0000000000623169
AUTHOR
A. M. Mukhamedzhanov
Proton-Hydrogen Charge Exchange and Elastic Scattering in the Faddeev Approach
Results of the application of Faddeev-type integral equations to proton-hydrogen collisions are reported. The approach, realized in the impact parameter representation, incorporates the exact two-particle off-shell Coulomb T-matrices in all ‘triangle’ contributions to the effective potentials. Calculatedtotal and differential electron-transfer as well as differential elastic scattering cross sections show very good agreement with experiment, over a wide range of incident energies.
Three-Body Coulomb Effects in the Direct Coulomb Breakup of 8B into 7Be + p in the Field of a 208Pb Ion
The amplitude for the Coulomb breakup of a light nucleus in the field of a highly charged ion is considered in the framework of the distorted wave approach, with particular emphasis being laid on correctly taking into account the three-body Coulomb interactions in the final state. Numerical calculations have been performed for the double differential cross section for the reaction 208Pb(8B, 7Be p)208Pb. They clearly demonstrate the importance of long-range three-body Coulomb correlations in the astrophysically interesting regime when the ejectiles have the extremely small relative energies.
Calculation of Proton-Deuteron Elastic Scattering at 10 MeV with a Realistic Potential
We present the first results of a calculation of the differential cross section and of polarization observables for proton-deuteron elastic scattering at 10thinspthinspMeV proton laboratory energy, for the Paris potential. The method used is the {open_quotes}screening and renormalization approach{close_quotes} which allows one to correctly take into account the Coulomb repulsion between the two protons. Comparison is made with the precise experimental data of Sagara {ital et al.}thinspthinsp[Phys.thinspthinspRev.thinspthinspC {bold 50}, 576 (1994)] and of Sperison {ital et al.}thinspthinsp[Nucl.thinspthinspPhys.thinspthinsp{bold A422}, 81 (1984)]. {copyright} {ital 1998} {ital The American …
Three-body approach to proton-hydrogen charge exchange and elastic scattering
The impact-parameter Faddeev approach to atomic three-body collisions which has been developed for, and successfully applied to, ion-atom scattering processes, has now been developed further by including, instead of the Coulomb potentials, the full two-particle off-shell Coulomb {ital T} matrices in all {open_quotes}triangle{close_quotes} contributions to the effective potentials. Results of calculations of proton-hydrogen collisions with only the ground states of the hydrogen retained in both the direct and the rearrangement channels are presented. Total and differential electron transfer, as well as differential elastic scattering cross sections, are obtained simultaneously in very good a…
First measurement of the 18O(p,α)15N cross section at astrophysical energies
International audience; The 18O(p,α)15N reaction rate has been deduced by means of the Trojan horse method. For the first time the contribution of the 20 keV resonance has been directly evaluated, giving a value about 35% larger than the one in the literature. Moreover, the present approach has allowed to improve the accuracy by a factor 8.5, as it is based on the measured strength instead of spectroscopic measurements. The contribution of the 90 keV resonance has been also determined, which turned out to be of negligible importance to astrophysics.
Exact and approximate triangle amplitudes for (in-)elastic three-body processes with charged particles
The triangle amplitudes, which within the framework of the multiple-scattering approach represent the leading contribution to the amplitude for three-body elastic and inelastic reactions, contain the off-shell Coulomb T-matrix describing the intermediate-state scattering of the projectile off each of the target particles. We present results of the exact numerical calculation of that amplitude in which the rescattering particles have charges of opposite sign (`attractive case'), for several atomic processes. This is facilitated by a `new' representation of the Coulomb T-matrix which turns out to be very effective for numerical purposes. One interesting result is that the charge sensitivity o…
Three-Body Coulomb Final-State Interaction Effects in the Coulomb Breakup of Light Nuclei
Coulomb breakup of a projectile in the Coulomb field of a fully stripped heavy nucleus is at present one of the most popular experimental methods to obtain information on reactions of interest in nuclear astrophysics. Its theoretical interpretation presents, however, considerable difficulties, due to the three-body nature and the infinite range of the Coulomb forces involved. Among the uncertainties affecting present analyses, the possible modification of the dissociation cross section by three-body Coulomb final-state interactions plays a major role. Various methods which have been proposed to deal with it are briefly reviewed. However, none of them is based on a consistent and mathematica…
Few-body problems in nuclear astrophysics
Few-body methods provide very useful tools to solve different problems important for nuclear astrophysics. Some of them are discussed below.
Triangle amplitude with off-shell CoulombTmatrix for exchange reactions in atomic and nuclear physics
The lowest-order rescattering contribution (triangle amplitude) in three-body models of exchange reactions with charged particles contains the off-shell two-body T matrix describing the intermediate-state Coulomb scattering of charged subsystems. General properties of the exact exchange triangle amplitude, when the incoming and outgoing particles are on the energy shell, are derived. This includes the analytic behavior, i.e., the positions and characters of its leading singularities, in the cos\ensuremath{\vartheta} plane, where \ensuremath{\vartheta} is the scattering angle, in the vicinity of the forward- and backward-scattering directions. Since for computational reasons the Coulomb T ma…
A novel approach to measure the cross section of the 18O(p, α)15N resonant reaction in the 0-200 keV energy range
The 18O(p, ?)15N reaction is of primary importance to pin down the uncertainties, due to nuclear physics input, affecting present-day models of asymptotic giant branch stars. Its reaction rate can modify both fluorine nucleosynthesis inside such stars and oxygen and nitrogen isotopic ratios, which allow one to constrain the proposed astrophysical scenarios. Thus, an indirect measurement of the low-energy region of the 18O(p, ?)15N reaction has been performed to access, for the first time, the range of relevance for astrophysical application. In particular, a full, high-accuracy spectroscopic study of the 20 and 90 keV resonances has been performed and the strengths deduced to evaluate the r…
Three-body Coulomb interaction effects in the final state of thePb208(B8,Be7p)Pb208Coulomb breakup reaction
The photodissociation reaction $^{8}\mathrm{B}+\ensuremath{\gamma}\ensuremath{\rightarrow}^{7}\mathrm{Be}+p$ is used to provide information on the astrophysical ${S}_{17}$ factor of the inverse radiative capture reaction, knowledge of which is crucial for an estimation of the high-energy neutrino flux from the sun. Since, at present, the Coulomb field of a fully stripped nucleus serves as the source of the photons, an adequate analysis requires a genuine three-body treatment of this reaction. Among the uncertainties still affecting present analyses, the possible modification of the dissociation cross section by the post-decay acceleration of the fragments $^{7}\mathrm{Be}$ and p in the targ…
About Compactness of Faddeev Integral Equations for Three Charged Particles
Momentum space three-body integral equations of the Faddeev type can not be used for Coulomb-like potentials, for energies above the breakup threshold. The reason is the occurrence of singularities in their kernels which destroy the compactness properties known to exist for purely short-range interactions. Using the rigorously equivalent formulation in terms of an effective-two- body theory, we prove that the nondiagonal kernels occurring therein possess on and off the energy shell only integrable singularities, provided all three particles have charges of the same sign (ie., only repulsive Coulomb interactions). In contrast, if some of the charges have opposite signs the nondiagonal kernel…
Final State Three-Body Coulomb Effects in thePb208(B8,Be7p)Pb208Coulomb Breakup Reaction
We present results of the first calculation of the double differential cross section for the 208Pb(8B,(7)Bep)208Pb Coulomb breakup reaction which treats the postdecay acceleration of the ejectiles within a genuine three-body approach. From this we conclude that, in order to minimize postdecay Coulomb acceleration effects, experiments should be performed at as small as possible scattering angles, not too low 7Be-p relative energies, and high incident energy.
Approximate triangle amplitude for three-body charge exchange processes.
The single-rescattering contribution to the amplitude pertaining to three-body charge exchange reactions (triangle amplitude) contains the off-shell Coulomb {ital T}-matrix {ital T}{sup {ital C}} describing the intermediate-state Coulomb scattering of charged subsystems. For ease of computation, the latter is usually replaced by the potential {ital V}{sup {ital C}} which, however, is unsatisfactory in many cases. An alternative approximation, obtained by {open_quote}{open_quote}renormalizing{close_quote}{close_quote} the {open_quote}{open_quote}triangle{close_quote}{close_quote} contribution with {ital V}{sup {ital C}} instead of {ital T}{sup {ital C}} by a simple analytic expression, is sh…
Energetic collisions of charged projectiles with atomic bound states
Abstract Use of the multiple-scattering expansion of the three-body amplitude for atomic direct and exchange reactions requires the evaluation of multidimensional integrals involving the two-body Coulomb T-operator. We present here numerical results for the first-order terms, both for the attractive and repulsive case. Furthermore, easy-to-calculate approximations are described which in their domain of validity (i) reproduce the exact amplitudes to high accuracy, and (ii) also serve to derive interesting theoretical results.
New High-Precision Measurement of the Reaction Rate of the 18O(p, α)15N Reaction via THM
The 18O(p,alpha)15N reaction rate has been extracted by means of the Trojan-Horse method. For the first time the contribution of the 20-keV peak has been directly evaluated, giving a value about 35% larger than previously estimated. The present approach has allowed to improve the accuracy of a factor 8.5, as it is based on the measured strength instead of educated guesses or spectroscopic measurements. The contribution of the 90-keV resonance has been determined as well, which turned out to be of negligible importance to astrophysics.
Proton-Deuteron Elastic Scattering for E > 0
We report on the first reliable numerical results for proton-deuteron elastic scattering observables for energies above the deuteron breakup thresh- old, for the Paris potential. The calculations have been performed within the screening and renormalisation approach. The theoretical results are compared with recent experimental data.
Momentum space integral equations for three charged particles: Nondiagonal kernels
Standard solution methods are known to be applicable to Faddeev-type momentum space integral equations for three-body transition amplitudes, not only for purely short-range interactions but also, after suitable modifications, for potentials possessing Coulomb tails provided the total energy is below the three-body threshold. For energies above that threshold, however, long-range Coulomb forces have been suspected to give rise to such severe singularities in the kernels, even of the modified equations, that their compactness properties are lost. Using the rigorously equivalent formulation in terms of an effective-two-body theory we prove that, for all energies, the nondiagonal kernels occurr…