Nucleons In Deuteron Research Articles

Real and Imaginary Phase Shifts for Nucleon–Deuteron Scattering Using Phase Function Method

Real and Imaginary Phase Shifts for Nucleon–Deuteron Scattering Using Phase Function Method

An Interactive Simulation of the Nucleon-Core Interacting Using the Fourth-Order Runge-Kutta Method for Studying Nuclear Physics

Nuclear physics is one of the theories in the field of physics that aims to study the structure of atomic nuclei, the interactions between the compilers of atomic nuclei, and the underlying forces. This study aims to obtain a model of interaction that occurs between nucleons. The interactions between these nucleons are modeled by a binary center of mass system (two objects) and their potential experience is expressed by the Woods-Saxon potential with certain parameters. The obtained model equations are then solved using the fourth-order Runge Kutta numerical method that programmed in the Matlab programming language. In this study, this model used has been simulated on the interaction of nucleons in Deuteron, Triton, Helium-3 isotope, and Helium works well, but it did not work well in Lithium atom.

Towards high-order calculations of three-nucleon scattering in chiral effective field theory

We discuss the current status of chiral effective field theory in the three-nucleon sector and present selected results for nucleon–deuteron scattering observables based on semilocal momentum-space-regularized chiral two-nucleon potentials together with consistently regularized three-nucleon forces up to third chiral order. Using a Bayesian model for estimating truncation errors, the obtained results are found to provide a good description of the experimental data. We confirm our earlier findings that a high-precision description of nucleon–deuteron scattering data below pion production threshold will require the theory to be pushed to fifth chiral order. This conclusion is substantiated by an exploratory study of selected short-range contributions to the three-nucleon force at that order, which, as expected, are found to have significant effects on polarization observables at intermediate and high energies. We also outline the challenges that will need to be addressed in order to push the chiral expansion of three-nucleon scattering observables to higher orders.

Two-Pion Exchange Three-Nucleon Force Effects in Elastic Nucleon–Deuteron Scattering Cross Sections

Differential cross sections for elastic nucleon–deuteron scattering at intermediate energies are calculated by solving the Faddeev equation in coordinate space using interaction models consisting of a two-nucleon potential and three-nucleon potentials based on the exchange of two pions among three nucleons. Attractive effects of the pion-exchange at medium range region in the three-nucleon potential are taken into account by using a larger cutoff mass parameter and by adding phenomenological repulsive three-nucleon potentials as a counterpart. It is shown that these effects increase the cross sections at backward angles, which tends to reduce discrepancies between theoretical calculations and experimental data.

Application of Semilocal Coordinate-Space Regularized Chiral Forces to Elastic Nd Scattering and Breakup

We solve three-nucleon (3N) Faddeev equations with nucleon–nucleon (NN) and three-nucleon forces (3NF) derived consistently in the framework of chiral perturbation theory, taking the semilocal coordinate-space regularized chiral N^4LO NN potential supplemented by the chiral N^2LO 3NF regularized in the same way. Based on these solutions the nucleon–deuteron (Nd) elastic scattering and deuteron breakup reactions are studied. We checked that the elastic Nd scattering cross section can be used as an alternative observable to the doublet neutron–deuteron (nd) scattering length to fix, together with the ^3H binding energy, the strengths of the contact terms of the N^2LO 3NF. We investigated the predicted 3NF effects in 3N continuum reactions putting an emphasis on the A_y puzzle in low energy nd elastic scattering and on cross sections in the symmetrical-space-star and quasi-free-scattering breakup configurations. We found that the N^2LO 3NF provides effects comparable to those of standard, (semi-)phenomenological 2pi -exchange Tucson-Melbourne 3NF.

Fate of the neutron–deuteron virtual state as an Efimov level

The emergence of Efimov levels in a three-body system is investigated near the unitarity limit characterized by a resonant two-body interaction. No direct evidence of Efimov levels is seen in the three-nucleon system since the triton is the only physical bound state. We provide a model-independent analysis of nucleon–deuteron scattering at low energy by formulating a consistent effective field theory. We show that virtual states evolve into shallow bound states, which emerge as excited triton levels as we drive the system towards unitarity. Even though we consider this specific system, our results for the emergence of the Efimov levels are universal.

Dual Ion Species Plasma Expansion from Isotopically Layered Cryogenic Targets.

A dual ion species plasma expansion scheme from a novel target structure is introduced, in which a nanometer-thick layer of pure deuterium exists as a buffer species at the target-vacuum interface of a hydrogen plasma. Modeling shows that by controlling the deuterium layer thickness, a composite H^{+}/D^{+} ion beam can be produced by target normal sheath acceleration (TNSA), with an adjustable ratio of ion densities, as high energy proton acceleration is suppressed by the acceleration of a spectrally peaked deuteron beam. Particle in cell modeling shows that a (4.3±0.7) MeV per nucleon deuteron beam is accelerated, in a directional cone of half angle 9°. Experimentally, this was investigated using state of the art cryogenic targetry and a spectrally peaked deuteron beam of (3.4±0.7) MeV per nucleon was measured in a cone of half angle 7°-9°, while maintaining a significant TNSA proton component.

Modern Chiral Forces Applied to the Nucleon\u2013Deuteron Radiative Capture

The chiral nucleon–nucleon interaction with semi-local regularization up to the fifth order of chiral expansion is applied to the nucleon–deuteron radiative capture process. Our theoretical approach is based on the formalism of Faddeev equations and the Siegert theorem is exploited to construct the electromagnetic current operator. The very weak dependence of the differential cross section on values of the regularization parameter is observed. This suggests that the improved chiral two-body interaction is a promising starting point to study electromagnetic processes at low energies.

Investigation of the reaction 4Нe(γ, pn)d at energies below the meson-production threshold

Themomentum distributions of deuterons and nucleons from the reaction 4Не(γ, pn)d induced by bremsstrahlung photons whose spectrum extends up to the endpoint energy of 150 MeV weremeasured by means of a diffusion chamber placed in a magnetic field. These measurements were performed in four photon-energy intervals for deuterons and in the energy range between 100 and 150 MeV for nucleons. Angular and energy correlations of nucleons were measured at photon energies in the interval between 50 and 70 MeV. The results obtained in this way were analyzed on the basis of the quasideuteron model. The probability for final-state nucleon–deuteron interaction was estimated.

Measurement of the 2H(p, n) Breakup Reaction at 170 MeV and the Three-Nucleon Force Effects

The effects of three nucleon force (3NF) have been actively studied via the nucleon–deuteron (Nd) scattering states. The differential cross sections and the vector analyzing powers A y of the 2H(p, n) inclusive breakup reaction at 170 MeV were measured for the study of 3NF effects in the intermediate energy region. The polarized proton beam of 170 MeV was injected to the deuterated polyethylene (CD2) target and the energy of scattered neutrons were measured by using TOF method. The data were compared with the Faddeev calculations based on modern nucleon–nucleon (NN) forces with and without the 3NF. Concerning the differential cross sections, we can see large discrepancies between the data and the calculations in the region of scattered neutron energies are low, which is similar to the results of the 2H(p, p) inclusive breakup reaction at 250 MeV.

Low-Energy Parameters of the Nucleon–Nucleon Scattering and Deuteron Properties, Electromagnetic Interactions with Bound Systems

One more application of the method of unitary clothing transformations (UCT’s) in the theory of nucleon–nucleon (N − N) interaction has been presented. We have extended our previous analysis (Dubovik and Shebeko in Few-Body Syst 48:109–142, 2010) of the N − N scattering below the pion production threshold to treat the neutron–proton (n − p) scattering at low energies and the deuteron static properties. Our calculations of deuteron magnetic and quadrupole moments have been carried out in the framework of a gauge independent description of electromagnetic (EM) interactions with nuclei (bound systems) using the clothed particle representation of the Hamiltonian, the boost and EM current density operators for the n–p system.

3H at Next-to-Next-to-Next-to Leading Order of the Chiral Expansion

The chiral three-nucleon force (3NF) at next-to-next-to-next-to leading order (N3LO) is used to calculate the triton wave function and the doublet nucleon–deuteron scattering length. This allows us to fix the values of the low-energy constants which are free parameters of the theory. The obtained values of these parameters, the expectation values of the kinetic energy, two- and three-body potentials and individual contributions of different parts of 3NF are given.

Coulomb Effect in Nucleon–Deuteron Elastic Scattering

We have applied the quark-model nucleon–nucleon interaction fss2 to the nucleon–deuteron scattering. The screened cutoff Coulomb force in the momentum space has been incorporated to the proton–deuteron scattering by extending the matching condition, which is proposed by Vincent and Phatak for the sharply cutoff Coulomb problem. The model fss2 can reproduce the overall characteristics of the experimental data. It is found that fss2 partially incorporates the attractive feature, which accords with the good reproduction of the triton binding energy and neutron–deuteron doublet scattering length. This attractive feature is due to the off-shell effect related to the quark-model description of the short-range repulsion of the two-nucleon force.

Off-shell Effect of the Quark-model NN Interaction in the Nd Scattering

Low- and medium-energy nucleon–deuteron (Nd) scattering less than the incident energy 65 MeV per nucleon is examined by using the quark-model nucleon–nucleon (NN) interaction fss2. The off-shell effect of this non-local interaction yields a part of the attractive effect given by the three-nucleon force in the standard description by the meson-exchange potentials. The triton binding energy and the spin-doublet scattering length are well described by fss2 without introducing the three-nucleon force. The nucleon analyzing power is slightly improved from the results by the AV18 potential, but the so-called Ay puzzle in the low-energy region is not essentially solved nor is the similar deficiency of the peak heights seen in the vector analyzing power of the deuteron, iT11(θ). Other observables are rather similar to the predictions by meson-exchange potentials, including disagreements of the deuteron breakup differential cross sections with experiment for some particular kinematical configurations. The space-star anomaly of the nd and pd scattering at EN = 13 MeV is not improved. The accurate and systematic KVI data of the \({^{1}H(\overrightarrow{d}, 2p)n}\) scattering at Ed = 130 MeV are compared with the predictions by fss2 for the breakup differential cross sections and the deuteron analyzing powers.

The Method of Unitary Clothing Transformations in Relativistic Quantum Field Theory: Recent Applications for the Description of Nucleon–Nucleon Scattering and Deuteron Properties

The clothing procedure, put forward in quantum field theory by Greenberg and Schweber, is applied for the description of nucleon–nucleon (N–N) scattering below the pion production threshold and deuteron properties. We consider pseudoscalar (π and η), vector (ρ and ω) and scalar (δ and σ) meson fields interacting with N and \({\bar N}\) ones via the Yukawa-type couplings to introduce trial interactions between “bare” particles. The subsequent unitary clothing transformations (UCTs) are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. We will also show a worked example where the UCTs method is used in the framework of a gauge-independent field-theoretical treatment of electromagnetic interactions of deuterons (bound systems).

Nucleon–Deuteron Breakup Differential Cross Sections Derived from the Quark-Model NN Interaction

The nd and pd breakup differential cross sections for E N ≤ 65 MeV are examined using the energy- independent quark-model nucleon-nucleon interaction fss2. The Coulomb effect is incorporated by the sharp cut-off Coulomb force, acting between quarks, without the phase-shift renormalization for the breakup ampli- tudes. Our model yields the results very similar to the meson-exchange potentials, including disagreement for some specific kinematical configurations. This includes the notorious space star anomaly of the nd and pd scattering at E N = 13 MeV. The KVI data for the breakup differential cross sections of Ed = 130 MeV dp scattering are reasonably reproduced by taking the Coulomb cut-off radius ρ = 16 fm.

Measurements of the Cross Sections and A y for D(p, n) Inclusive Breakup Reaction at 170 MeV

The effects of three-nucleon force (3NF) has been actively studied by using the nucleon–deuteron (Nd) scattering states. The differential cross sections of the elastic Nd scattering at the energy below 150 MeV can be well reproduced by incorporating 3NF in the Faddeev calculation based on modern nucleon–nucleon (NN) interactions. On the other hand, the differential cross sections of Nd elastic and inelastic scatterings at 250 MeV show large discrepancies between the data and the Faddeev calculations with 3NF. It indicates the presence of the missing features of the three nucleon system at this energy region. For the systematic study about the energy dependence of this large discrepancies, we measured the differential cross sections and the vector analyzing power Ay for the 2H(p, n) inclusive breakup reaction at 170 MeV. The experiment was carried out at RCNP by detecting scattered neutrons by using the neutron detector NPOL3. The data was compared with the results of the Faddeev calculations with and without the 3NF.

Configuration-Space Faddeev Calculation for Proton–Deuteron Elastic Scattering Observables

A new computational method for solving the nucleon–deuteron breakup scattering problem has been applied to study the elastic nucleon–deuteron scattering on the basis of the configuration-space Faddeev–Noyes–Noble–Merkuriev equations. The Merkuriev–Gignoux–Laverne approach has been generalized for arbitrary nucleon–nucleon potentials and with an arbitrary number of partial waves. The nucleon–deuteron observables at the incident nucleon energy 3 MeV have been calculated using the charge-independent AV14 nucleon–nucleon potential including the Coulomb force for the proton–deuteron scattering. Results have been compared with those of other authors and with experimental proton–deuteron scattering data.

Quasi-elastic and elastic charge-exchange differential cross sections (critical review)

More than 50 years ago the charge-exchange of one nucleon in the quasi-elastic nucleon deuteron scattering was proposed to determine the spin independent, or the spin dependent parts of the elastic backward neutron proton differential cross section. For this purpose two measurements are to be performed using unpolarized particles only. Such a suggestion was very attractive for experimentalists, since at that time polarized beams were rare and polarized targets were nonexistent. One experiment consists in the inclusive measurement of the charge-exchange quasi-elastic nucleon deuteron differential cross section. The energy of the fast outgoing nucleon is to be approximately the same as that of the incident nucleon. The intrinsic momenta of the remaining two identical nucleons should be small. The impulse approximation has been assumed, i.e. in the final state of the two nucleons their interaction can be neglected. The quasi-elastic result is to be compared with the elastic np differential cross section in the backward direction at the same energy. The theory related the ratio RQE(π) of the quasi-elastic to the elastic np charge-exchange differential cross sections to the spin dependent part of the np backward elastic scattering amplitude. Several experiments in the nucleon kinetic energy interval below 1 GeV were carried out, where the RQE(π) values were determined. Recently the energy interval was extended up to 2 GeV by successful experiments at the JINR VBLHE Nuclotron. The quasi-elastic results can be compared with the values of the analogous quantity Rnp(π) for the np elastic scattering, calculated from the phase shift analyses below 1.3 GeV. The present paper is a critical review checking expressions for Rnp(π) in different amplitude representations, listing numerical values of elastic np quantities and results of existing quasi-elastic experiments. Conclusions and statements of some authors and the validity of the relevant theory is discussed.

Polarization phenomena in elastic backward p-D scattering

The elastic backward proton-deuteron scattering is analyzed including both relativistic effects in the deuteron and the reaction mechanism. It is shown that inclusion of the graphs corresponding to the emission, rescattering and absorption of the virtual pion by a deuteron nucleon in addition to the one-nucleon exchange graph allows for a rather satisfactory description of all the experimental data on the differential cross section, tensor analyzing power of the deuteron and transfer polarization in this reaction.