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 data.
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.
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.
Elastic lepton-deuteron scattering was considered within the limit of zero lepton mass. The deuteron wave function in the coordinate representation for the Reid93 potential was applied to numerical calculations. The angular-momentum dependence of values spin correlation coefficients $C_{xz}^{(0)}$, $C_{zz}^{(0)}$ and tensor asymmetries $A_{xx}^{(0)}$, $A_{xz}^{(0)}$, $A_{zz}^{(0)}$ have been evaluated in 3D format for Reid93 potential. These polarization observables are analyzed for different energies and scattering angles. Application of the obtained values allows better explanation and illus…
The general form of the cross section as well as the polarizations of electron-deuteron elastic scattering are given. Two-photon exchange effects are analyzed. Possible signatures of the two-photon exchange effects in the electron-deuteron elastic scattering are discussed.
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.
A study of the deuteron structure in the framework of relativistic quantum mechanics is presented. Point-form (PF) relativistic quantum mechanics (RQM) is applied to the elastic eD scattering. The deuteron wave function and neutron form factors are fitted to the electromagnetic deuteron form factors. We also compare results obtained by different realistic deuteron wave functions stemming from Nijmegen-I, Nijmegen-II, JISP16, CD-Bonn, Paris, Argonne, Idaho and Moscow (with forbidden states) potentials. It is shown that the electromagnetic deuteron form factors may be described without exchange …
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 present calculations of deuteron elastic and inelastic breakup cross sections and angular distributions at deuteron energies below 100 MeV obtained using the post-form DWBA approximation. The elastic breakup cross section was extensively studied in the past. Very few calculations of inelastic breakup have been performed, however. We also analyze the angular momentum - energy distributions of the cross section for formation of the compound nucleus after inelastic breakup.
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 reaction of the elastic electron-deuteron scattering at high momentum transfer is investigated within the Bethe-Salpeter approach. The relativistic covariant Graz II separable kernel of nucleon-nucleon interactions is used to analyze the deuteron structure functions, form factors and tensor of polarization components. The modern data for the electromagmetic nucleons structure from the double polarization experiments as well as some other models of the nucleon form factors are considered.
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…
What range of momentum components in the deuteron wave function are available e d elastic scattering data sensitive to ? This question is addressed within the context of a model calculation of the deuteron form factors, based on realistic interactions and currents. It is shown that the data on the $A(q)$, $B(q)$, and $T_{20}(q)$ observables at $q \leq 6$ fm$^{-1}$ essentially probe momentum components up to $\simeq 4 m_π$.
A calculation of the deuteron polarization observables $A^d_y$, $A_{yy}$, $A_{xx}$, $A_{xz}$ and the differential cross-section for elastic nucleon-deuteron scattering at incident deuteron energies 270 and 880 MeV in lab is presented. A comparison of the calculations with two different deuteron wave-functions derived from the Bonn-CD $NN$-potential model and the dressed bag quark model is carried out. A model-independent approach, based on an optical potential framework, is used in which a nucleon-nucleon $T$-matrix is assumed to be local and taken on the energy shell, but still depends on the…
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.
The general expressions for parity violation observables in elastic scattering of polarized and/or unpolarized electrons from unpolarized deuterons are given and are numerically evaluated for the kinematics of SAMPLE, PVA4 and G0 experiments. The dominant contribution from the interference of $γ$ and Z exchange as well as the smaller contributions from strangeness ($s{\bar{s}}$) components of the nucleon, parity odd admixtures in the deuteron wave function, anapole moments and radiative corrections are included and discussed in the context of parity violating electron scattering experiments of…
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…
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.
The general formalism for polarization observables in elastic electron deuteron scattering is extended to incorporate parity and time reversal violating contributions. Parity violating effects arise from the interference of $γ$ and $Z$ exchange as well as from the hadronic sector via a small parity violating component in the deuteron. In addition we have allowed for time reversal invariance violating contributions in the hadronic sector. Formal expressions for the additional structure functions are derived, and their decomposition into the various multipole contributions are given explicitly.
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.
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>/…
A calculation of vector and tensor polarization observables of a deuteron in an optical potential framework for elastic proton-deuteron scattering at the incident deuteron energy $E_d=880$ MeV is presented. The main aim is to point out the role of various effects in explaining the wide-range angle distribution of these observables. Under the investigation are a double-scattering mechanism in the optical potential, the influence of various $NN$-partial waves and as well a comparison of calculations with two different deuteron wave-functions derived from the Bonn-CD $NN$-potential model and dres…
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 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 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…
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…
We calculate elastic electron-deuteron scattering in a chiral effective field theory approach for few-nucleon systems based on a modified Weinberg power counting. We construct the current operators and the deuteron wave function at next-to-leading (NLO) and next-to-next-to-leading (NNLO) order simultaneously within a projection formalism. The leading order comprises the impulse approximation of photons coupling to point-like nucleons with an anomalous magnetic moment. At NLO, we include renormalizations of the single nucleon operators. To this order, no unknown parameters enter. At NNLO, one f…
We investigate the effect of the deuteron breakup on the optical potential for the elastic scattering of 56 MeV deuterons from $^{51}$V. The breakup probabilities calculated within the post-form distorted wave Born-approximation theory of breakup reactions are fitted to derive the contribution to the optical potential from the breakup channels. The breakup potentials are found to have large real as well as imaginary parts. Thus the dynamical polarization potential due to the breakup process is expected to modify strongly the real part of the optical potential calculated by the double folding m…
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 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 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.
Point-form relativistic quantum mechanics is applied to elastic electron-deuteron scattering. The deuteron is modeled using relativistic interactions that are scattering-equivalent to the nonrelativistic Argonne $v_{18}$ and Reid '93 interactions. A point-form spectator approximation (PFSA) is introduced to define a conserved covariant current in terms of single-nucleon form factors. The PFSA is shown to provide an accurate description of data up to momentum transfers of 0.5 ${\rm GeV}^2$, but falls below the data at higher momentum transfers. Results are sensitive to the nucleon form factor p…
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.
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 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 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.
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.
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 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…
The elastic backward proton-deuteron scattering is analyzed including relativistic effects in the deuteron and the mechanism of this reaction which includes 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. It allows one to obtain 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.
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 contributions to the reaction cross section from the elastic and inelastic breakup processes, calculated within the post-form distorted wave Born-approximation theory, are used as constraints to determine the contributions to the imaginary part of the deuteron optical potentials (IPDOP) due to the breakup channels. The Coulomb part of this potential due to the elastic breakup process is seen to account for the long range absorption in the optical potential. The nuclear parts of the IPDOP due to the elastic and inelastic breakup modes peak in different regions of the nuclear surface, with t…
We investigate exchange current contributions to elastic electron-deuteron scattering using exactly Poincaré invariant quantum mechanics with a null-plane kinematic symmetry. Our model exchange current is motivated by one-pion-exchange physics. Exact current conservation and current covariance are satisfied by using this current to compute a linearly independent set of current matrix elements. The remaining current matrix elements are generated from the independent matrix elements using the covariance and current conservation constraints. The presence of the exchange current increases the sens…
Fully converged calculations of deuteron-deuteron elastic scattering observables are performed at energies above three- and four-body breakup threshold. Differential cross sections and analyzing powers are obtained using realistic nucleon-nucleon force models together with the Coulomb repulsion between protons. For all observables we find a very reasonable agreement with the available experimental data limited to deuteron beam energies up to 25.3 MeV.
We calculated response functions of the deuteron for charge exchange processes, including the final state interaction between two protons. Using them we evaluated the double differential cross section and polarization observables of $d(\vec{p},\vec{n})2p$ by means of plane wave impulse approximation with an optimal factorization. Calculation well reproduced the shape of the energy spectra of the cross section, though somewhat overestimated the magnitude. It also reproduced the spin observables well.
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…
We investigate the importance of the three-nucleon (3N) force contact terms in elastic nucleon-deuteron (Nd) scattering by applying the N$^4$LO$^+$ chiral semi-local momentum space (SMS) regularized nucleon-nucleon (NN) chiral potential supplemented by N$^2$LO and all subleading N$^4$LO three-nucleon force (3NF) contact terms. Strength parameters of the contact terms were obtained by least squares fitting of theoretical predictions to cross section and analyzing powers data at three energies of the impinging nucleon. Although the N$^3$LO contributions to the 3N force were completely neglected,…
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…
Spin-dependent total pbar-d cross sections are considered using the optical theorem. For this aim the full spin dependence of the forward pbar-d elastic scattering amplitude is considered in a model independent way. The single-scattering approximation is used to relate this amplitude to the elementary amplitudes of pbar-p and pbar-n scattering and the deuteron form factor. A formalism allowing to take into account Coulomb-nuclear interference effects in polarized pbar-d cross sections is developed. Numerical calculations for the polarized total pbar-d cross sections are performed at beam energ…
