Three-body Breakup Research Articles

Dissociation of methanol by ion-impact: Breakup dynamics, bond rearrangement and kinetic energy release

The dissociation dynamics of multiply charged methanol molecules formed in collision with 1.2 MeV Ar 8+projectiles is studied. Using coincidence mapping techniques, we can separate out the different dissociation pathways between carbon, oxygen and hydrogen ionic fragments as well as two- and three-body breakup events. Reactions involving intramolecular bond rearrangements within the CH 3 group of the dissociative molecule are discussed in detail. A signature of hydrogen migration in doubly charged methanol is observed. Kinetic energy releases of different breakup channels are reported here and compared with values calculated from a Coulomb explosion model. The shape and orientation of the islands in the coincidence map give further information about the momentum balance in the fragmentation process of two- or many-body dissociation pathways.

Full coupled-channel description of three-body and four-body breakup reactions

Recent development of the continuum-discretized coupled-channels method (CDCC) is reported with introducing the eikonal CDCC method (E-CDCC) and four-body CDCC. The former is applied to analysis of 8B breakup by 208Pb at 52 A MeV and the astrophysical factor S 17 ( 0 ) for the 7Be( p , γ ) 8B reaction is extracted with the asymptotic normalization coefficient method. We obtain S 17 ( 0 ) = 20.9 −1.9 +2.0 eV b , which is significantly larger than the previous one, S 17 ( 0 ) = 18.9 ± 1.8 eV b , determined from an analysis with the virtual photon theory. The difference between the two values is found to be due to the contributions from nuclear breakup and higher-order processes. The latter, four-body CDCC, is applied to 6He+ 209Bi scattering near the Coulomb barrier energy and found to reproduce the elastic cross sections well, in contrast to the standard three-body CDCC. Accurate treatment of the three-body continuum states of 6He turns out to be essential to correctly describe the 6He+ 209Bi scattering.

Four-nucleon system with Δ-isobar excitation

The four-nucleon bound state and scattering below three-body breakup threshold are described based on the realistic coupled-channel potential CD Bonn+Δ which allows the excitation of a single nucleon to a Δ isobar. The Coulomb repulsion between protons is included. In the four-nucleon system the two-baryon coupled-channel potential yields effective two-, three- and four-nucleon forces, mediated by the Δ isobar and consistent with each other and with the underlying two-nucleon force. The effect of the four-nucleon force on the studied observables is much smaller than the effect of the three-nucleon force. The inclusion of the Δ isobar is unable to resolve the existing discrepancies with the experimental data.

Three-body kinematical correlation in the dissociative recombination ofCH2+by three-dimensional imaging

A three-dimensional imaging technique installed at the Heidelberg Test Storage Ring (TSR) has been used to investigate the three-body breakup channels occurring in the dissociative recombination process of the methylene ion ${\text{CH}}_{2}^{+}$. By selecting dissociation planes perpendicular to the molecular beam direction the dissociation kinematics could be measured with unprecedented momentum resolution. Release energies, the relative branching ratio, and the kinematical correlations between the three fragments were determined for the two energetically allowed channels: $\text{C}(^{3}P)+\text{H}(^{2}S)+\text{H}(^{2}S)$ and $\text{C}(^{1}D)+\text{H}(^{2}S)+\text{H}(^{2}S)$.

Three-Body Breakup in the Dissociative Recombination of the Covalent Triatomic Molecular IonO3+

We report the first observation of almost exclusive three-body breakup in the dissociative recombination of a covalent triatomic molecular ion O3+. The three-body channel, constituting about 94% of the total reactivity, has been investigated in detail. The atomic fragments are formed in only the first two electronic states, 3P and 1D, while formation in the 1S state has not been observed. The breakup predominantly proceeds through dissociative states with linear geometry.

Operation of the Faddeev Kernel in Configuration Space

We present a practical method to solve Faddeev three-body equations at energies above the three-body breakup threshold as integral equations in coordinate space. This is an extension of a previously used method for bound states and scattering states below three-body breakup threshold energy. We show that breakup components in three-body reactions produce long-range effects on Faddeev integral kernels in coordinate space, and propose numerical procedures to treat these effects. Using these techniques, we solve Faddeev equations for neutron-deuteron scattering to compare with benchmark solutions.

Single and triple differential cross sections for double photoionization ofH−

The hydride anion ${\mathrm{H}}^{\ensuremath{-}}$ would not be bound in the absence of electron correlation. Since the double-photoionization process is exquisitely sensitive to electron correlation, one expects electron correlation effects to leave a strong signature on the double-ionization cross sections for ${\mathrm{H}}^{\ensuremath{-}}$. We present fully differential cross sections for the three-body breakup of ${\mathrm{H}}^{\ensuremath{-}}$ by single-photon absorption. The absolute triply and singly differential cross sections were obtained from ab initio calculations making use of exterior complex scaling within a discrete-variable-representation partial-wave basis. Results calculated at photon energies of 18 and $30\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ are compared with reported cross sections for helium calculated at $20\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ above the double-ionization threshold. These comparisons show a clear signature of initial-state correlations that differentiate the He and ${\mathrm{H}}^{\ensuremath{-}}$ cases.

Wave-packet continuum discretization method for solving the three-body scattering problem

We generalize the wave-packet continuum discretization method previously developed for the scattering problem to the three-body system. For each asymptotic channel, we construct a basis of three-body wave packets given by square-integrable functions. We show that the projections of the channel resolvents on the subspace of three-body wave packets are determined by diagonal matrices, whose eigenvalues we find explicitly. We express the amplitudes of 2→2 processes explicitly in terms of “wave-packet” finite-dimensional projections of the full resolvent. To illustrate our formalism, we calculate the differential cross section of elastic deuteron scattering on a heavy nucleus above the three-body breakup threshold and the s-wave quartet (n-d)-scattering amplitude. The results of the calculations agree well with the results obtained by other methods. In terms of complexity, the proposed scheme for solving the three-body scattering problem is comparable to solving a similar problem for bound states.

Four-nucleon scattering:Ab initiocalculations in momentum space

The four-body equations of Alt, Grassberger, and Sandhas are solved for $n\text{\ensuremath{-}}$$^{3}\mathrm{H}$ scattering at energies below three-body breakup threshold using various realistic interactions including one derived from chiral perturbation theory. After partial wave decomposition the equations are three-variable integral equations that are solved numerically without any approximations beyond the usual discretization of continuum variables on a finite momentum mesh. Large number of two-, three-, and four-nucleon partial waves are considered until the convergence of the results is obtained. The total $n\text{\ensuremath{-}}$$^{3}\mathrm{H}$ cross section data in the resonance region is not described by the calculations which confirms previous findings by other groups. Nevertheless the numbers we get are slightly higher and closer to the data than previously found and depend on the choice of the two-nucleon potential. Correlations between the ${A}_{y}$ deficiency in $n\text{\ensuremath{-}}d$ elastic scattering and the total $n\text{\ensuremath{-}}$$^{3}\mathrm{H}$ cross section are studied.

Three-body approaches for inclusive breakup reactions

The formal problem of three-body breakup in nuclear reactions is addressed. Two alternative treatments, namely, the direct breakup and transfer to the continuum approaches, are discussed and compared. Calculations for the reactions 8B+ 58Ni at 26 MeV and 6He + 208Pb at 22 MeV are presented and compared with existing data.

Bent dissociative states of CO22+

The geometry of the excited states of dicationic CO2 undergoing a three-body break-up has been estimated by momentum imaging of fragment ions. The momentum of the neutral fragment has been deduced from the momentum balance in the break-up. Our analysis shows that CO22+ has two electronic states with bent geometries which lead to three-body break-ups. We further propose that one of the dissociation channels follows from a bent symmetric stretch and the other from a bent asymmetric stretch. Analysis of the kinetic energy of the ions and of the momentum of the neutral fragment favours the proposition.

Coulomb breakup of the two-neutron halo nucleus 11Li

Coulomb breakup of the two-neutron halo nucleus 11Li has been investigated in a kinematically complete measurement of three-body breakup of 11Li on a Pb target at approximately 70 MeV/nucleon at RIKEN. Cross-talk events have been excluded without affecting the efficiency very much up to very low relative energy. The resultant preliminary B(E1) spectrum has revealed high (E1) strength at Erel (three-body relative energy) ∼0.3 MeV, which was missing in the previous measurements. This E1 strength with the help of the E1 cluster sum-rule indicates a significant neutron–neutron correlation in the ground state of 11Li.

Coulomb breakup effects on the elastic cross section ofHe6+Bi209scattering near Coulomb barrier energies

We accurately analyze the $^6$He+$^{209}$Bi scattering at 19 and 22.5 MeV near the Coulomb barrier energy, using the continuum-discretized coupled-channels method (CDCC) based on the $n$+$n$+$^4$He+$^{209}$Bi four-body model. The three-body breakup continuum of $^6$He is discretized by diagonalizing the internal Hamiltonian of $^6$He in a space spanned by the Gaussian basis functions. The calculated elastic and total reaction cross sections are in good agreement with the experimental data, while the CDCC calculation based on the di-neutron model of $^6$He, i.e., the $^2n$+$^{4}$He+$^{209}$Bi three-body model, does not reproduce the data.

ONE-PROTON AND TWO-PROTON RADIOACTIVITY OF THE (21+) ISOMER IN 94Ag

The properties observed for the one-proton and two-proton radioactivity of the (21+) isomer in 94 Ag are briefly summarized. The occurrence of both types of radioactivity from one and the same nuclear state is a unique phenomenon on the entire chart of nuclides. In particular, the first observation of energy correlations for two-proton radioactivity is discussed in comparison with predictions obtained from of a three-body breakup model. On the basis of this comparison it is tentatively suggested that the two protons are emitted simultaneously either from one of the poles or from opposite poles of a strongly deformed nucleus. Future experimental and theoretical studies are sketched which may help to explain this puzzling result.

Dissociative recombination of protonated methanol

The branching ratios of the different reaction pathways and the overall rate coefficients of the dissociative recombination reactions of CH3OH2+ and CD3OD2+ have been measured at the CRYRING storage ring located in Stockholm, Sweden. Analysis of the data yielded the result that formation of methanol or deuterated methanol accounted for only 3 and 6% of the total rate in CH3OH2+ and CD3OD2+, respectively. Dissociative recombination of both isotopomeres mainly involves fragmentation of the C-O bond, the major process being the three-body break-up forming CH3, OH and H (CD3, OD and D). The overall cross sections are best fitted by sigma = 1.2 +/- 0.1 x 10(-15) E(-1.15 +/- 0.02) cm2 and sigma = 9.6 +/- 0.9 x 10(-16) E(-1.20 +/- 0.02) cm2 for CH3OH2+ and CD3OD2+, respectively. From these values thermal reaction rate coefficients of k(T) = 8.9 +/- 0.9 x 10(-7) (T/300)(-0.59 +/- 0.02) cm3 s(-1) (CH3OH2+) and k(T) = 9.1 +/- 0.9 x 10(-7) (T/300)(-0.63 +/- 0.02) cm3 s(-1) (CD3OD2+) can be calculated. A non-negligible formation of interstellar methanol by the previously proposed mechanism via radiative association of CH3+ and H2O and subsequent dissociative recombination of the resulting CH3OH2+ ion to yield methanol and hydrogen atoms is therefore very unlikely.

Dissociative recombination of the weakly bound NO-dimer cation: Cross sections and three-body dynamics

Dissociative recombination (DR) of the dimer ion (NO)(2) (+) has been studied at the heavy-ion storage ring CRYRING at the Manne Siegbahn Laboratory, Stockholm. The experiments were aimed at determining details on the strongly enhanced thermal rate coefficient for the dimer, interpreting the dissociation dynamics of the dimer ion, and studying the degree of similarity to the behavior in the monomer. The DR rate reveals that the very large efficiency of the dimer rate with respect to the monomer is limited to electron energies below 0.2 eV. The fragmentation products reveal that the breakup into the three-body channel NO+O+N dominates with a probability of 0.69+/-0.02. The second most important channel yields NO+NO fragments with a probability of 0.23+/-0.03. Furthermore, the dominant three-body breakup yields electronic and vibrational ground-state products, NO(upsilon=0)+N((4)S)+O((3)P), in about 45% of the cases. The internal product-state distribution of the NO fragment shows a similarity with the product-state distribution as predicted by the Franck-Condon overlap between a NO moiety of the dimer ion and a free NO. The dissociation dynamics seem to be independent of the NO internal energy. Finally, the dissociation dynamics reveal a correlation between the kinetic energy of the NO fragment and the degree of conservation of linear momentum between the O and N product atoms. The observations support a mechanism in which the recoil takes place along one of the NO bonds in the dimer.

Three-body scattering at intermediate energies

The Faddeev equation for three-body scattering at arbitrary energies is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial-wave decomposition. In its simplest form, the Faddeev equation for identical bosons, which we are using, is a three-dimensional integral equation in five variables, magnitudes of relative momenta and angles. This equation is solved through Pad\'e summation. Based on a Malfliet-Tjon-type potential, the numerical feasibility and stability of the algorithm for solving the Faddeev equation is demonstrated. Special attention is given to the selection of independent variables and the treatment of three-body breakup singularities with a spline-based method. The elastic differential cross section, semiexclusive $d(N,{N}^{'}$) cross sections, and total cross sections of both elastic and breakup processes in the intermediate-energy range up to about 1 GeV are calculated and the convergence of the multiple-scattering series is investigated in every case. In general, a truncation in the first or second order in the two-body t matrix is quite insufficient.

P−dscattering with a nonlocal nucleon-nucleon potential below the breakup threshold

A short-range nonlocal nucleon-nucleon potential, which previously provided a better description for the three-nucleon bound states {sup 3}H and {sup 3}He then the local-potential models, is tested in p-d scattering calculations at energies below the three-body breakup threshold. This potential again provides an equivalent or better description of the experimental data than the local Argonne+3N force model.

Measurement of the asymmetries in 3 $ \overrightarrow{\sf He}$ (¯e, e′p)d and 3 $ \overrightarrow{\sf He}$ (¯e, e′p)np

The electron-target-asymmetries A_parallel and A_perpendicular with target spin parallel and perpendicular to the momentum transfer q were measured for both the two-- and three-body breakup of 3He in the 3He(e,e'p)-reaction. Polarized electrons were scattered off polarized 3He in the quasielastic regime in parallel kinematics with the scattered electron and the knocked-out proton detected using the Three-Spectrometer-Facility at MAMI. The results are compared to Faddeev calculations which take into account Final State Interactions as well as Meson Exchange Currents. The experiment confirms the prediction of a large effect of Final State Interactions in the asymmetry of the three-body breakup and of an almost negligible one for the two-body breakup.

Benchmark calculation for proton-deuteron elastic scattering observables including the Coulomb interaction

Two independent calculations of proton-deuteron elastic scattering observables including Coulomb repulsion between the two protons are compared in the proton laboratory energy region between 3 and 65 MeV. The hadron dynamics is based on the purely nucleonic charge-dependent AV18 potential. Calculations are done in both coordinate space and momentum space. The coordinate-space calculations are based on a variational solution of the three-body Schr\"odinger equation using a correlated hyperspherical expansion for the wave function. The momentum-space calculations proceed via the solution of the Alt-Grassberger-Sandhas equation using the screened Coulomb potential and the renormalization approach. Both methods agree to the order of 1% on all observables, showing the reliability of both numerical techniques in that energy domain. At energies below the three-body breakup threshold, the coordinate-space method remains favored; at energies higher than 65 MeV, the momentum-space approach seems to be more efficient.