Session SM: Nuclear Theory IV: Structure and formal developments

Survey of ab initio Gamow-Teller observables in the \textit{p} shell

\textit{Ab initio} nuclear theory strives to make quantitative predictions of nuclear observables, such as Fermi and Gamow-Teller strengths. The no-core configuration interaction (NCCI) method solves the quantum many-body problem, starting with the internucleon interaction, and gives wave functions representing approximate eigenstates of the nuclear Hamiltonian. These wave functions can then be used to evaluate transition matrix elements. However, the calculated results can depend heavily on the choice of single-particle basis and the choice of truncation needed to solve the problem numerically. We therefore survey impulse-approximation weak (Fermi and Gamow-Teller) transition observables in the \textit{p}-shell and explore the convergence behavior of both the individual transition matrix elements and the mixing ratios. This in turn will serve as a baseline when considering corrections to the operator arising from meson-exchange current (MEC) contributions derived in chiral effective field theory ($\chi$EFT).   

Searching for the Origin of Symplectic Symmetry Within the Chiral Effective Potential

Nuclei have been known to exhibit remarkable features, such as rotational structure and enhanced deformation, that have been shown through first-principles structure calculations to be tied to almost perfect symplectic symmetry in nuclear dynamics [1]. We aim to understand the origins of these features by examining the underlying chiral potentials in the framework of the symmetry-adapted no-core shell model. As a first step, we compute the wavefunctions of light nuclei using a subset of the diagrams up to next-to-next-to-leading order, to gain insight into which parts of the chiral nucleon-nucleon forces respect symplectic symmetry, and which of them break it. This allows one to examine how collective modes in nuclei emerge from the chiral nucleon-nucleon forces, and provide complementary information to the recent global sensitivity analysis of the binding energy and charge radius of $^{\mathrm{16}}$O [2]. [1] T. Dytrych, K. D. Launey, J. P. Draayer, et al., Phys. Rev. Lett. 124, 042501 (2020) [2] A. Ekstr\"{o}m and G. Hagen, Phys. Rev. Lett. 123, 252501 (2019)   

Exploring the Relationship Between Nuclear Matter and Finite Nuclei with Chiral Two- and Three-Nucleon Forces.

We address the connection between the saturating behavior of infinite nuclear matter and the description of finite nuclei based on state-of-the-art chiral two- and three-nucleon forces. We observe that chiral two- and three-nucleon interactions (at N2LO and at N3LO) which have been found to predict realistic binding energies and radii for a wide range of finite nuclei (from p-shell nuclei up to nickel isotopes) are unable to saturate infinite nuclear matter. On the other hand, it has been shown that, when the fits of the cD and cE couplings of the chiral three-nucleon interactions include the constraint of nuclear matter saturation in addition to, as is typically the case, the triton binding energy, medium-mass nuclei are underbound and their radii are systematically too large. We discuss this apparent inconsistency and perform test calculations for various scenarios to shed light on the issue.   

The Zero Mode Effect on Critical Coupling for 1+1 $\phi^4$ Theory

Evaluating the effect of the zero momentum mode in discretized light cone quantization (DLCQ) approach for light front field theory is a long standing problem. Using 1+1 dimension $\phi^4$ theory, we compare the critical coupling calculated in light front with zero mode excluded and included. The critical coupling without zero mode was previously obtained by solving the theory in DLCQ, and the critical coupling with zero mode included was recently obtained by solving the theory in light front using a symmetric polynomial basis which was claimed to circumvent the zero mode problem [1]. The critical coupling from these two methods can be compared, and conclusion can be drawn on whether the zero mode has a significant effect for the DLCQ critical coupling result. We then further compare the zero mode included and excluded cases after their critical coupling is converted to the corresponding value in equal time scheme. Finally, we discuss the consistency of these converted values with critical coupling obtained by equal time quantization approaches in literature. [1] M. Burkardt, et al., Phys. Rev. D94, 065006(2016)   

Properties of a Two-Dimensional Scalar Field Theory with a $\phi^4$ Interaction

We investigate properties of a two-dimensional scalar field theory with a $\phi^4$ interaction in the broken phase using the method of Discretized Light-Cone Quantization (DLCQ). Our goal is to extrapolate the critical coupling for vanishing mass gap (with respect to the perturbative vacuum) to infinite longitudinal momentum K in the odd particle sector, the even particle sector, and the degenerate mass of the odd and even sectors of DLCQ. We will present results with both periodic and anti-periodic boundary conditions to elicit effects of neglecting the zero mode in the periodic case.   

Manifestation of quantum correlations in the interpolating helicity amplitudes between the instant form dynamics and the light-front dynamics for the annihilation/production process of two spin-1 particles

Two fundamental spin-1/2 particles can combine to yield either a scalar particle with the anti-symmetric spin structure invariant under the rotation and boost or a vector particle with three helicity states with the symmetric spin-structure not invariant in general. In particular, the symmetric helicity-0 state of the vector particle distinguishes its quantum correlation effect from the antisymmetric helicity-0 state of the scalar particle. We manifest such clear difference between spin-1 and spin-0 particles, using the previous investigation of spin-1/2 particle's generalized helicity interpolating between the instant form dynamics (IFD) and the light-front dynamics (LFD). As the Jacob and Wick helicity defined in IFD is not invariant under the boost while the light-front helicity defined in LFD is invariant under the boost, we found that the quantum correlation effect manifests itself as the helicity boundary between the IFD and the LFD which appears in the helicity amplitudes of scattering processes by boosting the reference frame. To illustrate this characteristic manifestation, we exhibit the boundaries corresponding to the phase changes due to the distinguished quantum correlation effects between the scalar and vector particles in pair annihilation/production processes.   

Fermion-mass and charge renormalization using the relativistic, time-dependent Dirac equation.

The time-dependent electromagnetically self-coupled Dirac equation is solved numerically by means of the staggered-leap-frog algorithm. The stability region of the method versus the interaction strength and the ratio of the spatial-grid size over the time-step is established. The expectation values of several dynamic operators are evaluated as functions of time. These include the fermion and electromagnetic or strong interaction energies and the fermion dynamic mass. There is a characteristic time-dependence leading to asymptotic constants of these expectation values. In the case of the fermion mass and charge this amounts to renormalization. The dependence of the expectation values on the spatial-grid size is evaluated and yields finite results due to the finiteness and continuity of the spinor. The contribution of positive and negative energy states to the asymptotic values and the gauge fields is analyzed, particularly for charge renormalization. A statistical method, employing a canonical ensemble whose temperature is the inverse of the spatial-grid size, is used to remove the momentum-dependence. A result for each spatial-grid size value is obtained. The continuum limit is taken to calculate both the fermion mass and charge. The renormalization mass correction is 10{\%} and the charge correction is about 30{\%}.   

Revision of Some Mathematical Descriptions of Nuclear Phenomena Needed To Account for Newly Discovered Nuclear MotionsD

Nuclear motion, especially vibration discovered about 1960, may alter some previous mathematical descriptions of nuclear phenomena. Thus, a nucleus when created may exhibit no motion, linear, rotational and/or vibratory motion in some combination which may be later altered by outside forces: $E=mc^2 + 1/2mv^2 + 1/2I\omega^2 + 1/2kx^2$. Because the nuclear barrier height is position dependent, current descriptions must include this factor. The classical barrier height is given by $V= kQ_1Q_2/r.$ Assuming the nucleus is a 3 dimensional equal amplitude oscillator $r= ([(AcosX)^2 +(AcosY)^2 +(AcosZ)^2])^(1/2).$ For no motion $V= infinitely high $. For average oscillation, $r=RMScos$ and $r=1.22A$ , RMS average, and if $cos=1$, $r=1.707A$. The nuclear barrier height then ranges from infinitly high, average RMS $ V= 0.816Q_1Q_2A/r$. A low value will be $0.576Q_1Q_2A/r$. A is the average nuclear vibration. Random nuclear vibrations also create a variable nuclear cross sections . If $b= Acosy)$ is the impact parameter in 1 dimension, then cross section $\sigma = \pi(AcosY)^2$ if A =amplitude of nuclear vibration. Therefore, $\sigma = \pi(A)^2$ maximum, $\sigma = \pi(0.707A)^2$ RMS average and $\sigma= 0$ minimum values for the variable nuclear cross sections per nucleus.