Session PH: Nuclear Theory

Variational Monte Carlo calculation of n+3H scattering

The quantum Monte Carlo (QMC) methods have a long history of successful bound state calculations in light systems but so far have seen very little application to unbound systems.  In this talk we describe a numerical method that improves the efficiency and accuracy of scattering calculations in QMC. We present an initial test case of n+³H using variational Monte Carlo (VMC) wave functions with various two- and three-body potentials, including the Norfolk family of potentials. The method consists of inferring long-range amplitudes in the wave function from integrals over the short-ranged region of interaction. Specifically, we compute spectroscopic overlaps and scattering observables using these integrals and report improvement relative to direct evaluation of the same wave function. Compared with previous QMC scattering calculations, the new method avoids difficulties associated with precise computation of energy differences and with convergence outside the interaction region. It also enables calculation of approximate phase shifts over a range of energies from a single wave function. This initial test-case applies the Norfolk chiral potentials to A>2 scattering, and it paves the way for use with more-precise Green’s function Monte Carlo wave functions.   

Nuclear Josephson-like γ-emission

Nucleon pair transfer processes between superfluid nuclei in heavy ion reactions are considered as possible analogues of the transfer of Cooper pairs of electrons through Josephson Junctions (JJ). In this contribution we present a novel approach to the study of this analogy, based on the alternating current (ac) Josephson effect and associated electromagnetic radiation emitted in the process, for which the consideration of one nuclear Cooper pair transfer, together with the corresponding one-nucleon transfer process, leads to a direct identification of the nuclear Josepson-like effect. It is based on the nuclear Cooper pair coherence length and on the γ-radiation emitted in the transfer process. In this work we implement the quantum mechanical description of the coupling of the electric dipole associated with the (2n)-transfer reaction process, establishing the connection between the dynamics of the collision process and the number and energy dependence of the emitted γ photons, thus providing a robust quantitative signature of the (ac) Josephson-like nature of the phenomenon. Two important quantities emerge as conserved properties: the Cooper pair coherence length, and the length and orientation of the effective dipole associated with the two transferred neutrons.   

Investigating Resonant State Modification with a Coulomb Trajectory Model

Unstable nuclei in isolation decay with well-defined energy distributions parameterized by their intrinsic energy and lifetime; resonant states are experimentally identified by examining relative energies between two or more daughter particles. When ejected from an excited parent, long-lived resonant states decay unperturbed while very short-lived states decay in the vicinity of the parent; this proximity introduces non-negligible Coulomb interactions which modify the observed energy. Previous work investigating resonant state modification has shown that the phenomenon can be reproduced qualitatively. Through the development of a C++/ROOT Coulomb trajectory model, we investigate the nature of these effects by examining simulated relative energy distributions of common short-lived ejectiles such as 8Be (2+) and 5Li (3/2-) emitted from excited heavy nuclei. Building upon previous work, this model implements nuclear surface stabilization as a function of inter-nuclear distance between the decay components in an attempt to more accurately replicate experimental results.   

Calculation of the 3He(α,γ)7Be astrophysical S factor using the no-core shell model with continuum including three-nucleon forces

The ³He(α,γ)⁷Be radiative-capture reaction rates between 20 and 500 keV are essential in understanding the primordial ⁷Li abundance in the universe. The Coulomb repulsion between the fusing nuclei suppresses the capture cross section at these low energies, making it difficult to measure directly. Theoretical calculations are needed to guide the extrapolation to the solar energies of interest. To this end, we present NCSMC calculations of ³He(α,γ)⁷Be reaction within the NCSMC starting from two- and three-nucleon chiral interactions.   

Nuclear Shell Model to the Rescue: Efforts to Resolve a Mystery in Beta Delayed Neutron Emission

Nuclei far from stability can be studied by producing specific short-lived nuclei by beta decay and measuring the subsequent emission of neutrons and gammas. Such experiments are being planned at both Argonne Nat. Lab and at FRIB (Facility for Rare Isotopes, Michigan State University). Meanwhile, some initial experiments found a surprising overabundance of gamma emission. This has broad implications for predictions made in nuclear astrophysics and other applications. It is our goal to understand this overabundance and improve our theoretical description of short-lived nuclei to account for it. To this end, we will discuss our work integrating microscopic calculations of beta decay and other nuclear properties within the shell model framework with a contemporary nuclear reaction model code. We overcome the computational barrier of large shell model dimensions by deploying our newly developed many-body basis truncation method.   

Self-Consistent HFB+QRPA Calculations for Selected Mo Isotopes

Nuclear reactions play a fundamental role in the universe, driving stellar evolution and nucleosynthesis for the formation of the elements, and in applied areas such as medical isotopes production. In aspect of nuclear astrophysics, Mo is an interesting element for studying its reactions because its isotopes are produced by a variety of nucleosynthetic processes. Nuclear reaction cross sections are a key to understand these processes. For example, neutron capture cross sections are necessary to simulate astrophysical processes such as the r-process and to better understand the production mechanisms for nuclei heavier than iron. Successful descriptions for this process require knowledge of nuclear structure of related nuclear states, and the transition mechanisms between ground and excited states. Many theoretical models have been developed for the successful description of structural properties of nuclei and their reaction. The new experimental radioactive ion beam facilities provide great opportunities for the exploration of the properties of exotic nuclei, far away from the β-stability line.

 We have performed fully consistent calculations of excited states in both spherical and axially-deformed nuclei using the Quasi-particle Random Phase Approximation (QRPA) built on Hartree-Fock-Bololiubov (HFB) states with the Gogny D1M finite-range effective interaction, implemented in an axially-symmetric deformed harmonic-oscillator (HO) basis. We will present the ground-state nuclear shapes for the even-even molybdenum isotopes, from ⁸⁰Mo to ¹³⁰Mo. We will also discuss results for monopole, dipole, quadrupole and octupole responses and transition densities for selected spherical and deformed cases and compare with the experimental data.   

Effects of a Single-particle versus a Coulomb interaction in bubble nuclei.

The detailed investigation of microscopic mechanisms leading to the formation of bubble structures in the nuclei has been performed in the framework of covariant density functional theory. The main emphasis of this study is on the role of single-particle degrees of freedom and Coulomb interaction. In general, the formation of bubbles lowers the Coulomb energy. However, in nuclei, this trend is counteracted by the quantum nature of the single-particle states: only specific single-particle states with specific density profiles can be occupied with increasing proton and neutron numbers. A significant role of the central classically forbidden region at the bottom of the wine bottle potentials in the formation of nuclear bubbles (via primarily the reduction of the densities of the s states at r = 0) has been revealed for the first time. Their formation also depends on the availability of low-l single-particle states for occupation since single-particle densities represent the basic building blocks of total densities. Nucleonic potentials disfavor the occupation of such states in hyperheavy nuclei and this contributes to the formation of bubbles in such nuclei. Existing bubble indicators are strongly affected by single-particle properties and thus they cannot be reliable measures of bulk properties (such as the Coulomb interaction). The additivity rule for densities has been proposed for the first time. It was shown that the differences in the densities of bubble and at-density nuclei follow this rule in the A 40 mass region and in superheavy nuclei with comparable accuracy. This strongly suggests the same mechanism of the formation of a central depression in bubble nuclei of these two mass regions. Nuclear saturation mechanisms and self-consistency effects also affect the formation of bubble structures. The detailed analysis of different aspects of bubble physics strongly suggests that the formation of bubble structures in superheavy nuclei is dominated by single-particle effects. The role of the Coulomb interaction increases in hyperheavy nuclei but even for such systems, we do not nd strong arguments that the formation of bubble structures is dominated by it.   

Separable pairing in covariant density functional theory and its isospin dependence[1]

A systematic global investigation of pairing properties based on all available experimental data on pairing indicators has been performed for the first time in the framework of covariant density functional theory. It is based on separable pairing interaction of Ref. [2]. The optimization of the scaling factors of this interaction to experimental data clearly reveals its isospin dependence in neutron subsystem. However, the situation is less certain in proton subsystem since similar accuracy of the description of pairing indicators can be achieved both with isospin-dependent and mass-dependent scaling factors. The differences in the functional dependencies of scaling factors lead to the uncertainties in the prediction of proton and neutron pairing properties which are especially pronounced at high isospin and could have a significant impact on some physical observables. For a given part of nuclear chart the scaling factors for spherical nuclei are smaller than those for deformed ones: this feature exists also in non-relativistic density functional theories. 

    

Exploring Singular Value Decompositions within the In-Medium Similarity Renormalization Group Framework

One of the main challenges for ab initio nuclear many-body theory in the coming decade is the growth of computational and storage costs as calculations are extended to increasingly heavy, exotic and structurally complex nuclei. Here we investigate the factorization of nuclear interactions in m-scheme as a mean to address this issue. We perform Singular Value Decompositions of nuclear Hamiltonians in normal-ordered form and develop and implement their In-Medium Similarity Renormalization Group (IMSRG) evolution in term of the relevant singular values

We discuss structural features of the Hamiltonians that emerge upon their projection into suitably chosen low-rank space, and show that a small number of relevant components from the first space can be sufficient to capture important characteristics of the evolution.  We also explore implications for the storage and computational complexity of the IMSRG framework.   

Global Sensitivity Analysis of Collective Observables for 6Li and 12C

The importance of collectivity in nuclear dynamics is well-established from first-principles investigations [1, 2]. We combine the symmetry-adapted no-core shell model with global sensitivity methods to explore how observables in light nuclei respond to changes in the chiral effective NN interaction [3]. By generating a statistically significant set of unique parametrizations of this interaction and solving for the wave functions, we can determine which low-energy constants are the most important to accurately calculate and predict nuclear collective properties. In this talk, I will discuss such a sensitivity analysis performed on the excitation energies, point-proton RMS radii, and quadrupole moments for low-lying states in ⁶Li and ¹²C. We find that a small subset of the parameters has a dominant impact on these observables, suggesting a pathway to optimizing chiral potentials to constrain uncertainties in ab initio calculations.

[1] T. Dytrych, K. D. Launey, J. P. Draayer, et al., Phys. Rev. Lett. 124, 042501 (2020)

[2] Kristina D. Launey, Alexis Mercenne, and Tomas Dytrych, Ann. Rev. Nucl. Part. Sci. 71, 253 (2022)

[3] A. Ekström and G. Hagen, Phys. Rev. Lett. 123, 252501 (2019)