that differential rotation can substantially increase the maximum mass, yielding configurations consistent with the mass range inferred from GW 190814. However, a sufficiently soft EoS fails to satisfy the constraint from PSR~J0740+6620 (346 Hz) even with differential rotation applied. We also present a systematic analysis of the internal structure of the resulting equilibrium configurations. Furthermore, we demonstrate the existence of quasi-toroidal configurations and present equilibrium sequences incorporating the full baryon octet under extreme differential rotation.

We investigate the influence of medium effects on strange quark matter and their consequences for the structural properties of compact stars. In this study, the bag constant, in the MIT bag model equation of state, is reformulated as a function of the chemical potential of quark. Imposing the Bodmer-Witten stability criterion, the parameter space is constrained by evaluating the energy per baryon. The Tolman-Oppenheimer-Volkoff equations are then solved to obtain the maximum mass-radius configurations. Our analysis shows that an increase in chemical potential leads to a reduction in the effective value of bag constant, resulting in a stiffer equation of state and correspondingly higher value of maximum stellar mass. Furthermore, we examine the chemical potential dependence of the tidal Love number and tidal deformability. The results demonstrate that, for the chosen set of parameters, the constraint from the GW170817 event, namely $\Lambda < 800$, is consistently satisfied. In this paper, we have tried to establish how chemical potential $(\mu)$ affects the maximum mass and tidal deformability of strange stars.

Tensor-polarized parton distribution functions (PDFs) are calculated for the deuteron by using a convolution formalism, where the tensor-polarized PDFs are given by the corresponding nucleon's unpolarized PDFs convoluted with the tensor-polarized nucleon momentum distribution in the deuteron. These distributions are obtained at $Q^2=2.5$ GeV$^2$ in order to compare with the tensor-polarized PDFs which were determined by HERMES $b_1$ data. The obtained distributions are very different from the ones determined from the HERMES data, which indicates further studies are needed to clarify the difference, possibly by considering a new mechanism beyond the simple bound system of a proton and a neutron. The obtained PDFs $\delta_T q $ and $\delta_T \bar q$ are converted to the PDFs of the Trento convention $f_{1LL}^{\, q}$ and $f_{1LL}^{\, \bar q}$, and they are used for estimating the twist-3 PDFs $f_{LT}^{\, q}$ and $f_{LT}^{\, \bar q}$ by using a Wandzura-Wilczek-like relation. Because deep-inelastic-scattering experiments are under preparation for structure functions with a tensor-polarized deuteron target at the Thomas Jefferson National Accelerator Facility, and a Drell-Yan experiment will be possible at hadron accelerator facilities, such as the Fermi National Accelerator Laboratory, the obtained tensor-polarized PDFs will be tested experimentally.

We perform a Diffusion Monte Carlo study of fully light hexaquark containing three $u$ quarks and three $d$ quarks within a constituent-quark model. Both compact and baryon--baryon-like arrangements were considered separately. All compact hexaquark configurations are found well above their corresponding baryon--baryon thresholds, suggesting that deeply bound compact six-quark states are not favored in the light-quark sector within this model. By contrast, several dibaryon-like configurations lie close, but above, to the $NN$, $N\Delta$, and $\Delta\Delta$ thresholds and show spatial structures compatible with molecular states. One configuration exhibits two well-defined nucleon-like subclusters separated by several femtometers, closely resembling the spatial structure of the deuteron, although its calculated energy remains slightly above the corresponding threshold.

We study the effects of the running of the QCD coupling on the anti-collinear resummation in JIMWLK evolution in the linear (BFKL) regime. We determine the appropriate scale choice for the coupling entering the JIMWLK kernel, and derive the anti-collinearly resummed BFKL kernel, which includes running-coupling effects both in the resummation equation (i.e. DGLAP) and in the JIMWLK kernel proper. We find that the running of the coupling generally further slows down BFKL evolution, as expected. Surprisingly however the value of the generalized characteristic function at $\gamma=1$ is unaffected by the running coupling owing to subtle cancellations. We develop an approximation that allows us to use the generalized characteristic function to study the BFKL Green's function. Within this approximation we find that the Pomeron intercept in the anti-collinear regime is significantly reduced by both, the resummation and the running of the coupling.

We investigate the forces acting on a proton vortex in superconducting neutron-star matter composed of neutrons, protons, and electrons, accounting for Fermi-liquid interactions in the neutron-proton subsystem. While the force arising from electron scattering by the vortex magnetic field is well known, we demonstrate that normal neutrons also exert a force on proton vortices due to Fermi-liquid coupling with superconducting protons. Using a kinetic approach based on Landau Fermi-liquid theory, we show that neutron quasiparticles scatter off a proton vortex through the spatially varying condensate momentum, giving rise to a longitudinal force proportional to the relative neutron-vortex velocity. In contrast to the electron contribution, this force has no transverse component and vanishes in the absence of neutron-proton Fermi-liquid interaction. Within a simple model, we analyze the main properties of this force and provide physically motivated estimates of its magnitude.

The study of nuclear shape evolution and coexistence provides key insight into the nuclear interaction, particularly in semi-magic systems expected to be spherical. A high-precision Coulomb-excitation measurement of $^{116}$Sn yields a comprehensive set of electromagnetic matrix elements, enabling the determination of quadrupole moments of the $2_{1,2,3}^+$ states and intrinsic deformations of the $0_{1,2,3}^+$ states. The results provide an unambiguous and direct proof of the rare phenomenon of multiple-shape coexistence, revealing a weakly deformed ground state incompatible with the spherical shape.

We present a closed analytical description of the spin distributions of the fragments produced in low-energy induced and spontaneous fission. In our model the high fragment spins and the relative orbital angular momentum arise from the zero-point transverse wriggling and bending oscillations of the two pre-fragments, under the postulate that the fissioning system remains ``cold'' up to scission -- its available energy being stored as non-equilibrium deformation rather than as heat. From the probability distributions of the two modes we derive a closed expression for the spin distribution of each fragment and for its mean value. The decisive quantities are the fragment moments of inertia, which we evaluate in the hydrodynamic model from the non-equilibrium scission deformations reconstructed from the measured prompt-neutron multiplicities. Confronted with the recent data on $\rm ^{232}Th(n, f)$, $\rm ^{238}U(n, f)$, and $\rm ^{252}Cf(sf)$, the model reproduces both the magnitude of the mean spins and their characteristic sawtooth dependence on the fragment mass. Comparison with the statistical and microscopic approaches indicates that the differences for individual fragments can be traced largely to the deformation dependence of the moments of inertia.

Some atomic nuclei exhibit enhanced octupole collectivity, reflected in finite reflection-asymmetric multipole correlations rather than necessarily in a rigid static pear-shaped ground state. Low-energy studies indicate finite octupole strength in uranium-238, commonly interpreted as soft or vibrational in nature, in addition to its large prolate quadrupole collectivity~\cite{MCGOWAN1994569,KIBEDI:2002wxc}, in addition to its large prolate quadrupole collectivity. Here we investigate how such octupole correlations can be encoded in the initial geometry of relativistic heavy-ion collisions and mapped to final-state flow observables. Using state-of-the-art hydrodynamic calculations, we demonstrate quantitative sensitivity to octupole-induced features encoded in the initial-state geometry and suggest a modest octupole collectivity in uranium-238, confirmed by the latest high-energy experimental measurements~\cite{STAR:2025elk}. These findings provide as a complementary probe of odd-order nuclear collectivity and help constrain quark-gluon plasma initial conditions.

The nature of octupole deformation, whether static or vibrational, remains an open question in nuclear physics. Here, we propose a scaling approach to probe this ambiguity by triangular flow fluctuations using multi-particle cumulants, $c_{3,\varepsilon}\{4\}$, in relativistic $^{238}$U+$^{238}$U collisions. We demonstrate that both $|c_{3,\varepsilon}\{4\}|$ and the ratio $|c_{3,\varepsilon}\{4\}/c^2_{3,\varepsilon}\{2\}|$ scale linearly with the fourth-order moment of octupole deformation, $\langle \beta^4_{3,\mathrm{U}} \rangle$. Combined with the known linear relation of $c_{3,\varepsilon}\{2\}$ to $\langle \beta^2_{3,\mathrm{U}} \rangle$, this new relation provides a direct extraction of both the mean and variance of the octupole deformation fluctuations, finally discriminating between static and dynamic origins. This work establishes a new tool to probe the static and dynamic collective modes in high-energy nuclear collisions, advancing a significant step toward refining the initial conditions of quark-gluon plasma.

The observed shift of the $\Delta(1232)$ resonance peak in $\pi$-$p$ femtoscopic correlations challenges the conventional Breit-Wigner description of resonances in femtoscopy. We revisit the Koonin-Pratt framework by formulating femtoscopy in the momentum-space representation. By employing the T-matrix approach to disentangle on-shell and off-shell contributions, we show that the finite spatial extent of the emission source naturally induces sensitivity to off-shell scattering dynamics. Using a Friedrichs-Lee model constrained by low-energy $\pi$-$p$ scattering data, we numerically demonstrate that this off-shell sensitivity leads to a peak shift accompanied by a dip on the high-momentum side of the peak. The predicted high-momentum side dip is absent in the data, pointing to source properties beyond the simple Gaussian approximation.

We propose simultaneous $\alpha\beta$ decay as a novel mode of nuclear instability that involves the strong and weak interactions in a single quantum transition. We develop a theoretical framework to predict its branching ratios and $\alpha$-energy spectra, establishing exclusive and inclusive criteria based on whether the individual $\alpha$ and $\beta$ channels are closed or open. A global survey of the nuclear chart identifies five exclusive $\alpha\beta^-$ candidates, all predicted to be experimentally inaccessible, and ranks the leading inclusive candidates for both the $\alpha\beta^-$ and $\alpha\beta^+$ modes. Remarkably, six of the top $\alpha\beta^+$ candidates coincide with known $\beta$-delayed-$\alpha$ precursors. The observed $\alpha$ spectra are naturally accounted for by simultaneous $\alpha\beta^+$ emission, suggesting direct decay as the dominant underlying mechanism. Our findings establish simultaneous $\alpha\beta$ decay as a distinct radioactive process and a sensitive probe of the interplay between the strong and weak interactions.