Treatment of Coulomb Interaction in Momentum Space for p-3He Elastic Scattering

Applying the method proposed by C.M.Vincent and S.C.Phatak to p-³He elastic scattering,we studied the treatment of Coulomb interaction in momentum space.The differetial cross sections and spin observables at 500,400,300 and 200MeV are calculated.The present results are discussed and compared with previous results and experimental data.     

p－~3He弹性散射动量空间库仑作用的处理

将Ｒ．Ｃｒｅｓｐｏ和Ｊ．Ａ．Ｔｏｓｔｅｖｉｎ提出的方法，推广应用于自旋的散射，研究了ｐ—３Ｈｅ弹性散射动量空间库仑作用的处理．计算了２００－５００ＭｅＶ的微分散射截面和自旋观测量，并将其结果与Ｖ—Ｐ方法所得结果及实验结果进行了比较，显示出这种方法与Ｖ—Ｐ方法相比可应用的角动量和动量转移的范围更宽些．     

Treatment of Coulomb Interaction in Momentum Space for p-3He Elastic Scattering

Applying the method proposed by R.Crespo and J.A.Tostevin to p-³He elastic scattering,we study the treatment of Coulomb interaction of momentum space.The differential cross sections and spin observables at 500 and 300 MeV are calculated with R=7fm.The present results are compared with those given in V-P method.It shows that the applicable range of angular momentum and momentum transfer in R-J method are wider than those in V-P method.     

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.     

COULOMB CORRECTION OF THE p-4He LOW ENERGY SCATTERING PHASE SHIFTS

A simple approach of Coulomb correction to the p-⁴He low energy scattering phase shifts is proposed,in which the channel radius of each partial wave is taken as an adjustable parameter.By using the Coulomb correction the n-⁴He scattering observables predicted from p-⁴He scattering phase shifts are in excllent agreement with experiment.Our calculations show that the neutron polarization depends sensitively on the channel radius of p waves and the obtained channel radius are adeguate to the different sets of phase shifts.     

Recent developments in ab-initio few-body scattering calculations including the Coulomb interaction

Recent progress on the solution of ab-initio three- and four-nucleon scattering equations in momentum space that include the correct treatment of the Coulomb interaction is reviewed; results for specific observables in reactions initiated by p + d, p + ³He and n + ³He are shown. In addition three-body calculations of d + ¹²C reactions are compared with equivalent CDCC calculations.     

The A(y) problem for p-3He elastic scattering

We present evidence that numerically accurate quantum calculations employing modern internucleon forces do not reproduce the proton analyzing power, A(y), for p- 3He elastic scattering at low energies. These calculations underpredict new measured analyzing powers by approximately 30% at E(c.m.) = 1.20 MeV and by 40% at E(c.m.) = 1.69 MeV, an effect analogous to a well-known problem in p-d and n-d scattering. The calculations are performed using the complex Kohn variational principle and the (correlated) hyperspherical harmonics technique with full treatment of the Coulomb force. The inclusion of the three-nucleon interaction does not improve the agreement with the experimental data.     

Proton-proton scattering without Coulomb force renormalization

We demonstrate numerically that proton-proton (pp scattering observables can be determined directly by standard short-range methods using a screened pp Coulomb force without renormalization. In the examples the appropriate screening radii are given. We also numerically investigate solutions of the 3-dimensional Lippmann-Schwinger (LS) equation for a screened Coulomb potential alone in the limit of large screening radii and confirm analytically predicted properties for off-shell, half-shell and on-shell Coulomb t -matrices. These 3-dimensional solutions will form a basis for a novel approach to include the pp Coulomb interaction into the 3N Faddeev framework.     

Experimental Studies of Few-nucleon Systems at Intermediate Energies

Systems composed of 3 nucleons are a subject of precise experimental studies for many years. At the first stage the investigations were mainly focused on elastic nucleon-deuteron scattering, slowly extending to systematic measurements of the deuteron breakup reaction. Intermediate energies, below the threshold for pion production, deserve special attention: it is the region where comparison with exact theoretical calculations is possible, while the sensitivity to various aspects of interaction, like subtle effects of the dynamics beyond the pairwise nucleon-nucleon force, is significant. Moreover, the Coulomb interaction and relativistic effects show their influence in the observables of the breakup reaction. All these effects vary with energy and appear with different strength in certain observables and phase space regions, what calls for systematic investigations of a possibly rich set of observables determined in a wide range of energies. The next step in complication of the system are studies of reactions involving 4 nucleons—more sensitive, as expected, to subtle dynamics beyond the pairwise interaction. A brief survey of recent and planned experiments in the 3- and 4-nucleon systems is given.     

Ab-Initio Calculations of Four-Nucleon Elastic Scattering

We present microscopic calculations of low-energy scattering observables in all possible four-nucleon systems: n-³H, p-³He, and p-³H. Results were obtained by solving Faddeev-Yakubovski equations in configuration space, appropriately modified to include Coulomb and three-nucleon forces.     

Electromagnetic contributions to proton- and neutron-4He scattering

A proper treatment of various electromagnetic contributions toN-⁴He scattering enables one to determinen(p)-⁴He observables fromp(n)-⁴He data. Several calculations ofn-⁴He observables considering different electromagnetic effects are presented. It is shown that the contribution of thep-⁴He Coulomb corrections ton-⁴He polarizations and differential cross sections dominates over other electromagnetic effects forθ _c.m.≧30°. For smaller scattering angles, neutron magnetic scattering is important and produces a divergingn-⁴He differential cross section atθ=0° and a large peak (Mott-Schwinger effect) in the polarization. The influence of thep- andn-⁴He vacuum polarizations on then-⁴He observables is found to be small.     

Energy dependence of nucleon-deuteron elastic scattering observables and its bearing on the3 P J nucleon-nucleon interactions

The energy dependence of neutron-deuteron elastic scattering observables has been calculated from 5 to 45 MeV via rigorous three-nucleon calculations using the Bonn B nucleon-nucleon interaction. The goal of these calculations was to identify energy and angular regions that may be investigated experimentally to study the question of charge-symmetry breaking in the³ P _J nucleon-nucleon forces and/or Coulomb interactions. It was found that the measurement of the neutron-deuteron elastic analyzing power at 16 and 22.7 MeV and its comparison to proton-deuteron data obtained at the same incident energy is the most promising case for studying the issue of charge-symmetry breaking in the³ P _J nucleon-nucleon forces and/or Coulomb interactions.     

Selected Topics in Correlated Hyperspherical Harmonics

Correlated hyperspherical-harmonic basis functions are used to expand the three- and four-nucleon wave functions. Bound and scattering states are considered. Results for the binding energies of ³H, ³He, and ⁴He calculated using modern two- and three-nucleon forces are given and discussed. For scattering states, results for N-d differential cross section and vector analyzing powers are shown. The importance of the Coulomb and magnetic moment effects are discussed.     

Investigation of low-energy scattering in the nnpp system on the basis of differential equations for Yakubovsky components in configuration space

The s-wave differential equations for the Yakubovsky components characterizing the nnpp system have been solved by the method of cluster reduction. Two-cluster scattering at energies below the three-particle threshold in the singlet and triplet spin states has been considered. The MT I–III potential model has been used to simulate nucleon-nucleon interaction, and the Coulomb interaction between the protons has been taken into account. The singlet and triplet scattering lengths have been calculated for proton interaction with the triton (³H) and for neutron interaction with the ³He nucleus, and the deuteron-deuteron scattering length has also been determined. The low-energy behavior of the phase shifts and inelasticity factors in the corresponding scattering channels has been investigated. The features of the 0⁺ resonance in the ⁴He nucleus have been determined.     

P-Matrix approach and parameters of low-energy scattering in the presence of a Coulomb potential

The scattering of two charged strongly interacting particles is described on the basis of the P-matrix approach. In the P matrix, it is proposed to isolate explicitly the background term corresponding to purely Coulomb interaction, whereby it becomes possible to improve convergence of the expansions used and to obtain a correct asymptotic behavior of observables at high energies. The expressions for the purely Coulomb background P matrix, its poles and residues, and purely Coulomb eigenfunctions in the P-matrix approach are obtained. The nuclear-Coulomb parameters of the low-energy scattering of two charged hadrons are investigated on the basis of this approach combined with the method for isolating the background P matrix. Simple explicit expressions for the nuclear-Coulomb scattering length and effective range in terms of the residual P matrix are derived. For models of short-range strong interaction, these expressions give a general form of nuclear-Coulomb parameters for low-energy scattering. Specific applications of the general expressions derived in this study are exemplified by considering, on the basis of these expressions, some exactly solvable models of strong interaction, including the hard-core model, and, for these models, the nuclear-Coulomb parameters for low-energy scattering at arbitrary values of the orbital angular momentum are found explicitly for the first time. In particular, the nuclear-Coulomb scattering length and effective range are obtained explicitly for the boundary-condition model, the model of a hard-core delta-shell potential, the Margenau model, and the model of square-well hard-core potential.     

Proton-3He elastic scattering: A phase-shift analysis by a separable potential model

All the available experimental data (cross sections, projectile and target polarizations, polarization transfer coefficients) on p-³He elastic scattering up to ~10 MeV are analyzed on a unified basis in the framework of a separable potential model. This allows a phase-shift analysis which is model dependent, but is averaged over a wide energy interval (757 experimental points are reproduced by 27 model parameters). The calculations confirm some indications, already present in the literature, of a weak S-D tensor mixing, and strong singlet-triplet mixing in the P-states. Our conclusions are that probably the leading non-central effect is given by the coupling s₁ · l between the incident proton spin s₁ and the orbital angular momentum of relative motion. Finally, the phase shifts and observables are recalculated using the p-³He potential parameters, but switching off the Coulomb interaction. The results are compared with the (few) n-³H experimental cross sections of the literature, and the agreement is good, as expected on the basis of the charge-symmetry law.     

Annihilation of slow antiprotons in flight and in traps

The antiproton-nucleus annihilation in two possible experimental situations (low energy in-flight annihilation and annihilation in a trap) is investigated taking into account the Coulomb interaction. For these two cases, the formulas giving the relation between the antiproton-nucleus scattering lengtha _cs and observables (annihilation cross section and antiprotons time-of-life in a trap) are obtained. These relations are proposed to determinea _cs.     

Calculation of proton-deuteron breakup reactions including the Coulomb interaction between the two protons

The Coulomb interaction between the two protons is fully included in the calculation of proton-deuteron breakup with realistic interactions for the first time. The hadron dynamics is based on the purely nucleonic charge-dependent (CD) Bonn potential and its realistic extension CD Bonn +Delta to a coupled-channel two-baryon potential, allowing for single virtual Delta-isobar excitation. Calculations are done using integral equations in momentum space. The screening and renormalization approach is employed for including the Coulomb interaction. The Coulomb effect on breakup observables is seen at all energies in particular kinematic regimes.     

Investigating neutron polarizabilities through Compton scattering on 3He

We examine manifestations of neutron electromagnetic polarizabilities in coherent Compton scattering from the helium-3 nucleus. We calculate gamma3He elastic scattering observables using chiral perturbation theory to next-to-leading order [O(e2Q)]. We find that the unpolarized differential cross section can be used to measure neutron electric and magnetic polarizabilities, while two double-polarization observables are sensitive to different linear combinations of the four neutron spin polarizabilities.