Nuclear Hamiltonian Research Articles

Relativistic corrections to the correlated basis function effective nuclear Hamiltonian

Relativistic corrections to the correlated basis function effective nuclear Hamiltonian

The giant dipole resonance (GDR) in odd-mass 181–195Pt nuclei

Abstract This manuscript theoretically examines the Giant Dipole Resonance (GDR) in odd-mass 181-195Pt nuclei with the Translational and Galileo Invariant Qusiparticle Phonon Nuclear Model (TGI-QPNM) for the first time. TGI-QPNM includes axially symmetric Woods-Saxon potential, isovector dipole-dipole interaction and restoration forces for spontaneously broken Galilean and Translation symmetries of the nuclear Hamiltonian. Therefore, TGI-QPNM makes eliminating the spurious contributions in the E1 spectrum possible. The obtained results show that the odd-mass 181-195Pt isotopes have a two-peak structure. In 181-187Pt isotopes, while the second peak is higher than the first, in 189-195Pt isotopes, it’s the opposite. The photo-absorption result for the 195Pt is in reasonably good agreement with the experimental data.

Extracting the Geometric Phase from the Ensemble of Trajectories.

Traditionally, methods designed to investigate the effects of the geometric phase in reaction dynamics, such as including a vector potential in the nuclear Hamiltonian, necessitate the explicit manipulation of geometric phase-related terms in the adiabatic representation. In contrast, the diabatic representation provides an alternative approach that implicitly addresses the geometric phase and nonadiabatic issues. In this study, we present a method to directly extract the phase information on the geometric phase from the ensemble of interdependent trajectories utilizing the diabatic representation. This approach presents a direct means of quantitatively examining the geometric phase effects in dynamics and has the potential to yield observables suitable for experimental measurement.

Distilling the Essential Elements of Nuclear Binding via Neural-Network Quantum States.

To distill the essential elements of nuclear binding, we seek the simplest Hamiltonian capable of modeling atomic nuclei with percent-level accuracy. A critical aspect of this endeavor consists of accurately solving the quantum many-body problem without incurring an exponential computing cost with the number of nucleons. We address this challenge by leveraging a variational MonteCarlo method based on a highly expressive neural-network quantum state ansatz. In addition to computing binding energies and charge radii of nuclei with up to A=20 nucleons, by evaluating their magnetic moments, we demonstrate that neural-network quantum states are able to correctly capture the self-emerging nuclear shell structure. To this end, we introduce a novel computational protocol based on adding an external magnetic field to the nuclear Hamiltonian, which allows the neural network to learn the preferred polarization of the nucleus within the given magnetic field.

Targeting spectroscopic accuracy for dispersion bound systems from abinitio techniques: Translational eigenstates of Ne@C70.

We investigate the endofullerene system Ne@C70 by constructing a three-dimensional Potential Energy Surface (PES) describing the translational motion of the Ne atom. This is constructed from electronic structure calculations from a plethora of methods, including MP2, SCS-MP2, SOS-MP2, RPA@PBE, and C(HF)-RPA, which were previously used for He@C60 in Panchagnula et al. [J. Chem. Phys. 160, 104303 (2024)], alongside B86bPBE-25X-XDM and B86bPBE-50X-XDM. The reduction in symmetry moving from C60 to C70 introduces a double well potential along the anisotropic direction, which forms a test of the sensitivity and effectiveness of the electronic structure methods. The nuclear Hamiltonian is diagonalized using a symmetrized double minimum basis set outlined in Panchagnula and Thom [J. Chem. Phys. 159, 164308 (2023)], with translational energies having error bars ±1 and ±2 cm-1. We find no consistency between electronic structure methods as they find a range of barrier heights and minima positions of the double well and different translational eigenspectra, which also differ from the Lennard-Jones (LJ) PES given in Mandziuk and Bačić [J. Chem. Phys. 101, 2126-2140 (1994)]. We find that generating effective LJ parameters for each electronic structure method cannot reproduce the full PES nor recreate the eigenstates, and this suggests that the LJ form of the PES, while simple, may not be best suited to describe these systems. Even though MP2 and RPA@PBE performed best for He@C60, due to the lack of concordance between all electronic structure methods, we require more experimental data in order to properly validate the choice.

Ab initio description of monopole resonances in light- and medium-mass nuclei

Giant resonances (GRs) are a striking manifestation of collective motions in mesoscopic systems such as atomic nuclei. Until recently, theoretical investigations have essentially relied on the (quasiparticle) random phase approximation ((Q)RPA), and extensions of it, based on phenomenological energy density functionals (EDFs). As part of a current effort to describe GRs within an ab initio theoretical scheme, the present work promotes the use of the projected generator coordinate method (PGCM). This method, which can handle anharmonic effects while satisfying symmetries of the nuclear Hamiltonian, displays a favorable (i.e. mean-field-like) scaling with system’s size. Presently focusing on the isoscalar giant monopole resonance (GMR) of light- and medium-mass nuclei, PGCM’s potential to deliver wide-range ab initio studies of GRs in closed- and open-shell nuclei encompassing pairing, deformation, and shape coexistence effects is demonstrated. The comparison with consistent QRPA calculations highlights PGCM’s unique attributes and sheds light on the intricate interplay of nuclear collective excitations. The present paper is the first in a series of four and focuses on technical aspects and uncertainty quantification of ab initio PGCM calculations of GMR using the doubly open-shell 46\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{46}$$\\end{document}Ti as an illustrative example. The second paper displays results for a set of nuclei of physical interest and proceeds to the comparison with consistent (deformed) ab initio QRPA calculations. While the third paper analyzes useful moments of the monopolar strength function and different ways to access them within PGCM calculations, the fourth paper focuses on the effect of the symmetry restoration on the monopole strength function.

Maximally local two-nucleon interactions at N3LO in Δ -less chiral effective field theory

We present new maximally local two-nucleon interactions derived in Δ-less chiral effective field theory up to next-to-next-to-next-to-leading order (N3LO), which include all contact and pion-exchange contributions to the nuclear Hamiltonian up to this order. Our interactions are fit to nucleon-nucleon phase shifts using a Bayesian statistical approach, and explore a wide cutoff range from 0.6–0.9 fm (≈660–440MeV). These interactions can be straightforwardly employed in quantum Monte Carlo methods, such as the auxiliary field diffusion Monte Carlo method. Together with local three-nucleon forces, calculations with these new interactions will provide improved benchmarks for the structure of atomic nuclei and serve as crucial input to analyses of astrophysical phenomena of neutron stars, such as binary neutron-star mergers. Published by the American Physical Society 2024

On the Eigenvalues of a Soluble Model of Coupled Molecular and Nuclear Hamiltonians

In this paper, a special type of soluble model corresponding to a coupled molecular and nuclear Hamiltonians H, the so-called generalized Friedrichs model, is considered. We aim to determine and provide the most important properties of the well-known Faddeev operator corresponding to H accommodating a number of discrete eigenvalues. Furthermore, we provide a formula for counting the multiplicity of discrete eigenvalues of H.

Translational eigenstates of He@C60 from four-dimensional abinitio potential energy surfaces interpolated using Gaussian process regression.

We investigate the endofullerene system 3He@C60 with a four-dimensional potential energy surface (PES) to include the three He translational degrees of freedom and C60 cage radius. We compare second order Møller-Plesset perturbation theory (MP2), spin component scaled-MP2, scaled opposite spin-MP2, random phase approximation (RPA)@Perdew, Burke, and Ernzerhof (PBE), and corrected Hartree-Fock-RPA to calibrate and gain confidence in the choice of electronic structure method. Due to the high cost of these calculations, the PES is interpolated using Gaussian Process Regression (GPR), owing to its effectiveness with sparse training data. The PES is split into a two-dimensional radial surface, to which corrections are applied to achieve an overall four-dimensional surface. The nuclear Hamiltonian is diagonalized to generate the in-cage translational/vibrational eigenstates. The degeneracy of the three-dimensional harmonic oscillator energies with principal quantum number n is lifted due to the anharmonicity in the radial potential. The (2l + 1)-fold degeneracy of the angular momentum states is also weakly lifted, due to the angular dependence in the potential. We calculate the fundamental frequency to range between 96 and 110 cm-1 depending on the electronic structure method used. Error bars of the eigenstate energies were calculated from the GPR and are on the order of ∼±1.5 cm-1. Wavefunctions are also compared by considering their overlap and Hellinger distance to the one-dimensional empirical potential. As with the energies, the two abinitio methods MP2 and RPA@PBE show the best agreement. While MP2 has better agreement than RPA@PBE, due to its higher computational efficiency and comparable performance, we recommend RPA as an alternative electronic structure method of choice to MP2 for these systems.

An integrable model of a planar tri-atomic molecule

A model of a planar tri-atomic molecule is presented, which is integrable in the Born–Oppenheimer adiabatic approximation. The molecular Hamiltonian is the sum of a nuclear vibrational energy operator and an electronic Hamiltonian, where vibrations of nuclei are defined to be motions with vanishing total angular momentum in the center-of-mass system, and where the electronic Hamiltonian is assumed to be a traceless 2 × 2 Hermitian matrix defined on Ṙ3, the shape space of the planar three-body system. Once an eigenvalue of the electronic Hamiltonian is chosen, vibrational-electronic interaction is introduced through covariant differential operators acting on sections of the eigen-line bundle associated with the chosen eigenvalue. The Hamiltonian for nuclear motion coupled with electronic state is then described in terms of these covariant differential operators together with the chosen eigenvalue as a potential for nuclear motion. The eigenvalues of the nuclear Hamiltonian are evaluated for bound states. In the case that vibrational-electronic interaction is restricted to small vibrational-electronic one around a symmetric configuration of the nuclei, a remark is made on a relation to a well-known Hamiltonian describing the dynamic Jahn–Teller effect for a planar tri-atomic molecule X3.

On the microscopic shell-model version of the Bohr-Mottelson collective model

The recently proposed microscopic shell-model version of the Bohr-Mottelson (BM) collective model is considered in more detail in the coordinate representation. The latter possesses a clear and transparent physical meaning, which reveals several features of the new version of the collective model missed in the previous formulation. The relationship to the original BM model is considered, along with the relationships between the different limiting submodels of the microscopic version of the BM model, which closely resemble the relationships of the original Wilets-Jean and rotor models. The kinematically correct many-particle wave functions of the microscopic version of the BM model, conserving the experimentally observed integrals of motion, are shown to consist of collective irrotational-flow and intrinsic components in accordance with the original BM unified model. The general BM Hamiltonian is obtained as a contraction limit of the microscopic many-particle nuclear Hamiltonian, or, alternatively, by restricting the latter to the scalar irreducible collective space.

Analysis of experimental spectra of phosphine in the Tetradecad range near 2.3 μm using ab initio calculations

Due to its major interest for the chemistry of planetary atmospheres and exobiology, accurate spectroscopy data of phosphine are required for the search of signatures of this molecule in astronomical observations. In this work, high resolution infrared laboratory spectra of phosphine were analyzed for the first time in the full Tetradecad region (3769–4763 cm−1) involving 26 rotationally resolved bands. Overall, 3242 lines were assigned in spectra previously recorded by Fourier transform spectroscopy at temperatures 200 K and 296 K, using a combined theoretical model based on ab initio calculations. The total nuclear motion Hamiltonian of PH3 including ab initio potential energy surface, was reduced to an effective Hamiltonian using the high-order contact transformation method adapted to vibrational polyads of the AB3 symmetric top molecules, followed by empirical optimization of the parameters. At this step, the experimental line positions were reproduced with a standard deviation of 0.0026 cm−1 that provided unambiguous identification of observed transitions. The effective dipole transition moments of the bands were obtained by fitting to the intensities obtained from variational calculations using the ab initio dipole moment surface. The assigned lines were used to newly determine 1609 experimental vibration-rotational levels up to Jmax = 18 with energy in the range 3896–6037 cm−1 that represents significant extension towards higher energies compared to previous works. Transitions for all 26 sublevels of the Tetradecad were identified but with noticeably fewer transitions for fourfold excited bands because of their weaker intensity. At the final step, pressure-broadened half widths were attached to each transition and a composite line list adopting ab initio intensities and empirical line positions corrected to the accuracy of about 0.001 cm−1 for strong and medium transitions was validated against experimental spectra available in the literature.

Modewise Johnson–Lindenstrauss embeddings for nuclear many-body theory

In this work, we explore modewise Johnson-Lindenstrauss embeddings (JLEs) as a tool to reduce the computational cost and memory requirements of nuclear many-body methods. JLEs are randomized projections of high-dimensional data tensors onto low-dimensional subspaces that preserve key structural features. Such embeddings allow for the oblivious and incremental compression of large tensors, e.g., the nuclear Hamiltonian, into significantly smaller random sketches that still allow for the accurate calculation of ground-state energies and other observables. Their oblivious character makes it possible to compress a tensor without knowing in advance exactly what observables one might want to approximate at a later time. This opens the door for the use of tensors that are much too large to store in memory, e.g., complete two-plus three-nucleon Hamiltonians in large, symmetry-unrestricted bases. Such compressed Hamiltonians can be stored and used later on with relative ease. As a first step, we analyze the JLE's impact on the second-order Many-Body Perturbation Theory (MBPT) corrections for nuclear ground-state observables. Numerical experiments for a wide range of closed-shell nuclei, model spaces and state-of-the-art nuclear interactions demonstrate the validity and potential of the proposed approach: We can compress nuclear Hamiltonians hundred- to thousand-fold while only incurring mean relative errors of 1\% or less in ground-state observables. Importantly, we show that JLEs capture the relevant physical information contained in the highly structured Hamiltonian tensor despite their random characteristics. In addition to the significant storage savings, the achieved compressions imply multiple order-of magnitude reductions in computational effort when the compressed Hamiltonians are used in higher-order MBPT or nonperturbative many-body methods.

Confining CO2 inside sI clathrate‐hydrates: The impact of the CO2–water interaction on quantized dynamics

We report new results on the translational-rotational (T-R) states of the CO2 molecule inside the sI clathrate-hydrate cages. We adopted the multiconfiguration time-dependent Hartree methodology to solve the nuclear molecular Hamiltonian, and to address issues on the T-R couplings. Motivated by experimental X-ray observations on the CO2 orientation in the D and T sI cages, we aim to evaluate the effect of the CO2 -water interaction on quantum dynamics. Thus, we first compared semiempirical and ab initio-based pair interaction model potentials against first-principles DFT-D calculations for ascertaining the importance of nonadditive many-body effects on such guest-host interactions. Our results reveal that the rotational and translational excited states quantum dynamics is remarkably different, with the pattern and density of states clearly affected by the underlying potential model. By analyzing the corresponding the probability density distributions of the calculated T-R eigenstates on both semiempirical and ab initio pair CO2 -water nanocage potentials, we have extracted information on the altered CO2 guest local structure, and we discussed it in connection with experimental data on the orientation of the CO2 molecule in the D and T sI clathrate cages available from neutron diffraction and solid-state NMR studies, as well as in comparison with previous molecular dynamics simulations. Our calculations provide a very sensitive test of the potential quality by predicting the low-lying T-R states and corresponding transitions for the encapsulated CO2 molecule. As such spectroscopic observables have not been measured so far, our results could trigger further detailed experimental and theoretical investigations leading to a quantitative description of the present guest-host interactions.

Theoretical Study of the d(d, p)^{3}H and d(d, n)^{3}He Processes at Low Energies.

We present a theoretical study of the processes d(d,p)^{3}H and d(d,n)^{3}He at energies of interest for energy production and for big-bang nucleosynthesis. We accurately solve the four body scattering problem using the abinitio hyperspherical harmonics method, starting from nuclear Hamiltonians which include modern two- and three-nucleon interactions, derived in chiral effective field theory. We report results for the astrophysical S factor, the quintet suppression factor, and various single and double polarized observables. A first estimate of the theoretical uncertainty for all these quantities is provided by varying the cutoff parameter used to regularize the chiral interactions at high momentum.

Trends of Neutron Skins and Radii of Mirror Nuclei from First Principles.

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion MonteCarlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference between neutron and proton radii of mirror nuclei and quantify the effect of charge symmetry breaking terms in the nuclear Hamiltonian. Our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.

Nuclear Structure Investigations of Even–Even Hf Isotopes

The mass region of rare-earth nuclei in the nuclear chart is riddled with well-deformed nuclei, exhibiting rotational properties and many interesting nuclear structure-related phenomena. The scarcity of experimental data as the neutron number increases and the exotic phenomena such as shape coexistence, which are strongly connected with the underlying symmetries of the Hamiltonian and are predicted to take place in this region, make this mass region a fertile ground for experimental and theoretical studies of nuclear structure. In this work, we investigate the structure of the even–even 162–184Hf (hafnium) isotopes through a calculation of various observables such as B(E2;01+→21+) reduced transition matrix elements and quadrupole moments. Six different nuclear models are employed in the calculations of the observables for these nuclei, the shapes of which deviate from spherical symmetry, and as such, are characterized by Hamiltonians, which break the rotational invariance of the exact nuclear many-body Hamiltonian. The results of the present study are expected to establish some concrete guidelines for current and future experimental endeavors. Along these lines, the results for the 162–180Hf isotopes are compared with existing experimental data where available, showing an overall good agreement.

Modeling Neutron Star Matter in the Age of Multimessenger Astrophysics

The interpretation of available and forthcoming data obtained from multimessenger astrophysical observations—potentially providing unprecedented access to neutron star properties—will require the development of novel, accurate theoretical models of dense matter. Of great importance, in this context, will be the capability for devising a description of thermal effects applicable to the study of quantities other than the equation of state, such as the transport coefficients and the neutrino mean free path in the nuclear medium. A formalism based on correlated basis states and the cluster expansion technique has been previously employed to derive a well-behaved effective interaction—suitable for use in standard perturbation theory—from a state-of-the-art nuclear Hamiltonian, including phenomenological two- and three-nucleon potentials. Here, we provide a comprehensive and self-contained account of the extension of this approach to the treatment of finite-temperature effects, and report the results of numerical calculations of a number of properties of nuclear matter with arbitrary neutron excess and temperature up to 50 MeV.

Magnetic-translational sum rule and approximate models of the molecular Berry curvature.

The Berry connection and curvature are key components of electronic structure calculations for atoms and molecules in magnetic fields. They ensure the correct translational behavior of the effective nuclear Hamiltonian and the correct center-of-mass motion during molecular dynamics in these environments. In this work, we demonstrate how these properties of the Berry connection and curvature arise from the translational symmetry of the electronic wave function and how they are fully captured by a finite basis set of London orbitals but not by standard Gaussian basis sets. This is illustrated by a series of Hartree-Fock calculations on small molecules in different basis sets. Based on the resulting physical interpretation of the Berry curvature as the shielding of the nuclei by the electrons, we introduce and test a series of approximations using the Mulliken fragmentation scheme of the electron density. These approximations will be particularly useful in ab initio molecular dynamics calculations in a magnetic field since they reduce the computational cost, while recovering the correct physics and up to 95% of the exact Berry curvature.

Statistical nuclear spectroscopy with [formula omitted]-normal and bivariate [formula omitted]-normal distributions and [formula omitted]-hermite polynomials

Statistical nuclear spectroscopy (also called spectral distribution method), introduced by J.B. French in late 60’s and developed in detail in the later years by his group and many other groups, is based on the Gaussian forms for the state (eigenvalue) and transition strength densities in shell model spaces with their extension to partial densities defined over shell model subspaces. The Gaussian forms have their basis in embedded random matrix ensembles with nuclear Hamiltonians consisting of a mean-field one-body part and a residual two-body part. However, following the recent random matrix results for the so called Sachdev–Ye–Kitaev model due to Verbaarschot et al, embedded random matrix ensembles with k-body interactions are re-examined and it is shown that the density of states, transition strength densities and strength functions (partial densities) in fact follow more closely the q-normal distribution (the parameter q is related to the fourth moment of these distributions with q=1 giving Gaussian and q=0 giving semi-circle form). The q-normal has the important property that it is bounded for 0≤q<1. The q-normal (also its bivariate and general multi-variate extensions) and the associated q-Hermite polynomials are studied for their properties by Bryc, Szablowski and others. Following these, in the present article, developed is statistical nuclear spectroscopy based on q-normal (univariate and bivariate) distributions and the associated q-Hermite polynomials. In particular, formulation is presented for nuclear level densities, shell model orbit occupancies, transition strengths (for electromagnetic and β and double β-decay type operators) and strength sums.