Coupled Reaction Channel Calculations Research Articles

Pickup coupling effects in deuteron scattering: The case ofd+Ca40

The dynamic polarization potential (DPP) contribution to the effective deuteron-nucleus interaction is evaluated by means of coupled reaction channel (CRC) calculations followed by $S$-matrix-to-potential inversion. The full coupled channel $S$ matrix ${S}_{{l}^{'}l}^{J}$ is inverted using the iterative-perturbative algorithm to yield a potential that includes a complex ${T}_{R}$ tensor term as well as central and spin-orbit components. The differences between the various components of the inverted potential and the corresponding terms in the bare potential of the CRC calculation constitute a local equivalent representation of the complete DPP that is generated by the reaction channel coupling. The magnitude of the DPP, the real part in particular, is much less than that found in earlier calculations in which the nonorthogonality terms were omitted. The characteristic features of the tensor part of the DPP were traced to breakup and reorientation processes in the entrance deuteron channel that had been included with the pickup. The contribution of stripping to the deuteron-nucleus interaction is also discussed.

Strong pickup-channel coupling effects in proton scattering: The case ofp+Be10

The dynamic polarization potential (DPP) contribution to the effective proton-nucleus interaction, that is due to the coupling of deuteron channels, is evaluated by applying ${S}_{\mathit{lj}}\ensuremath{\rightarrow}V(r)$ inversion to the elastic channel $S$-matrix from coupled reaction channel calculations of proton elastic scattering. This was done for protons scattering from $^{10}\mathrm{Be}$ at 12, 13, 14, 15, and 16 MeV; nonorthogonality corrections were included. We find a consistent pattern of a repulsive real and an absorptive imaginary DPP, with the absorption shifted to a larger radius. This is consistent with what has been found for proton scattering from the neutron skin nucleus $^{8}\mathrm{He}$. The DPP is not of a form that can be represented by a renormalization of the bare potential, and has properties suggesting an underlying nonlocal process. We conclude that deuteron channels cannot be omitted from a full theoretical description of the proton-nucleus interaction (optical potential).

Single neutron transfer coupling effects on sub-barrier elastic scattering and near-barrier fusion ofC15

To date, the possible effects of coupling to nucleon transfer reactions on the elastic scattering and fusion of weakly bound exotic nuclei have been largely neglected. The $^{15}\mathrm{C}$ nucleus presents a virtually unique opportunity to test these effects for an almost pure s${}_{1/2}$ single neutron halo nucleus. We present a series of coupled reaction channel calculations of the sub-barrier elastic scattering and single neutron transfer reactions, plus near-barrier excitation functions of the total fusion cross section for the $^{12}\mathrm{C}$, $^{13}\mathrm{C}$, and $^{15}\mathrm{C}+^{208}\mathrm{Pb}$ systems. The method is validated against data for $^{12}\mathrm{C}$ and $^{13}\mathrm{C}+^{208}\mathrm{Pb}$. A large effect on the sub-barrier elastic scattering due to coupling to the ($^{15}\mathrm{C}$,$^{14}\mathrm{C}$) single neutron stripping reaction is found, ascribed to the 2s${}_{1/2}$ halo nature of the $^{15}\mathrm{C}$ ground state, in contrast to the two stable carbon isotopes. We also find a significant diminution of the above barrier total fusion cross section for $^{15}\mathrm{C}$ due to this coupling, again in contrast to the stable isotopes.

Failure of the Woods-Saxon nuclear potential to simultaneously reproduce precise fusion and elastic scattering measurements

A precise fusion excitation function has been measured for the $^{12}\mathrm{C}$+$^{208}\mathrm{Pb}$ reaction at energies around the barrier, allowing the fusion barrier distribution to be extracted. The fusion cross sections at high energies differ significantly from existing fusion data. Coupled reaction channels calculations have been carried out with the code FRESCO. A bare potential previously claimed to uniquely describe a wide range of $^{12}\mathrm{C}$+$^{208}\mathrm{Pb}$ near-barrier reaction channels failed to reproduce the new fusion data. The nuclear potential diffuseness of 0.95 fm which fits the fusion excitation function over a broad energy range fails to reproduce the elastic scattering. A diffuseness of 0.55 fm reproduces the fusion barrier distribution and elastic scattering data, but significantly overpredicts the fusion cross sections at high energies. This may be due to physical processes not included in the calculations. To constrain calculations, it is desirable to have precisely measured fusion cross sections, especially at energies around the barrier.

Generation of a repulsive dynamic polarization potential by transfer couplings

A series of coupled reaction channels calculations for the $^{9}\mathrm{Be}+^{209}\mathrm{Pb}$ system at near-barrier energies is presented. Single neutron stripping couplings leading to several states in $^{209}\mathrm{Pb}$ together with coupling to the direct breakup of $^{9}\mathrm{Be}$ using a $^{5}\mathrm{He}+\ensuremath{\alpha}$ cluster model are included. We find that the transfer couplings give rise to a dynamic polarization potential with the same characteristics in the nuclear surface region as that produced by breakup.

Tensor analyzing powers forLi7induced transfer breakup reactions

The ${T}_{20}$ analyzing powers have been measured for the $^{120}\mathrm{Sn}(^{7}\mathrm{Li},^{8}\mathrm{Be}\ensuremath{\rightarrow}2\ensuremath{\alpha})^{119}\mathrm{In}$ and $^{120}\mathrm{Sn}(^{7}\mathrm{Li},^{6}\mathrm{Li}^{*}\ensuremath{\rightarrow}\ensuremath{\alpha}+d)^{121}\mathrm{Sn}$ transfer breakup reactions, using a $70\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$ beam. The data exhibit excellent agreement with the results of coupled reaction channels calculations, providing an important test of these calculations when applied to the transfer breakup reaction mechanism.

Solution to a long-standing problem:12C(14N,13N)13C1/2+

The failure of finite-range distorted-wave Born approximation (DWBA) calculations to describe neutron transfer to ${2s}_{1/2}$ states in nuclei such as ${}^{13}\mathrm{C}{,}^{13}\mathrm{N}{,}^{17}\mathrm{O},$ and ${}^{27}\mathrm{Mg}$ is a long-standing problem. Detailed coupled-channels Born approximation and coupled-reaction-channels (CRC) calculations failed to improve on the much simpler DWBA calculations. This work presents results suggesting that the vital step necessary to obtain agreement between CRC calculations and data in the case of the ${2s}_{1/2}$ state in ${}^{13}\mathrm{C}$ is an increase in the radius of the potential binding the neutron to the ${}^{12}\mathrm{C}$ core, leading to a considerable extension of the neutron radial wave function. The source of this extension is shown to arise from the deformation of the ${}^{12}\mathrm{C}$ core.

Coupled reaction channel analysis of elastic, inelastic, transfer, and fusion cross sections for12C+208Pb

Elastic, inelastic, and transfer angular distributions were measured for ${}^{12}\mathrm{C}{+}^{208}\mathrm{Pb}$ in the energy range from 58.9 to 84.9 MeV. While the fission fragment angular distributions were measured over the energy range from 58.9 to 79 MeV, the residue cross sections after $2n$ evaporation from the compound nucleus ${(}^{220}\mathrm{Ra})$ were measured by $\ensuremath{\alpha}$ counting at 58.9, 60.9, and 62.9 MeV. Combining the above data with the ones from the literature, the fusion cross sections have been obtained. Quasielastic excitation function at $170\ifmmode^\circ\else\textdegree\fi{}$ was also measured to obtain the fusion barrier distribution. Optical model analysis of the elastic scattering data, using both phenomenological and microscopic models, brought out the pronounced energy dependence of the optical potential at near barrier energies. A simultaneous description of the elastic and all the nonelastic channels was obtained from the coupled reaction channel (CRC) calculations using a consistent set of parameters at all the energies. The effective nucleus-nucleus real potential, obtained from CRC calculations, explained the observed energy dependence of the real part of the optical potential. Thus, the real potential used in these calculations with such a large number of constraints can be considered as the bare nucleus-nucleus potential.

Absorption matrix for fusion in coupled reaction channel calculations

The absorption of flux for fusion from a coupled channels system has been examined over a wide range of energies. The full absorption matrix for fusion, consisting of the diagonal absorption and the fusion in transition, is presented. The fusion in transition is at times more than the removal of flux while propagating in the physical channels. The absorption matrix is obtained also for the case of purely real coupling potentials. The absorption matrix method is shown to be superior to the usual method of difference of cross sections used in some of the present coupled channels fusion codes. The flux absorbed within a given channel has been resolved into the constituent subchannels of the total angular momentum. Using this approach, the isocentrifugal approximation has been examined for various cases.

Threshold anomaly in12C+209Biscattering

Elastic scattering angular distributions have been measured for the system ${}^{12}\mathrm{C}{+}^{209}\mathrm{Bi}$ at ten energies between 58.9 to 87.4 MeV. Optical model analysis of these, together with existing data at 118 MeV, using both phenomenological and microscopic models, shows a pronounced energy dependence of the optical potential. Fusion cross sections have been deduced, by a barrier penetration model and by subtracting the direct reaction contributions from the reaction cross sections. Threshold anomaly of the optical potential has been explained both by dispersion relation and by coupled reaction channel (CRC) calculations. The CRC calculations, including inelastic excitation and transfer channels, reproduce simultaneously the elastic, inelastic, and transfer angular distributions measured at 61.9, 63.9, and 87.4 MeV. Comparison of threshold anomaly results for ${}^{4}\mathrm{He},{ }^{11}\mathrm{B},{ }^{16}\mathrm{O}{+}^{209}\mathrm{Bi}$ systems along with the present case indicates that the degree of anomaly increases with the projectile mass.

Direct charge-exchange versus sequential nucleon transfers in the 14C( 6Li, 6He) 14N reaction at 93 MeV

The 14C( 6Li, 6He) 14N reaction was investigated at a 6Li ion energy of 93 MeV. The angular distributions for several natural and unnatural parity states of the 14N nucleus were compared with the DWBA and Coupled Reaction Channels (CRC) calculations assuming direct charge exchange and two-step sequential nucleon transfers. It was shown that the direct charge-exchange mechanism dominates for the transitions to the ground and excited ( E x = 3.95 MeV) 1 4 states of the 14N nucleus up to angles of 50°–70°. The sequential nucleon transfers must be taken into account at larger angles for these states and in the full angular range for the other states (2.31 MeV (0 +, T = 1), 5.11 MeV (2 −), 5.69 MeV (1 −) + 5.83 MeV (3 −), 7.03 MeV (2 +) and 8.49 MeV (4 −)).

Strong enhancement of two-proton transfer in the 40Ca(37Cl,39K)38Ar - reaction

Measurements of one- and two-proton transfer in the system 37Cl + 40Ca at energies close to the Coulomb barrier have been performed. The two-proton transfer to ground states attains cross sections which are comparable to the one-proton transfer. The strong enhancement of the proton-pair transfer is interpretedinterms of a combined actionofstatic and dynamic proton-proton correlations, for example in the 2+ state of 38Ar andin the 0+ ground state of40Ca which are introducedbymixing of shell model configurations across two major shells with hω = 2 and 3 of different parities (s1/2, d3/2 and f7/2, p3/2). This effect, which is called hybridization, induces a strong spatial polarization of the nucleons in the two-proton wave-function and enhances the two-proton transfer cross section. Coupled reaction channel calculations reproduce consistently the one and two proton transfer using spectroscopic information from light ion reactions.

Modified WKB transmission for fusion

In the optical model (OM) approach for fusion, absorption of flux occuring beyond the barrier position is presented in detail at low energies. It has been shown that the OM transmission can be well approximated as a sum of the WKB transmission and a long range absorption (LRA) contribution. Owing to absence of LRA, the fusion predictions of coupled channel codes based on transmission approach like the CCFUS code, do not agree with the predictions of complete coupled reaction channel (CRC) calculations based on OM approach using the code FRESCO. The CCFUS code with a modified transmission which includes LRA contribution is shown to be consistent with the CRC results using FRESCO. The static deformation of the colliding nuclei strongly influences the fusion imaginary potential and therefore the deep sub-barrier fusion cross sections.

Optical model approach for heavy ion fusion.

The differences between optical model (OM) and the barrier transmission approaches for fusion are studied in detail at low energy. In the heavy ion case at deep subbarrier energies, the absorption mean square spin of an optical model calculation using a short ranged imaginary potential differs significantly from the results of the WKB transmission method. This discrepancy of OM results is shown to be due to absorption occurring beyond the barrier position. The coupled reaction channel calculations for fusion based on OM approach are shown to be sensitive to the choice of imaginary fusion potentials, whereas the coupling effects on fusion are dominant for energies only around the barrier. \textcopyright{} 1996 The American Physical Society.

Evidence of projectile polarisation effects on the reaction 208Pb( 17O, 16O) 209Pb

Coupled reaction channels calculations (CRC) of the reactions 208Pb( 17O, 16O) 209Pb leading to different states of 209Pb are compared with DWBA predictions at projectile energies of 78, 86 and 102 MeV. The calculations exhibit strong effects of multistep processes on Q-value and angular-momentum-mismatched transfer reactions. It is shown that the contribution to the transfer through the inelastic excitation of 17O contains a major part of the multistep effect. A simple three-channel model comprising the elastic, inelastic and transfer channels is constructed which simulates the CRC effects on the transfer cross sections. The polarization effects of the eliminated channels give rise to effective potentials which are mainly imaginary.

The12C(t,α)11B reaction at 33 MeV

Differential cross sections for the 12C(t, alpha )11B reaction at 33 MeV have been measured and analysed for the transition to the 0.0, 2.125, 4.445, 5.021, 6.743, 7.286, 7.978 and 8.559 MeV states in 11B. The results of CRC (coupled reaction channels) calculations are compared with DWBA (distorted wave Born approximation) and CCBA (coupled channels Born approximation) calculations for the single-step and two-step transitions respectively. The CRC calculations resulted in improved agreement with the experimental data for the strong transitions.

Do we understand deuteron scattering at all?: The polarization potential due to mass-three channels

The contribution to the deuteron effective local optical potential arising from coupling to triton and helion channels has been evaluated by performing finite-range coupled reaction channel calculations with the pickup channels at sum rule strength. The effective local polarization potential is evaluated by inversion of the CRC S-matrix elements. The effect is very large, with indications of underlying l-dependence. The significance of these large contributions will be discussed.

Finite-range coupled reaction channel calculation of pickup contribution to the proton optical-model potential

Finite-range calculations indicate that deutron channel coupling contributes a much weaker repulsive contribution to the proton optical potential in contrast to zero-range calculations which indicate strong repulsion. Finite-range coupled reaction channel calculations and an accurate inversion procedure are used to explain this in more detail and it is shown that finite range corrections quench the repulsion at the nuclear centre, but the overall repulsive effect remains substantial.

Inelastic two-step processes in (d,Li6) reactions onMg24andMg26nuclei

Evidence is given that two-step processes are largely involved in (d,$^{6}\mathrm{Li}$) reaction on light deformed nuclei. Coupled reaction channels calculations can reproduce the experimental data in rather good agreement with the theoretical spectroscopic amplitudes.

A study of the 26Mg( 12C, 12B) 26Al charge-exchange reaction

The reaction 26Mg( 12C, 12B) 26A1(5 +, 3 +) has been studied using a beam of 102 MeV of 12C. Shell-model, microscopic direct model and finite-range coupled reaction channel (CRC) calculations including recoil effects, have been performed, for comparison with the experimental data. DWBA calculations were performed for the intermediate states of interest in the 11B + 27Al and in the 13C + 25Mg channels and these results were also compared with the experimental ones. The dominant reaction mechanism for 26Mg( 12C, 12B) 26Al(5 +, 3 +) appears to be the sequential mode.