Coupled Reaction Channels Method Research Articles

Reactions induced by 30 MeV 3He beam on 9Be : cluster transfer reactions* *Supported by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (AP14870958)

An experiment was conducted for studying the cluster structure of Be induced by He ions at an energy of 30 MeV. As results of the nuclear reaction 3He + 9Be, the differential cross sections for the exit channels – elastic, inelastic, α + 8Be, 6He + 6Be, 6Li + 6Li, and 7Be + 5He – were measured. Elastic and inelastic scattering data were treated within both the optical model and coupled channel method. A new set of optical potentials was considered for the elastic scattering. The deformation parameter was established for the transition . Cluster transfer reactions were analyzed via the coupled reaction channel method. The nuclear reactions with the exit channels 6He + 6Be, 6Li + 6Li, and 7Be + 5He were complemented by two-step transfer mechanisms. The contribution of each reaction mechanism were shown and compared with the findings of other authors.

Analysis of 6Li+16O system using different theoretical methods

In this paper, we report on the [Formula: see text] system to which the crystal model (CM), the coupled reaction channel method (CRC), and continuum discretized coupled channel (CDCC) method were applied in addition to the distorted waves-Born approximation (DWBA), which was also applied to the [Formula: see text] system. Also, CM is folded with inelastic scattering. The analysis of the experimental data was performed simply with elastic and inelastic scattering in a first step. Then transfers have been studied like pp, nn, dd, [Formula: see text] and [Formula: see text]B using the CRC method. The CRC method was used to study many suggested combinations of transfers with elastic scattering. The analyses were performed for 6Li elastically scattered from [Formula: see text]O in the energy range of 13–50[Formula: see text]MeV. The cluster structure of [Formula: see text] has been examined during the CDCC method in addition to the breakup of the weakly bound structure of the same nucleus. A dynamic polarization potential (DPP) was used at [Formula: see text][Formula: see text]MeV. A comparison between different models was performed. A general agreement was found between the experimental data and the proposed theoretical methods.

Пружне та непружне розсіяння іонів 15N ядрами 10В при енергії 81 МеВ. ізотопічні ефекти в розсіянні ядер 15N + 10В, 15N + 11В, 14N + 10В

New experimental data of angular distributions for the elastic and inelastic scattering of 15N ions by 10B nuclei were obtained at the energy Elab(15N) = 81 MeV. The experimental data were analyzed within the coupled-reaction channels method (CRC). The Woods - Saxon optical potentials were used for nuclei interactions in the calculations. The potential's parameters for the interaction of 15N + 10В nuclei were deduced as well as it was measured the angular distribution of the elastic scattering for these nuclei. The experimental data of the 15N + 10В elastic scattering are compared with data of the 15N + 11В and 14N + 10В scatterings. It was discovered isotopic effects in the scatterings of these three nuclear couples due to the difference in the optical potentials of the interaction of these nuclei and their structure. New experimental data of inelastic scattering of 15N + 10В nuclei for 0.718 - 3.587 МеV states of 10В nucleus and for 5.270 - 6.324 МеV states of 15N nucleus were measured. These data were analyzed within the CRC method using the translation-invariant shell model for collective excitations of 15N and 10B nuclei. Information about deformations of these nuclei was obtained.

Investigation the elastic scattering of isobar nuclei 6Li and 6He by 12C using different nuclear potentials

The available experimental data for the elastic scattering of isobar nuclei 6Li and 6He on [Formula: see text]C nuclei have been reanalyzed in a wide energy range of energy from 5.8[Formula: see text]MeV to 600[Formula: see text]MeV using the optical model with Distorted Wave Born Approximation (DWBA), and coupled reaction channel method (CRC) where inelastic scattering and transfer have been involved during calculations. A semi-microscopic potential, namely double-folding cluster model (DFC) has been used to investigate the cluster structure for both projectiles and target which was folded with Distorted Wave Born Approximation (DWBA) as a real part of potential where the imaginary part was taken in Woods–Saxon (WS) shape. The crystal model method has been applied to 6Li, 6He elastically scattered by [Formula: see text]C, and reliable analysis of the considered experimental data has been obtained.

Analysis of the alpha-transfer reaction in the 12C + 16O system using the semi-microscopic algebraic cluster model

In this work, we revisit the experimental data for elastic, inelastic and $\alpha$-transfer in the 12C + 16O system at 80 and 84 MeV using the coupled reaction channel method to analyze the angular distributions. The spectroscopic amplitudes relevant for the $\alpha$-transfer channel have been calculated from the semi-microscopic algebraic cluster model. The imaginary term of the optical potential was fitted to the experimental elastic scattering data at forward angles. Our calculations describe reasonable well the absolute cross sections for the inelastic scattering and $\alpha$-transfer. We discuss the effect of couplings on the transfer channel.

Mechanism of the 11B($\alpha$α,t)12C reaction at an energy of 40 MeV, role of exchange processes and collective excitations

The differential cross sections of triton from the 11B($\alpha$,t) reaction with transitions to the ground (0+) and excited states of the 12C nucleus at $ E_{x} = 4.44$ MeV (2+), 7.65 MeV (0+), 9.64 MeV (3-) and 14.08 MeV (4+) have been measured at an $\alpha$-particles energy of 40 MeV. Analysis of the measured angular distributions was carried out in the framework of the coupled reaction channels method considering the contribution of the 8Be cluster exchange mechanism. It is shown that the direct mechanism with proton transfer dominates at an energy of 40 MeV, and the heavy particle transfer is noticeable only at large angles. An exception is the transition to the 14.08 MeV (4+) state, which is possible only by the transfer of the 8Be cluster. It is established that the couplings between the excited states of 12C, arising from the nonsphericity of the nucleus, have little effect on the $ (\alpha, t)$ reaction cross sections in the forward hemisphere, but strongly affect the cross sections at large angles.

Elastic and inelastic scattering of 6Li + 18O versus 7Li + 18O and 6Li + 16O

Inverse kinematics scattering of 18 O on 6 Li at E lab ( 18 O) = 114 MeV was measured to obtain elastic and inelastic scattering cross sections. In this way cross sections for excited states in 6 Li and 18 O were determined. The data were analyzed within the optical model and coupled reaction channel method. The 6 Li + 18 O optical potential as well as the 6 Li and 18 O deformation parameters were deduced. Contributions of different nuclear processes to the 6 Li + 18 O elastic and inelastic scattering were explored. The isotopic differences between the 6,7 Li + 18 O and 6 Li + 16,18 O potential parameters were determined.

Effects of t- and α-transfer on the spectroscopic information from the reaction

Abstract Angular distributions of differential cross sections have been measured for elastic, inelastic scattering and the ( He 3 , d ) reaction on 6Li nuclei at the E lab ( He 3 ) = 34 MeV energy. The new and early obtained elastic scattering data at 34, 50, 60 and 72 MeV have been analyzed with Coupled Reaction Channels Method (CRC) taking into account triton transfer mechanism. The spectroscopic factors for t + He 3 configuration of 6Li were extracted. Parameters for real part of potential have been also calculated microscopically with double folding model. The differential cross sections for proton stripping to the 7Be ground and first excited states have been analyzed by modified DWBA and CRC methods at 34 MeV. The effect of triton and α exchange on proton transfer reaction Li 6 ( He 3 , d ) Be 7 for both ground and excited state is discussed. Spectroscopic factors and asymptotical normalization coefficients for p + Li 6 configuration of 7Be have been obtained from the experimental data.

Role of channel coupling and deuteron-exchange mechanisms in anomalous alpha-particle scattering on 6Li

A unified description of existing experimental data on alpha-particle scattering by 6Li over the broad energy range from 18 to 166 MeV was obtained with allowance for channel-coupling effects and mechanisms involving the exchange of a deuteron cluster. Angular distributions were analyzed on the basis of the optical model and the coupled reaction channels method. It was shown that the inclusion of channel coupling and the contributions from one- and two-step exchangemechanismsmakes it possible to describe special features of the behavior of differential cross sections for both elastic and inelastic scattering in a full energy range. Optimum values found for the parameters of optical potentials agree with the parameters of the global potential proposed previously for nuclei in the mass region A > 12.

Mechanisms of charge-exchange in the 12C( 7Li, 7Be) 12B reaction at the beam energy of 82 MeV

Angular distributions for the transitions to the ground and excited states of 12B from the 12C( 7Li, 7Be) 12B reaction at 82 MeV were measured. The data were analyzed in the framework of distorted wave born approximation for the direct charge-exchange and coupled reaction channels method for the two-step sequential nucleon transfers. It was shown that the two-step sequential nucleon transfer is the dominant mechanism in the investigated angular range and the direct mechanism becomes important only for small angles ( θ cm < 10 ° ).

Analysis of deuteron elastic scattering on 6,7Li up to 50 MeV

An analysis of the elastic scattering of deuterons on 6,7Li, for energies up to 50 MeV, has been carried out by using a phenomenological optical potential. Energy-dependent average parameters of the optical model potential have been obtained in the analysis of the corresponding real and imaginary volume integrals, pointing out an “anomalous” behavior of the real potential when the imaginary part approaches zero. This could be a consequence of the dispersion relations, but may be also related to the non-locality of the basic real potential term which introduces a slow and smooth energy dependence. On the other hand, the coupled reaction channels method has been used in order to describe the Li 6 ( d , d 0 ) Li 6 experimental angular distributions including the backward hemisphere at 14.7 and 19.6 MeV but not at 50 MeV. The comparison between the experimental and calculated elastic scattering angular distributions proves the reliability of the present average optical potentials, at variance with the extrapolation of the deuteron global potentials to other mass and energy domains.

Feshbach formalism, coupled reaction channels, and effective interactions

The Feshbach effective Hamiltonian for unsymmetrized rearrangement channels is used to obtain coupled reaction channels equations with effective interactions. Operators are introduced which solve nonorthogonality to all orders. Two representations of the effective Schr\"odinger equation are obtained with solved nonorthogonality. These equations have unique solutions, even when the basis used is overcomplete. The effective interactions in these equations are compared with those defined by Goldflam and Kowalski. Implications for the coupled reaction channels method are discussed.NUCLEAR REACTIONS Feshbach formalism for rearrangement channels. Coupled reaction channels. Nonorthogonality and overcomplete bases. Effective interactions.

The non-orthogonality problem of the coupled reaction channels method

The coupled reaction channels method is formulated as a two-step procedure. In the first step, the eigenvalue problem of the overlap operator is solved. In the second step, an off-shell transformation is applied to the coupled reaction channels equation. The transformed equation has an energy-independent interaction. Redundant solutions which arise when the test function space is linearly dependent, are removed from the physical part of the spectrum and become positive energy bound states at chosen (unphysical) energies. The non-orthogonality of test functions of different channels is related to the appearance of implicit distortion corrections.