New articles on Nuclear Theory

[1] 2311.16391

Variation of multi-Slater determinants in antisymmetrized molecular dynamics and its application to $^{10}$Be with various clustering

We propose a method to optimize the multi-Slater determinants of the antisymmetrized molecular dynamics (AMD) in the linear combination form and apply it to the neutron-rich $^{10}$Be nucleus. The individual Slater determinants and their weights in the superposition are determined simultaneously according to the variational principle of the energy of the total wave function. The multi-AMD basis states of $^{10}$Be show various cluster structures as well as the shell-model type. In the cluster configurations, different intercluster distances are superposed automatically indicating the role of the generator coordinates. We further introduce a procedure to obtain the configurations for the excited states imposing the orthogonal condition to the ground-state configurations. In the excited states of $^{10}$Be, the linear-chain-like structure is confirmed consisting of various clusters. The energy spectrum using the obtained basis states reproduces the experiments. The present framework can be the method to find the optimal multi-configuration for nuclear ground and excited states.

[2] 2311.16425

Exotic nonaxial-octupole shapes in $N=184$ isotones from covariant density functional theories

The nonaxial octupole shape in some nuclei with $N = 184$, namely, $^{284}$Fm, $^{286}$No, $^{288}$Rf, and $^{290}$Sg, is investigated using covariant density functional theories. Employing the density-dependent point-coupling covariant density functional theory with the parameter set DD-PC1 in the particle-hole channel, it is found that the ground states of $^{284}$Fm, $^{286}$No, $^{288}$Rf, and $^{290}$Sg have pure nonaxial octupole shapes with deformation parameters $\beta_{31} \approx 0.08$ and $\beta_{33} \approx -0.01 \sim -0.03$. The energy gain due to the $\beta_{31}$ and $\beta_{33}$ distortion is $\sim$ 1 MeV. The occurrence of the nonaxial octupole correlations is mainly from the proton orbitals $1i_{13/2}$ and $2f_{7/2}$, which are close to the proton Fermi surface. The dependence of the nonaxial octupole effects on the form of the energy density functional and on the parameter set is also studied.

[3] 2311.16837

The Hoyle and associated excited states from the viewpoint of pocket resonances in alpha + 8Be reactions

We examine the production of the Hoyle and associated excited states from the viewpoint of pocket resonances in the reaction of an $\alpha$-particle on a ground state prolate $^8$Be nucleus within the optical model coupled-channel framework. The predicted reaction cross sections, as a function of the center-of-mass energy $E_{\rm cm}$, show prominent resonances, including the Hoyle resonance. The positions and widths of these resonances are sensitive to the target deformation ($\beta_2$ parameter) and the parity of the nuclear surface potential $-$ deeper for the even-parity $L$ partial waves relative to those for the odd-parity $L$ partial waves at the surface region because of the Bose-Einstein exchange of the $\alpha$-bosons. Decomposing the reaction cross sections to different partial waves, we find that the resonance energies and widths reasonably agree with the available experimental data and previous hyperspherical calculations for the $0_2^+$ (Hoyle state), $0_3^+$, $1_1^-$ and $3_1^-$ states of $^{12}$C, except for the narrow theoretical width of the $2_2^+$ state. Analyzing the wavefunctions and the resonance widths, we identify the narrow and sharp $0_2^+$, $3_1^-$ and $2_2^+$ resonances as pocket resonances -- resonances which occur below the potential barrier, while the broad $0_3^+$ and $1_1^-$ resonances as above-the-barrier resonances. For astrophysical applications, we also evaluate the astrophysical $S(E_{\rm cm})$-factor for $E_{\rm cm}$ $<$ 1.0 MeV, for the fusion of $\alpha$+$^8$Be into the $^{12}$C$(2^+)$ state based on our estimated $s$-wave $\alpha$+$^8$Be reaction cross section and the associated $\gamma$- and $\alpha$-decay widths for the decay of $^{12}$C excited states in the potential pocket.

[4] 2311.16929

Universality in Ground State Masses of Nuclei

The beautiful and profound result that the first eigenvalue of Schroedinger operator can be interpreted as a large deviation of certain kind of Brownian motion leads to possible existence of universality in the distribution of ground state energies of quantal systems. Existence of such universality is explored in the distribution of the ground state energies of nuclei with Z $\ge$ 8 and N $\ge$ 8. Specifically, it has been demonstrated that the nuclear masses follow extreme-value statistics, implying that the nuclear ground state energies indeed can be treated as extreme values in the sense of the large deviation theory of Donsker and Varadhan.

[5] 2311.16969

Adding Corrections to Global Spherical Potentials for Use in a Coupled-Channel Formulation

The coupled-channel technique augments a non-relativistic distorted wave born approximation scattering calculation to include a coupling to virtual states from the negative energy region. It has been found to be important in low energy nucleon-nucleus scattering. We modify the nucleon-nucleus standard optical potentials, not designed for a coupled-channel space, so they can be used in that setting. The changes are small and systematic. We use a standard scattering code to adjust a variety of optical potentials and targets such that the original fit to scattering observables are maintained as we incorporate the coupled-channel environment. Overall over forty target nuclei were tested from $A=12$ to $A=205$ and nucleon projectile energies from 1 MeV to 200 MeV. There is excellent improvement in fitting the scattering observables, especially for low energy neutron scattering.The corrections were found to be unimportant for projectile energies greater than 200 MeV. The largest changes are to the surface amplitudes while the real radii and the real central amplitude are modified by only a few percent, every other parameter is unchanged. This technique is general enough to be applied to a variety of inelastic theoretical calculations.

[6] 2311.16297

Quantum-classical simulation of quantum field theory by quantum circuit learning

We employ quantum circuit learning to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, we encounter significant challenges due to the technical limitations of quantum devices when implementing the Hamiltonian using Pauli spin matrices. To address this challenge, we leverage quantum circuit learning, employing a compact configuration of qubits and low-depth quantum circuits to predict real-time dynamics in quantum field theories. The key advantage of this approach is that a single-qubit measurement can accurately forecast various physical parameters, including fully-connected operators. To demonstrate the effectiveness of our method, we use it to predict quench dynamics, chiral dynamics and jet production in a 1+1-dimensional model of quantum electrodynamics. We find that our predictions closely align with the results of rigorous classical calculations, exhibiting a high degree of accuracy. This hybrid quantum-classical approach illustrates the feasibility of efficiently simulating large-scale QFTs on cutting-edge quantum devices.

[7] 2311.16402

A unified description of DGLAP, CSS, and BFKL: TMD factorization bridging large and small x

This paper introduces a transverse-momentum dependent (TMD) factorization scheme designed to unify both large and small Bjorken-x regimes. We compute the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to the gluon TMD operator for an unpolarized hadron within this proposed scheme. This leads to the emergence of a new TMD evolution, incorporating those in transverse momentum, rapidity, and Bjorken-x. When matched to the collinear factorization scheme, our factorization scheme faithfully reproduces the well-established Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and Collins-Soper-Sterman (CSS) evolutions. Conversely, matching with high-energy factorization not only yields the Balitsky-Fadin-Kuraev-Lipatov (BFKL) evolution but also reveals distinctive signatures of CSS logarithms. The development of this novel TMD factorization scheme, capable of seamlessly reconciling disparate Bjorken-x regimes and faithfully reproducing established QCD evolution equations, has the potential to significantly advance our comprehension of high-energy processes and three-dimensional parton structures of hadrons.

[8] 2311.16537

More on the gauge principle and nonobservability of some quantum numbers characterizing the Landau eigen-states

The eigen-states of the Landau Hamiltonian in the symmetric gauge are characterized by two integers $n$ and $m$. Here, $n$ denotes the familiar Landau quantum number, while $m$ represents the eigen-value of the canonical orbital angular momentum (OAM) operator $\hat{L}^{can}_z$. On the other hand, the eigen-states in the 1st Landau gauge are characterized by two integers $n$ and $k_x$, here $n$ is the Landau quantum number, while $k_x$ is the eigen-value of the canonical momentum operator $\hat{p}^{can}_x$. Since the canonical momentum and the canonical OAM are both gauge-variant quantities, their eigenvalues $k_x$ and $m$ are standardly believed not to correspond to observables. However, this wide-spread view was suspected in a recent paper based on the logical development of the gauge-potential-independent formulation of the Landau problem, which predicts the existence of two conserved momenta $\hat{p}^{cons}_x$ and $\hat{p}^{cons}_y$ and one conserved OAM $\hat{L}^{cons}_z$. They are regarded as Noether charges of the Landau Hamiltonian, the conservation of which is guaranteed {\it independently} of the choice of the {\it auge potential}. In particular, on the basis of novel covariant gauge transformation properties of these conserved operators, the eigen-values of which are characterized by the quantum numbers $k_x$, $k_y$, and $m$, it was claimed that these quantum numbers correspond to observables at least in principle. The purpose of the present paper is to show that this claim is not justified, regardless of the differences in the two theoretical formulations of the Landau problem, i.e. the traditional formulation and the gauge-potential-independent formulation.

[9] 2311.16561

Cost of inferred nuclear parameters towards the f-mode dynamical tide in binary neutron stars

Gravitational Wave (GW) observations from Neutron Stars (NS) in a binary system provide an excellent scenario to constrain the nuclear parameters. The investigation of Pratten et al. (2022) has shown that the ignorance of f-mode dynamical tidal correction in the GW waveform model of the binary neutron star (BNS) system can lead to substantial bias in the measurement of NS properties and NS equations of state (EOS). In this work, we investigate the bias in the nuclear parameters resulting from the ignorance of dynamical tidal correction. In addition, this work demonstrates the sensitivity of the nuclear parameters and the estimated constraints on them from future GW observations. We infer the nuclear parameters from GW observations by describing the NS matter within the relativistic mean field model. For a population of GW events, we notice that the ignorance of dynamical tide predicts a lower median for nucleon effective mass ($m^*$) by $\sim6\%$ compared to the scenario when dynamical tidal correction is considered. Whereas at a 90\% credible interval(CI), $m^*$ gets constrained up to $\sim 5\%$ and $\sim 3\%$ in A+ (the LIGO-Virgo detectors with a sensitivity of 5th observing run) and Cosmic Explorer (CE) respectively. We also discuss the resulting constraints on all other nuclear parameters, including compressibility, symmetry energy, and slope of symmetry energy, considering an ensemble of GW events. We do not notice any significant impact in analyzing nuclear parameters other than $m^*$ due to the ignorance of f-mode dynamical tides.

[10] 2311.16938

New insights into the doubly charmed exotic mesons

Using effective Lagrangians constrained by the heavy quark spin symmetry and chiral symmetry, for the light quarks, we analyze the $D^0 D^0\pi^+$, $\bar{D}^0D^0\pi^0$ and $D^0\bar{D}^{*0}$ invariant mass spectra. Performing a simultaneous analysis of the doubly charmed and charm-anti-charm states gives further insights into the nature of the $T^+_{cc}$ and $\chi^0_{c1}(3872)$, exotic hadrons. We find that both states lie below the respective open-charm $DD^*$/$D\bar{D}^*$ thresholds. This finding, together with the fact that the contributions of the triangle and box diagrams are negligible, suggests that both resonances are likely to be genuine bound states. We also predict the decay rates for their possible charge partners.