Three-body Cross Sections Research Articles

Electron-heliumS-wave model benchmark calculations. II. Double ionization, single ionization with excitation, and double excitation

The propagating exterior complex scaling (PECS) method is extended to all four-body processes in electron impact on helium in an S-wave model. Total and energy-differential cross sections are presented with benchmark accuracy for double ionization, single ionization with excitation, and double excitation (to autoionizing states) for incident-electron energies from threshold to 500 eV. While the PECS three-body cross sections for this model given in the preceding article [Phys. Rev. A 81, 022715 (2010)] are in good agreement with other methods, there are considerable discrepancies for these four-body processes. With this model we demonstrate the suitability of the PECS method for the complete solution of the electron-helium system.

Bare-nucleus astrophysical factor of theHe3(d,p)He4reaction via the “Trojan horse” method

The $^{3}\mathrm{He}$($d,p$)$^{4}\mathrm{He}$ reaction has been studied from ${E}_{c.m.}=600$ keV down to astrophysical energies by means of the ``Trojan horse'' method using the $^{6}\mathrm{Li}$($^{3}\mathrm{He}$,$p\ensuremath{\alpha}$)$^{4}\mathrm{He}$ three-body reaction at ${E}_{\mathrm{lab}}=5$ and 6 MeV. Coincidence spectra were measured in kinematic conditions favoring the quasifree $^{3}\mathrm{He}+^{2}\mathrm{H}$ process. The bare astrophysical factor ${S}_{b}(E)$ for the $^{3}\mathrm{He}$($d,p$)$^{4}\mathrm{He}$ reaction was extracted from the three-body cross section in the modified plane-wave Born approximation. Comparison with the ${S}_{b}$ extrapolation from the free two-body data is presented. The independent estimate of the screening potential as obtained with the present work seems to confirm the theoretical adiabatic limit.

TheB11(p,α0)Be8reaction at sub-Coulomb energies via the Trojan-horse method

The $^{11}\mathrm{B}(p,{\ensuremath{\alpha}}_{0})^{8}\mathrm{Be}$ reaction was studied from $1\phantom{\rule{0.3em}{0ex}}\text{MeV}$ down to astrophysical energies by means of the Trojan-horse method applied to the $^{2}\mathrm{H}(^{11}\mathrm{B},{\ensuremath{\alpha}}_{o}^{8}\mathrm{Be})n$ three-body reaction performed at an incident energy of $27\phantom{\rule{0.3em}{0ex}}\text{MeV}$. Coincidence spectra measured in a kinematically complete experiment show the presence of the quasifree $^{11}\mathrm{B}\penalty1000-\hskip0ptp$ process. The astrophysical factor $S(E)$ for the $^{11}\mathrm{B}(p,{\ensuremath{\alpha}}_{0})^{8}\mathrm{Be}$ reaction was extracted from the three-body cross section at low neutron momentum. The result was compared with the behavior of the astrophysical factor from the directly measured two-body reaction.

Theory of the Trojan-Horse Method

The Trojan-Horse method is an indirect approach to determine the energy dependence of S factors of astrophysically relevant two-body reactions. This is accomplished by studying closely related three-body reactions under quasi-free scattering conditions. The basic theory of the Trojan-Horse method is developed starting from a post-form distorted wave Born approximation of the T-matrix element. In the surface approximation the cross section of the three-body reaction can be related to the S-matrix elements of the two-body reaction. The essential feature of the Trojan-Horse method is the effective suppression of the Coulomb barrier at low energies for the astrophysical reaction leading to finite cross sections at the threshold of the two-body reaction. In a modified plane wave approximation the relation between the two-body and three-body cross sections becomes very transparent. Applications of the Trojan Horse Method are discussed. It is of special interest that electron screening corrections are negligible due to the high projectile energy.

Theory of the Trojan–Horse method

The Trojan–Horse method is an indirect approach to determine the energy dependence of S factors of astrophysically relevant two-body reactions. This is accomplished by studying closely related three-body reactions under quasi-free scattering conditions. The basic theory of the Trojan–Horse method is developed starting from a post-form distorted wave Born approximation of the T-matrix element. In the surface approximation the cross-section of the three-body reaction can be related to the S-matrix elements of the two-body reaction. The essential feature of the Trojan–Horse method is the effective suppression of the Coulomb barrier at low energies for the astrophysical reaction leading to finite cross-sections at the threshold of the two-body reaction. In a modified plane wave approximation the relation between the two- and three-body cross-sections becomes very transparent. The appearing Trojan–Horse integrals are studied in detail.

Quasifree processes in the 6Li breakup reactions by alpha particles

The differential cross sections for the 6Li(α, 2α) 2H and the 6Li(α, 3He 5He) 2H reactions have been measured at the bombarding energy of 118.4 MeV. For both reactions, enhanced quasifree peaks were observed. The angular dependences of the two-body cross sections, deduced from the three-body cross sections by using DWIA, were compared with the free cross sections. For the 6Li(α, 2α) 2H reaction, the angular dependence for the quasifree scattering was similar to that for the free elastic scattering and the absolute cross sections were explained with a reasonable αd cluster probability in 6Li. So the quasifree scattering process seems consistent with the free scattering. For the 6Li(α, 3He 5He) 2H reaction, the angular dependence for the quasifree reaction process agreed with that for the free reaction; however, the absolute cross sections were about twice as large as those for the free reactions. This might be due to three-body structure effects in 6Li.

Pion absorption by 3He at the Delta -resonance energy.

Pion absorption by 3He was studied at Tπ=165 MeV in a kinematically complete experiment. The cross section for absorption on a (pn) pair of nucleons, σpn(π+), was found to be 17.0±2.6 mb; that for absorption on a (pp) pair, σpp(π-), 0.91±0.20 mb. The angular distribution in the πNN center-of-mass system for σpn(π+) resembles that for the π++d→p+p reaction while the angular distribution for σpp(π-) is strongly backward peaked. Evidence that a significant fraction of the absorptions involves all three target nucleons is seen in the angular correlation between the two detected nucleons as well as in the momentum distribution of the unobserved nucleon. For π+ and π- absorption, the three-body cross sections were found to be 9.6±2.1 and 4.2±01.2 mb, respectively. Neither initial- nor final-state interactions appear to be major contributors to the observed three-body absorption, though initial-state interactions may be contributing to the enhancement of the three-body π+ absorption at the Δ resonance.