Coupled-channel Calculations Research Articles

Analysis of 4He+40Ca and 4He+44Ti scattering using different optical model potentials

Elastic scattering of 4He+40Ca and 4He+44Ti reactions at backward angles has been analyzed using two differentmodels, microscopic and semimicroscopic folding potentials. The derived real potentials supplemented with phenomenological Woods–Saxon imaginary potentials, provide good agreement with the experimental data at energy Ec.m. = 21.8 MeV without need to renormalize the potentials. Coupledchannels calculations are used to extract the inelastic scattering cross section to the low-lying state 2+ (1.083 MeV) of 44Ti. The deformation length is obtained and compared with the electromagnetic measurement values as well as those obtained from previous studies.

Evidence for a dynamically refracted primary bow in weakly boundBe9rainbow scattering fromO16

We present for the first time evidence for the existence of a dynamically refracted primary bow for $^{9}$Be+$^{16}$O scattering. This is demonstrated through the use of coupled channel calculations with an extended double folding potential derived from the density-dependent effective two-body force and precise microscopic cluster wave functions for $^{9}$Be. The calculations reproduce the experimental Airy structure in $^{9}$Be+$^{16}$O scattering well.It is found that coupling of a weakly bound $^{9}$Be nucleus to excited states plays the role of a booster lens, dynamically enhancing the refraction over the {\it static} refraction due to the Luneburg lens mean field potential between the ground states of $^{9}$Be and $^{16}$O.

Hyperspherical coupled channel calculations of energy and structure of 4He–4He–Li+ and its isotopic combinations

The ground state vibrational energy and spatial features of (4)He-(4)He-Li(+) and its triatomic isotopic complexes are studied using the slow variable discretization (SVD) method in the hyperspherical coordinates for the zero total angular momentum. Our results show that the dominant structure of the system is an isosceles triangle with the shorter side associated with the two Li(+)-He distances using the sum-of-potential approximation. Corrections caused by the induced dipole-induced dipole interactions on the He atoms are also investigated. The effects are seen to be small and have a minor influence on the binding energy and the structure of present system. The results are also compared with the full ab initio calculations including all the three-body interactions and information of three-body corrections is obtained.

Anharmonicity of multi–octupole-phonon excitations inPb208: Analysis with multireference covariant density functional theory and subbarrier fusion ofO16+Pb208

We discuss anharmonicity of the multi-octupole-phonon states in $^{208}$Pb based on a covariant density functional theory, by fully taking into account the interplay between the quadrupole and the octupole degrees of freedom. Our results indicate the existence of a large anharmonicity in the transition strengths, even though the excitation energies are similar to those in the harmonic limit. We also show that the quadrupole-shape fluctuation significantly enhances the fragmentation of the two-octupole-phonon states in $^{208}$Pb. Using those transition strengths as inputs to coupled channels calculations, we then discuss the fusion reaction of $^{16}$O+$^{208}$Pb at energies around the Coulomb barrier. We show that the anharmonicity of the octupole vibrational excitation considerably improves previous coupled-channels calculations in the harmonic oscillator limit, significantly reducing the height of the main peak in the fusion barrier distribution.

Probing systematic model dependence of complete fusion for reactions with the weakly bound projectilesLi6,7

Background: Complete fusion cross section measurements involving weakly bound projectiles show suppression at above-barrier energies compared to coupled-channels (CC) calculations, but no definite conclusion could be drawn for sub-barrier energies. Different CC models often lead to contrasting results.Purpose: We aim to investigate the differences in the fusion cross sections predicted by commonly used CC calculations, using codes such as fresco and ccfull, when compared to experimental data.Methods: The fusion cross sections are normalized to a dimensionless form by isolating the effect of only dynamic channel couplings calculated by both fresco and ccfull, by the method of fusion functions, and compared to a universal fusion function. This acts as a probe for obtaining the model dependence of fusion.Results: A difference is observed between the predictions of fresco and ccfull for all the reactions involving $^{6,7}\mathrm{Li}$ as projectiles, and it is noticeably more for systems involving $^{7}\mathrm{Li}$.Conclusions: With the theoretical foundations of the two CC models being different, their calculation of fusion is different even for the same system. The conclusion about the enhancement or suppression of fusion cross sections is model dependent.

Sub-barrier fusion excitation function data and energy dependent Woods–Saxon potential

This paper analyzed the role of intrinsic degrees of freedom of colliding nuclei in the enhancement of sub-barrier fusion cross-section data of various heavy ion fusion reactions. The influences of inelastic surface vibrations of colliding pairs are found to be dominant and their couplings result in the significantly larger fusion enhancement over the predictions of the one dimensional barrier penetration model at sub-barrier energies. The theoretical calculations are performed by using energy dependent Woods–Saxon potential model (EDWSP model) in conjunction with the one dimensional Wong formula. The effects of dominant intrinsic channels are entertained within framework of the coupled channel calculations obtained by using the code CCFULL. It is quite interesting to note that the energy dependence in Woods–Saxon potential simulates the effects of inelastic surface vibrational states of reactants wherein significantly larger value of diffuseness parameter ranging from a = 0.85fm to a = 0.95fm is required to address the observed fusion excitation function data of the various heavy ion fusion reactions.

Probing transfer to unbound states of the ejectile with weakly boundLi7onNb93

The two-step process of transfer followed by breakup is explored by measuring a rather complete set of exclusive data for reaction channels populating states in the ejectile continua of the $^7$Li+$^{93}$Nb system at energies close to the Coulomb barrier. The cross sections for $\alpha+\alpha$ events from one proton pickup were found to be smaller than those for $\alpha+d$ events from one neutron stripping and $\alpha+t$ events from direct breakup of $^7$Li. Coupled channels Born approximation and continuum discretized coupled channels calculations describe the data well and support the conclusion that the $\alpha+d$ and $\alpha+\alpha$ events are produced by direct transfer to unbound states of the ejectile.

Interplay of the elastic and inelastic channels in the 16O+27Al scattering at Elab = 280 MeV

Recent data indicated a nuclear rainbow-like pattern in the elastic scattering of 16O + 27Al at $ E_{lab}=100$ MeV that arises from couplings of the ground to the low-lying states of the 27Al nucleus. Similar effect was identified in the elastic angular distribution of 16O + 12C at $ E_{lab}=281$ and 330 MeV. These experiments show a crucial role of microscopic details of nuclear structure in the elastic scattering of heavy ions at energies well above the Coulomb barrier. In this work we investigate the 16O + 27Al system at $ E_{lab}=280$ MeV for which a coupled channel calculation predicts a pronounced nuclear rainbow-like structure. Obtained experimental data show evidences of an important coupling of the elastic channel to the inelastic. Coupled channel calculations reproduce the experimental angular distributions when a re-normalization factor on the real part of the optical potential is introduced. A proper theoretical approach still requires a high degree of accuracy for the nuclear structure models and new tools to deal with collective excitations.

Differential cross sections of positron–hydrogen collisions**Project supported by the Nanyang Normal University Science Foundation of China (Grant No. ZX2013017) and the National Natural Science Foundation of China (Grant Nos. 11174066, 61306007, and U1304114).

We make a detailed study on the angular differential cross sections of positron–hydrogen collisions by using the momentum-space coupled-channels optical (CCO) method for incident energies below the H ionization threshold. The target continuum and the positronium (Ps) formation channels are included in the coupled-channels calculations via a complex equivalent-local optical potential. The critical points, which show minima in the differential cross sections, as a function of the scattering angle and the incident energy are investigated. The resonances in the angular differential cross sections are reported for the first time in this energy range. The effects of the target continuum and the Ps formation channels on the different cross sections are discussed.

Role of projectile breakup effects and intrinsic degrees of freedom on fusion dynamics**Supported by Dr. D. S. Kothari Post-Doctoral Fellowship Scheme sponsored by University Grants Commission (UGC), New Delhi, India

This article analyzes the fusion dynamics of loosely bound and stable projectiles with Zr-target isotopes within the context of the coupled channel approach and the energy-dependent Woods-Saxon potential model (EDWSP model). In the case of the 28Si + 90Zr reaction, the coupling to the inelastic surface excitations results in an adequate description of the observed fusion dynamics while in case of the 28Si + 94Zr reaction, the coupling to collective surface vibrational states as well as the neutron (multi-neutron) transfer channel is necessary in the coupled channel calculations to reproduce the below-barrier fusion data. However, the EDWSP model calculation provides an accurate explanation of the fusion data of 28Si + 90,94Zr reactions in the domain of the Coulomb barrier. In the fusion of the 6Li + 90Zr reaction, the inclusion of the nuclear structure degrees of freedom recovers the observed sub-barrier fusion enhancement but results in suppression of the above barrier fusion data by 34% with respect to the coupled channel calculations. Using EDWSP model calculations, this suppression factor is reduced by 14% and consequently, the above-barrier fusion data of 6Li + 90Zr reaction is suppressed by 20% with reference to the EDWSP model calculations. Such fusion suppression at above-barrier energies can be correlated with the breakup of the projectile (6Li) before reaching the fusion barrier, as a consequence of low binding energy.

Influence of experimental conditions on the spectroscopy investigation of 14Be by Coulomb breakup reaction**Supported by National Natural Science Foundation of China (11205036)

The two-body (core+2n) cluster structure was implemented to describe the two-neutron halo nucleus 14Be, where the core 12Be was assumed inert and at a ground state and the dineutron was assumed at a pure 2S0 state. Based on such a structure the three-body continuum-discretized coupled-channel (CDCC) calculation was successfully used to deal with the 14Be breakup reactions of 14Be + Pb at 35 MeV/u. Consequently, we modeled the kinematically complete measurement experiment of this reaction with the help of Geant4. With the simulation data the relative energy spectrum was constructed by the invariant mass method and B(E1) spectrum was extracted using the virtual photon model. The influence of the target thickness and detector performance on the energy spectroscopy was investigated.

Elastic and inelastic angular distributions of the 7Li+120Sn system for energies near the Coulomb barrier

The reaction of 7Li+120Sn has been measured at bombarding energies of 21, 24 and 27 MeV. The -ray transition in 120Sn was observed and the angular distribution for the 2+ excited state was obtained. Coupled channels and coupled-reaction channels calculations, including the dynamical polarization potential due to the projectile break-up, obtained from continuum discretized coupled channel calculations, were performed. The comparison between the existing experimental elastic angular distribution with the coupled-reaction channels calculations indicates that the 1n stripping transfer is the most intense channel to be coupled and the 2n stripping reaction occurs sequentially rather than directly, however, further data must be analyzed to confirm this indication. The experimental elastic and inelastic scattering data were well described by the calculations, but some discrepancies in these channels may indicate the need for corrections to the nuclear potential and/or the necessity to incorporate further channels.

Adiabatic and coupled channels calculations for near barrier fusion of 16O +238U using realistic nucleon–nucleon interaction

We investigate the fusion cross-section and the fusion barrier distribution of [Formula: see text]O[Formula: see text]U at near- and sub-barrier energies. We use an interaction potential generated by the semi-microscopic double folding model-based on density dependent (DD) form of the realistic Michigan-three-Yukawa (M3Y) Reid nucleon–nucleon (NN) interaction. We studied the role of both the static and dynamic deformations of the target nucleus on the fusion process. Rotational and vibrational degrees of freedom of [Formula: see text]U-nucleus are considered. We found that the deformation and the octupole vibrations in [Formula: see text]U enhance its sub-barrier fusion cross-section. The signature of the the octupole vibrational modes of [Formula: see text]U appears clearly in its fusion barrier distribution profile.

Target-charge dependence of the breakup coupling effects in the elastic scattering of 8B

We perform continuum discretized coupled-channels calculations for the elastic scattering of 8B on different targets to trace where the Coulomb-nuclear breakup coupling effects start to be dominant in the interaction of the proton halo nuclei. We observe a qualitative difference in angular distributions when the charge of the target increases as seen in the case of neutron halos, but the Coulomb-nuclear interference peak begins to disappear clearly at a relatively smaller value of Z T for the proton halos.

One-neutron stripping fromBe9toTm169,Ta181, andRe187at near-barrier energies

We report the measurement of one-neutron stripping of $^{9}\text{Be}$ to the $^{169}\text{Tm},\phantom{\rule{0.16em}{0ex}}^{181}\text{Ta}$, and $^{187}\text{Re}$ nuclei, in the range from subbarrier to above-barrier energies. The activation technique was used, with the detection of off-line $\ensuremath{\gamma}$ rays. The results show that the transfer cross sections for the three systems investigated are very similar and are much larger than the corresponding fusion cross sections at subbarrier energies, whereas fusion predominates at energies above the barrier. Data are in good agreement with our coupled reaction channel calculations. We also investigate the ratio, as a function of energy, between experimental transfer and fusion cross sections. The role of transfer couplings on the fusion excitation functions is also discussed.

Revised analysis ofCa40+Zr96fusion reactions

Fusion data for $^{40}$Ca+$^{96}$Zr are analyzed by coupled-channels calculations that are based on a standard Woods-Saxon potential and include couplings to multiphonon excitations and transfer channels. The couplings to multiphonon excitations are the same as used in a previous work. The transfer couplings are calibrated to reproduce the measured neutron transfer data. This type of calculation gives a poor fit to the fusion data. However, by multiplying the transfer couplings with a $\sqrt{2}$ one obtains an excellent fit. The scaling of the transfer strengths is supposed to simulate the combined effect of neutron and proton transfer, and the calculated one- and two-nucleon transfer cross sections are indeed in reasonable agreement with the measured cross sections.

Analysis of 6Li Scattering at 240 MeV Using Different Nuclear Potentials

Angular distributions of the elastic and inelastic scattering cross sections of 6Li projectile on different heavy ion target nuclei including the 24Mg, 28Si, 48Ca, 58Ni, 90Zr, and 116Sn at energy of 240 MeV have been analyzed by using two different folded potentials based on the CDM3Y6 and Sao Paulo potentials for the real part of the optical potential, while the imaginary parts have a phenomenological Woods-Saxon shape. Coupled channel calculations for the low-lying 2+ state at 1.369, 1.779, 3.832, 1.454, 2.186, and 1.29 MeV for 24Mg, 28Si, 48Ca, 58Ni, 90Zr, and 116Sn, respectively, have been carried out, and the best fit values for B(EL) with the above models have been extracted by fitting the inelastic scattering cross section and compared with the values of previous works. The total reaction cross section and real and imaginary volume integrals have also been investigated.

Microscopic study ofCa40+Ni58,64fusion reactions

Background: Heavy-ion fusion reactions at energies near the Coulomb barrier are influenced by couplings between the relative motion and nuclear intrinsic degrees of freedom of the colliding nuclei. The time-dependent Hartree-Fock (TDHF) theory, incorporating the couplings at the mean-field level, as well as the coupled-channels (CC) method are standard approaches to describe low energy nuclear reactions. Purpose: To investigate the effect of couplings to inelastic and transfer channels on the fusion cross sections for the reactions $^{40}$Ca+$^{58}$Ni and $^{40}$Ca+$^{64}$Ni. Methods: Fusion cross sections around and below the Coulomb barrier have been obtained from coupled-channels (CC) calculations, using the bare nucleus-nucleus potential calculated with the frozen Hartree-Fock method and coupling parameters taken from known nuclear structure data. The fusion thresholds and neutron transfer probabilities have been calculated with the TDHF method. Results: For $^{40}$Ca+$^{58}$Ni, the TDHF fusion threshold is in agreement with the most probable barrier obtained in the CC calculations including the couplings to the low-lying octupole $3_1^{-}$ state for $^{40}$Ca and to the low-lying quadrupole $2_1^{+}$ state for $^{58}$Ni. This indicates that the octupole and quadrupole states are the dominant excitations while neutron transfer is shown to be weak. For $^{40}$Ca+$^{64}$Ni, the TDHF barrier is lower than predicted by the CC calculations including the same inelastic couplings as those for $^{40}$Ca+$^{58}$Ni. TDHF calculations show large neutron transfer probabilities in $^{40}$Ca+$^{64}$Ni which could result in a lowering of the fusion threshold. Conclusions: Inelastic channels play an important role in $^{40}$Ca+$^{58}$Ni and $^{40}$Ca+$^{64}$Ni reactions. The role of neutron transfer channels has been highlighted in $^{40}$Ca+$^{64}$Ni.

Semiclassical treatment of fusion and breakup processes of $$^{6,8}$$ 6 , 8 He halo nuclei

A semiclassical approach has been used to study the effect of channel coupling on the calculations of the total fusion reaction cross section \(\sigma _\text{fus}\), and the fusion barrier distribution \(D_\text{fus}\) for the systems \(^{6}\)He \(+^{238}\)U and \(^{8}\)He \(+^{197}\)Au. Since these systems invloves light exotic nuclei, breakup states channel play an important role that should be considered in the calculations. In semiclassical treatment, the relative motion between the projectile and target nuclei is approximated by a classical trajectory while the intrinsic dynamics is handled by time-dependent quantum mechanics. The calculations of the total fusion cross section \(\sigma _\text{fus}\), and the fusion barrier distribution \(D_\text{fus}\) are compared with the full quantum mechanical calculations using the coupled-channels calculations with all order coupling using the computer code and with the available experimental data.

Charge-exchange processes in collisions ofH+,H2+,H3+,He+, andHe2+ions with CO andCO2molecules at energies below 1000 eV

Absolute measurements of charge-exchange cross sections of ${\mathrm{H}}^{+},\phantom{\rule{0.16em}{0ex}}{\mathrm{H}}_{2}^{+},\phantom{\rule{0.16em}{0ex}}{\mathrm{H}}_{3}^{+},\phantom{\rule{0.16em}{0ex}}{\mathrm{He}}^{+}$, and ${\mathrm{He}}_{2}^{+}$ ions in CO and ${\mathrm{CO}}_{2}$ have been made for energies below 1000 eV, an equivalent of the energy of ionized particles at typical solar-wind conditions. An attenuation method for the case of complex ions of a molecule, taking into account the influence on the ion beam composition of the processes of disintegration of the primary ions into secondary ones with different charge-exchange cross sections, is described. Also the secondary effects, like three-body collisions and re-ionization processes that could emerge at higher pressures of the gas layer, are discussed. Dependence of the cross sections on the number of atomic centers in the projectile have been explained on the basis of the energy defect of the reactions and asymmetric near-resonant charge-exchange process between the ion and target molecule including the Doppler broadening in the interaction of the monoenergetic ion beam and target molecules having an isotropic Maxwellian velocity distribution corresponding to room temperature. Using the semiempirical approach based on the parametrized numerical coupled-channel two-state calculations, we have extrapolated the cross sections to a broader range of velocities.