Hyperspherical Harmonic Method Research Articles

Baryonic thermal screening mass at NLO

We determine the resummed 1-loop correction to a baryonic thermal screening mass. The calculation is carried out in the framework of a dimensionally reduced effective theory, where quarks are heavy fields due to their non-zero Matsubara frequencies. The correction due to interactions is computed at O(g2) in the coupling constant. In order to solve a 3-body Schrödinger equation, we exploit a two-dimensional generalization of the hyperspherical harmonics method. At electroweak scale temperatures, the NLO correction represents a ∼ 4.6% increase of the free-theory value 3πT of the screening mass.

Trions in two-dimensional monolayers within the hyperspherical harmonics method: Application to transition metal dichalcogenides

Trions in two-dimensional monolayers within the hyperspherical harmonics method: Application to transition metal dichalcogenides

Study of the d(d, p) 3H and d(d, n) 3He processes at low energies

The processes d(d, p) 3H and d(d, n) 3 He at energies of interest for energy production and for big-bang nucleosynthesis are studied using the hyperspherical harmonic method. The interactions include modern two- and three-nucleon interactions, derived in chiral effective field theory. We report results for the astrophysical S-factor and the quintet suppression factor.

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.

Geometrical properties of ΩNN three-body states by realistic NN and first principles Lattice QCD ΩN potentials

The Faddeev equations in coordinate space are solved to study the ΩNN and ΩΩN three-body systems using the latest ΩNS25 and ΩΩ S01 interactions developed by the HAL QCD Collaboration. We recalculate the binding energy of the ΩNN system by examining three NN potentials, i.e., modern realistic AV18 potential, Yukawa-type Malfliet-Tjon (MT) interaction, and Gogny-Pires-Tourreil (GPT) soft and local potential. We take into account the contribution of the Coulomb potential. Our numerical calculations for Ωd(T=0) in maximum spin 5/2+ confirm ground state binding energy of 20.953, 19.368, and 20.439 MeV and a matter radius of 1.097, 1.373, and 1.309 fm using MT, GPT, and AV18 NN potentials, respectively. In the case of Ωd(0)5/2+ system, our numerical analysis shows that considering higher partial waves than s wave in NN interactions leads to an increase of about 0.2 MeV using GPT and about 0.1 MeV reduction with AV18 potentials. We study the convergence of three-body binding energies in a cluster model using the hyperspherical harmonics method and investigate the geometrical properties of Ωd(0)5/2+ ground states.

Nuclei with Up to $$\varvec{A=6}$$ Nucleons with Artificial Neural Network Wave Functions

The ground-breaking works of Weinberg have opened the way to calculations of atomic nuclei that are based on systematically improvable Hamiltonians. Solving the associated many-body Schr\"odinger equation involves non-trivial difficulties, due to the non-perturbative nature and strong spin-isospin dependence of nuclear interactions. Artificial neural networks have proven to be able to compactly represent the wave functions of nuclei with up to $A=4$ nucleons. In this work, we extend this approach to $^6$Li and $^6$He nuclei, using as input a leading-order pionless effective field theory Hamiltonian. We successfully benchmark their binding energies, point-nucleon densities, and radii with the highly accurate hyperspherical harmonics method.

N+H3, p+He3, p+H3, and n+He3 scattering with the hyperspherical harmonic method

The $n+^{3}\mathrm{H},$ $p+^{3}\mathrm{He},$ $p+^{3}\mathrm{H},$ and $n+^{3}\mathrm{He}$ elastic and charge exchange reactions at low energies are studied by means of the hyperspherical harmonic method. The considered nuclear Hamiltonians include modern two- and three-nucleon interactions, and in particular results are reported in case of chiral two-nucleon potentials, with and without the inclusion of chiral three-nucleon (3N) interactions. A detailed study of the convergence and numerical stability of the method is presented. We have found that the effect the 3N force is in general tiny except for $p+^{3}\mathrm{H}$ scattering below the opening of the $n+^{3}\mathrm{He}$ channel. In such a case, the effect of 3N forces is appreciable and a clear dependence on the cutoff used to regularize the high-momentum tail of the interactions is observed. Such a dependence is related to the presence of the poorly known sharp ${0}^{+}$ resonance, considered to be the first excited state of $^{4}\mathrm{He}$.

Benchmark calculations of electromagnetic sum rules with a symmetry-adapted basis and hyperspherical harmonics

We demonstrate the ability to calculate electromagnetic sum rules with the \textit{ab initio} symmetry-adapted no-core shell model. By implementing the Lanczos algorithm, we compute non-energy weighted, energy weighted, and inverse energy weighted sum rules for electric monopole, dipole, and quadrupole transitions in $^4$He using realistic interactions. We benchmark the results with the hyperspherical harmonics method and show agreement within $2\sigma$, where the uncertainties are estimated from the use of the many-body technique. We investigate the dependence of the results on three different interactions, including chiral potentials, and we report on the $^4$He electric dipole polarizability calculated in the SA-NCSM that reproduces the experimental data and earlier theoretical outcomes. We also detail a novel use of the Lawson procedure to remove the spurious center-of-mass contribution to the sum rules that arises from using laboratory-frame coordinates. We further show that this same technique can be applied in the Lorentz integral transform method, with a view toward studies of electromagnetic reactions for light through medium-mass nuclei.

The Hyperspherical Harmonics Method: A Tool for Testing and Improving Nuclear Interaction Models

The Hyperspherical Harmonics (HH) method is one of the most accurate techniques to solve the quantum mechanical problem for nuclear systems with $A\le 4$. In particular, by applying the Rayleigh-Ritz or Kohn variational principle, both bound and scattering states can be addressed, using either local or non-local interactions. Thanks to this versatility, the method can be used to test the two- and three-nucleon components of the nuclear interaction. In the present review we introduce the formalism of the HH method, both for bound and scattering states. In particular, we describe the implementation of the method to study the $A=3$ and $4$ scattering problem. Second, we present a selected choice of results of the last decade, most representative of the latest achievements. Finally, we conclude with a discussion of what we believe will be the most significant developments within the HH method for the next five-to-ten years.

Non-symmetrized Hyperspherical Harmonics Method for Non-equal Mass Three-Body Systems

The non-symmetrized hyperspherical harmonics method for a three-body system, composed by two particles having equal masses, but different from the mass of the third particle, is reviewed and applied to the $^3$H, $^3$He nuclei and $^3_{\Lambda}$H hyper-nucleus, seen respectively as $nnp$, $ppn$ and $NN\Lambda$ three-body systems. The convergence of the method is first tested in order to estimate its accuracy. Then, the difference of binding energy between $^3$H and $^3$He due to the difference of the proton and the neutron masses is studied using several central spin-independent and spin-dependent potentials. Finally, the $^3_{\Lambda}$H hypernucleus binding energy is calculated using different $NN$ and $\Lambda N$ potential models. The results have been compared with those present in the literature, finding a very nice agreement.

Trions in bulk and monolayer materials: Faddeev equations and hyperspherical harmonics

The negatively T− and positively T+ charged trions in bulk and monolayer semiconductors are studied in the effective mass approximation within the framework of a potential model. The binding energies of trions in various semiconductors are calculated by employing the Faddeev equation with the Coulomb potential in 3D configuration space. Results of calculations of the binding energies for T− are consistent with previous computational studies, while the T+ is unbound for all considered cases. The binding energies of trions in monolayer semiconductors are calculated using the method of hyperspherical harmonics by employing the Keldysh potential. It is shown that 2D T− and T+ trions are bound and the binding energy of the positive trion is always greater than for the negative trion due to the heavier effective mass of holes. Our calculations demonstrate that screening effects play an important role in the formation of bound states of trions in 2D semiconductors.

Benchmark Results for Few-Body Hypernuclei

The Non-Symmetrized Hyperspherical Harmonics method (NSHH) is introduced in the hypernuclear sector and benchmarked with three different ab-initio methods, namely the Auxiliary Field Diffusion Monte Carlo method, the Faddeev-Yakubovsky approach and the Gaussian Expansion Method. Binding energies and hyperon separation energies of three- to five-body hypernuclei are calculated by employing the two-body $\Lambda$N component of the phenomenological Bodmer-Usmani potential, and a hyperon-nucleon interaction simulating the scattering phase shifts given by NSC97f. The range of applicability of the NSHH method is briefly discussed.

Trion and Biexciton in Monolayer Transition Metal Dichalcogenides

We study the trion and biexciton in transition metal dichalcogenides monolayers within the framework of a nonrelativistic potential model using the method of hyperspherical harmonics (HH). We solve the three- and four-body Schr\"odinger equations with the Keldysh potential by expanding the wave functions of a trion and biexciton in terms of the antisymmetrized HH. Results of the calculations for the ground state energies are in good agreement with similar calculations for the Keldysh potential and in reasonable agreement with experimental measurements of trion and biexciton binding energies.

Erratum: Three-cluster dynamics within anab initioframework [Phys. Rev. C88, 034320 (2013)

In this study, we introduce a fully antisymmetrized treatment of three-cluster dynamics within the ab initio framework of the no-core shell model/resonating-group method. Energy-independent nonlocal interactions among the three nuclear fragments are obtained from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrodinger equation is solved with bound-state boundary conditions by means of the hyperspherical-harmonic method on a Lagrange mesh. We discuss the formalism in detail and give algebraic expressions for systems of two single nucleons plus a nucleus. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we apply the method to a 4He+n+n description of 6He and compare the results to experiment and to a six-body diagonalization of the Hamiltonian performed within the harmonic-oscillator expansions of the no-core shell model. Differences between the two calculations provide a measure of core (4He) polarization effects.

Three-body calculations for the K−pp system within potential models

We present three-body nonrelativistic calculations within the framework of a potential model for the kaonic cluster K−pp using two methods: the method of hyperspherical harmonics in the momentum representation and the method of Faddeev equations in configuration space. To perform numerical calculations, different NN and antikaon–nucleon interactions are applied. The results of the calculations for the ground-state energy for the K−pp system obtained by both methods are in reasonable agreement. Although the ground-state energy is not sensitive to the pp interaction, it shows very strong dependence on the K−p potential. We show that the dominant clustering of the system in the configuration Λ (1405) + p allows us to calculate the binding energy to good accuracy within a simple cluster approach for the differential Faddeev equations. The theoretical discrepancies in the binding energy and width for the K−pp system related to the different pp and K−p interactions are addressed.

Study of theKKK̅system in hyperspherical formalism

The three-body kaonic system KKK is studied in the framework of a single-channel potential nonrelativistic model using the method of hyperspherical harmonics in momentum representation. Calculations are performed with two sets of KK and KK potentials. A quasibound state for the KKK system with spin-parity 0− and isospin 1/2 is found below the three-kaon threshold.

K̅ppandK̅K̅pClusters

The three-body kaonic K pp and K K p clusters are studied using the method of hyperspherical harmonics (HH) in momentum representation and differential Faddeev equations (DFE). We use different NN and K N interactions. Results obtained by the methods of HH and DFE are in reasonable agreement. The binding energy and the width show very strong dependence on the K N potential. We have two different classes of results: the results based on phenomenological strong K N potential, and the results obtained with much weaker chiral SU(3)-based K N potential.

Understanding the proton radius puzzle: Nuclear structure effects in light muonic atoms

We present calculations of nuclear structure effects to the Lamb shift in light muonic atoms. We adopt a modern ab-initio approach by combining state-of-the-art nuclear potentials with the hyperspherical harmonics method. Our calculations are instrumental to the determination of nuclear charge radii in the Lamb shift measurements, which will shed light on the proton radius puzzle.

Non-Symmetrized Hyperspherical Harmonics Method Applied to Light Hypernuclei

The present work is conducted in the field of few-body methods and it concerns the extension of the Non-Symmetrized Hyperspherical Harmonics method in order to treat quantum systems with different species of particles and additional degrees of freedom, like particle mixing. The aim is to introduce it as a new tool in the ab-initio study of light hypernuclei, and, more in general, of few-body quantum systems composed by a variety of different objects. To this end precise benchmark results for light hypernuclei with A=3-5 are provided and the perspectives of applications to systems with A>5 and the employment of the most recent hypernuclear interactions are discussed.

He 4 4He + n + n continuum within an ab initio framework.

The low-lying continuum spectrum of the (6)He nucleus is investigated for the first time within an ab initio framework that encompasses the (4)He + n + n three-cluster dynamics characterizing its lowest decay channel. This is achieved through an extension of the no-core shell model combined with the resonating-group method, in which energy-independent nonlocal interactions among three nuclear fragments can be calculated microscopically, starting from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with three-body scattering boundary conditions by means of the hyperspherical-harmonics method on a Lagrange mesh. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we find the known J(π) = 2(+) resonance as well as a result consistent with a new low-lying second 2(+) resonance recently observed at GANIL at 2.6 MeV above the (6)He ground state. We also find resonances in the 2(-), 1(+), and 0(-) channels, while no low-lying resonances are present in the 0(+) and 1(-) channels.