The pd break-up amplitude in the Faddeev scheme is calculated by employing a three-dimensional method without partial wave decomposition (PWD). In a first step and in view of higher energies only the leading term is evaluated and this for the process d(p,n)pp. A comparison with the results based on PWD reveals discrepancies in the cross section around 200 MeV. This indicates the onset of a limitation of the partial wave scheme. Also, around 200 MeV relativistic effects are clearly visible and the use of relativistic kinematics shifts the cross section peak to where the experimental peak is located. The theoretical peak height, however, is wrong and calls first of all for the inclusion of rescattering terms, which are shown to be important in a nonrelativistic full Faddeev calculation in PWD.
The Kohn variational principle is formulated for calculating elastic proton-deuteron scattering amplitudes at energies above the deuteron breakup threshold. The use of such a principle with an expansion of the wave function on the (correlated) hyperspherical harmonic basis is discussed.
The complex Kohn variational principle and the (correlated) hyperspherical harmonics method are applied to study the proton-deuteron elastic scattering at energies above the deuteron breakup threshold. Results for the elastic cross section and various elastic polarization observables have been obtained by fully taking into account the long-range effect of the Coulomb interaction and using a realistic nucleon-nucleon interaction model. Detailed comparison between the theoretical predictions and the accurate and abundant proton-deuteron experimental data can now be performed.
We extend our approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) Faddeev calculations from elastic proton-deuteron (pd) scattering to the breakup process. The main new ingredient is a 3-dimensional screened pp Coulomb t-matrix obtained by a numerical solution of the 3-dimensional Lippmann-Schwinger equation. We demonstrate numerically that the proton-deuteron breakup observables can be determined from the resulting on-shell 3N amplitudes increasing the screening radius. However, contrary to the pd elastic scattering, the screening limit exists only after r…
We consider T-violating P-conserving proton-deuteron forward elastic scattering amplitude in a frame of the Glauber multiscattering theory, proceeding from T-odd, P-even N-N interaction.
Deuteron-proton elastic scattering is studied in the multiple scattering expansion formalism. The four contributions are taken into account: one-nucleon-exchange, single- and double scattering, and $Δ$-isobar excitation. The presented approach was applied to describe the differential cross sections at deuteron energies between 500 and 1300 MeV in a whole angular range. The obtained results are compared with the experimental data.
The $dp\to dp$ and $dd\to ^3He n$ reactions are considered in the energy range from few hundred MeV up to 1 GeV. The approach is based on the multiple-scattering theory, where the few-body collisions are presented through two-body ones. The high-energy nucleon-nucleon interactions are described by t-matrix, which is parameterized in accordance with the modern phase-shift analysis data. The special attention is given to investigation of the rescattering effects in these reactions. The theoretical predictions are obtained for the differential cross sections, vector and tensor analyzing powers. A…
The deuteron-proton elastic scattering has been studied in the multiple scattering expansion formalism. The essential attention has been given to such relativistic problem as a deuteron wave function in a moving frame and transformation of spin states due to Wigner rotation. Parameterization of the nucleon-nucleon $t$-matrix has been used to take the off-energy shell effects into account. The vector, $A_y,$ and tensor, $A_{yy}$, analyzing powers of the deuteron have been calculated at two deuteron kinetic energies: 395 MeV and 1200 MeV. The obtained results are compared with the experimental d…
The Coulomb interaction between the protons is included in the description of proton-deuteron scattering using the screening and renormalization approach in the framework of momentum-space integral equations. Two new calculational schemes are presented that confirm the reliability of the perturbative approach for treating the screened Coulomb interaction in high partial waves, used by us in earlier works.
We propose a novel approach to incorporate the proton-proton (pp) Coulomb force into the three-nucleon (3N) Faddeev calculations. The main new ingredient is a 3-dimensional screened pp Coulomb t-matrix obtained by a numerical solution of the 3-dimensional Lippmann-Schwinger (LS) equation. We demonstrate numerically and provide analytical insight that the elastic proton-deuteron (pd) observables can be determined directly from the resulting on shell 3N amplitude increasing the screening radius. The screening limit exists without the need of renormalisation not only for observables but for the e…
Collective flows of protons and deuterons for Au + Au collisions at beam energy $E_{beam}$ = 1.23 $A$ GeV were simulated by an Isospin dependent Quantum Molecular Dynamics (IQMD) model. Two coalescence models, namely naive coalescence and dynamical coalescence models, for the formation of deuterons are compared. After reasonable match of rapidity spectra of protons and deuterons to the High Acceptance DiElectron Spectrometer (HADES) data is reached, we apply an event-plane method to calculate the first four-order collective flow coefficients as well as the ratios of $<v_4>/<v_2>^2$ and $<v_3>/…
The deuteron fragmentation by fast protons has been studied both near the kinematics of quasi-free proton - proton scattering and far away from it. We have concentrated on the interplay between different reaction mechanisms associated with the antisymmetrization of the initial and final states and rescattering contributions. A multiple-scattering-expansion technique has been applied to evaluate the reaction amplitude. An essential element of this approach in the momentum representation is the use of the effective nucleon- nucleon interaction constructed by Love and Franey as a two-body t-matri…
The article is devoted to the relativistic study of elastic $pD$ backward scattering based on the one-nucleon exchange diagram. Calculations were performed using relativistic deuteron wave functions obtained by solving the Bethe-Salpeter equation in the Minkowski space with relativistic separable potentials. The unpolarized differential cross section as well as some polarization observables of the reaction for initial proton momentum up to 7.3 GeV were calculated. The obtained results are compared with the calculations of other authors.
We present a practical method to solve the proton-deuteron scattering problem at energies above the three-body breakup threshold, in which we treat three-body integral equations in coordinate space accommodating long-range proton-proton Coulomb interactions. The method is examined for phase shift parameters, and then applied to calculations of differential cross sections in elastic and breakup reactions, analyzing powers, etc. with a realistic nucleon-nucleon force and three-nucleon forces. Effects of the Coulomb force and the three-nucleon forces on these observables are discussed in comparin…
The elastic proton-deuteron backward reaction is analyzed within a covariant approach based on the Bethe-Salpeter equation with realistic meson-exchange interaction. Lorentz boost and other relativistic effects in the cross section and spin correlation observables, like tensor analyzing power and polarization transfer etc., are investigated in explicit form. Results of numerical calculations for a complete set of polarization observables are presented.
A modified version of the Faddeev three-body equation to accommodate the Coulomb interaction, which was used in the study of three-nucleon bound states, is applied to the proton-deuteron scattering problem at energies below the three-body breakup threshold. A formal derivation of the equation in a time-independent scattering theory is given. Numerical results for phase shift parameters are presented to be compared with those of another methods and results of the phase shift analysis. Differential cross sections and nucleon analyzing powers are calculated with the effects of three-nucleon force…
The relation between the differential cross section of the charge-exchange breakup of a fast deuteron d+p -> (pp)+n and the differential cross section of the charge transfer process n+p -> p+n is discussed taking into account the effects of the proton identity and of the Coulomb and strong interactions of protons in the final state. The distribution of the relative momenta of the protons is found in the framework of the impulse approach. It is shown that the use of polarized initial deuterons and protons allows one to separate two spin-dependent terms in the amplitude of the charge transfer re…
The elastic backward proton-deuteron scattering is analyzed within a fully covariant approach based on the invariant expansion of the reaction amplitude. The method of calculation of any observables for any reaction mechanism is developed. The cross section and spin observables, like tensor analyzing power and polarization transfer coefficient etc., are investigated in explicit form within framework of the impulse approximation using different kinds of the relativistic deuteron wave function (DWF) with P-wave components. Our results of numerical calculation for complete set of polarization obs…
The low-energy parameters describing the np scattering in the 3S1 + 3D1 partial waves, the deuteron parameters, and their relations are discussed. These parameters can be determined quite accurately in the energy-dependent Nijmegen partial-wave analyses of the np data and are also given by the high-quality Nijmegen potentials. The newest values for these parameters are presented.
Faddeev calculations have been performed for nucleon-deuteron photodisintegration of 3He(3H) and proton-deuteron radiative capture. The bulk of the results is based on the AV18 nucleon-nucleon force and the Urbana IX three-nucleon force together with explicit exchange currents or applying the Siegert approach. Three-nucleon force effects are predicted for both processes and supported by most of the data.
Recent data on the reaction pD -> (pp) n with a fast forward pp pair with very small excitation energy is analyzed within a covariant approach based on the Bethe-Salpeter formalism. It is demonstrated that the minimum non-relativistic amplitude is completely masked by relativistic effects, such as Lorentz boost and the negative-energy P components in the 1S_0 Bethe-Salpeter amplitude of the pp pair.
The charge-exchange reaction pd->npp at 1 GeV projectile proton energy is studied in the multiple-scattering expansion technique. This reaction is considered in a special kinematics, when the transfer momentum from the beam proton to fast neutron is close to zero. The differential cross section and a set of polarization observables are calculated. It was shown that contribution of the final state interaction between two protons is very significant.
The elastic backward proton-deuteron scattering is analyzed within a covariant approach based on the invariant expansion of the reaction amplitude. The relativistic invariant equations for all the polarization observables are presented. Within the impulse approximation the relation of the tensor analyzing power $T_{20}$ and the polarization transfer $κ_0$ to $P$-wave components of the deuteron wave function is found. The comparison of the theoretical calculations with experimental data is presented. An experimental verification of the reaction mechanism is suggested by constructing some combin…
The differential cross section for radiative capture of protons by deuterons is calculated using different realistic NN interactions. We compare our results with the available experimental data below $E_x = 20 MeV$. Excellent agreement is found when taking into account meson exchange currents, dipole and quadrupole contributions, and the full initial state interaction. There is only a small difference between the magnitudes of the cross sections for the different potentials considered. The angular distributions, however, are practically potential independent.
The process p+d \leftrightarrow 3He + γ* at intermediate energies is described using a covariant and gauge-invariant model, and a realistic pd3He vertex. Both photodisintegration of 3He and proton-deuteron capture with production of e+e- pairs are studied, and results for cross sections and response functions are presented. The effect of time-like formfactors on the dilepton cross sections is investigated as well.
We present the results of a calculation of differential cross sections and polarization observables for proton-deuteron elastic scattering, for proton laboratory energies from 2.5 to 22.5 MeV. The Paris potential parametrisation of the nuclear force is used. As solution method for the charged-composite particle equations the 'screening and renormalisation approach' is adopted which allows to correctly take into account the Coulomb repulsion between the two protons. Comparison is made with the precise experimental data of Sagara et al. [Phys. Rev. C 50, 576 (1994)] and of Sperison et al. [Nucl.…
The eigenphase shifts and mixing parameters for elastic p-d scattering below the deuteron-breakup threshold are calculated for the AV14 two-body potential using two different numerical methods. The excellent agreement confirms that it is possible to perform accurate numerical studies of p-d scattering as well as n-d scattering for low energies. The numerical results can be considered as benchmarks for future calculations.
The elastic backward proton-deuteron scattering is analyzed within a covariant approach based on the Bethe-Salpeter equation with realistic meson-exchange interaction. Contributions of the one-nucleon and one-pion exchange mechanisms to the cross section and polarization observables are investigated in explicit form. Results of numerical calculations for the cross section, tensor analyzing power and spin transfers are presented. The one-pion exchange contribution is essential for describing the spin averaged cross section, while in polarization observables it is found to be less important.
A new method for solving the configuration-space Faddeev equations for elastic p-d scattering below the deuteron-breakup threshold is described. Numerical solutions that demonstrate the convergence and accuracy of the method are given. The number of channels and the value of the matching radius required to obtain an accurate solution are also investigated. These calculations demonstrate that this method can efficiently solve the large matrix equations required for the three-body scattering problem.
The reactions of nucleon and polarized deuteron scattered off a heavy target at large impact parameter with intermediate energies have been investigated by using the improved quantum molecular dynamics model. It is found that, due to the difference effect of isovector potential on proton and neutron, there is a significant difference between the angle distribution of elastic scattering protons and neutrons. To overcome the lack of monochromatic neutron beam, the reaction of polarized deuteron peripherally scattered off the heavy target is used to replace the reaction of individual proton and n…
The astrophysical factor S_pp(0) for the solar proton burning, p + p -> D + positron + neutrino, is recalculated in the relativistic field theory model of the deuteron (RFMD). We obtain S_pp(0) = 4.08 x 10^{-25} MeV b which agrees good with the recommended value S_pp(0) = 4.00 x 10^{-25} MeV b. The amplitude of low-energy elastic proton-proton (pp) scattering in the singlet S-wave state with the Coulomb repulsion contributing to the amplitude of the solar proton burning is described in terms of the S-wave scattering length and the effective range. This takes away the problem pointed out by Bah…
We consider two basic nuclear reactions: Radiative capture of neutrons by protons, $n+p\to γ+~d$ and its time-reversed counterpart, photodisintegration of the deuteron, $γ+d\to n+p$. In both of these cases we assume that the incoming beam of neutrons or photons is "twisted" by having an azimuthal phase dependence, {\it i.e.}, it carries an additional angular momentum along its direction of propagation. Taking a low-energy limit of these reactions, we derive relations between corresponding transition amplitudes and cross sections with plane-wave beams and twisted beams. Implications for experim…
The target tensor analyzing powers of the process $γd -> π^{-}pp$ had been studied in the plane wave impulse approximation, if both ejected protons are detected in coincidence and in the directions, symmetrical respect to the incoming photon momentum, being in the proton plane. The matrix elements of the studied reaction become essentially simple, if the magnitudes of the proton momenta p1 = p2 = p are equal. That proton kinematics keeps the ejected pion angle near zero, therefore the one body pion production operator does not include the spin-non-flip term. Moreover, the transition to the tri…
Contributions of three-nucleon forces (3NF) to proton-deuteron scattering observables at energies below the deuteron breakup threshold are studied by solving the Faddeev equation that includes the Coulomb interaction. At E_p=3.0 MeV, we find that the central part of a two-pion exchange 3NF removes the discrepancy between measured cross sections and the calculated ones by two-nucleon forces, and improves the agreement with T_{22} experimental data. However, the tensor part of the 3NF fails in reproducing data of the analyzing power T_{21} by giving worse agreement between the measured and the c…
The relativistic field theory model of the deuteron (RFMD) is applied to the calculation of the astrophysical factor S_{pp}(0) for the process of the solar proton burning p + p -> D + e^+ + ν_e and the cross sections for the disintegration of the deuteron by photons gamma + D -> n + p and anti-neutrinos \barν_e + D -> e^+ + n + n. Our theoretical value of the astrophysical factor S_{pp}(0) = 4.02 x 10^{-25} MeV b agrees with the classical result obtained by Bahcall and Kamionkowski S_{pp}(0) = 3.89 x 10^{-25} MeV b in the potential model approach (PMA). The cross sections for the disintegratio…
The role of the short-range part (repulsive core) of the proton-neutron ($pn$) potential in deuteron elastic breakup processes is investigated. A simplified one-range Gaussian potential and the Argonne V4' (AV4') central potential are adopted in the continuum-discretized coupled-channels (CDCC) method. The deuteron breakup cross sections calculated with these two potentials are compared. The repulsive core is found not to affect the deuteron breakup cross sections at energies from 40 MeV to 1 GeV. To understand this result, an analysis of the peripherality of the elastic breakup processes conc…
Relativistic nuclear response theory is formulated for the proton-neutron pairing, or deuteron transfer, channel. The approach is based on the meson-nucleon Lagrangian of Quantum Hadrodynamics (QHD) and advances the relativistic field theory to connect consistently the high-energy scale of heavy mesons, the medium-energy range of the pion and the low-energy domain of emergent collective vibrations (phonons) in a parameter-free way. Mesons and phonons build up the in-medium nucleon-nucleon interaction in spin-isospin transfer channels, in particular, the phonon-exchange part takes care of the l…
We present a unitary and gauge-invariant model with coupled channels, which provides a consistent description of pion photoproduction off nucleons in the E$_{0+}$ channel and eta-meson photoproduction off protons and deuterons. An effective field theory with hadrons and photons is constructed, which includes non-resonant Born terms as well as the S$_{11}$(1535) and S$_{11}$(1650) baryon resonances. Due to the coupling between the channels, the production of eta-mesons is strongly affected by the S$_{11}$(1650) although its direct coupling to the $η$N channel is negligible. The rho- and omega-m…
The integrated cross section $\widetildeσ$ for a special type of double polarized proton-deuteron scattering constitutes a null test forvtime-invariance violating but P-parity conserving effects. Using the Glauber theory for the $pd$ elastic scattering and different types of phenomenological T-odd P-even NN-interactions we show that the contribution of the lowest mass meson exchange, i.e. the $ρ$-meson, to the null-test signal $\widetildeσ$ vanishes. Variation of the cross section $\widetildeσ$ due to strong hadronic and Coulomb interaction is studied and its energy dependence is calculated in…
A theoretical analysis using an impact-parameter description of the collisions of deuterons with nuclei is carried out in the high-energy diffraction approximation. It is used to obtain the intensities and integrated cross sections for elastic scattering, for the emergence of the two incident nucleons from the collision whether they appear as an elastically scattered deuteron or as two unbound nucleons, and for the diffraction-induced dissociation of the deuteron into a free neutron and a free proton, as well as the total cross section. The cross section for collisions in which one or both of …
We discuss two approaches which, by applying the screening method, permit one to include the long range proton-proton (pp) Coulomb force in proton-deuteron (pd) momentum-space scattering calculations. In the first one, based on Alt-Grassberger-Sandhas (AGS) equation, presented in Phys. Rev. C{\bf{71}}, 054005 (2005) and {\bf{73}}, 057001 (2006), one needs to renormalize elastic scattering amplitude before calculating observables. In the second treatment, proposed by us in Eur. Phys. Journal A {\bf{41}}, 369 (2009), {\bf{41}}, 385 (2009), and arXiv:2310.03433 [nucl.th], this renormalization is …
Two independent calculations of proton-deuteron elastic scattering observables including Coulomb repulsion between the two protons are compared in the proton lab energy region between 3 MeV and 65 MeV. The hadron dynamics is based on the purely nucleonic charge-dependent AV18 potential. Calculations are done both in coordinate space and momentum space. The coordinate-space calculations are based on a variational solution of the three-body Schrödinger equation using a correlated hyperspherical expansion for the wave function. The momentum-space calculations proceed via the solution of the Alt-G…
The hadron-deuteron correlation function has attracted many interests as a potential method to access the three-hadron interactions. However, the weakly-bound nature of deuteron has not been considered in the preceding studies. In this study, the breakup effect of deuteron on the deuteron-$Ξ^-$ ($d$-$Ξ^-$) correlation function $C_{dΞ^-}$ is investigated. The $d$-$Ξ^-$ scattering is described by a nucleon-nucleon-$Ξ$ three-body reaction model. The continuum-discretized coupled-channels method, which is a fully quantum-mechanical and non-perturbative reaction model, is adopted. $C_{dΞ^-}$ turns …
The effects of parity violation in the interaction of relativistic polarized protons and deuterons are discussed. Within Glauber's approach, estimates are obtained for P-odd asymmetries in the total and elastic scattering cross sections, in the deuteron dissociation cross section, and in the inelastic cross section with meson production in a final state. It is shown that, from the point of view of the magnitude of the P-odd effects, the interaction of polarized deuterons with unpolarized protons has an advantage over the interaction of polarized protons with unpolarized deuterons. A significan…
Background: Eclipse effect of the neutron and proton in a deuteron target is essential to correctly describe high-energy deuteron scattering. The nucleus-deuteron scattering needs information not only on the nucleus-proton but also the nucleus-neutron interaction, for which no direct measurement of the nucleus-neutron cross sections is available for unstable nuclei. Purpose: We systematically evaluated the total reaction cross sections by a deuteron target to explore the feasibility of extracting the nucleus-neutron interaction from measurable cross sections. Methods: High-energy nucleus-deute…
Time reversal invariance violating parity conserving (TVPC) effects are calculated for elastic proton deuteron scattering with proton energies up to $2~$MeV. Distorted Wave Born Approximation is employed to estimate TVPC matrix elements, based on hadronic wave functions, obtained by solving three-body Faddeev-Merkuriev equations in configuration space with realistic potentials.
In recent time the deuteron structure at short distances is often treated from the point of view nonnucleonic degrees of freedom. In this paper the measurements of T-odd polarization observables using tensor polarized deuteron beam and polarized proton target or proton polarimeter are proposed to search the quark configurations inside the deuteron.
The cross sections for the M1-capture n + p -> D + gamma, the photo-magnetic and anti-neutrino disintegration of the deuteron are evaluated in the relativistic field theory model of the deuteron (RFMD). The cross section for M1-capture is evaluated by taking into account the contributions of chiral one-meson loop corrections and the Delta(1232) resonance. The cross sections for the photo-magnetic and anti-neutrino disintegration of the deuteron are evaluated by accounting for final-state interaction of the nucleon pair in the spinsinglet S-wave state. The amplitudes of low-energy elastic np an…
Coulomb effects in the neutron-deuteron and proton-deuteron polarization-transfer coefficients $K_y^{y'}$, $K_z^{x'}$, $K_y^{x'x'-y'y'}$ and $K_y^{z'z'}$ are studied at energies above the deuteron breakup threshold. Theoretical predictions for these observables are evaluated in the framework of the Kohn Variational Principle using correlated basis functions to expand the three-nucleon scattering wave function. The two-nucleon Argonne $v_{18}$ and the three-nucleon Urbana IX potentials are considered. In the proton-deuteron case, the Coulomb interaction between the two protons is included expli…
The isoscalar $pn$ pair is expected to emerge in nuclei having the similar proton and neutron numbers but there is no clear experimental evidence for it. We aim to clarify the correspondence between the $pn$ pairing strength in many-body calculation and the triple differential cross section (TDX) of proton-induced deuteron knockout ($p,pd$) reaction on $^{16}$O. The radial wave function of the isoscalar $pn$ pair with respect to the center of $^{16}$O is calculated with the energy density functional (EDF) approach and is implemented in the distorted wave impulse approximation (DWIA) framework.…
A new computational method for solving the nucleon-deuteron breakup scattering problem has been applied to study the elastic neutron- and proton-deuteron scattering on the basis of the configuration-space Faddeev-Noyes-Noble-Merkuriev equations. This method is based on the spline-decomposition in the angular variable and on a generalization of the Numerov method for the hyperradius. 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 …
The deuteron break-up exclusive reaction $p+d \to N(180^{\circ}) + (NN)(0^{\circ})$ is considered in the framework of the one-nucleon-exchange mechanism at the incident proton kinetic energy 0.2--2 GeV and the relative energy of nucleons in the forward going final NN-pair $E_{NN}=0$--20 MeV, that is close to the kinematical conditions of the planned experiment at COSY. The off-energy-shell effects resulting, in particular, in the node of the half-off-shell $^1S_0$-state partial NN-scattering amplitude and the role of higher partial waves in the subprocess $pN\to pN$ are analysed and found to b…
It is shown that the ratio of the deuteron and proton analysing powers in proton-deuteron elastic scattering at small angles is sensitive to subtle effects in a theoretical description. These include the transverse spin-spin term in the elementary nucleon-nucleon amplitudes and double-scattering corrections. On the other hand there is far less sensitivity to the spin-orbit amplitude and to binding or other kinematic effects associated with the use of the deuteron, as either target or projectile. The available data are in agreement with the results of a refined Glauber theory model.
