Nucleon System Research Articles

Experimental Studies of the Three Nucleon System Dynamics in the Proton Induced Deuteron Breakup at 108 MeV

Experimental Studies of the Three Nucleon System Dynamics in the Proton Induced Deuteron Breakup at 108 MeV

The validity of the [formula omitted] lattice calculations for the finite asymmetric [formula omitted] matter using the central potentials

The lattice version of the lowest order constrained variational (LOCV) approach at the three-body cluster approximation is applied to the finite asymmetric nucleonic matter (ASM) in the periodic boxes (PBLOCV). The PBLOCVASM three- to two-body cluster energy ratios (R), using the central Bethe homework and (AV′8)c potentials, are obtained for small cubic PBs. The smallness of the ratios R could be considered evidence for the validity of the lowest order approximation. It is demonstrated that the truncation of the energy cluster expansion at the lowest order is confirmed for the Bethe homework interaction case. Also, the finite size effects and their impact on the symmetry energy coefficient are investigated. It is observed that using simple potentials and small finite nucleonic systems, one cannot reproduce the experimental prediction of the symmetry energy coefficient, even by including the three-body cluster energy contribution.

Quasibound state in the K¯NNN system

The attractive nature of the antikaon-nucleon interaction suggests that few-body systems of antikaons and nucleons can exist. The author presents a new study of the exotic $\overline{K}\phantom{\rule{0}{0ex}}N\phantom{\rule{0}{0ex}}N\phantom{\rule{0}{0ex}}N$ system. Four-body Faddeev-type equations are used to evaluate the binding energy and the width of the quasi-bound state in the system. The dependence of the results on the two-body antikaon-nucleon and nucleon-nucleon interactions is quantified.

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory

We present a study of the two-photon-exchange (2upgamma -exchange) corrections to the S-levels in muonic (mu D) and ordinary (D) deuterium within the pionless effective field theory (EFT). Our calculation proceeds up to next-to-next-to-next-to-leading order (N3LO) in the EFT expansion. The only unknown low-energy constant entering the calculation at this order corresponds to the coupling of a longitudinal photon to the nucleon–nucleon system. To minimise its correlation with the deuteron charge radius, it is extracted using the information about the hydrogen–deuterium isotope shift. We find the elastic 2upgamma -exchange contribution in mu D larger by several standard deviations than obtained in other recent calculations. This discrepancy ameliorates the mismatch between theory and experiment on the size of 2upgamma -exchange effects, and is attributed to the properties of the deuteron elastic charge form factor parametrisation used to evaluate the elastic contribution. We identify a correlation between the deuteron charge and Friar radii, which can help one to judge how well a form factor parametrisation describes the low-virtuality properties of the deuteron. We also evaluate the higher-order 2upgamma -exchange contributions in mu D, generated by the single-nucleon structure and expected to be the most important terms beyond N3LO. The uncertainty of the theoretical result is dominated by the truncation of the EFT series and is quantified using a Bayesian approach. The resulting extractions of the deuteron charge radius from the mu D Lamb shift, the 2S{-}1S transition in D, and the 2S{-}1S hydrogen–deuterium isotope shift, with the respective 2upgamma -exchange effects evaluated in a unified EFT approach, are in perfect agreement.

Closed form wave profiles of the coupled-Higgs equation via the ϕ6-model expansion method

The coupled-Higgs equation, which depicts a system of preserved scalar nucleons cooperating with unbiased scalar mesons, is investigated using the [Formula: see text]-model expansion approach in this paper. We want to look at the various particles that are created when scalar nucleons collide with unbiased scalar mesons. The modulus of the elliptic function [Formula: see text] and [Formula: see text] is used to obtain the trigonometric and hyperbolic functions. Under the stated limited constraints, all found solutions are used to validate the partial differential equation. We displayed 3D surfaces and 2D visuals of selected solutions produced with the assistance of a computer program to shed more light on the dynamic behavior of the acquired solutions.

Spectrum of light nuclei in a finite volume

Lattice quantum chromodynamics calculations of multi-baryon systems with physical quark masses would start a new age of ab initio predictions in nuclear physics. Performed on a finite grid, such calculations demand extrapolation of their finite volume numerical results to free-space physical quantities. Such extraction of the physical information can be carried out fitting effective field theories (EFTs) directly to the finite-volume results or utilizing the L\"uscher free-space formula or its generalizations for extrapolating the lattice data to infinite volume. To understand better the effect of periodic boundary conditions on the binding energy of few nucleon systems we explore here light nuclei with physical masses in a finite box and in free space. The stochastic variational method is used to solve the few-body systems. Substantial optimizations of the method are introduced to enable efficient calculations in a periodic box. With the optimized code, we perform accurate calculations of light nuclei $A \le 4$ within leading order pionless EFT. Using L\"uscher formula for the two-body system, and its generalization for 3- and 4-body systems, we examine the box effect and explore possible limitations of these formulas for the considered nuclear systems.

Charged lepton flavor violation associated with heavy quark production in deep inelastic lepton-nucleon scattering via scalar exchange

We study charged lepton flavor violation (CLFV) associated with heavy quark pair production in lepton-nucleon deep-inelastic scattering ℓiN → ℓjq overline{q} X. Here ℓi and ℓj denote the initial and final leptons; N and X are respectively the initial nucleon and arbitrary final hadronic system. We employ a model Lagrangian in which a scalar and pseudoscalar mediator generates the CLFV. We derive heavy quark structure functions for scalar and pseudoscalar currents and compute momentum distributions of the final lepton for the process. Our focus is on the heavy quark mass effects in the final lepton momentum distribution. We clarify the necessity of inclusion of the heavy quark mass to obtain reliable theory predictions for the CLFV signal searches in the deep-inelastic scattering.

Study of Matter Density Distributions, Elastic Electron Scattering Form factors and Root Mean Square Radii of 9C, 12N, 23Al, 11Be and 15C Exotic Nuclei

The ground state densities of neutron-rich (11Be,15C) and proton-rich (9C,12N,23Al) exotic nuclei are investigated using a two-body nucleon density distribution (2BNDD) with two frequency shells model (TFSM). The structure of the valence one-neutron of 11Be is in pure (1p1/2) and of 15C in pure (1d5/2) configuration, while the structure of valence one-proton configuration is in 9C,12N are to be in a pure (1p1/2) and 23Al in a pure (2s1/2) . For our studied nuclei, an efficient (2BNDD) operator for point nucleon system folded with two-body correlation operator's functions is used to investigate nuclear matter density distributions, elastic electron scattering form factors, and root-mean square (rms) radii. The effect of the strong tensor force (TC) in nucleon-nucleon forces is taken into account in the correlation. The wave functions of a single particle harmonic oscillator are used with two different oscillator size parameters, βc and βv, the former for core (inner) orbits and the latter for valence (halo) orbits. The measured matter density distributions of these nuclei clearly show the long tail results. The plane wave born approximation (PWBA) is used to investigate the elastic electron scattering form factors for these exotic nuclei.

Quantum statistics effects near the critical point in systems with different interparticle interactions

Equation of state with quantum statistics corrections is derived for systems of the Fermi and Bose particles by using their van der Waals (vdW) and effective density-dependent Skyrme mean-field interactions. The first few orders of these corrections over a small quantum-statistics parameter, $\ensuremath{\varepsilon}\ensuremath{\approx}{\ensuremath{\hbar}}^{3}n{(mT)}^{\ensuremath{-}3/2}{g}^{\ensuremath{-}1}$, where $n$ and $T$ are the particle number density and temperature, $m$ and $g$ are the mass and degeneracy factor of particles, are analytically obtained. For an interacting system of nucleon and $\ensuremath{\alpha}$ particles, a small impurity of $\ensuremath{\alpha}$ particles to a nucleon system at leading first order in both $\ensuremath{\alpha}$- particle and nucleon small parameters $\ensuremath{\varepsilon}$ does not change the basic results for the symmetric nuclear matter in the quantum vdW consideration much. Our approximate analytical results for the quantum vdW and Skyrme mean-field approaches are in a good agreement with accurate numerical calculations.

Level density within a micro-macroscopic approach

Statistical level density ρ(E,A) is derived for nucleonic system with a given energy E, particle number A and other integrals of motion in the micro-macroscopic approximation beyond the standard saddle-point method of the Fermi gas model. This level density reaches the two limits; the well-known Fermi gas grand-canonical ensemble limit for a large entropy S related to large excitation energies, and the finite micro-canonical limit for a small combinatorical entropy S at low excitation energies. The inverse level density parameter K as function of the particle number A in the semiclassical periodic orbit theory, taking into account the extended Thomas-Fermi and Strutinsky shell corrections, is calculated and compared with experimental data.

Semiclassical shell-structure micro-macroscopic approach for the level density

Level density $\rho(E,A)$ is derived for a one-component nucleon system with a given energy $E$ and particle number $A$ within the mean-field semiclassical periodic-orbit theory beyond the saddle-point method of the Fermi gas model. We obtain $~~\rho \propto I_\nu(S)/S^\nu$, with $I_\nu(S)$ being the modified Bessel function of the entropy $S$. Within the micro-macro-canonical approximation (MMA), for a small thermal excitation energy, $U$, with respect to rotational excitations, $E_{\rm rot}$, one obtains $\nu=3/2$ for $\rho(E,A)$. In the case of excitation energy $U$ larger than $E_{\rm rot}$ but smaller than the neutron separation energy, one finds a larger value of $\nu=5/2$. A role of the fixed spin variables for rotating nuclei is discussed. The MMA level density $\rho$ reaches the well-known grand-canonical ensemble limit (Fermi gas asymptotic) for large $S$ related to large excitation energies, and also reaches the finite micro-canonical limit for small combinatorial entropy $S$ at low excitation energies (the constant "temperature" model). Fitting the $\rho(E,A)$ of the MMA to the experimental data for low excitation energies, taking into account shell and, qualitatively, pairing effects, one obtains for the inverse level density parameter $K$ a value which differs essentially from that parameter derived from data on neutron resonances.

Renormalization of $$\textit{NN}$$ Chiral EFT: My Personal Mixed Feelings

We are celebrating thirty-years from the seminal papers from Weinberg proposing to use the rules of Chiral Perturbation Theory to nucleon systems. His proposal was to build an Effective Field Theory (EFT) with Chiral symmetry as a key property. A big effort on this line have been made during these three decades, however the issue of renormalization of the theory is not settled. I will briefly review my path on this issue and give my personal view.

Quantum gravity corrections to the mean field theory of nucleons

In this paper, we analyze the correction to the mean field theory potential for a system of nucleons. It will be argued that these corrections can be obtained by deforming the Schrödinger’s equation describing a system of nucleons by a minimal length in the background geometry of space-time. This is because such a minimal length occurs due to quantum gravitational effects, and modifies the low energy quantum mechanical systems. In fact, as the mean field potential for the nucleons is represented by the Woods–Saxon potential, we will explicitly analyze such corrections to this potential. We will obtain the corrections to the energy eigenvalues of the deformed Schrödinger’s equation for the Woods–Saxon potential. We will also construct the wave function for the deformed Schrödinger’s equation.

Studies of Deuteron\u2013Proton Collisions at 100 MeV

Differential cross section for the ^1H(d,pp)n reaction is sensitive to various dynamical ingredients and allows for thorough tests of theoretical potentials describing the interaction in the three nucleon systems. The analysis of the experimental data collected for the breakup reaction at the beam energy of 100 MeV has been performed and the first cross section results for selected configurations are presented in this paper. They are in good agreement with calculations based on the realistic potentials. Studies at this relatively low energy will also be important for examining awaited calculations within the Chiral Effective Field Theory.

Matter Density Distributions, Root-mean Square Radii and Elastic Electron Scattering Form Factors of Some Exotic Nuclei (17B, 11Li, 8He)

The two-neutron halo-nuclei (17B, 11Li, 8He) was investigated using a two-body nucleon density distribution (2BNDD) with two frequency shell model (TFSM). The structure of valence two-neutron of 17B nucleus in a pure (1d5/2) state and in a pure (1p1/2) state for 11L and 8He nuclei. For our tested nucleus, an efficient (2BNDD's) operator for point nucleon system folded with two-body correlation operator's functions was used to investigate nuclear matter density distributions, root-mean square (rms) radii, and elastic electron scattering form factors. In the nucleon-nucleon forces the correlation took account of the effect for the strong tensor force (TC's). The wave functions of single particle harmonic oscillator are used with two different oscillator size parameters βc and βv, where the former is for the core (inner) orbits and the latter is for the valence (halo) orbits. The measured matter density distributions of these nuclei clearly showed long tail results. To investigate elastic electron scattering form factors the plane wave born approximation (PWBA) with two body nucleon density distribution (2BNDD's) was use.

α-Like quartetting in the excited states of proton-neutron pairing Hamiltonians

Previous studies have shown that the ground state of systems of nucleons composed by an equal number of protons and neutrons interacting via proton-neutron pairing forces can be described accurately by a condensate of α-like quartets. Here we extend these studies to the low-lowing excited states of these systems and show that these states can be accurately described by breaking a quartet from the ground state condensate and replacing it with an “excited” quartet. This approach, which is analogous to the one-broken-pair approximation employed for like-particle pairing, is analyzed for various isovector and isovector-isoscalar pairing Hamiltonians which can be solved exactly by diagonalization.

Quantum Boltzmann equation for fermions: An attempt to calculate the NMR relaxation and decoherence times using quantum field theory techniques

Extracting macroscopic properties of a system from microscopic interactions has always been an interesting topic with the most diverse applications. Here, we use the quantum Boltzmann equation to investigate the density matrix evolution of a system of nucleons. Using the quantum field theory tools for constructing the density matrix operators and calculating the interactions is the main advantage of this equation. The right-hand side of this equation involves forward scattering and usual collision terms. As examples of application, we calculate the standard Bloch equations for the nucleon system in the presence of a constant and an oscillating magnetic field from the forward scattering term. We find the longitudinal and transverse (decoherence) relaxation times from the collision term by considering the nucleon-nucleon scattering.

Dynamical interaction geometries for physics with models

The MINT-Wigris Tool bag is presented with its models for color charges as a G-compass the hedgehog for the energy exchange of a nucleon system with its environment, an inner quark-gluon flow in it as 6-roll mill, two nucleon tetrahedrons for the gluon exchange between nucleons quarks, a radial contraction/expansion pulsation for deuteron, two fusion states of the tetrahedrons, a neutrino Gleason operator bound geometry and oscillation dynamics.

Fermions with long and finite-range interactions on a quantum ring

Background: Idealised systems are commonly used in nuclear physics and condensed matter. For instance, the construction of nuclear energy density functionals involves properties of infinite matter, while neutron drops are used to test nuclear interactions and approximations to the nuclear many-body problem. In condensed matter, quantum rings are also used to study properties of electron systems. Purpose: To investigate the possibility to use quantum rings with systems of nucleons including many-body correlations. Methods: A quantum ring model of a finite number of same spin fermions is developed. Several attractive and repulsive interactions with finite and infinite ranges are considered. Quantum Monte Carlo calculations are used to provide exact ground-state energies. Comparisons with analytical Hartree-Fock solutions are used to get an insight into the role of correlations. Results: Hartree-Fock results with no breaking of space translational symmetry are able to describe many systems. However, additional spatial correlations are required in the case of dense systems with a strong short-range repulsion, or with attractive interactions in large rings. Conclusions: Self-bound systems of fermions with spatial correlations produced by basic features of the nuclear interactions can be described on a quantum ring, encouraging applications with realistic interactions, as well as investigations with higher dimensional geometries such as spherium.

E1 moments from a coherent set of measured photoneutron cross sections

Recently, the $E1$ photoneutron cross sections were measured consistently using quasimonochromatic laser Compton-scattering $\ensuremath{\gamma}$-ray beams at NewSUBARU (Japan) for a set of ten odd-even nuclei, spherical as well as deformed, covering relatively widely light to heavy species and at energies ranging between the neutron threshold and 40 MeV. This consistent set of experimental photoneutron cross sections allow us to estimate the total $E1$ photoabsorption cross sections, through validated theoretical models, by excluding the quasideuteron component and by including the missing low-energy and charged-particle emission contributions. In turn, the total $E1$ photoabsorption cross sections are used to derive the three main moments of the $E1$ distributions, namely the integrated cross section, the centroid energy, and the polarizability. These so-called model-dependent experimental moments follow a rather smooth trend with atomic mass, as theoretically expected, except for the specific case of $^{209}\mathrm{Bi}$ which presents a surprising 10% increase of both the integrated strength and the polarizability with respect to its even-even spherical neighbor $^{208}\mathrm{Pb}$. A rather consistent value for the enhancement factor of the $E1$ energy-weighted sum rule could be extracted from the present experimental data. The experimentally derived moments are compared for the ten odd-even systems with calculations based on the mean-field plus quasiparticle random phase approximation (QRPA). Spherical as well as axially deformed predictions based on the Skyrme and Gogny interactions are considered to discuss the results. Special attention is also paid to the approximate treatment of odd systems of nucleons in this context. It is found that in general theoretical predictions can rather well describe the data for the full set of nuclei, except for $^{209}\mathrm{Bi}$ presenting a kink in all the three main $E1$ moments with respect to the well-studied $^{208}\mathrm{Pb}$ case. Such an experimental determination cannot be explained by mean-field plus QRPA calculations. New measurements of photoabsorption cross section on $^{208}\mathrm{Pb}$ and $^{209}\mathrm{Bi}$ in the 14--19 MeV range as well as future theoretical calculations, in particular of odd-even systems, may help to solve such a mystery. The present data are also used to reinvestigate the correlation between the nuclear matter symmetry energy and its slope at saturation density. The analysis based on both Skyrme and Gogny Hartree-Fock-Bogolyubov (HFB) plus QRPA calculations confirm previous results, though quantitatively larger variations of the correlation parameters are found.