Three-body Breakup Research Articles

Solutions to the three-body collisions breakup: A Sturmians approach

We study the dynamics of a three-body collisions breakup process. We write the solution as a sum of a scattered wave function and a defined initial state, which leads to a non-homogeneous Schrödinger equation. The scattering term is expanded in a basis of positive energy Sturmian functions with outgoing wave boundary conditions. The non-homogeneous Schrödinger equation is transformed into an algebraic problem which is solved with standard matrix techniques. We show that our wave function converges and gives excellent results when compared with simple, exact analytical models.

Dissociation dynamics of multiply charged CO2 by low energy ion impact using coincidence mapping

Dissociation dynamics of multiply charged CO2 has been studied by 1.2 MeVAr8+. The geometry of the excited states of the precursors undergoing three-body break-up has been estimated by Monte-Carlo simulation. It has been found that when more electrons are removed from the peripheral O atoms, bent dissociative structure of the parent molecular ion comes into play which gives non-zero momentum contribution to the central C atom.

Photodisintegration ofHe4intop+t

The two-body photodisintegration of $^4$He into a proton and a triton has been studied using the CEBAF Large-Acceptance Spectrometer (CLAS) at Jefferson Laboratory. Real photons produced with the Hall-B bremsstrahlung-tagging system in the energy range from 0.35 to 1.55 GeV were incident on a liquid $^4$He target. This is the first measurement of the photodisintegration of $^4$He above 0.4 GeV. The differential cross sections for the $\gamma$$^4$He$\to pt$ reaction have been measured as a function of photon-beam energy and proton-scattering angle, and are compared with the latest model calculations by J.-M. Laget. At 0.6-1.2 GeV, our data are in good agreement only with the calculations that include three-body mechanisms, thus confirming their importance. These results reinforce the conclusion of our previous study of the three-body breakup of $^3$He that demonstrated the great importance of three-body mechanisms in the energy region 0.5-0.8 GeV .

Quantum scattering theory on the momentum lattice

A new approach based on the wave-packet continuum discretization method recently developed by the present authors for solving quantum-mechanical scattering problems for atomic and nuclear scattering processes and few-body physics is described. The formalism uses the complete continuum discretization scheme in terms of the momentum stationary wave-packet basis, which leads to formulation of the scattering problem on a lattice in the momentum space. The solution of the few-body scattering problem can be found in the approach from linear matrix equations with nonsingular matrix elements, averaged on energy over lattice cells. The developed approach is illustrated by the solution of numerous two- and three-body scattering problems with local and nonlocal potentials below and well above the three-body breakup threshold.

Coulomb Breakup Reactions in Complex-Scaled Solutions of the Lippmann-Schwinger Equation

We propose a new method to describe three-body breakups of nuclei, in which the Lippmann-Schwinger equation is solved in combination with the complex scaling method. The complex-scaled solutions of the Lippmann-Schwinger equation (CSLS) enable us to treat boundary conditions of many-body open channels correctly and to describe a manybody breakup amplitude from the ground state. The Coulomb breakup cross section from the 6 He ground state into 4 He+n+n three-body decaying states as a function of the total excitation energy is calculated using CSLS, and the result well reproduces the experimental data. Furthermore, the two-dimensional energy distribution of the E1 transition strength is obtained and the importance of the 5 He(3/2 � ) resonance is confirmed. It is shown that CSLS is a promising method to investigate correlations of subsystems in three-body breakup reactions of weakly bound nuclei. Subject Index: 213, 221, 227

Big Bang Nucleosynthesis Reactions Catalyzed by a Long Lived Negatively Charged Leptonic Particle

An accurate quantum three-body calculation is performed for the new type of big-bang nucleosynthesis (BBN) reactions that are catalyzed by a long-lived negatively-charged, massive leptonic particle (called X^-) such as the supersymmetric (SUSY) particle stau. The reactions studied here includes, i) 4He-transfer reactions such as (4He X)+d --> 6Li+X, ii) radiative capture reactions such as (7Be X)+ p --> (8B X) + gamma, iii) three-body breakup reactions such as (7Li X)+ p --> 4He+4He+X, iv) charge-exchange reactions such as (p X)+4He -->(4He X) +p, and v) neutron induced reactions such as (8Be X)+ n -->9Be+X, where (A X) denotes a Coulombic bound state of a nucleus A and X^-. In recent papers it has been claimed that some of the catalyzed BBN reactions have significantly large cross sections so as to markedly change the abundances of some elements, not only giving a solution to the 6Li-7Li problem (calculated underproduction of 6Li by a factor of 1000 and overproduction of 7Li+7Be by a factor of nearly 3) but also imposing strong restrictions on the lifetime and the primordial abundance of X^-. However, most of the calculations of these reaction cross sections in the literature were performed assuming too naive models or approximations that are unsuitable for the complicated low-energy nuclear reactions. We use a high-accuracy few-body calculational method developed by the authors, and provide precise cross sections and rates of these catalyzed BBN reactions for use in the BBN network calculation.

CALCULATION OF PROTON-DEUTERON SCATTERING WITH COULOMB FORCE EFFECTS

A modified version of the Faddeev three-body equation to accommodate the long-range Coulomb interaction is applied to the proton-deuteron scattering problem at energies above the three-body breakup threshold. Numerical results for elastic and breakup cross sections in proton-deuteron scattering with effects of three-nucleon forces are compared with experimental data.

FOUR-NUCLEON BOUND STATE AND SCATTERING: EFFECT OF MANY-NUCLEON FORCES

The four-nucleon bound state and scattering below three-body breakup threshold are described. The description is based on a realistic coupled-channel potential which allows the excitation of a single nucleon to a Δ isobar. In the four-nucleon system the Δ isobar mediates effective two-, three- and four-nucleon forces. The effect of the four-nucleon force is found to be much smaller than the effect of the three-nucleon force.

COUPLED-CHANNELS ANALYSES OF 6He BREAKUP REACTIONS

We present analyses of breakup effects of 6 He on the elastic scattering by the continuum-discretized coupled-channels method, in which the reaction system is described as a four-body model, n+n+4 He +target. In this analysis, three-body breakup continuum of 6 He is discretized by daiagonalizing the internal Hamiltonian of 6 He in a space spanned by the Gaussian basis functions. The calculated elastic cross sections are in good agreement with the experimental data, which shows that nuclear and Coulomb breakup effects are significant.

Solving three-body scattering problems in the momentum lattice representation

A brief description of the novel approach toward solving few-body scattering problems in a finite-dimensional functional space of the ${L}_{2}$ type is presented. The method is based on the complete few-body continuum discretization in the basis of stationary wave packets. This basis, being transformed to the momentum representation, leads to the cell-lattice-like discretization of the momentum space. So the initial scattering problem can be formulated on the multidimensional momentum lattice, which makes it possible to reduce the solution of any scattering problem above the breakup threshold (where the integral kernels include, in general, some complicated moving singularities) to convenient simple matrix equations that can be solved on the real energy axis. The phase shifts and inelasticity parameters for the three-body $\mathit{nd}$ elastic scattering with MT I-III $\mathit{NN}$ potential both below and above the three-body breakup threshold calculated with the proposed wave-packet technique are in a very good agreement with the previous accurate benchmark calculation results.

Surface-integral formulation of scattering theory

We formulate scattering theory in the framework of a surface-integral approach utilizing analytically known asymptotic forms of the two-body and three-body scattering wavefunctions. This formulation is valid for both short-range and long-range Coulombic interactions. New general definitions for the potential scattering amplitude are presented. For the Coulombic potentials, the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the Coulomb three-body breakup amplitude are derived. This resolves the problem of the inability of the conventional scattering theory to define the post form of the breakup amplitude for charged particles. The new definitions can be written as surface-integrals convenient for practical calculations. The surface-integral representations are extended to amplitudes of direct and rearrangement scattering processes taking place in an arbitrary three-body system. General definitions for the wave operators are given that unify the currently used channel-dependent definitions.

Peripheral fragmentation of relativistic nuclei 11B in nuclear track emulsion

Data obtained from a nuclear track photoemulsion exposed to a beam of 11B nuclei with a momentum of 2.75 GeV/c per nucleon are reported. Peripheral interactions where the total charge of particles emitted within the forward cone of relativistic fragmentation is equal to the charge of the projectile nucleus are analyzed to study the clustering of the 11T nucleus. It is found that the three-body breakup of 2 + 2 + 1 charge configuration is a leading process. Tritons are revealed to play a crucial role in the most peripheral interactions of this type. Events interpreted as charge exchange of the 11B nucleus to excited states of the 11C* nucleus above the nucleon-coupling threshold were observed for the first time. Prospects for studying the 11C nucleus are discussed.

On account of Coulomb excitations of a target for the three-body break-up

The three-body break-up wavefunction asymptotics is reformulated to take into account only leading terms of the infinite number of Coulomb excitations of the target. The infinite tail of the Coulomb excitation contribution is summed up by the exact representation for the projection onto the subspace of Coulomb bound states.

Δ-isobar effects in the four-nucleon system

The four-nucleon bound state and scattering below three-body breakup threshold are described. The description is based on a realistic coupled-channel potential which allows the excitation of a single nucleon to a Δ isobar. In the four-nucleon system the Δ isobar mediates effective two-, three- and four-nucleon forces. The effect of the four-nucleon force is found to be much smaller than the effect of the three-nucleon force.

Momentum-space description of four-nucleon scattering

Four-nucleon scattering equations are solved in momentum space. The Coulomb interaction between the protons is included using the screening and renormalization approach. Realistic potentials are used between nucleon pairs. Results are obtained for all four-nucleon elastic and transfer reactions below three-body breakup threshold.

Collective Multipole Expansions and the Perturbation Theory in the Quantum Three-Body Problem

The perturbation theory with respect to the potential energy of three particles is considered. The first-order correction to the continuum wave function of three free particles is derived. It is shown that the use of the collective multipole expansion of the free three-body Green function over the set of Wigner $D$-functions can reduce the dimensionality of perturbative matrix elements from twelve to six. The explicit expressions for the coefficients of the collective multipole expansion of the free Green function are derived. It is found that the $S$-wave multipole coefficient depends only upon three variables instead of six as higher multipoles do. The possible applications of the developed theory to the three-body molecular break-up processes are discussed.

Three-body breakup in dissociative electron attachment to the water molecule

We report the results of ab initio calculations on dissociative electron attachment to water that demonstrate the importance of including three-body breakup in the dissociation dynamics. While three-body breakup is ubiquitous in the analogous process of dissociative recombination, its importance in low-energy dissociative electron attachment to a polyatomic target has not previously been quantified. Our calculations indicate that three-body breakup is a major component of the observed ${\mathrm{O}}^{\ensuremath{-}}$ cross section. Our studies suggest that the local complex potential model provides a generally accurate picture of the experimentally observed features in this polyatomic system.

Theoretical Model Calculation for d + 8Li Reaction

Based on the theoretical models for light nuclei, the calculations of reaction cross sections and the angular distributions for d + 8Li reaction are performed. Since all of the particle emissions are from the compound nucleus to the discrete levels, the angular momentum coupling effect in pre-equilibrium mechanism is taken into account. The three-body break-up process and the recoil effect are involved. The theoretical calculated results are compared to existing experimental data.

Three-Nucleon Continuum by Means of the Hyperspherical Adiabatic Method

This paper investigates the possible use of the Hyperspherical Adiabatic basis in the description of scattering states of a three-body system. In particular, we analyze a 1+2 collision process below the three-body breakup. The convergence patterns for the observables of interest are analyzed by comparison to a unitary equivalent Hyperspherical Harmonic expansion. Furthermore, we compare and discuss two different possible choices for describing the asymptotic configurations of the system, related to the use of Jacobi or hyperspherical coordinates. In order to illustrate the difficulties and advantages of the approach two simple numerical applications are shown in the case of neutron-deuteron scattering at low energies using s-wave interactions. We found that the optimization driven by the Hyperspherical Adiabatic basis is not as efficient for scattering states as in bound state applications.

Fragmentation dynamics of the methanol dication

Formation of di- and tri-atomic hydrogen molecular ions during the fragmentation of methanol dication is investigated by coincidence momentum imaging. Site-specific probability for such associative break-ups is determined. Two-body and three-body break-up channels involving association and migration of H atoms are identified. Three-body associative break-ups are found to occur sequentially, triggered by the loss of one H atom, followed by separation of charges. Based on the fragment momentum distributions we propose that H atom migration is induced in the first stage of a three-body sequential break-up, and suggest a structure for the intermediate dication.