Motivated by forthcoming high-energy experiments at Jefferson Lab and the Electron-Ion Collider, this dissertation develops a novel relativistic formulation of nuclear structure. While previous scattering models were updated to include nucleon-nucleon short-range correlations (SRCs) to explain cross-section plateaus, modern high-kinematics experiments require a relativistic approach. We reformulate conventional tools into a light-front-quantized framework, utilizing density functional theory and similarity renormalization group techniques. Our calculations successfully reproduce nuclear binding energies, shell structure, and SRC physics. However, we show that a purely nucleonic description fails to fully capture inclusive electron-nucleus data or the plateaus at high Bjorken-$x_B$. This demonstrates the critical importance of inelastic final-state interactions currently omitted by standard SRC phenomenology.

WIMP scattering from 40Ar is investigated using a self-consistent Skyrme Hartree-Fock-Bogoliubov (HFB) approach. Nuclear form factors relevant to dark matter direct detection are calculated from the resulting one-body density matrix elements and compared with shell-model predictions. Good agreement is found for the spin-independent response, while significant differences are observed for the spin-orbit response due to variations in single-particle occupancies. The effects of particle-number projection are shown to be small for 40Ar. These results demonstrate the sensitivity of certain dark matter response channels to the underlying nuclear structure model and establish a framework for extending mean-field calculations to nuclei beyond the reach of large-scale shell-model studies.

There is a conundrum regarding the binding of $\alpha$ particles in nuclei. On one hand, auxiliary-field Monte Carlo simulations of Hamiltonians on discrete spatial lattices proposed that attractive two-nucleon potentials, alone or together with attractive three-nucleon potentials, yield accurate nuclear binding. On the other hand, such Hamiltonians typically overbind all but the lightest nuclei in continuum-space approaches. We address this puzzle by performing Hartree-Fock computations of the light nuclei $^4$He, $^8$Be, $^{12}$C, and $^{16}$O, and of nuclear and neutron matter using established lattice Hamiltonians. These variational upper bounds for the ground-state energies show that the Hamiltonians with only two-nucleon potentials do not yield accurate binding, in contrast to the results from auxiliary-field Monte Carlo simulations. The case is different for Hamiltonians with three-nucleon potentials although it is the dense packing on the lattice -- and not repulsive potentials -- that yield a constant binding energy per nucleon.

In this review, we discuss the most recent developments and applications of the Subtracted Second RPA (SSRPA), an extension of the Second RPA (SRPA), which overcomes its pathological issues encountered within the Energy Density Functional theory. After recalling the formal properties of the SRPA and SSRPA, the anomalous behavior of SRPA is shown and discussed by presenting several applications with different kinds of nuclear interactions. The most recent pathology-free SSRPA studies are then presented both for charge-conserving and charge-exchange nuclear excitations. The comparison with experimental data is presented to assess and quantify the improvement introduced by the SSRPA with respect to the RPA and SRPA. The impact of beyond-mean-field correlations induced in SSRPA is also qualitatively estimated in connection with the modeling of the nuclear equation of state. We conclude by discussing the future perspectives of the SSRPA, focusing on its potential connections with some current experimental challenges and outlining necessary theoretical extensions and numerical developments.

Contemporary theoretical descriptions of nuclear structure rely mainly on microscopic, single-particle frameworks often in competition with collective degrees of freedom, especially when deformation plays a dominant role. Such phenomena are prominent in the rare-earth region, where rotational band structures and enhanced electric quadrupole transitions are systematically examined. The Confined beta-Soft (CBS) rotor model, introduced by N. Pietralla and O.M. Gorbachenko, bridges the gap between the X(5) critical point and the rigid-rotor limit in the region where the R_4/2 = E(4+)/E(2+) ratio lies between 2.904 and 3.333. In the present work, the CBS framework is employed to calculate ground-state band energies, associated B(E2) transition rates, and beta-band excitations of even-even nuclei in the rare-earth region. The theoretical results are systematically compared with available experimental data, and predictions are provided for nuclear observables that have not yet been measured, offering guidance for future experimental investigations.

The high-frequency gravitational waves emitted by a binary neutron star merger remnant carry information on matter at densities and temperatures beyond those reached in isolated neutron stars. We quantify how tightly current multi-messenger constraints already determine the dominant post-merger frequency $f_{2,\rm mean}$. Adopting a set of cold equations of state (EOSs) constrained jointly by gravitational-wave tidal deformability, NICER mass--radius measurements, massive-pulsar masses, chiral effective field theory at low density, and perturbative QCD at asymptotically high density, for each binary mass we select the softest and stiffest models of the multi-messenger posterior and follow their coalescence with fully general-relativistic hydrodynamics simulations. Together with a broad set of EOSs drawn from the literature ($82$ models in total), these simulations show that, once the binary mass and a single measure of the stellar compactness ($\Lambda$ or $R$) are held fixed, the residual spread of $f_{2,\rm mean}$ is only $\sim 100\,{\rm Hz}$, a factor of several below the $\gtrsim 500\,{\rm Hz}$ range spanned by an EOSs set including those already disfavored by the data. This tight calibration of the cold-matter prediction implies that a future high-frequency detection departing from it would point directly to additional physics, such as a hadron--quark transition occurring at finite temperature. We further confirm the quasi-universal relation $(f_1+f_3)/2 \approx f_{2,\rm mean}$ to within $\sim 116\,{\rm Hz}$, which provides a model-independent estimate of $f_{2,\rm mean}$ from the secondary spectral peaks.

The Electron-Ion Collider (EIC) will enable a series of measurements at unprecedented energies and luminosities, providing new opportunities to investigate the microscopic structure of nucleons and nuclei at small $x_B$. Exclusive processes such as Deeply Virtual Compton Scattering (DVCS) offer unique access to the three-dimensional structure of hadrons through Generalized Parton Distributions (GPDs), while polarized electron and ion beams further enable detailed studies of spin-dependent structure. A model for coherent DVCS on polarized $^3$Heis developed and applied to simulations of for $9\times166$-GeV $e^3$He collisions at the EIC. Using this framework, the statistical precision achievable is estimated for measurements of beam-spin asymmetries and for the extraction of the Compton Form Factors (CFFs) $\mathcal H_{^3\mathrm{He}}$ and $\tilde{\mathcal H}_{^3\mathrm{He}}$. Early EIC data are found to enable precise differential measurements of the unpolarized CFF $\mathcal H_{^3\mathrm{He}}$ and to provide significant constraints on its real and imaginary components. By contrast, meaningful constraints on the polarized CFF $\tilde{\mathcal H}_{^3\mathrm{He}}$ require substantially larger integrated luminosities. The kinematics of the recoil $^3$He nucleus are also examined, and the far-forward detector capabilities at the EIC required to tag the intact nucleus and perform fully exclusive measurements of coherent nuclear DVCS are discussed.

We solve exactly the relativistic finite-difference equation for the quantum three-dimensional ring-shaped Quesne oscillator potential. Our investigation is based on a finite-difference version of relativistic quantum mechanics. So-called relativistic configurational r-space is a key concept here. We show that the radial wavefunctions and angular wavefunctions are expressed through the continuous dual Hahn polynomials and Jacobi polynomials, respectively. A discrete energy spectrum has been found. The radial wave functions and energy spectrum have the correct nonrelativistic limit. We also build a dynamical symmetry group SU (1, 1) for the radial part of the equation of motion, which allows us to find the energy spectrum purely algebraically.

We use effective field theory to factorize production matrix elements that appear in the NRQCD framework for quarkonium cross sections. By applying a Hubbard-Stratonovich transformation and appropriate field redefinitions, we show that the soft and ultrasoft sectors of NRQCD can be decoupled from the heavy quark and antiquark fields in a hybrid vNRQCD/pNRQCD Lagrangian at leading order in the velocity power-counting. This enables us to re-factorize quarkonium production matrix elements in terms of matrix elements of color-singlet composite fields, which we can write as the wave-function at the origin, and state independent vacuum correlators of chromo-electric and chromo-magnetic gluon fields. This approach verifies powerful relationships between the LDMEs of different S-wave quarkonia originally derived using pNRQCD. Additionally, it allows us to derive new relationships for the production matrix elements used in the transverse momentum dependent factorization (TMD) framework, known as TMD soft transition functions, providing a much stronger set of constraints on these nonperturbative operators. This work significantly advances our understanding of quarkonium production, particularly in the TMD framework.

Background: Lithium is of broad interest in nuclear astrophysics, fusion energy research, and nuclear technology. From a theoretical perspective, the nucleus $^7$Li presents a remarkable challenge, as its bound and resonant states can exhibit contributions from both the $^4$He + $^3$H cluster configuration and configurations involving a neutron or proton coupled to a $^6$Li or $^6$He core, respectively. Purpose: We aim to achieve a unified ab initio description of bound-state and continuum properties of $^7$Li by explicitly including simultaneously the coupled mass/charge partitions $^4$He + $^3$H, $^6$Li + $n$, and $^6$He + $p$. Specifically, we investigate the effect of inter-partition coupling on the spectrum of $^7$Li and calculate cross sections for the $^6$Li($n,p)^6$He, $^6$He($p,n)^6$Li, and $^6$He($p,t)^4$He reactions. Method: We employ the no-core shell model with continuum for the first time in a calculation that couples three mass/charge partitions of the aggregate nucleus $^7$Li, using a chiral nucleon-nucleon interaction as input. Results: The calculated spectrum reproduces all the experimentally observed states of $^7$Li in the correct order and predicts additional resonances. The calculation also reproduces the overall energy dependence of the $^6$Li$(n,p)^6$He cross section. Improved agreement with measured cross sections is obtained after phenomenological adjustment of resonance energies. Conclusions: The present results show that coupling the relevant mass/charge partitions is important for a consistent description of the $^7$Li spectrum and reaction cross sections, and offers a useful framework for interpreting existing data and guiding future measurements.

A comprehensive investigation of nonradial oscillations in neutron star (NS) admixed with gravitationally bounded dark matter (DM) is carried out within the framework of full general relativity. The relativistic mean field (RMF) formalism is employed to illustrate the hadronic equation of state (EOS), while a physically motivated, gravitationally captured, non-uniform fermionic Higgs-portal DM component is incorporated to model DM-admixed NS. The DM distribution is characterized by two free parameters: $\alpha M_\chi$, an effective control parameter that combines the DM concentration and the DM candidate mass, and $\beta$, a steepness parameter controlling the DM density distribution. The quasi normal mode (QNM) characteristics such as fundamental ($f$) mode frequency and its corresponding gravitational-wave (GW) damping time ($\tau$) is calculated for DM-admixed NS by solving the general relativistic perturbed equations involving axial as well as polar modes. The study demonstrates how the inclusion of DM distribution modifies the $f$-mode frequency and enhances the damping rate, reflecting a stronger coupling between matter and spacetime perturbations. Considering DM effects, the correlation analysis among DM model parameters, NS observables and QNM characteristics also carried out. Analytic fits for the $f-C-\tau$ and $f-\Lambda -\tau$ relations are constructed and calibrated for DM-admixed NS models. Building upon asteroseismic universal relations (URs), multimessenger constraint from the GW170817 event is employed by mapping the tidal deformability $\Lambda_{1.4}$ into the $(f_{1.4},\tau_{1.4})$ space, thereby providing observational bounds on the oscillation properties of canonical DM-admixed NS model.

Recently, new quark mass dependent three-nucleon (3N) forces have been identified, whose contributions in nuclear matter exceed expectations of Weinberg power-counting arguments. In this work, we investigate the impact of the most dominant new interaction term, characterized by the coupling $F_2$, in ab initio calculations of medium-mass nuclei. For this, we combine the new $F_2$ interaction with established 3N interactions up to next-to-next-to-leading order (N$^2$LO) and next-to-next-to-next-to-leading order (N$^3$LO) in chiral effective field theory. We explore two fit strategies for the low-energy couplings. The first is based only on few-body observables, while the second also incorporates information from $^{16}$O. Generally, we find that the $F_2$ interaction has a significant impact on energies and radii, however mainly due to changes in the short-range couplings. Overall, we do not find systematic improvements in the reproduction of medium-mass nuclei when the additional $F_2$ interaction is included.

In the present work, we propose an improved harmonic oscillator model to systematically evaluate the proton radioactivity half-lives in spherical nuclei, incorporating centrifugal potential effects. By fitting the experimental data, the centrifugal parameter $d = 0.143$ for the correction term $dl(l+1)$ and nuclear potential depth $V_0 = 62.4$ MeV are obtained. The model integrates the relativistic mean field (RMF) theory with the BCS method based on the DD-ME2 force to determine spectroscopic factors $S_p$. Moreover, by verifying the linear relationship between the logarithm of the normalized width $\log_{10}{\gamma^2}$ and fragmentation potential $V_{frag}$, the connection between nuclear structure and tunneling dynamics is confirmed, and an analytical expression for the adjustable parameter $d$ corresponding to the centrifugal potential is derived as $d^{\rm{Ae}}$ $\approx$ 0.167. Compared with $d^{\rm{Ae}}$, the modified model based on $d$ yields results in better agreement with experimental half-lives, and is able to control the error of the experimental data within a factor of 2.4. Furthermore, the extended improved model is used to predict the half-lives of some possible proton radioactivity candidates in NUBASE2020 that are energetically allowed or have been observed but not yet quantified. This work improves the accuracy of proton radioactivity studies and provides a robust theoretical framework for future nuclear structure research.

We introduce a no-reaction-plane (no-RP) method for extracting directed (\(v_1\)) and elliptic (\(v_2\)) flows in heavy-ion collisions, which eliminates the need for event-plane reconstruction. %by scanning over fixed test angles and using simple count asymmetries. The method is validated with PHSD model simulations of Au+Au collisions at \(\sqrt{s_{NN}} = 9.2\) GeV at freeze-out (for impact parameters \(b = 4-8\) fm). We demonstrate that the two asymmetries for each harmonic contribute equally, i.e., \(\langle A_{\mathrm{ud}}^2\rangle \approx \langle A_{\mathrm{lr}}^2\rangle\) and \(\langle A_1^2\rangle \approx \langle A_2^2\rangle\), so that a single asymmetry measurement suffices for a good flow estimate. Event-by-event comparisons with direct calculations using the true reaction plane yield Pearson correlation coefficients of 0.956 for \(v_2\) and 0.834 for \(v_1\), confirming that the no-RP method captures flow fluctuations well enough.

The structure of the ground $(2^+)$ and excited $(1^+)$ bound states of the $^8$B and $^8$Li nuclei is studied within the framework of the $\alpha+^3$He($^3$H)+$p(n)$ three-body potential cluster model based on the hyperspherical Lagrange-mesh method. The two-body realistic potentials have been applied from the literature. Convergent theoretical estimates for the three-body binding energy and matter radius have been obtained with the maximal hypermomentum $K_{max}=22$ and 28 for the ground and excited $1^+$ states, respectively. The ANC value of the virtual transition of the $^8$B nucleus is estimated self-consistently by matching the overlap integral of the $^8$B three-body and the $^7$Be two-body wave functions with it's asymptotics. The obtained values are $0.211$~fm$^{-1/2}$ and $0.739$~fm$^{-1/2}$ in the spin 1 and spin 2 channels, respectively. For the ANC values of the $^8$Li nucleus the estimates $0.220$~fm$^{-1/2}$ and $0.774$~fm$^{-1/2}$ are extracted. The ratio $C^2(^8 {\rm B})/C^2(^8 {\rm Li})=0.912$ implies a breaking of the mirror symmetry of the strong nuclear forces of order 27\% due to the Coulomb interaction and the dynamical three-body effects. For the $S_{17}(0)$ -factor an estimate $22.492\pm0.014$ eV b was obtained based on the asymptotic theory developed by D. Baye [Phys. Rev. C {\bf 62},065803 (2000)]. The spin 2 channel contributes with $S^{(2)}_{17}(0)=20.838 \pm 0.014$ eV b, while the spin 1 channel yields $S^{(1)}_{17}(0)=1.654 \pm 0.003$ eV b. These results for $S_{17}(0)$ are in a good agreement with the estimate $20.8\pm0.7{\rm(th)}\pm1.4{\rm(exp)}$ eV b of the SF II, but larger than the recommended value $20.5\pm0.70$ eV b of the SF III. At the same time, our estimate is very close to the value 22.4 eV b used in the most successful Solar Model BAR2M [W.~Yang and Z.~Tian, AJ {\bf 970} (2024), 38].

Global control provides a promising route to implementing multi-qubit gates without individual qubit addressing. This is especially appealing for permutation-invariant (PI) gates, whose symmetry is often broken when they are compiled into individually addressed one- and two-qubit gates. Important examples include SWAP, $\sqrt{i\text{SWAP}}$, and the n-qubit controlled-Z gate, which is equivalent, up to two single-qubit Hadamard gates, to the multi-qubit Toffoli gate. Motivated by this global-control perspective, we show that all PI unitaries on an arbitrary number of qubits can be realized using the Tavis-Cummings (TC) interaction, the multi-qubit version of the Jaynes-Cummings interaction, together with global uniform z and x fields. Here, the $n$ qubits are identically coupled to a single bosonic mode (oscillator), which is initialized in and returned to its vacuum state. A corollary is that all PI states, including GHZ and Dicke states, can be prepared using the same global control. For the case n=2 qubits, which is particularly important in quantum computing, we also find explicit pulse sequences for implementing all PI qubit unitaries that conserve angular momentum in the z direction, using only the TC interaction and global z fields. This includes controlled-Z, SWAP, and $\sqrt{i\text{SWAP}}$.

Directly probing light-quark Yukawa couplings and their flavor structure remains a major challenge due to their smallness and overwhelming QCD backgrounds. In this Letter, we propose a theoretical framework to access these couplings at lepton colliders through transverse spin dependent azimuthal modulations in dihadron fragmentation. These modulations arise from the interference between Higgs mediated and standard model amplitudes in $e^-e^+\to q\bar{q}Z$, producing angular structures that are linearly sensitive to the Yukawa couplings $y_q$, in contrast to conventional observables that scale as $y_q^2$. By combining channels with an identified accompanying single hadron, $h^\prime=\pi^\pm,K^\pm$, and $p/\bar{p}$, this approach cleanly disentangles the up- and down-quark Yukawa contributions, yielding typical limits at the $\mathcal{O}(10^{-4}\sim 10^{-3})$ level and establishing fragmentation dynamics as a novel and complementary probe of the Higgs flavor structure.

We investigate the phase structure of the single-flavor Gross--Neveu model with Wilson fermions using the Grassmann corner transfer matrix renormalization group (CTMRG). The path integral is formulated as a two-dimensional Grassmann tensor network and approximately contracted by the Grassmann CTMRG algorithm. We investigate the phase diagram by varying the fermion mass and the four-fermion coupling, using the pseudoscalar condensate as an order parameter for the $\mathbb{Z}_{2}$ parity symmetry breaking phase. The universality classes of the phase boundaries are identified through the central charge $c$ obtained via scaling analysis of the entanglement entropy. Furthermore, we extract the quantity related to the entanglement spectrum from the converged CTMRG environments, allowing us to distinguish the topological insulator phase and the trivial phase. The resulting phase structure suggests that the Aoki phase is separated from the other phases by critical lines characterized by $c=1/2$, while the critical lines with $c=1$ separate the topological insulating and trivial phases. Our numerical results also indicate that the Aoki phase does not persist in the strong-coupling regime for the single-flavor theory.

We propose a scheme to correctly incorporate the contribution of the chiral anomaly in the D3/D7 model to calculate chiral transport phenomena. To ensure the D7-brane wraps S^5 appropriately and the Wess-Zumino term is switched on, we allow the D7-brane to rotate in the compactified extra directions and perform the analysis accordingly. To demonstrate that this calculation procedure works well, we specifically compute the magnetoresistance in the D3/D7 model. We find that a finite axial chemical potential is realized and the negative magnetoresistance is enhanced by the anomaly contribution.