Two-step Contributions Research Articles

Extracting the asymptotic normalization coefficient for the C14→B13+p overlap from the C14(B11,C12)B13 reaction

The availability of a comparatively complete data set for the elastic and inelastic scattering of a 45-MeV beam of $^{11}\mathrm{B}$ ions from a $^{14}\mathrm{C}$ target, together with an angular distribution for the $^{14}\mathrm{C}(^{11}\mathrm{B},^{12}\mathrm{C})^{13}\mathrm{B}$ proton pickup reaction enables a determination of the $\ensuremath{\langle}^{14}\mathrm{C}\ensuremath{\mid}^{13}\mathrm{B}+p\ensuremath{\rangle}$ asymptotic normalization coefficient (ANC) using the coupled reaction channel (CRC) technique. The complete nature of the data set allows two-step contributions to the reaction mechanism to be controlled while a set of $\ensuremath{\langle}^{12}\mathrm{C}\ensuremath{\mid}^{11}\mathrm{B}+p\ensuremath{\rangle}$ overlaps obtained from a consistent analysis of ($d,^{3}\mathrm{He}$) and ($e,{e}^{\ensuremath{'}}p$) data fixes the projectile overlaps. We find that the level of completeness of the modeling of the reaction mechanism has a significant effect on the value obtained for the ANC, with a distorted wave Born approximation analysis yielding a significantly larger ANC than the full CRC calculation. The final result obtained, when compared with the theoretical value calculated within the source term approach, is in accord with trends for proton removal from similar $p$-shell nuclei.

Investigation of two-photon emission in strong field QED using channeling in a crystal

We investigate the 2nd order process of two photons being emitted by a high-energy electron dressed in the strong background electric field found between the planes in a crystal. The strong crystalline field combined with ultra relativistic electrons is one of very few cases where the Schwinger field can be experimentally achieved in the electron's rest frame. The radiation being emitted, the so-called channeling radiation, is a well studied phenomenon. However only the first order diagram corresponding to emission of a single photon has been studied so far. We elaborate on how the 2 photon emission process should be understood in terms of a two-step versus a one-step process, i.e., if one can consider one photon being emitted after the other, or if there is also a contribution where the two photons are emitted 'simultaneously'. From the calculated full probability we see that the two-step contribution is simply the product of probabilities for single photon emission while the additional one-step terms are, mainly, interferences due to several possible intermediate virtual states. These terms can contribute significantly when the crystal is thin. Therefore, in addition, we see how one can, for a thick crystal, calculate multiple photon emissions quickly by neglecting the one-step terms, which represents a solution of the problem of quantum radiation reaction in a crystal beyond the usually applied constant field approximation. We explicitly calculate an example of 180 GeV electrons in a thin Silicon crystal and argue why it is, for experimental reasons, more feasible to see the one-step contribution in a crystal experiment than in a laser experiment.

Pionic enhancement in quasielastic(p⃗,n⃗)reactions at345MeV

Differential cross sections and a complete set of polarization observables have been measured for quasielastic $(\stackrel{P\vec}{p},\stackrel{P\vec}{n})$ reactions on $^{12}\mathrm{C}$ and $^{40}\mathrm{Ca}$ at a bombarding energy of $345\phantom{\rule{0.3em}{0ex}}\text{MeV}$. The laboratory momentum transfers are ${q}_{\text{lab}}\ensuremath{\simeq}1.2$, 1.7, and $2.0\phantom{\rule{0.3em}{0ex}}{\text{fm}}^{\ensuremath{-}1}$ for $^{12}\mathrm{C}$ and ${q}_{\text{lab}}\ensuremath{\simeq}1.7\phantom{\rule{0.3em}{0ex}}{\text{fm}}^{\ensuremath{-}1}$ for $^{40}\mathrm{Ca}$. In these momentum transfer regions, the isovector spin-longitudinal interaction is attractive where the one-pion exchange is dominant. The spin-longitudinal and spin-transverse polarized cross sections, $I{D}_{q}$ and $I{D}_{p}$, are deduced. The theoretically expected enhancement in the spin-longitudinal mode is observed at ${q}_{\text{lab}}\ensuremath{\simeq}1.7$ and $2.0\phantom{\rule{0.3em}{0ex}}{\text{fm}}^{\ensuremath{-}1}$. The observed $I{D}_{q}$ is consistent with the pionic enhanced $I{D}_{q}$ evaluated in distorted wave impulse approximation (DWIA) calculations employing random phase approximation (RPA) response functions. The enhanced $I{D}_{q}$ implies the existence of a precursor to pion condensation in nuclei. On the other hand, the theoretically predicted quenching in the spin-transverse mode is not observed. The observed $I{D}_{p}$ is not quenched, but rather enhanced relative to that predicted via the $\mathrm{DWIA}+\mathrm{RPA}$ calculations. Two-step contributions are responsible in part for the enhancement of $I{D}_{p}$.

Production of exotic Λ hypernuclei via mesonic beams

We study the production of neutron-rich hypernuclei Λ 12 Be, Λ 16 C, and Λ 10 Li by the (π −, K +) and (K −, π +) reactions in flight and treat two different mechanisms of production. The first mechanism is a two-step process with meson charge exchange (e.g., π − p → π 0 n, π 0 p → K +Λ). The other mechanism is one-step production (π − p → K +Σ−) proceeding via a small Σ− component, arising in Λ hypernuclei due to ΛN–ΣN coupling, as a doorway state. Typically, the two-step mechanism is more productive. The forward differential cross section of the 10B(π −,K +) reaction is about 70 nb/sr at an incident momentum of 1.05 GeV/c. On the other hand, the one-step process can serve as a direct measurement of the Σ admixture if the two-step contribution is suppressed by a suitable choice of the reaction kinematics.

Three-nucleon mechanisms in photoreactions

The 12C(γ,ppn) reaction has been measured for Eγ=150–800 MeV in the first study of this reaction in a target heavier than 3He. The experimental data are compared to a microscopic many body calculation. The model, which predicts that the largest contribution to the reaction arises from final state interactions following an initial pion production process, overestimates the measured cross sections and there are strong indications that the overestimate arises in this two-step process. The selection of suitable kinematic conditions strongly suppresses this two-step contribution leaving cross sections in which up to half the yield is predicted to arise from the absorption of the photon on three interacting nucleons and which agree with the model. The results indicate (γ,3N) measurements on nuclei may be a valuable tool for obtaining information on the nuclear three-body interaction.

Two-step contribution to the spin-longitudinal and spin-transverse cross sections of the quasielastic(p,n)reactions

The two-step contribution to the spin-longitudinal and the spin-transverse cross sections of ^{12}C,^{40}Ca(p,n) reactions at 494 MeV and 346 MeV is calculated. We use a plane-wave approximation and evaluate the relative contributions from the one-step and the two-step processes. We found that the ratios of the two-step to the one-step processes are larger in the spin-transverse cross sections than in the spin-longitudinal ones. Combining these results with the distorted-wave impulse approximation (DWIA) results we obtained considerable two-step contributions to the spin-longitudinal and the spin-transverse cross sections. The two-step processes are important in accounting for the underestimation of the DWIA results for the spin-longitudinal and the spin-transverse cross sections.

Cross sections and polarization observables for the40Ca(p,n)reaction at 345 MeV and multistep contributions in the continuum

The double-differential cross sections and analyzing powers over an angular range of $30\ifmmode^\circ\else\textdegree\fi{}l~{\ensuremath{\theta}}_{\mathrm{lab}}l~75\ifmmode^\circ\else\textdegree\fi{},$ and the induced polarizations P and polarization transfer values ${D}_{\mathrm{NN}}$ at $30\ifmmode^\circ\else\textdegree\fi{}$ and $40\ifmmode^\circ\else\textdegree\fi{}$ for the ${}^{40}\mathrm{Ca}(p,n)$ reaction are measured at a bombarding energy of 345 MeV. The data are compared with theoretical calculations in a semiclassical distorted wave (SCDW) model employing through three- and two-step contributions for cross sections and polarization observables, respectively. At forward angles, the SCDW calculations reproduce the observed cross sections fairly well around the quasielastic peak. The one-step contribution is dominant at ${\ensuremath{\theta}}_{\mathrm{lab}}=30\ifmmode^\circ\else\textdegree\fi{},$ while the two- and three-step contributions become more important with increasing reaction angle. At backward angles the calculations underestimate the cross sections in the whole region, which indicates the significance of higher-step contributions. The ${D}_{\mathrm{NN}}$ values, which are sensitive to the effective nucleon-nucleon interaction in the nuclear medium, are close to those calculated with the G-matrix interaction parametrized by the Melbourne group.

Two-Step Contribution to Intermediate Energy (p, p') and (p, n) Reactions

We calculate the two-step contribution to (p,p') and (p,n) reactions at intermediate energy. We describe the motion of the incident nucleon with plane wave and compare the contribution from the two-step processes with that from the one-step processes. To describe the two-step processes, we extende the response functions into the nondiagonal ones with respect to the momentum transfer q. We performed a numerical calculation for the cross sections of the $^{12}$C, $^{40}$Ca(p,p') scatterings and the spin longitudinal and the spin transverse cross sections of the $^{12}$C,$^{40}$Ca(p,n) reactions at 346 MeV and 494 MeV. We found that the two-step contribution is appreciable in comparison with the one-step processes in higher energy transfer region for the spin longitudinal and the spin transverse (p,n) reactions. We also found that the two-step processes give larger contribution to the spin transverse (p,n) reaction than to the spin longitudinal reaction. This finding is very encouraging to interpret the discrepancy between the DWIA calculation and the experimental results of the spin longitudinal and the spin transverse cross sections.

Theoretical developments in (e,2e) studies of excited states and in (e,3e) spectroscopy

The theory of single and double ionization of atoms deals with one of the most difficult problems in quantum mechanics: the scattering of a few charged particles. A large number of different (e,2e) experiments and theoretical calculations have helped us to understand the main physical mechanisms and their effect on the shape of triple differential cross section (TDCS). Recently the first deeply asymmetric (e,2e) experiments, leaving the residual ion in an excited state (which we indicate in this paper by (e,2e)*), and (e,3e) experiments have been performed. These offer new challenges to the theory. A very preliminary survey of main theoretical methods currently used to explain the experimental measurements is presented here. It will be shown that small differences in the choice of initial and final state models employed by different authors lead to large effects in both the shape and absolute size of the TDCS in the case of excitation ionization, even if these models give almost identical results for the (e,2e) case. A few physical mechanisms contributing to the (e,2e)* process are discussed in this paper. Special attention is given to the multichannel close-coupling method. (e,3e) experiments allow us to study the final state wave function with two continuum electrons. We obtain two unexpected results. First, we found that the two-step mechanism contribution is comparable and even bigger than that of shake-off. Second, the algorithms exploiting the angular decompositions of many-body continuum wave functions do not work in the case of long-range potentials; this is a result of the failure of the widely used diagonalization approximations in this case. The physical considerations that support these and other results are presented in this paper.

Glauber isovector spin responses for (p

The separated isovector spin-longitudinal and spin-transverse responses from a recent (p,n) quasifree experiment at 494 MeV are analyzed in a Glauber theory framework up to two-step contributions. Nuclear correlations are treated in the continuum random phase approximation, accounting for the spreading width of the particle-hole states. A good description of the spin-longitudinal response is achieved, hinting at some evidence of pionic effects in the quasielastic region. The spin-transverse response is underestimated and we show that multistep contributions, while sizable, are not sufficient to provide an explanation of the discrepancy.

Proton inelastic scattering to continuum studied with antisymmetrized molecular dynamics.

The intermediate energy (p,p\ensuremath{'}x) reaction is studied with antisymmetrized molecular dynamics (AMD) in the cases of ${\mathrm{Ni}}^{58}$ target with ${\mathrm{E}}_{\mathrm{p}}$=120 MeV and ${\mathrm{C}}^{12}$ target with ${\mathrm{E}}_{\mathrm{p}}$=200 and 90 MeV. Angular distributions for various ${\mathrm{E}}_{\mathrm{p}\ensuremath{'}}$ energies are shown to be reproduced well without any adjustable parameter, which shows the reliability and usefulness of AMD in describing light-ion reactions. Detailed analyses of the calculations are made in the case of ${\mathrm{Ni}}^{58}$ target and the following results are obtained: Two-step contributions are found to be dominant in some large angle region and to be indispensable for the reproduction of data. Furthermore, the reproduction of data in the large angle region \ensuremath{\theta}\ensuremath{\gtrsim}120\ifmmode^\circ\else\textdegree\fi{} for ${\mathrm{E}}_{\mathrm{p}\ensuremath{'}}$=100 MeV is shown to be due to three-step contributions. Angular distributions for ${\mathrm{E}}_{\mathrm{p}\ensuremath{'}}$\ensuremath{\gtrsim}40 MeV are found to be insensitive to the choice of different in-medium nucleon-nucleon cross sections ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{NN}}$ and the reason for this insensitivity is discussed in detail. On the other hand, the total reaction cross section and the cross section of evaporated protons are found to be sensitive to ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{NN}}$. In the course of the analyses of the calculations, comparison is made with the distorted wave approach.

A study of the reactions 14C(→d, d′) 14C and 14C(→d, p) 15C at 16.0 MeV

Cross-section and vector-analyzing-power measurements for 14C(d, d′) and 14C(d, p) reactions have been carried out for E d = 16 MeV. The inelastic-scattering data have been analyzed using the DWBA with a collective and a microscopic model form-factor and also by using the coupled-channels formalism with a vibrational model form-factor. It is observed that while the cross-section angular-distribution data for the two 2 + states at E x = 7.012 and 8.318 MeV are very similar, the corresponding vector analyzing powers are quite different. The results of the analyses indicate that the distinctive characteristics probably arise from the difference in the relative importance of the proton and neutron components in the transition amplitude. The 3 − state at E x = 6.728 MeV is identified as predominantly a 1p-3h state. Although the deformation parameters are relatively large, the single-particle structure aspects play a more dominant role than channel-coupling effects in populating the inelastic states. The transfer reaction data have been analyzed using the DWBA for bound and unbound states. The importance of two-step processes has been investigated via coupled-reaction-channels calculations. The g.s. and the states with excitation energies 0.770, 3.103 and 4.78 MeV in 15C are populated primarily by a one-step process with a small two-step contribution in the case of the 3.103 MeV state. The 4.22 MeV state is populated predominantly by two-step processes. The 4.78 and the 5.83 MeV states have been identified as 1p-2h and 3p-4h, 3/2 + state, respectively, in an earlier report. There is close similarity in the level structures and reaction mechanisms between the states of 15C and 17O populated via the (d, p) reaction.

Quasielastic nuclear scattering: a Glauber analysis

The nuclear quasielastic response in a continuum random phase approximation framework is discussed. Both (p,n) and (p,p′) reactions are considered, including one- and two-step contributions within a Glauber description.

Quasielastic nuclear response.

We explore the nuclear responses at intermediate energies, particularly in the spin longitudinal and spin transverse isovector channels, within the continuum random phase approximation framework. We also employ an extension of the standard random phase approximation to account for the spreading width of the single particle states through the inclusion of a complex and energy-dependent nucleon self-energy. The nuclear responses are then used as the basic ingredient to calculate hadronic reactions in the Glauber theory framework. Here both one and two-step contributions to the multiple scattering series in the quasi-elastic peak region are taken into account. We find evidence for shell effects in the one-step response and a strong dependence on the momentum regime of the two-step contribution.

Observation of two-step processes in the quasi-elastic reaction 12C(e, e′ p) 11B

The contribution of two-step processes in the reaction 12C(e, e′ p) 11B has been studied under quasi-elastic conditions. Cross sections were measured for the transitions to the 5 2 − state at an excitation energy of 4.445 MeV and the ( 7 2 −, 1 2 +) -doublet at 6.767 MeV in the missing momentum range between 140 MeV/ c and 220 MeV c. The excitation of the 5 2 − states, which was never observed before in (e, e′ p) experiments on 12C, can be quantitatively described as being due to a two-step process. A good description of the excitation of the ( 7 2 − , 1 2 +) doublet is obtained with a coupled-channels calculation includi both direct knock-out and two-step contributions.

The two-body electrodisintegration of 4He studied through the (e, e′p) reaction

Coincidence cross sections obtained with the (e, e′p) reaction are presented for the 4He nucleus. From the measurements, performed in non-parallel kinematics at a relative p- 3H kinetic energy in the center-of-mass system of 75 MeV, the proton-triton momentum distribution for recoil momenta up to 350 MeV/ c has been extracted. The results show a strong dependence on the kinematical configuration. In order to study this in more detail we extended the 4He(e,e′p) 3H experiments to other kinematics, both parallel and non-parallel, and compare these data to phenomenological and microscopic calculations. The phenomenological treatment consists of a distorted-wave impulse approximation (DWIA) analysis using an optical potential. Charge-exchange effects in the final state are accounted for through coupled-channels calculations using the Lane formalism. These phenomenological calculations do not agree with the data. The microscopic calculation, which employs a diagrammatic treatment including the charge-exchange process (e, e′n)(n, p), proton rescattering effects and the contributions from meson-exchange currents, accounts fairly well for the empirical observations. The momentum dependence of the data is compared with theoretical calculations obtained with the VMC and ATMS variational methods for the Urbana and RSC nucleon-nucleon potentials. The results for the Urbana V14 NN potential, including corrections to PWIA using the microscopic model, are in good agreement with the data. The (e, e′n)(n, p) two-step contribution turns out to be an important ingredient for obtaining a satisfactory description of the 4He(e, e′p) 3H cross sections. Sum-rule results are presented and the data are compared to results of (p, 2p) and other (e, e′p) experiments.

Bleaching of the bacteriochlorophyll monomer band: can absorption kinetics distinguish virtual from two-step electron transfer in bacterial photosynthesis?

The significance of absorption kinetics data in distinguishing between two-step and virtual mechanisms for the primary charge separation in reaction centers of photosynthetic bacteria is examined. A simple class of models is presented in which the transfer may occur predominantly by a virtual process and in which the intermediate state develops some small, but nonzero, transient population. The simplicity of the model allows both virtual and two-step contributions to the intermediate state population to be easily calculated. The authors find that the peak intermediate state population can be either close to 1 or very small (< 10{sup {minus}2}), depending on the system parameters such as electronic matrix elements, the energy denominator, and the lifetimes and dephasing rates in the electronic states. In particular, purely virtual transfer can yield a peak intermediate-state population of 10%. These calculations imply that observation of a small amount of bleaching in the bacteriochlorophyll monomer band does not necessarily rule out a virtual process.

Measurement of magnetic monopole transition in electron scattering from 16O as direct test of dispersive effects.

For the first time an experiment has been performed to measure a magnetic monopole transition in inelastic electron scattering. In $^{16}\mathrm{O}$ the ${0}^{+}$\ensuremath{\rightarrow}${0}^{\mathrm{\ensuremath{-}}}$ transition to the level at ${\mathit{E}}_{\mathit{x}}$=10.957 MeV has been observed with a cross section of d\ensuremath{\sigma}/d\ensuremath{\Omega}=(5.4\ifmmode\pm\else\textpm\fi{}3.8)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}37}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$/sr. Measurement of this transition is a direct signature of two-step contributions in electron scattering. Our measurement is in good agreement with the strength calculated for this transition.

The Imaginary Part of Channel-Coupling Potentials for 6Li-Induced Reactions

A microscopic estimate of imaginary coupling potentials used in coupled-channels calculations is performed for the 6Li+,oCa and 6Li+ Pb system in the framework of the Feshbach formalism. Two-step contributions to the imaginary potentials are calculated by taking account of the excitation of the target collective states in the intermediate states. The estimated strength of the potential is found to be too small by a factor of about 3 in comparison with the phenomenological one used in the microscopic coupled-channels analyses of 6Li scattering data by Sakuragi et a!.

The (p,d) reaction on 56Fe at 24.6 MeV

The authors have studied the (p,d) reaction on 56Fe, initiated by a 24.6 MeV polarised proton beam. Cross sections and analysing powers were obtained for nine states in the final nucleus 55Fe. These were compared with DWBA and CRC calculations, confirming spin and parity assignments. As opposed to the situation in 58Ni(p,d) no large two-step contributions were necessary for obtaining agreement with calculations.