Deuteron Breakup Differential Cross Sections and Analyzing Powers of {\overrightarrow{d} + p} Scattering at E d = 16 and 130 MeV

Deuteron breakup differential cross sections and analyzing powers for ${\overrightarrow{d} + p}$ scattering at E _d  = 16 and 130 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 amplitudes. Our results are very similar to those by the meson-exchange potentials, including disagreement for some specific kinematical configurations. The accurate and systematic KVI data at E _d  = 130 MeV are reasonably reproduced by taking the Coulomb cut-off radius ρ ≥ 16 fm.     

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 amplitudes. 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 E _d  = 130 MeV dp scattering are reasonably reproduced by taking the Coulomb cut-off radius ρ = 16 fm.     

Calculations of Three-Nucleon Reactions

Faddeev calculations using the chiral three-nucleon force in next-to-next-to-next-to-leading-order show that this force is too weak to provide an explanation for the low-energy A _y puzzle. The large discrepancy between data and theory for the neutron–neutron quasi-free-scattering cross section in low energy neutron–deuteron breakup requires a modification of the ${^{1}S_0}$ neutron–neutron force. We discuss the consequences that a bound ${^{1}S_0}$ state of two neutrons has on neutron–deuteron scattering observables. At higher energies we compare the solutions of the non-relativistic three-nucleon Faddeev equations with three-nucleon force included to the solutions of its Poincaré invariant version.     

Vector and Tensor Analyzing Powers in Deuteron�CProton Breakup

High precision data for vector and tensor analyzing powers of the ${^1{\rm {H}}(\vec{\rm{d}},\rm{{pp}})\rm{n}}$ breakup reaction at 130 and 100?MeV deuteron beam energies have been measured in a large fraction of the phase space. They are compared to the theoretical predictions based on various approaches to describe the three nucleon (3N) system dynamics. Theoretical predictions describe very well the vector analyzing power data, with no need to include any three-nucleon force effects for these observables. Tensor analyzing powers can be also very well reproduced by calculations in most of the studied region, but locally certain discrepancies are observed. At 130?MeV for A _xy such discrepancies usually appear, or are enhanced, when model 3N forces are included. Predicted effects of 3NFs are much lower at 100?MeV and at this energy equally good consistency between the data and the calculations is obtained with or without 3NFs.     

Quark-Model Nucleon–Nucleon Interaction Applied to Nucleon-Deuteron Scattering

We have examined the neutron-deuteron low-energy effective-range parameters, differential cross sections and spin polarization observables of the elastic nucleon-deuteron scattering up to the incident nucleon energy E _N  = 65 MeV, using the quark-model nucleon–nucleon interaction fss2. These observables are consistently described without introducing three nucleon forces except for the nucleon analyzing power A _y (θ) and the deuteron vector analyzing power iT ₁₁(θ) in the low-energy region E _N  ≤ 25 MeV. The long-standing A _y puzzle is slightly improved, but still remains. We have incorporated the screened Coulomb force to the proton-deuteron scattering, modifying the Vincent–Phatak approach for the sharp cutoff Coulomb force. The Coulomb effect on the elastic scattering observables is discussed.     

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 A _y 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.     

Relativistic Effects in Neutron�CDeuteron Elastic Scattering and Breakup

We solved the Faddeev equation in a Poincaré invariant model of the three-nucleon system. Two-body interactions are generated so that when they are added to the two-nucleon invariant mass operator (rest energy) the two-nucleon S matrix is identical to the experimental S matrix modeled with a given nucleon?Cnucleon interaction. Cluster properties of the three-nucleon S-matrix determine how these two-nucleon interactions are embedded in the three-nucleon mass operator. Differences in the predictions of the relativistic and corresponding non-relativistic models for elastic and breakup processes are investigated. Of special interest are effects of relativity on the elastic scattering angular distribution and total cross sections, the lowering of the A _y maximum in elastic nucleon-deuteron (Nd) scattering below ??25?MeV caused by the Wigner spin rotations and the significant changes of the breakup cross sections in certain regions of the phase-space.     

Four-Body Faddeev–Yakubovsky Equations Using Two-Cluster RGM Kernels: Applications to 4N and 4α Systems

Four-cluster Faddeev–Yakubovsky calculations using two-cluster RGM kernels are carried out for identical clusters. A precise ground-state energy of the α-particle, predicted by the quark-model nucleon–nucleon (NN) interaction fss2, is E _α  = ?26.61 MeV, including approximate effects of the Coulomb force and the charge dependence of the 2N force. The missing ?1.7 MeV in the experimental value ?28.3 MeV is about half of 3–4 MeV, predicted by modern meson-exchange 2N potentials, implying that almost half of 3–4 MeV is attributed to the off-shell effect of our nonlocal NN interaction fss2. As to the applications to four-α system, a method to eliminate the Faddeev redundant components from the basic Faddeev–Yakubovsky equations is proposed.     

Measurement of all Deuteron Analyzing Powers for {\overrightarrow{d} + p} Elastic Scattering at 294 MeV/Nucleon

We have measured all deuteron analyzing powers ${(A_{y}^{d}, A_{yy}, A_{xx}, A_{xz})}$ for deuteron-proton elastic scattering at 294 MeV/nucleon in order to study the properties of three nucleon forces (3 NFs). Measurement was made at in an angular range of ${\theta_{{\rm c.m.}} = 35.6^{\circ} - 163.0^{\circ}}$ . Obtained data were compared with Faddeev calculations with and without the 3 NFs. At ${\theta_{{\rm c.m.}}\lesssim 120^{\circ}}$ all the data have general agreement with the calculations, while the measured data at ${\theta_{{\rm c.m.}} \gtrsim 120^{\circ}}$ are not explained by any theoretical calculations. These results were consistent with those at 250 MeV/nucleon.     

Neutron–Deuteron Scattering Observables at E lab = 14.1 MeV

Inelastic neutron–deuteron scattering is studied on the basis of configuration-space Faddeev equations. Calculated are neutron–deuteron breakup amplitudes using AV14 nucleon–nucleon potential at incident neutron energy of 14.1 MeV. The results of calculations are presented for the differential cross sections under quasi free scattering and space–star configurations, and compared with those of the previous calculations and experimental data. The choice of the cutoff radius R _cutoff for asymptotic conditions is discussed.     

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.     

Experimental photoneutron cross sections of natural zirconium from 8 MeV to 134 MeV

The inclusive partial photoneutron cross sections and the total photoneutron cross section \(\sigma ^{(1)} (E_\gamma ) = \sum\limits_{i = 1}^{i_{\max } } {\sigma (\gamma ,in...)} \) for natural Zr have been measured from 8 MeV to 134 MeV, with monochromatic photons obtained by in flight annihilation of monoenergetic positrons. The integrated total photoneutron cross section up tillE _γ=140 MeV is (1.59±0.11)σ ₀, whereσ ₀ is the Thomas-Reiche-Kuhn sum-rule. The integrated total photonuclear absorption cross section is evaluated to be (1.73±0.15)σ ₀. The behaviour of the total photoneutron cross section as a function of Eγ, in the 40 MeV <E _γ<140 MeV energy range, is well described by a modified version of the quasideuteron model.     

Neutral pion photoproduction on tensor-polarized deuterium on the VEPP-3 storage ring

An experiment to measure component T ₂₀ of the tensor analyzing power for the coherent photo-production of neutral pions on polarized deuterons is described. The measurements cover the photon energies in the ranges E _γ = 200–500 MeV and E _γ = 300–600 MeV, and the emission angles of neutral pions in the ranges = \(\theta _{\pi ^0 }^{c.m.} \) = 100°–140° and = \(\theta _{\pi ^0 }^{c.m.} \) = 60°–65°, respectively. The experiment uses a hyperfine internal gas polarized target. Detectors of neutral pions and deuterons register these particles in coincidence. The target’s degree of polarization and luminosity is measured by detecting elastic electron-deuteron scattering at low momentum transfer. A selection of the preliminary results is presented.     

Investigations of Few-Nucleon System Dynamics in Medium Energy Domain

Precise and large set of cross sections, vector A _x , A _y and tensor A _xx , A _xy , A _yy analyzing powers for the ¹ H(d, pp)n breakup reactions were measured at 100 and 130 MeV deuteron beam energies with the use of the SALAD and BINA detectors at KVI and Germanium Wall setup at FZ-Jülich. Results are compared with various theoretical approaches which model the three-nucleon (3N) system dynamics. The calculations are based on different two-nucleon (2N) potentials which can be combined with models of the three-nucleon force (3NF) and other pieces of the dynamics can also be included like the Coulomb interaction and relativistic effects. The cross sections data reveal seizable 3NF and Coulomb force influence. In case of analyzing powers very low sensitivity to the effects was found and the data are well describe by 2N models only. At 130 MeV for A _xy serious disagreements appear when 3NF models are included into calculations.     

e08-008: Exclusive study of deuteron electrodisintegration near threshold

The study of threshold electrodisintegration of and elastic scattering on the only stable two nucleon system, the deuteron, can reveal specific aspects of the N-N interaction. The simplicity of electrodisintegration along with the simplicity of the deuteron makes this study most appropriate for revealing these interactions. By using an incident beam of polarized electrons and by measuring the polarization of the recoiling proton, the ratio of the electric (G _E ) and magnetic (G _M ) form factors for $d\left( {\vec e,e'\vec p} \right)$ (and $p\left( {\vec e,e'\vec p} \right)$ ) reactions may be extracted. This experiment was conducted in Hall A at Jefferson Lab in Newport News, Virginia using a beam of polarized electrons provided by the CEBAF Accelerator incident on a liquid deuterium (and hydrogen) target. The scattered electron and the recoiling (polarized) proton were detected using the High Resolution Spectrometers of Hall A. To determine the polarization of the recoil proton, an analyzing material was placed perpendicular to the protons trajectory through the spectrometer, in front of a set of straw chambers. Due to the spin-orbit interactions involved in the scattering of the proton from the analyzer material, asymmetries seen in the distribution of events detected by these straw chambers reveal the polarization of the recoil proton. By tracking the spin procession of the polarized protons from the straw chambers back to the target, the transferred and induced polarization of the proton may be determined. The (double-spin) asymmetries observed in the straw chambers will first be studied for the well-known elastic $p\left( {\vec e,e'\vec p} \right)$ process and compared to the asymmetries for $d\left( {\vec e,e'\vec p} \right)n\left( {x_B = 1} \right)$ . The analysis will then be repeated to determine how these asymmetries change with increasing x _B (to the kinematic limit for deuteron electrodisintegration).     

Spin Effects in the Interaction of Antiprotons with the Deuteron at Low and Intermediate Energies

Antiproton-deuteron scattering is analyzed within the Glauber theory, accounting for the full spin dependence of the underlying \({\bar{N}N}\) amplitudes. The latter are taken from the Jülich \({\bar{N}N}\) models and from a recently published new partial-wave analysis of \({\bar{p}p}\) scattering data. Predictions for differential cross sections and the spin observables \({A_y^d}\) , \({A_y^{\bar{p}}}\) , A _xx , A _yy are presented for antiproton beam energies up to about 300 MeV. The efficiency of the polarization buildup for antiprotons in a storage ring is investigated.     

Studies of the three-nucleon system dynamics: Cross sections of the deuteron-proton breakup at 130 MeV

The three-nucleon system is the simplest non-trivial testing ground in which the quality of modern nucleon-nucleon interaction models, as well as additional dynamical ingredients referred to as three-nucleon forces, can be probed quantitatively by means of a rigorous technique of solving the Faddeev equations. A large set of high precision, exclusive cross-section data for the $^1{\rm H}({\vec d},pp)n$ breakup reaction at 130?MeV was obtained at KVI, Groningen. It allowed to establish for the first time a clear evidence of the three-nucleon force contributions to the cross sections of the breakup process and to confirm recent predictions of sizable influences of the Coulomb force in this reaction.     

Relativistic effects in the 3N continuum and the A y puzzle

The three-nucleon (3N) Faddeev equation is solved in a Poincaré-invariant model of the three-nucleon system. Two-body interactions are generated so that when they are added to the two-nucleon invariant mass operator (rest energy) the two-nucleon S-matrix is identical to the non-relativistic S-matrix with a CD Bonn interaction. Cluster properties of the three-nucleon S-matrix determine how these two-nucleon interactions are embedded in the three-nucleon mass operator. Differences in the predictions of the relativistic and corresponding non-relativistic models for elastic and breakup processes are investigated. Of special interest are the lowering of the A _y maximum in elastic nucleon-deuteron (Nd) scattering below ≈25?MeV caused by the Wigner spin rotations and the significant changes of the breakup cross sections in certain regions of the phase space.     

Virtual breakup effects in elastic scattering of polarized deuterons

Elastic scattering of polarized deuterons at E_d = 56 MeV is investigated for ¹⁶O, ⁴⁰Ca, ⁵⁸Ni, ¹¹⁸Sn and ²⁰⁸Pb target nuclei by the use of folding interactions. Effects of virtual breakup of the deuteron to S- and D-states in the continuum region are taken into account by the CDCC method and are found to make indispensable contributions to cross sections and analyzing powers, where continuum-continuum couplings are substantial. The contribution of the D-state admixture in the ground state is important for the tensor analyzing powers. The calculated results agree well with experimental data. The invariant-amplitude method and the second-order sum rule study clarify the characteristic feature of the spin dependence of the effective interactions due to the virtual breakup. The near-side/far-side decomposition of scattering amplitudes illuminates the difference of the reaction mechanism between light and heavy target nuclei. The investigation for the ²⁰⁸Pb target at E_d = 21.5 MeV gives important information on the energy dependence of the effective interactions. The use of different parameter sets for the input nucleon-target optical potentials shows that the detailed results depend significantly on the choice of the parameter sets.     

Investigation of the Three-Nucleon System Dynamics in the Deuteron–Proton Breakup Reaction

Precise and large sets of cross section, vector A _x , A _y and tensor A _xx , A _xy , A _yy analyzing power data for the ¹ H(d, pp)n breakup reactions were measured at 100 and 130 MeV deuteron beam energies with the SALAD and BINA detectors at KVI and the Germanium Wall setup at FZ-Jülich. Results are compared with various theoretical approaches which model the three-nucleon system dynamics. The cross section data reveal a sizable three-nucleon force (3NF) and Coulomb force influence. In case of the analyzing powers very low sensitivity to these effects was found and the data are well describe by 2N models only. For A _xy at 130 MeV, serious disagreements were observed when 3NF models are included in the calculations.