Deuteron Binding Energy Research Articles

Radiative Corrections and the Renormalization Group for the Two-Nucleon Interaction in Effective Field Theory

We use a combination of effective field theory and the renormalization group to determine the impact of radiative corrections on the nucleon–nucleon potential and the binding energy of the deuteron. In order to do so, we present a modified version of pionless effective field theory inspired by earlier work in nonrelativistic quantum electrodynamics. The renormalization group improvement of the deuteron binding energy leads to a shift on the order of a few percent and is consistent with the experimental value. This work serves as a starting point for a dedicated study of radiative corrections in few-body systems relevant for precision tests of the Standard Model in an effective field theory framework.

The weakly bound states in Gaussian wells: From the binding energy of deuteron to the electronic structure of quantum dots

AbstractGaussian potentials serve as a valuable tool for the comprehensive modeling of short‐range interactions, spanning applications from Nuclear Physics to the artificial confinement of electrons within quantum dots. This study focuses on examining the lowest states within Gaussian wells, with particular emphasis on the weakly bound regime. The analysis delves into the asymptotic behavior of the exact wave function at both small and large distances, motivating the development of a few parametric Ansatz which is locally accurate and yields to a fast convergent basis set. To validate its efficacy, we assess its convergence rate using a toy model of Nuclear Physics, specifically for Deuteron. Furthermore, we employ the expansion of the energy close to the threshold to derive an analytical formula for the binding energy of the Deuteron whose accuracy improves as the effective parameter approaches the critical. To conclude our study, we test the ability of our Ansatz to describe relativistic corrections into a quantum dot and its performance as an orbital in the exploration of the electronic structure of a two‐electron quantum dot.

The Movement of Efimov States in 2n Halo Nucleus: probing the roles of mass asymmetry and short range of interaction

This brief communication presents the results of our work to study the movement of Efimov states in 2-neutron halo nuclei. We discuss the emergence and evolution of Efimov states in to resonances beyond the two-body (n-Core) breakup threshold and also the movement of the Efimov state in a 2-neutron halo nucleus to the region of the so called, Thomas Collapse. We especially, probe the roles of mass asymmetry of the three-body system (n-n-core) and the short range of the n-core interaction in the movement of the Efimov states. The analysis has been carried out within the framework of a three-body model, assuming two-body, non-local, separable potentials for the binary sub-systems, namely, the n-n and n-core systems. The primary motivation has been to scan the parameter space of the range parameter and determine the value(s) for which the system can support the Efimov states. The analysis shows that the value of the range parameter $\beta$ = 5.2$\alpha$ ( $\alpha$ being the energy parameter given in terms of the deuteron binding energy ) produces the realistic three-body binding energy for $^{20}$C and also generates the excited Efimov states. However, as the value of $\beta$ is increased corresponding to decrease in the range of the two-body (n-core) interaction the ground and excited state binding energies increase drastically. In other words, as the range of the two-body interaction tends to zero the system enters the Thomas Collapse region away from the Efimov region.

On u-d Quark Coulomb Origin of Nuclear Force

The origin of nuclear force is assigned to Coulomb interactions between quarks, u and d, in neighboring nucleons, replacing the current unspecified “residual” strong interaction assignment. The deuteron binding energy is correctly estimated using quasi-classical models for nucleons based upon SSI, the scalar strong interaction hadron theory. The next lightest nuclei are analogously treated. The Coulomb binding energies depend upon the small, in principle observable, internucleon distances between such u and d quarks whose positions in their respective host nucleons however depend upon intranucleon strong u - d potential that span over larger “hidden” distances.

QCSH: A full quantum computer nuclear shell-model package

The nuclear system is a promising area for demonstrating practical quantum advantage. A comprehensive computation of a nuclear system in a classical computer is beyond the capacity of current classical computers. With the rapid development of hardware, the prospect of using quantum computers in nuclear physics is close at hand. In this paper, we report a full quantum package, QCSH, for solving a nuclear shell model in a quantum computer. QCSH uses the linear combination of the unitary formalism of quantum computing and performs all calculations in a quantum computer. The complexities of qubit resource and the number of basic gates of QCSH are both polynomials to the number of nucleons in nuclei. For example, QCSH is used to calculate the binding energies of 12 light nuclei (i.e., 2H, 3H, 3He, 4He, 6Li, 7Li, 12C, 14N, 16O, 17O, 23Na, and 40Ca). Moreover, we experimentally demonstrate the calculation of deuteron binding energy using a superconducting quantum processor. The result indicates that QCSH can provide meaningful results already in near-term quantum devices.

Electron and neutrino scattering off the deuteron in a relativistic framework

We build a relativistic model to perform calculations of exclusive, semi-exclusive and inclusive unpolarized cross sections and various polarization observables in electron and neutrino scattering experiments with deuteron targets. The strong interaction dynamics is defined by an explicit dynamical unitary representation of the Poincar\'e group, where representations of space translations and rotations in the interacting and non-interacting representations are the same. The Argonne V18 potential is used to construct a relativistic nucleon-nucleon interaction reproducing the experimental deuteron binding energy and nucleon-nucleon scattering observables. Our formalism does not include the pion production channel and neglects two-body contributions in the electromagnetic as well as in the weak nuclear current operator. We show that it is applicable to processes at kinematics, where the internal two-nucleon energy remains below the pion production threshold but the magnitude of the three-momentum transfer extends at least to several GeV.

Relativistic nucleon\u2013nucleon potentials in a spin-dependent three-dimensional approach

The matrix elements of relativistic nucleon–nucleon (NN) potentials are calculated directly from the nonrelativistic potentials as a function of relative NN momentum vectors, without a partial wave decomposition. To this aim, the quadratic operator relation between the relativistic and nonrelativistic NN potentials is formulated in momentum-helicity basis states. It leads to a single integral equation for the two-nucleon (2N) spin-singlet state, and four coupled integral equations for two-nucleon spin-triplet states, which are solved by an iterative method. Our numerical analysis indicates that the relativistic NN potential obtained using CD-Bonn potential reproduces the deuteron binding energy and neutron-proton elastic scattering differential and total cross-sections with high accuracy.

Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei

Classes of two-nucleon ($2N$) contact interactions are developed in configuration space at leading order (LO), next-to-leading order (NLO), and next-to-next-to-next-to-leading order (N3LO) by fitting the experimental singlet $np$ scattering length and deuteron binding energy at LO, and $np$ and $pp$ scattering data in the laboratory-energy range 0--15 MeV at NLO and 0--25 MeV at N3LO. These interactions are regularized by including two Gaussian cutoffs, one for $T\,$=$\,0$ and the other for $T\,$=$\,1$ channels. The cutoffs are taken to vary in the ranges $R_0\,$=$(1.5$--2.3) fm and $R_1\,$=$(1.5$--3.0) fm. The 780 (1,100) data points up to 15 (25) MeV energy, primarily differential cross sections, are fitted by the NLO (N3LO) models with a $\chi^2$/datum about 1.7 or less (well below 1.5), when harder cutoff values are adopted. As a first application, we report results for the binding energies of nuclei with mass numbers $A\,$=$\,3$--6 and 16 obtained with selected LO and NLO $2N$ models both by themselves as well as in combination with a LO three-nucleon ($3N$) contact interaction. The latter is characterized by a single low-energy constant that is fixed to reproduce the experimental $^3$H binding energy. The inclusion of the $3N$ interaction largely removes the sensitivity to cutoff variations in the few-nucleon systems and leads to predictions for the $^3$He and $^4$He binding energies that cluster around 7.8 MeV and 30 MeV, respectively. However, in $^{16}$O this cutoff sensitivity remains rather strong. Finally, predictions at LO only are also reported for medium-mass nuclei with $A\,$=$\,40$, 48, and 90.

Novel regularization scheme for nucleon-nucleon lattice simulations with effective field theory

We propose a new regularization scheme to study the bound state of two-nucleon systems in Lattice Effective Field Theory. Inspired by continuum EFT calculation, we study an exponential regulator acting on the leading-order (LO) and next-to-leading order (NLO) interactions, consisting of local contact terms. By fitting the low-energy coefficients (LECs) to deuteron binding energy and the asymptotic normalization coefficient (ANC) on a lattice simulation, we extract the effective range expansion (ERE) parameters in the $^3S_1$ channel to order $p^2$. We explore the impact of different powers of the regulator on the extracted ERE parameters for the lattice spacing $a=1.97$ fm. Moreover, we investigate how the implementation of the regularization scheme improves the predicted ERE parameters on the lattice spacing in the range of $1.4 \le a \le 2.6$ fm. Our numerical analysis indicates that for lattice spacing greater than $2$ fm, the predicted observables are very close to the experimental data.

Practical quantum computation of chemical and nuclear energy levels using quantum imaginary time evolution and Lanczos algorithms

Various methods have been developed for the quantum computation of the ground and excited states of physical and chemical systems, but many of them require either large numbers of ancilla qubits or high-dimensional optimization in the presence of noise. The quantum imaginary-time evolution (QITE) and quantum Lanczos (QLanczos) methods proposed in Motta et al. (2020) eschew the aforementioned issues. In this study, we demonstrate the practical application of these algorithms to challenging quantum computations of relevance for chemistry and nuclear physics, using the deuteron-binding energy and molecular hydrogen binding and excited state energies as examples. With the correct choice of initial and final states, we show that the number of timesteps in QITE and QLanczos can be reduced significantly, which commensurately simplifies the required quantum circuit and improves compatibility with NISQ devices. We have performed these calculations on cloud-accessible IBM Q quantum computers. With the application of readout-error mitigation and Richardson error extrapolation, we have obtained ground and excited state energies that agree well with exact results obtained from diagonalization.

The charge-dependent Bonn potentials with pseudovector pion-nucleon coupling * * Supported by National Natural Science Foundation of China (11775119, 11405116, 11675083)

In order to use high-precision realistic nucleon-nucleon (NN) potentials in relativistic many-body problems, new versions of the charge-dependent Bonn (CD-Bonn) NN potential are constructed with pseudovector pion-nucleon coupling, instead of pseudoscalar coupling used in the original CD-Bonn potential as given by Machleidt . To describe precisely the charge dependence in the NN scattering data, two effective scalar mesons are introduced, whose coupling constants with nucleons are independently determined for each partial wave and for the total angular momentum . The coupling constants between the vector and pseudovector mesons and a nucleon are identical in all channels. Three revised CD-Bonn potentials with the pseudovector pion-nucleon coupling (pvCD-Bonn) are generated by fitting the Nijmegen PWA phase shift data and the deuteron binding energy with different pion-nucleon coupling strengths. The potentials reproduce the phase shifts in the spin-single channels and the low-energyNNscattering parameters very well, but result in significantly different mixing parameters in the spin-triplet channels. The D-state probabilities for the deuteron range from 4.22% to 6.05%, demonstrating that the potentials contain different components of the tensor force, which is useful when considering the role of the tensor force in nuclear few- and many-body systems.

Extended-soft-core baryon-baryon model ESC16. I. Nucleon-nucleon scattering

Background: The Nijmegen extended-soft-core (ESC) model ESC16, as well as its predecessors ESC04--ESC08, describe the nucleon-nucleon ($NN$), hyperon-nucleon ($YN$), and hyperon-hyperon/nucleon ($YY/\mathrm{\ensuremath{\Xi}}\phantom{\rule{4pt}{0ex}}N$) interactions in a unified way using broken SU(3) symmetry. SU(3) symmetry serves to connect the $NN$ with the $YN$ and the $YY$ channels. In the spirit of the Yukawa approach to the nuclear force problem, the interactions are studied from the meson-exchange picture viewpoint, using generalized soft-core Yukawa functions. The meson exchanges are supplemented with diffractive contributions due to multiple-gluon exchanges. The extended-soft-core (ESC) meson-exchange interactions consist of local and nonlocal potentials due to (i) one-boson exchanges (OBE), which are the members of nonets of pseudoscalar, vector, scalar, and axial-vector mesons, (ii) diffractive exchanges, (iii) two-pseudoscalar exchange (PS-PS), and (iv) meson-pair exchange (MPE). The OBE and MPE vertices are regulated by Gaussian form factors producing potentials with a soft behavior near the origin. The assignment of the cutoff masses for the BBM vertices is dependent on the SU(3) classification of the exchanged mesons for OBE and a similar scheme for MPE.Purpose: The evolution of the ESC approach to the ESC16 model for the baryon-baryon (BB) interactions of the SU(3) flavor octet of baryons (N, $\mathrm{\ensuremath{\Lambda}}$, $\mathrm{\ensuremath{\Sigma}}$, and $\mathrm{\ensuremath{\Xi}}$) is described and presented. In this first of a series of papers, the $NN$ model and results are reported in detail.Methods: Important nonstandard ingredients in the OBE sector in the ESC models are (i) the axial-vector meson potentials, and (ii) a zero in the scalar- and axial-vector meson form factors. Furthermore, the strange scalar $\ensuremath{\kappa}$ meson is treated within the scheme of the Gell-Mann-Okubo mass relations, and like the $\ensuremath{\rho}$ and $\ensuremath{\epsilon}$ treated as a broad meson. The multiple-gluon exchanges are elaborated further by adding contributions due to odd number of gluon exchanges. A novel contribution is the incorporation of structural effects due to the quark core of the baryons. In establishing the parameters of the model a simultaneous fit to $NN$ and $YN$ channels has been performed. The meson-baryon coupling constants are calculated via SU(3) using the coupling constants of the $NN\ensuremath{\bigoplus}YN$ analysis as input. In ESC16 the couplings are kept completely SU(3) symmetric. About 25 physical coupling parameters and 8 cutoff and diffractive masses were searched.Results: In the fit to $NN$ and $YN$ many parameters are essentially fixed by the $NN$ data. A few, but severely constrained parameters, e.g., $F/(F+D)$ ratios, are left for determination of the $YN$ interactions and the $YY$ experimental indications. The simultaneous fit of the ESC models to the $NN$- and $YN$-scattering data with a single set of parameters has achieved excellent results for the $NN$ and $YN$ data, and for the $YY$ data in accordance with the experimental indications for $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ and $\mathrm{\ensuremath{\Xi}}N$. In the case of ESC16, the version discussed here, the achievements are: (i) For the selected 4313 $pp$ and $np$ scattering data with energies $0\ensuremath{\le}{T}_{\text{lab}}\ensuremath{\le}350\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$, the model reaches a fit having ${\ensuremath{\chi}}^{2}/{N}_{\text{data}}=1.10$. (ii) The deuteron binding energy and all the $NN$ scattering lengths are fitted very nicely. (iii) The $YN$ data are described very well with ${\ensuremath{\chi}}^{2}/{N}_{\text{data}}=1.04$, giving at the same time a description of the $\mathrm{\ensuremath{\Xi}}N$ cross sections in agreement with the experimental indications.Conclusions: The ESC approach leads to an excellent description of the $NN$ and $YN$ data, and for the scarce $YY$ data. The added innovations as well as the treatment of mass broken SU(3) make it possible to keep the meson coupling parameters and the $F/(F+D)$ ratios of the model qualitatively in accordance with the predictions of the $^{3}P_{0}$-dominated quark-antiquark pair creation (QPC) model. The information about estimates of (i) the $\mathrm{\ensuremath{\Lambda}}$- and $\mathrm{\ensuremath{\Sigma}}$-nuclear well-depth, and (ii) the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$ hypernuclei played an important role in the form of using constraints. In particular, the experimental indications for the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}$-attraction and the $\mathrm{\ensuremath{\Sigma}}$-nuclear well-depth were directive.

The Expansion in Hadron Effective Field Theory**Supported by the National Natural Science Foundation of China under Grant No. 11305137

We study the Nc scalings of pion-nucleon and nucleon-nucleon scatterings in hadron effective field theory. By assuming Wittenʼs counting rules are applied to matrix elements or scattering amplitudes, which use the relativistic normalization for the nucleons, we find that the nucleon axial coupling is of order , and a consistent large Nc counting can be established for the pion-nucleon and nucleon-nucleon scatterings. We also justify the nonperturbative treatment of the low energy nucleon-nucleon interaction with the large Nc analysis and find that the deuteron binding energy is of order .

The Rank-One Separable Interaction Kernel for Nucleons with Scalar Propagator

In the paper the covariant kernel of the nucleon-nucleon interaction of particles with scalar propagators is analyzed. The Bethe-Salpeter equation for the T matrix is considered in the rank- one separable kernel. The parameters of the kernel for the specific partial-wave channels explicitly connect with the observables { low energy scattering parameters and phase shifts, deuteron binding energy. Covariant separable kernels forthe partial-wave channels with total angular momentum J = 0 (1S0, 3P0) and J = 1 (3S1 -3D1, 1P1, 3P1) are constructed.

Probing Long-Range Neutrino-Mediated Forces with Atomic and Nuclear Spectroscopy.

The exchange of a pair of low-mass neutrinos between electrons, protons, and neutrons produces a "long-range" 1/r^{5} potential, which can be sought for in phenomena originating on the atomic and subatomic length scales. We calculate the effects of neutrino-pair exchange on transition and binding energies in atoms and nuclei. In the case of atomic s-wave states, there is a large enhancement of the induced energy shifts due to the lack of a centrifugal barrier and the highly singular nature of the neutrino-mediated potential. We derive limits on neutrino-mediated forces from measurements of the deuteron binding energy and transition energies in positronium, muonium, hydrogen, and deuterium, as well as isotope-shift measurements in calcium ions. Our limits improve on existing constraints on neutrino-mediated forces from experiments that search for new macroscopic forces by 18 orders of magnitude. Future spectroscopy experiments have the potential to probe long-range forces mediated by the exchange of pairs of standard-model neutrinos and other weakly charged particles.

Cloud Quantum Computing of an Atomic Nucleus.

We report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.

Estimation of Minimal Length Using Binding Energy of Deuteron

We find the shift of ground state energy of deuteron caused by generalized uncertainty principle (GUP) using Yukawa potential as the binding force between the proton and neutron. This leads to an upperbound on minimal length of about 10 -18 m which is close to the values frequently found in literature.

On the Mechanism of Nucleon-Nucleon Attraction by Pion Exchange

A formula is derived for the central nucleon-nucleon potential, based on an analysis of the physical origin of the nucleon-nucleon attraction by pion exchange. The decrease of the dynamical mass of the interaction field, exchanged pion in this case, is the principal mechanism responsible for the nuclear attraction in a similar way that the decrease of the kinetic energy of the exchange electron in the diatomic molecule is directly responsible for the covalent molecular attraction. The minimum value of this central nucleon-nucleon potential and the position of the minimum are similar with the values reported in literature for a potential calculated by lattice QCD, which shares the features of the phenomenological nucleon-nucleon potentials. The Schrodinger equation with this central nucleon-nucleon potential was solved numerically for different values of the pion mass. The binding energy increases with the decrease of the pion mass. For masses higher than the real pion mass the nucleon-nucleon system is unbound. We discuss on the two pion exchange and hard core repulsion. The minimum value of the potential for two pion exchange is comparable with the minimum value of the CD Bonn potential. For a hard core radius of 0.5 fm the binding energy is equal to the deuteron binding energy.

Local chiral potentials with Δ -intermediate states and the structure of light nuclei

We present fully local versions of the minimally non-local nucleon-nucleon potentials constructed in a previous paper [M.\ Piarulli {\it et al.}, Phys.\ Rev.\ C {\bf 91}, 024003 (2015)], and use them in hypersperical-harmonics and quantum Monte Carlo calculations of ground and excited states of $^3$H, $^3$He, $^4$He, $^6$He, and $^6$Li nuclei. The long-range part of these local potentials includes one- and two-pion exchange contributions without and with $\Delta$-isobars in the intermediate states up to order $Q^3$ ($Q$ denotes generically the low momentum scale) in the chiral expansion, while the short-range part consists of contact interactions up to order $Q^4$. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database in two different ranges of laboratory energies, either 0--125 MeV or 0--200 MeV, and to the deuteron binding energy and $nn$ singlet scattering length. Fits to these data are performed for three models characterized by long- and short-range cutoffs, $R_{\rm L}$ and $R_{\rm S}$ respectively, ranging from $(R_{\rm L},R_{\rm S})=(1.2,0.8)$ fm down to $(0.8,0.6)$ fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.

Two-nucleon scattering in a modified Weinberg approach with a symmetry-preserving regularization

We consider the nucleon-nucleon scattering problem by applying time-ordered perturbation theory to the Lorentz invariant formulation of baryon chiral perturbation theory. Using a symmetry preserving higher derivative form of the effective Lagrangian, we exploit the freedom of the choice of the renormalization condition and obtain an integral equation for the scattering amplitude with an improved ultraviolet behavior. The resulting formulation is used to quantify finite regulator artifacts in two-nucleon phase shifts as well as in the chiral extrapolations of the S-wave scattering lengths and the deuteron binding energy. This approach can be straightforwardly extended to analyze few-nucleon systems and processes involving external electroweak sources.