Three-body Breakup Research Articles

Exploring three-body fragmentation of acetylene trication.

The three-body breakup of [C2H2]3+ formed in collision with Xe9+ moving at 0.5 atomic units of velocity is studied by using recoil ion momentum spectroscopy. Three-body breakup channels leading to (H+, C+, CH+) and (H+, H+, C2 +) fragments are observed in the experiment and their kinetic energy release is measured. The breakup into (H+, C+, CH+) occurs via concerted and sequential modes, whereas the breakup into (H+, H+, C2 +) shows only the concerted mode. By collecting events coming exclusively from the sequential breakup leading to (H+, C+, CH+), we have determined the kinetic energy release for the unimolecular fragmentation of the molecular intermediate, [C2H]2+. By using ab initio calculations, the potential energy surface for the lowest electronic state of [C2H]2+ is generated, which shows the existence of a metastable state with two possible dissociation pathways. A discussion on the agreement between our experimental results and these ab initio calculations is presented.

Pion absorption from the lowest atomic orbital in H2, H3 , and He3

The ${\ensuremath{\pi}}^{\ensuremath{-}}+^{2}\mathrm{H}\ensuremath{\rightarrow}n+n, {\ensuremath{\pi}}^{\ensuremath{-}}+^{3}\mathrm{H}\ensuremath{\rightarrow}n+n+n, {\ensuremath{\pi}}^{\ensuremath{-}}+^{3}\mathrm{He}\ensuremath{\rightarrow}n+d$, and ${\ensuremath{\pi}}^{\ensuremath{-}}+^{3}\mathrm{He}\ensuremath{\rightarrow}p+n+n$ capture reactions from the lowest $1S$ atomic orbitals are studied under full inclusion of final state interactions. Our results are obtained with the single-nucleon and two-nucleon transition operators derived at leading order in chiral effective field theory. The initial and final three-nucleon states are calculated with the chiral nucleon-nucleon semilocal momentum space potential up to ${\mathrm{N}}^{4}{\mathrm{LO}}^{+}$, augmented by the consistently regularized chiral ${\mathrm{N}}^{2}\mathrm{LO}$ three-nucleon potential. We found that absorption rates depend strongly on the nuclear pion absorption operator used, and its two-body parts change the rates by a few orders of magnitude. The final state interactions between nucleons generated by the two-nucleon forces are also important, while the three-nucleon interaction plays a visible role only in the ${\ensuremath{\pi}}^{\ensuremath{-}}+^{3}\mathrm{He}\ensuremath{\rightarrow}n+d$ reaction. Our absorption rate for the ${\ensuremath{\pi}}^{\ensuremath{-}}+^{2}\mathrm{H}\ensuremath{\rightarrow}n+n$ process is in good agreement with the experimental data from the hadronic ground-state broadening in pionic deuterium. The capture rates on $^{3}\mathrm{He}$ are also generally consistent with the spectroscopic data within error bars, though our central values are found to be systematically below the data. We show that for the three-body breakup processes the dominant contributions to the absorption rates arise from the quasi-free scattering and final-state interaction kinematical configurations.

Application of the Lagrange-mesh method in continuum-discretized coupled-channel calculations

We apply the Lagrange-mesh method to discretize continuum states of weakly bound nuclei for continuum-discretized coupled-channel (CDCC) calculations of three-body breakup reactions. This discretization method is compared with the bin method, which is regarded as the standard continuum discretization method, for the d and 6Li induced reactions. An improved Numerov algorithm is used to solve the coupled channels equations, which permits a fast integration of equations and a convenient treatment of the closed channels. A new CDCC model code named CDCC-R is developed. In all cases, the combination of the Lagrange-mesh method and the Numerov algorithm shows high efficiency and accuracy for the CDCC calculations of the elastic scattering and breakup reactions. Especially, various numerical and physical aspects are discussed for 6Li induced reactions. The coupling effects of the continuum states with high orbital angular momentum and closed channels are discussed. Moderate effects are found in the calculations for elastic scattering and breakup reaction when F- and G-wave continuum states are included in CDCC model space for 6Li induced reactions at the incident energies well above the Coulomb barrier. The closed channel effect is found to be indispensable for 6Li breakup reaction calculation when the incident energy is around the Coulomb barrier.

Bound and resonance states near the critical charge region in two-electron atoms

The critical nuclear charge ${Z}_{c}$ of the two-electron atoms below which the ground state transforms into a shape resonance and the critical stability of the system around ${Z}_{c}$ have been well established. However, the behavior of the shape resonance below ${Z}_{c}$ is still a mystery. By employing the complex-scaling method using Hylleraas configuration-interaction basis functions, we trace the trajectory of the shape resonance from ${Z}_{c}$ down to a very small nuclear charge. It is shown that at specific values of $Z$ far below ${Z}_{c}$ the resonance crosses over higher-lying one-electron thresholds, and when $Z$ is decreased below 0.316, the shape resonance lies above the three-body breakup threshold. We finally show that the imaginary part of the resonance energy at small nuclear charges can be modeled by the dispersion relation with a high-order Pad\'e approximant correction.

Electron-impact-like feature in triple fragmentation of CO23+ under slow proton impact

We have studied the three-body breakup of ${\mathrm{CO}}_{2}^{3+}$ created by the impact of slow ($v<1$ a.u.) protons on ${\mathrm{CO}}_{2}$. Employing the coincidence momentum imaging technique, we have obtained the correlated momenta of the three fragments, ${\mathrm{O}}^{+}+{\mathrm{C}}^{+}+{\mathrm{O}}^{+}$, and thence the kinetic energy release (KER) distribution. By examining the Dalitz plots for the three-body breakup, we separate the sequential and concerted breakup events and analyze the corresponding KER distributions. Based on the potential energy curves reported in the literature, we identify the possible transient states of ${\mathrm{CO}}_{2}^{3+}$ that lead to the different features in the KER distribution. We find that under ${\mathrm{H}}^{+}$ impact, the KER distribution shows a low-energy feature, which is seen in the case of electron impact, but not under the impact of slow or fast highly charged ions. This feature is identified as arising via the low-lying ${}^{2}\mathrm{\ensuremath{\Pi}}$ and ${}^{4}\mathrm{\ensuremath{\Pi}}$ states of the transient molecular ion. We further note that slow protons, which are the simplest of projectiles, are able to excite the ${\mathrm{CO}}_{2}$ molecule to a broad range of triply ionized transient states, spanning those accessed by the impact of slow highly charged ions and also those accessed by electron impact, but with varying probabilities.

Three-body breakup of 6He and its halo structure

The Borromean halo nucleus 6He has been studied by a kinematically complete measurement of Coulomb and nuclear breakup into α + 2n on Pb and C targets at 70 MeV/nucleon. Fully quantum-mechanical four-body breakup calculations reproduce the energy and angular differential cross sections below Erel∼1 MeV for both targets. The model used here reproduces the 6He ground-state properties as well as α-n and n-n scattering data and predicts an average opening angle 〈θnn〉 of 68∘ between the two halo neutrons. However, the model underestimates the breakup cross sections for higher Erel, indicating a possible contribution from the inelastic breakup. Alternatively, we examine the empirically modified calculations that reproduce the energy-differential cross sections for a wide range of scattering angles for both targets. The extracted B(E1) peaks at Erel∼1.4 MeV and amounts to 1.6(2) e2fm2 for Erel ≤ 20 MeV, resulting 〈θnn〉 = 56−10+9 degrees. In either interpretation, the current results show evidence of the dineutron spatial correlation in 6He.

A new technique for measurement of subrotational lifetime of molecular ions

Singly and multiply charged molecular ions are found in diverse environments and hold relevance for a wide range of research areas like combustion chemistry, accelerator physics, atmospheric sciences, plasma physics, astrophysics etc. Molecular dications are of special significance as they can be generated and studied comparatively easily in laboratory experiments. And they have enabled exploration of new and exciting phenomenon such as hydrogen migration, inter-atomic Coulombic decay, plasmonic excitations, orbital tomography etc. The lifetime of a molecular dication is one of its fundamental characteristics, whose measurement contributes to strengthening ab initio calculations and in predicting the concentration of its dissociation products. Most of the already reported lifetimes of molecular dications are in the range of nanoseconds to seconds and metastable states with lifetimes of the order of picoseconds have only been theoretical predicted and an experimental verification is pending. We present a method of measuring subrotational lifetimes of molecular dications formed in three-body sequential breakup of polyatomic molecular precursors. Specifically, we have measured the subrotational lifetime of hbox {SO}^{2+} , which is formed as an intermediate in the three-body sequential fragmentation of hbox {SO}_2^{3+}. The lifetime against dissociation is determined to be a fraction of the rotational period of hbox {SO}^{2+} and is of the order of few picoseconds. The method proposed is general and is not restricted to triatomic precursors.

Differentiating and Quantifying Gas-Phase Conformational Isomers Using Coulomb Explosion Imaging.

Conformational isomerism plays a crucial role in defining the physical and chemical properties and biological activity of molecules ranging from simple organic compounds to complex biopolymers. However, it is often a significant challenge to differentiate and separate these isomers experimentally as they can easily interconvert due to their low rotational energy barrier. Here, we use the momentum correlation of fragment ions produced after inner-shell photoionization to distinguish conformational isomers of 1,2-dibromoethane (C2H4Br2). We demonstrate that the three-body breakup channel, C2H4+ + Br+ + Br+, contains signatures of both sequential and concerted breakup, which are decoupled to distinguish the geometries of two conformational isomers and to quantify their relative abundance. The sensitivity of our method to quantify these yields is established by measuring the relative abundance change with sample temperature, which agrees well with calculations. Our study paves the way for using Coulomb explosion imaging to track subtle molecular structural changes.

Comprehensive measurements of cross sections and spin observables of the three-body break-up channel in deuteron-deuteron scattering at 65\xa0MeV/nucleon

Detailed measurements of five-fold differential cross sections and a rich set of vector and tensor analyzing powers of the ^{2}mathrm{H}({varvec{d}},dp){n} break-up process using polarized deuteron-beam energy of 65 MeV/nucleon with a liquid-deuterium target are presented. The experiment was conducted at the AGOR facility at KVI using the BINA 4pi -detection system. We discuss the analysis procedure including a thorough study of the systematic uncertainties. The results can be used to examine upcoming state-of-the-art calculations in the four-nucleon scattering domain, and will, thereby, provide further insights into the dynamics of three- and four-nucleon forces in few-nucleon systems. The results of coplanar configurations are compared with the results of recent theoretical calculations based on the Single-Scattering Approximation (SSA). Through these comparisons, the validity of SSA approximation is investigated in the Quasi-Free (QF) region.

Probing Few-Body Nuclear Dynamics via ^{3}H and ^{3}He (e,e^{'}p)pn Cross-Section Measurements.

We report the first measurement of the (e,e^{'}p) three-body breakup reaction cross sections in helium-3 (^{3}He) and tritium (^{3}H) at large momentum transfer [⟨Q^{2}⟩≈1.9 (GeV/c)^{2}] and x_{B}>1 kinematics, where the cross section should be sensitive to quasielastic (QE) scattering from single nucleons. The data cover missing momenta 40≤p_{miss}≤500 MeV/c that, in the QE limit with no rescattering, equals the initial momentum of the probed nucleon. The measured cross sections are compared with state-of-the-art abinitio calculations. Overall good agreement, within ±20%, is observed between data and calculations for the full p_{miss} range for ^{3}H and for 100≤p_{miss}≤350 MeV/c for ^{3}He. Including the effects of rescattering of the outgoing nucleon improves agreement with the data at p_{miss}>250 MeV/c and suggests contributions from charge-exchange (SCX) rescattering. The isoscalar sum of ^{3}He plus ^{3}H, which is largely insensitive to SCX, is described by calculations to within the accuracy of the data over the entire p_{miss} range. This validates current models of the ground state of the three-nucleon system up to very high initial nucleon momenta of 500 MeV/c.

Quasi-free limit in the deuteron-deuteron three-body break-up process

Detailed measurements of vector and tensor analyzing powers of the ^{2}{\rm H}(\vec d,dp){n} break-up process are presented. The data were obtained using a polarized deuteron-beam with an energy of 65 MeV/nucleon impinging on a liquid-deuterium target. The experiment was conducted at the AGOR facility at KVI using the BINA 4\piπ-detection system. The focus of this contribution is to analyze data of the dddd scattering process in the regime at which the neutron acts as a spectator, which we refer to as the quasi-free (QF) limit. To achieve this, events for which the final-state deuteron and proton are coplanar have been analyzed and the data have been sorted for various reconstructed momenta of the missing neutron. In the limit of vanishing neutron momentum and at small deuteron-proton momentum transfer, the data match very well with measured and predicted spin observables of the elastic deuteron-proton scattering process. The agreement deteriorates rapidly with increasing neutron momentum and deuteron-proton momentum transfer. The results of coplanar configurations in four-body phase space are compared with the results of recent available theoretical calculations based on the Single-Scattering Approximation.

Few-nucleon system dynamics studied via deuteron-deuteron collisions at 160 MeV

Four nucleon scattering at intermediate energies provides unique opportunities to study effects of the two key ingredients of the nuclear dynamics, the nucleon-nucleon P-wave (NNP-wave) and the three-nucleon force (3NF). This is possible only with systematic and precise data, in conjunction with exact theoretical calculations. Using the BINA detector at KVI Groningen, the Netherlands, a rich set of differential cross section of the ^{2}2H(d,dp)n breakup reaction at 160 MeV deuteron beam energy has been measured. Besides the three-body breakup, also cross sections of the ^{2}2H(d, ^{3}3He)n proton transfer reaction have been obtained. The data are compared to the recent calculations for the three-cluster breakup.

Breakdown of the Coulomb-explosion imaging technique induced by the ultrafast rotation of fragments

Coulomb-explosion imaging is a broadly employed technique to reconstruct the geometry of molecules from the direct multibody breakups of its ions. However, we reveal that this technique fails for a large class of systems, such as (${\mathrm{CO})}_{2}{}^{3+}$ and ${\mathrm{ArCO}}^{3+}$, since the events of the ``direct breakup channel'' are not the real direct breakups but the rapid sequential breakups with a short-lived and ultrafast-rotational fragment. Using Ar-CO as a prototype, we have investigated theoretically its Coulomb-explosion process. We find that due to the interfield between the metastable ${\mathrm{CO}}^{2+}$ and ${\mathrm{Ar}}^{+}$, ${\mathrm{ArCO}}^{3+}$ changes from its initial T shape into the more stable linear shape within 100 fs; such a rotation of ${\mathrm{CO}}^{2+}$ is hundreds of times faster than the field free case. Further, the advanced three-body surface hopping simulations indicate that the angle ${\ensuremath{\angle}}_{(\mathrm{Ar},\mathrm{CO})}$ has rotated from an initial ${95}^{\ensuremath{\circ}}$ to $110.6{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}$ on average before the Coulomb explosion, which agrees well with the one (${115}^{\ensuremath{\circ}}$) detected by Gong et al. [Phys. Rev. A 88, 013422 (2013)]. Furthermore, we point out that correct geometry of ArCO can be obtained from the three-body breakups with high kinetic-energy release ($>20$ eV).

Three body dissociation of

SynopsisMultiply charged ion impact induced three body fragmentation pathways of (q=3, 4) molecular ions have been studied using the technique of recoil ion momentum spectroscopy. An attempt has been made to distinguish the three-body breakup based on mechanism of dissociation, whether sequential or concerted.

Three-body breakup in deuteron-deuteron collisions at 160 MeV including quasifree scattering

A set of differential cross section of the three-body $^{2}$H($d$,$dp$)$n$ breakup reaction at 160 MeV deuteron beam energy are presented for 147 kinematically complete configurations near the quasi-free scattering kinematics. The experiment was performed at KVI in Groningen, the Netherlands using the BINA detector. The cross-section data have been normalized to the $^{2}$H($d$,$d$)$^{2}$H elastic scattering cross section. The data are compared to the recent single-scattering approximation (SSA) calculations for three-cluster breakup in deuteron-deuteron collisions. Confronting the SSA predictions with the experimental data shows that SSA provides the correct order of magnitude of the cross-section data. The studied energy is probably too low to meet the SSA assumptions which prevents better accuracy of the description.

Studies of Deuteron Breakup Reactions in Deuteron\u2013Deuteron Collisions at 160\xa0MeV with BINA

A rich set of differential cross section of the three-body ^{2}H(d,dp)n breakup reaction at 160 MeV deuteron beam energy has been measured over a large range of the available phase space. The experiment was performed at KVI in Groningen, the Netherlands, using the BINA detector. The cross-section data for the breakup reaction have been normalized to the simultaneously measured ^{2}H(d,d)^{2}H elastic scattering cross section. The breakup cross sections obtained for 147 kinematically complete configurations near the quasi-free scattering kinematics are compared to the recent approximate calculations for the three-cluster breakup in deuteron–deuteron collisions. The cross sections for 294 kinematic configurations of the quasi-free scattering regime, for which no theoretical calculations exist, are also presented. Besides the three-body breakup, semi-inclusive energy distributions for the four-body ^{2}H(d,pp)nn breakup are reported.

An Investigation of the Nuclear Reaction Near the Three-Body Break-up Threshold: As a Ultra Low Energy Nuclear Synthesis

We investigate the possibility of lanthanum (La)-nucleus creation via the reaction Cs(2d, gamma )La on the three-ion quasi-molecule hbox {CsD}_2 in the hbox {CsD}_2hbox {Pd}_{{12}}-cluster. In order to calculate d–Cs–d (or D–Cs–D) three-body bound states and wave functions, we adopt a very accurate three-body variational method with more than 80 figures. The hbox {CsD}_2 and La binding energies and wave functions are obtained with an S-wave trial functions. The wave function overlap (WFO) value between the La nuclear excited state and the several hbox {CsD}_2 quasi molecular modified states is calculated. It should be stressed that the WFO value is of critical importance for the existence of the electro-magnetic transition in the Cs(2d, gamma )La reaction. We found that the WFO value is very sensitive to the nuclear potential tail with a two- or three-body 1/r^2-type long range hadron potential, and gives a promising result for the reaction. The result is also followed by the three-body Faddeev calculation.

Making Sense of Coulomb Explosion Imaging.

A multifaceted agreement between ab initio theoretical predictions and experimental measurements, including branching ratios, channel-specific kinetic energy release, and three-body momentum correlation spectra, leads to the identification of new mechanisms in Coulomb-explosion (CE) induced two- and three-body breakup processes in methanol. These identified mechanisms include direct nonadiabatic Coulomb explosion responsible for CO bond-breaking, a long-range " inverse harpooning" dominating the production of H2+ + HCOH+, a transient proton migration leading to surprising energy partitioning in three-body fragmentation and other complex dynamics forming products such as H2O+ and H3+. These mechanisms provide general concepts that should be useful for analyzing future time-resolved Coulomb explosion imaging of methanol as well as other molecular systems. These advances are enabled by a combination of recently developed experimental and computational techniques, using weak ultrafast EUV pulses to initiate the CE and a high-level quantum chemistry approach to follow the resulting field-free nonadiabatic molecular dynamics.

Core-excitation effects in three-body breakup reactions studied using the Faddeev formalism

Previous studies of $(d,p)$ reactions in three-body (proton, neutron, nuclear core) systems revealed a nontrivial effect of the core excitation: the transfer cross section cannot be factorized into the spectroscopic factor and the single-particle cross section obtained neglecting the core excitation. This observable, up to a kinematic factor, is the angular distribution of the core nucleus in the $(p,d)$ reaction. The study of the core excitation effect for the most closely related observable in the $(p,pn)$ three-body breakup, i.e., the core angular distribution, is aimed in the present work. Breakup of the one-neutron halo nucleus in the collision with the proton is described using three-body Faddeev-type equations extended to include the excitation of the nuclear core. The integral equations for transition operators are solved in the momentum-space partial-wave representation. Breakup of 11Be nucleus as well as of model $A=11$ $p$-wave nuclei is studied at beam energies of 30, 60, and 200 MeV per nucleon. Angular and momentum distributions for the 10Be core in ground and excited states is calculated. In sharp contrast to $(p,d)$ reactions, the differential cross section in most cases factorizes quite well into the spectroscopic factor and the single-particle cross section. Due to different reaction mechanisms the core excitation effect in the breakup is very different from transfer reactions. A commonly accepted approach to evaluate the cross section, i.e., the rescaling of single-particle model results by the corresponding spectroscopic factor, appears to be reliable for breakup though it fails in general for transfer reactions.

Measurement of double-polarization asymmetries in the quasi-elastic [formula omitted] process

We report on a precise measurement of double-polarization asymmetries in electron-induced breakup of He3 proceeding to pd and ppn final states, performed in quasi-elastic kinematics at Q2=0.25(GeV/c)2 for missing momenta up to 250MeV/c. These observables represent highly sensitive tools to investigate the electromagnetic and spin structure of He3 and the relative importance of two- and three-body effects involved in the breakup reaction dynamics. The measured asymmetries cannot be satisfactorily reproduced by state-of-the-art calculations of He3 unless their three-body segment is adjusted, indicating that the spin-dependent part of the nuclear interaction governing the three-body breakup process is much smaller than previously thought.