Coupled-channel Framework Research Articles

Effects ofβ6deformation and low-lying vibrational bands on heavy-ion fusion reactions at sub-barrier energies

We study fusion reactions of $^{16}$O with $^{154}$Sm, $^{186}$W and $^{238}$U at sub-barrier energies by a coupled-channels framework. We focus especially on the effects of $\beta_{6}$ deformation and low-lying vibrational excitations of the target nucleus. It is shown that the inclusion of $\beta_{6}$ deformation leads to a considerable improvement of the fit to the experimental data for all of these reactions. For the $^{154}$Sm and $^{238}$U targets, the octupole vibration significantly affects the fusion barrier distribution. The effect of $\beta$ band is negligible in all the three reactions, while the $\gamma$ band causes a non-negligible effect on the barrier distribution at energies above the main fusion barrier. We compare the optimum values of the deformation parameters obtained by fitting the fusion data with those obtained from inelastic scatterings and the ground state mass calculations. We show that the channel coupling of high multipolarity beyond the quadrupole coupling is dominated by the nuclear coupling and hence higher order Coulomb coupling does not much influence the optimum values of $\beta_4$ and $\beta_6$ parameters. We also discuss the effect of two neutron transfer reactions on the fusion of $^{16}$O with $^{238}$U.

The JLM model for nucleon scattering off strongly deformed nuclei up to 200 MeV

In this work we introduce new developments of our nucleon-nucleus optical model potential (OMP) built from the nuclear matter (NM) approach of Jeukenne, Lejeune and Mahaux (JLM). Having selected prescriptions for the local density approximation (LDA) and using nuclear densities obtained from Hartree-Fock-Bogoliubov (HFB) calculations, the normalizations of the potential depth are carefully optimized and given functional forms that represent their variations with projectile energy over a broad mass and energy range for incident protons an neutrons. These OMPs, used in the coupled channel framework, produce good predictions of neutron and proton scattering and reaction measurements available up to 200 MeV for deformed rigid nuclei in the range A=80–240.

Klein-Gordon equation in a coupled channels description of elastic and inelastic scattering

We show that, in contrast to the case of elastic scattering of spinless particles from composite targets, Klein-Gordon dynamics is not a natural choice for the description of their inelastic scattering in the standard coupled channels method. We propose one way to overcome the difficulty, showing that Klein-Gordon dynamics may be used in practical calculations within the coupled channels framework provided that the optical potential is modified in a straightforward manner.

Breakup of 30 MeV/u- 16O in nuclear and Coulomb fields of 120Sn and 208Pb Nuclei

Coincidence measurements of α- 12C pairs collinearly emitted in the breakup of 30 MeV/u- 16O incident on 208Pb and 120Sn were performed with a two detector system set up along the focal plane of a magnetic spectrograph. Double differential cross sections for sequential breakup via the 2 2 + and 2 3 + states in 16O were analyzed within the framework of coupled-channels (CC) calculations which incorporated microscopic α- 12C cluster model wave functions for bound and unbound states of 16O. The experimental data are satisfactorily reproduced by the CC calculations to within a factor of two. The results are discussed in terms of the interference between nuclear- and Coulomb-breakup amplitudes.

Coupled channel folding model description of alpha scattering from 9Be.

Alpha scattering from $^{9}\mathrm{Be}$ at ${\mathit{E}}_{\mathrm{\ensuremath{\alpha}}}$= 65 MeV is described in the coupled channel framework with phenomenological as well as folded potentials. The multipole components of the deformed density of $^{9}\mathrm{Be}$ are derived from Nilsson model wave functions. Reasonably good agreements are obtained for the angular distributions of 3/${2}^{\mathrm{\ensuremath{-}}}$(g.s.) and 5/${2}^{\mathrm{\ensuremath{-}}}$(2.43 MeV) states of the ground state band with folded potentials. The deformation predicted by the model corroborates with that derived from the phenomenological analysis with potentials of different geometries.

Simultaneous microscopic description of 16O( gamma,n) and 16O( gamma,p) including Delta degrees of freedom.

The photonuclear reactions $^{16}\mathrm{O}$(\ensuremath{\gamma},n${)}^{15}$O and $^{16}\mathrm{O}$(\ensuremath{\gamma},p${)}^{15}$N are simultaneously described within a coupled channels framework based on a continuum shell model formulation that includes all nonlocalities arising from antisymmetrization. This large-scale conventional many-body calculation provides a good description of the medium energy data. The inclusion of \ensuremath{\Delta}(1232) degrees of freedom further, but slightly, improves the description of the available data. Complete quantitative agreement, however, is still lacking.

Polarization observables in pion photoproduction on 3He

The single polarization observables Σ, P and T are presented for the reaction 3He( γ, π +) 3H at various kinematics. The process is described in a recently developed nonlocal coupled-channel framework that employs three-body Faddeev amplitudes and incorporates two-step processes such as 3He( γ, π 0) 3He( π 0, π +) 3H. Enhancement effects of the contributions from small components of the 3He wave function as well as from the Δ-resonance E2 transition to the polarization observables have been found.

Coupled-channels study of polarized 6Li scattering at 44 MeV

Previously published coupled-channels (CC) analyses by Rusek et al. of polarized 6Li elastic scattering by 26Mg and 120Sn at Elab=44 MeV are analyzed. Excitations of 6Li to its three lowest T = 0 excited states are taken into account in the framework of continuum-discretized coupled-channels (CDCC). The analyses are made with the use of the projectile-target interactions based on the cluster-folding (CF) model and those on the double-folding (DF) one. It is shown that the coupling to the 6Li-excited states has large contributions to the vector and tensor analyzing powers of the elastic scattering. A test of the accuracy of the weak-binding-energy approximation (WBEA), which was used in the previous analyses, is made in comparison with the results of the CDCC calculation. It is also pointed out that there exists an ambiguity in the deuteron-target spin-orbit interaction, which affects the conclusion on the competition between the folding spin-orbit interaction and the projectile-excitation effects in the vector analyzing power.

Relativistic optical model analysis of 180 MeV p-bar+12C elastic and inelastic scattering.

In this paper we give the results of a relativistic analysis of elastic and inelastic scattering of 180 MeV antiprotons from {sup 12}C. The calculations are performed within a Dirac coupled-channel framework using a collective model for the transition potentials. While the presence of the inelastic data does seem to remove some of the ambiguity in the Dirac optical model potentials, the largest constraint comes from the elastic analyzing power measurements. In the Dirac approach for proton-nucleus scattering, spin observables are very important; this is also true for the determination of the antiproton-nucleus optical potential.

Effects of nonresonant breakup states in polarized 6Li scattering.

Effects of the coupling to $^{6}\mathrm{\ensuremath{\alpha}}$+d nonresonant continuum states on polarized $^{6}\mathrm{Li}$ scattering at ${\mathit{E}}_{\mathrm{lab}}$\ensuremath{\simeq}20--100 MeV are investigated in the framework of the continuum-discretized coupled-channels (CDCC) method which takes into account the resonant and nonresonant \ensuremath{\alpha}-d breakup states of $^{6}\mathrm{Li}$. A convergence of the calculated analyzing powers of $^{6}\mathrm{Li}$ elastic scattering against the size and the discretization of the breakup continuum is examined. The resulting model space of the breakup states consists of the \ensuremath{\alpha}-d S-wave (l=0), P-wave (l=1), and D-wave (l=2) states up to the \ensuremath{\alpha}-d relative momentum of k=1.2 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. The results of the CDCC calculation show that the effects of the nonresonant breakup states are quite as significant on the analyzing powers as those of the resonant breakup states.

Anomalous renormalization of cluster-folding interactions for 6Li-nucleus scattering at low energies

The validity of cluster-folding (CF) interactions for elastic scattering of 6Li by various nuclei is investigated in the α+d+target three-body model. The 6Li→α+d breakup process is taken into account in the framework of the continuum-discretized coupled-channels (CDCC). It is shown that, at low energies below E lab A p ≅10 MeV , the real part of the CF potentials has to be reduced by about (40–50)%, even when the resonant and non-resonant breakup channels are explicitly included in the CDCC calculations, while no renormalization is necessary for fits to scattering at higher energies.

Elastic and inelastic scattering of protons and alpha particles from stable even samarium isotopes

Differential cross sections have been measured for the elastic and inelastic scattering of 24 MeV protons from 148,150,152,154Sm and of 36 MeV alpha particles from 150,152Sm. The experimental results were analysed in the framework of coupled-channels and collective-model theories. 148,150Sm were assumed to be harmonic vibrators while 152,154Sm were treated as symmetric rotators. The octupole vibrational bands (1 − ,3 −,5 −) in 152,154Sm were satisfactorily analysed simultaneously with the ground-state band in the framework of the rotation-vibration model.

Vector polarized 6Li scattering from 12C and 16O.

The elastic scattering vector analyzing powers for /sup 6/Li+/sup 16/O at 25.7 MeV and /sup 6/Li+/sup 12/C at 30 MeV have been measured. In addition, measurement of the vector analyzing power for inelastic /sup 6/Li scattering has been made for the 2/sup +/ (4.44 MeV) state in /sup 12/C. Excitation function data for /sup 6/Li+/sup 16/O elastic and inelastic scattering have also been measured at five angles for /sup 6/Li lab energies through the range 15--28 MeV in 375 keV steps. These data show the system to be resonance free at 25.7 MeV. The data have been analyzed in the coupled channels framework, employing the double folding model for the real part of the nuclear scattering potential. The coupling strengths in the coupled channels calculations were determined from inelastic scattering cross-section data directly. The elastic scattering vector analyzing powers arise from a complicated interference between channel coupling and spin-orbit contributions, whereas the /sup 12/C, 2/sup +/ inelastic vector analyzing power arises from the spin-orbit potential only. Inelastic scattering analyzing powers may allow the shape and strength of heavy-ion spin-orbit potentials to be investigated more clearly than do the elastic scattering analyzing powers. The normalization of the double-folded real potential wasmore » found to be in the range 0.85--1.00 in the coupled channel calculations, thus bringing the normalization of /sup 6/Li scattering into agreement with other projectiles.« less

Inelastic α-particle scattering on doubly even selenium isotopes

Elastic and inelastic scattering of 25 MeV alpha particles by isotopically enriched targets of 76.78.80Se have been measured. Results have been analysed in the coupled-channel framework on the basis of two collective models: the harmonic vibrational model and the asymmetric rotational model. Deformation parameters were extracted for the first quadrupole and octupole states in each nucleus and compared with similar quantities obtained from other scattering experiments and Coulomb excitation measurements. Departure of the gamma parameter from the value deduced from the energy ratio E(22+)/E(21+) in the inelastic scattering of polarised protons by Matsuki et al (1983) is also indicated by the authors' data. The asymmetric rotational model provides a better description of the even-parity states than the harmonic vibrational model.

The deformation of23Na from inelastic alpha scattering

Inelastic scattering of 42 MeV alpha particles on 23Na has been measured to the low-lying members of the ground-state rotational band. Angular distributions for these states have been analysed in a coupled-channels framework to determine quadrupole and hexadecapole deformation lengths. The results indicate a deformation for 23Na comparable to the neighbouring 24Mg nucleus.

Effects of projectile breakup and target excitation in scattering of polarized 7Li

Abstract Scattering of polarized 7Li by 12C at Elab = 21 MeV and by 26Mg at Elab = 44 MeV is investigated by the use of the double-folding interaction in the coupled-channel framework where the breakup of 7Li to non-resonant continuum region and the excitation of 12C or 26Mg to the first 2+ state are taken into account in addition to the excitations of 7Li to the discrete levels so far considered. The effective interactions induced by the couplings between these channels are studied in detail by the invariant-amplitude method with fruitful results. For example, serious effects due to the projectile virtual excitation are observed in the central and third-rank tensor interactions in the elastic channel. The calculated cross sections and vector and tensor analyzing powers show overall good agreements with experimental data for the elastic scattering and the inelastic scattering to the 1 2 state of 7Li. The measured inelastic cross sections for the excitation of 26Mg and the mutual excitation to the 1 2 − state of 7Li and the 2+ state of 26Mg for the 7Li+26Mg scattering as well as the excitation of 12C for the 7Li+ 12C scattering are well described by the calculation. The target excitation accompanied by the mutual one and the non-resonant breakup of the projectile newly introduced are found to make important contributions to these physical quantities.

Analysis of the12C+12C inelastic scattering in the energy range 11?24 MeV/n

Elastic and inelastic scatterings cross-sections of12C+12C in the energy range 11–24 MeV/n have been analyzed within the coupled channels framework including appropriate symmetrization. The set obtained withr 0=1.01 fm,r I =0.86 fm for seven incident energies gave the best agreement with the data and could be, therefore, considered as really significant when compared with other sets. Coupled channels calculations have been made to fit the data and it has been found that they require a reduction of the imaginary potential. The total reaction cross-sectionσ R (E) determined from this analysis is in good agreement with a direct and recent measurement of σ R . Quadrupole deformation parameterβ 2 has been extracted and compared with those obtained for proton and alpha scatterings. Some small energy dependence of β2 over this energy range has been found, ¦β 2¦ ∼0.39–0.47. Finally, these calculations further confirm that β2 depends on the probe used in the various scattering experiments. For composite projectile such asα or12C,β 2 is clearly smaller than that one for nucleon as projectile.

Energy and target dependence of projectile breakup effect in elastic scattering of 6Li.

For a wide range of incident energy (${E}_{\mathrm{lab}=40--}$170 MeV) and target mass number (A=12--208), projectile breakup effects in elastic scattering of $^{6}\mathrm{Li}$ have been investigated in the microscopic coupled-channel framework; coupling with $^{6}\ensuremath{\rightarrow}\mathit{\ensuremath{\alpha}}$+d breakup process is taken into account by the method of coupled discretized continuum channels. $^{6}\mathrm{target}$ interactions are provided by folding of the M3Y effective nucleon-nucleon potential with nucleon densities of colliding nuclei. The calculation reproduces well experimental data of elastic scattering for all the targets and incident energies investigated, without any renormalization of the folding real potential. The breakup effect is found to depend little on the energy and target, which is shown by calculating dynamical polarization potentials induced by the breakup process. The dynamical polarization potential has a repulsive real part with strength of about 40% of the folding potential, the imaginary part being negligible, which explains well the empirical reduction factor of the single-channel double-folding model. The origin of repulsive nature of the breakup effect is discussed.

Contribution of multistep transfers to low-energy elastic and reaction cross sections

Two aspects of heavy-ion collisions at near-barrier energies deviate considerably from the predictions of simple potential models. Fusion cross sections are generally greatly underpredicted, and in a recent analysis of 16O elastic scattering on 208Pb the optical potential had a marked energy dependence. We show that the inclusion of both neutron and proton transfers in addition to inelastic excitation processes within a coupled channels framework can give a consistent description of the data.

Microscopic description of the backward rise of the elastic angular distribution of16O+28Si

The elastic angular distribution for the reaction16O+28Si is calculated for the bombarding energiesEc.m.=21.1 MeV and 22.7 MeV. The imaginary part of the ion-ion potential due to transfer reactions is calculated by making use of microscopic form factors. The depopulation of the entrance channel due to Coulomb excitation and inelastic processes is treated within the coupled-channel framework. By making use of a standard folding expression for the real part of the ion-ion potential the main features of the backward rise of the angular distribution are reproduced. Detailed agreement is obtained by introducing a very-short-range absorption and adjusting slightly the strength of the real potential.