Coupled-channel Born Approximation Research Articles

Quadrupole transfer strength studied through heavy-ion induced two-neutron transfer between the shape transitional nucleiOs190,192

A coupled-channels Born-approximation analysis of the reaction $^{192}\mathrm{Os}$($^{12}\mathrm{C}$, $^{14}\mathrm{C}$)$^{190}\mathrm{Os}$ at ${E}_{\mathrm{lab}}=70$ MeV demonstrates that the direct quadrupole transfer strength is very weak, in continuation of the trend found previously in a study of the tungsten nuclei. Elastic and inelastic scattering data for the $^{12}\mathrm{C}$ channel were also taken and analyzed in a conventional coupled-channels model to determine the relative motion.NUCLEAR REACTIONS $^{192}\mathrm{OS}$($^{12}\mathrm{C}$, $^{12}\mathrm{C}$), $^{192}\mathrm{OS}$($^{12}\mathrm{C}$, $^{14}\mathrm{C}$), ${E}_{\mathrm{lab}}=\mathrm{MeV}$, measured $\ensuremath{\sigma}(\ensuremath{\Theta})$. CCBA analysis. Demonstrated effect of shape transitions on quadrupole transfer strength.

Analysis of theGe74(O18,O16)Ge76andGe76(O16,O18)Ge74reactions in

An exact finite-range coupled-channel Born-approximation analysis of the $^{74}\mathrm{Ge}$($^{18}\mathrm{O}$, $^{16}\mathrm{O}$)$^{76}\mathrm{Ge}$ and $^{76}\mathrm{Ge}$($^{16}\mathrm{O}$, $^{18}\mathrm{O}$)$^{74}\mathrm{Ge}$ reactions has been performed. It shows that the shape change between the angular distributions of different final states is well reproduced by using BCS---random-phase-approximation wave functions to describe the Ge states. The measured transfer cross sections are rather well described by calculations using optical model parameters and deformation values which fit the experimental data on $^{18}\mathrm{O}$ and $^{16}\mathrm{O}$ elastic and inelastic scattering. It has been found that the excitation of the $^{18}\mathrm{O}^{*}$ ${2}^{+}$ state has to be included in the coupled-channel Born-approximation analysis in order to reproduce the experimental angular distributions of the $^{74}\mathrm{Ge}$ and $^{76}\mathrm{Ge}$ ground states. A unique factor of 2.3 can be used to normalize the calculated cross section to the experimental data.[NUCLEAR REACTIONS $^{74}\mathrm{Ge}$($^{18}\mathrm{O}$, $^{16}\mathrm{O}$), ($^{18}\mathrm{O}$, $^{18}\mathrm{O}$); $^{76}\mathrm{Ge}$($^{16}\mathrm{O}$, $^{18}\mathrm{O}$), ($^{16}\mathrm{O}$, $^{16}\mathrm{O}$); deduced optical model parameters; CCBA analysis.]

JDependence of the (F19,O16) Reaction and Spin-Orbit Forces in the Heavy-Ion Optical Potential

The shapes of the observed angular distributions for the reactions $^{28,30}\mathrm{Si}$($^{19}\mathrm{F}$, $^{16}\mathrm{O}$)$^{31,33}\mathrm{P}$ to ${\frac{3}{2}}^{+}$ and ${\frac{5}{2}}^{+}$ states differ strongly. A consistent description of this $j$ dependence and of the ground-state ${\mathrm{\textonehalf{}}}^{+}$ angular distributions is given by distorted-wave Born-approximation calculations which assume triton cluster transfer and include spin-orbit potentials in both entrance and exit channels. We find from coupled-channel Born-approximation calculations that inelastic excitation of $^{19}\mathrm{F}$ does not affect the shapes significantly.

One-proton transfer reactions induced byO16andC12onNi62target isotope

The ($^{16}\mathrm{O}$, $^{15}\mathrm{N}$) and ($^{12}\mathrm{C}$, $^{11}\mathrm{B}$) reactions on $^{62}\mathrm{Ni}$ target have been investigated with 56 MeV $^{16}\mathrm{O}$ and 48 MeV $^{12}\mathrm{C}$ beams. Angular distributions for transitions to the first five single particle states of $^{63}\mathrm{Cu}$ were obtained. An exact finite-range distorted-wave Born approximation analysis was performed, showing that the spectroscopic factors extracted agree fairly well with those obtained from light ion induced reactions. The role of multistep processes has also been investigated by performing exact finite-range coupled-channel Born approximation calculations which take into account the core excitation of the projectile or the target nucleus. It is found that in the case of the $^{62}\mathrm{Ni}$($^{12}\mathrm{C}$, $^{11}\mathrm{B}$)$^{63}\mathrm{Cu}$ reaction both the intensity and shape of the angular distributions are affected by including the multistep contributions due to projectile excitation. In particular, the behavior of the angular distributions at small angles is better described by the coupled-channel Born approximation calculations. The indirect routes involving the inelastic excitations of the $^{16}\mathrm{O}$ or $^{62}\mathrm{Ni}$ nuclei are shown to be unimportant.NUCLEAR REACTIONS $^{62}\mathrm{Ni}$($^{12}\mathrm{C}$, $^{11}\mathrm{B}$) ${E}_{^{12}\mathrm{C}}=48$ MeV; $^{62}\mathrm{Ni}$($^{16}\mathrm{O}$, $^{15}\mathrm{N}$) ${E}_{^{16}\mathrm{O}}=56$ MeV $\ensuremath{\sigma}(\ensuremath{\theta})$; EFR-DWBA and EFR-CCBA analysis; deduced spectroscopic factors; enriched targets.

One- and two-step processes in single-nucleon pickup

The reaction /sup 12/C(p,d)/sup 11/C at high momentum transfers (q > at approx = 200 MeV/c) has been examined with respect to single- and two-step processes. Our coupled-channel Born approximation analysis of the reaction at 185 MeV shows that peculiarities observed in experimental angular distributions can be explained with the two-step process or the interference between the single-step and two-step processes. The analysis requires the presence of small 1d and 1f/sub 7///sub 2/ admixtures in the /sup 12/C ground state along with the basic 1s/sup 4/1p/sup 8/ configuration. The different energy dependence in the single-step and two-step processes is discussed and illustrated by data at 185 and 700 MeV.

The 40Ca(p, t) 38Ca reaction and configuration mixing

The 40Ca(p, t) 38Ca reaction has been investigated at 51.9 MeV and angular distributions have been obtained for transitions leading to ten states in 38Ca. Several spin-parity assignments were made. The experimental angular distributions for the J π = 2 + states at 2.20 and 3.69 MeV were reproduced by distorted wave Born approximation (DWBA) calculations assuming simple configurations consistent with the analysis of the L = 0 transitions to the ground state and the 3.06 MeV state done previously. However, the normalization factor for the 3.69 MeV state was different from that for the other states. For the L = 0 transitions to the 3.06 MeV 0 + state a different choice of the radius parameter for the bound state potential was found to require a slightly different amplitude for the 4p-4h component in 40Ca(g.s.). The angular distribution for the 3.06 MeV state was analyzed by coupled channel Born approximation (CCBA) calculations. It is shown that two-step processes via the 2 + states of 40Ca(3.90 MeV) and 38Ca(2.20 MeV) make relatively large contributions to the transition. However, a satisfactory explanation could not be obtained by the channel coupling effects alone. It appears that the observed L = 2 angular distributions which rise at far forward angles can be explained by DWBA with configuration mixing. The role of configuration mixing in (p, t) reactions is investigated using the L = 0 transitions, and it is found that the configuration mixing causes effects similar to those obtained from a change in the radius of the bound state potentials.

Analysis of direct and indirect processes of two-proton-transfer reactions performed onNi64andMo100

The $^{64}\mathrm{Ni}$($^{16}\mathrm{O}$, $^{14}\mathrm{C}$)$^{66}\mathrm{Zn}$ and $^{100}\mathrm{Mo}$($^{12}\mathrm{C}$, $^{10}\mathrm{Be}$)$^{102}\mathrm{Ru}$ angular distributions have been measured between 13\ifmmode^\circ\else\textdegree\fi{} and 70\ifmmode^\circ\else\textdegree\fi{} (lab), respectively, at 56 and 48 MeV incident energies. Distorted-wave Born approximation and coupled-channel Born approximation analyses have been performed using exact finite range codes. The marked difference in the angular distributions between the $^{102}\mathrm{Ru}$ ground state and ${2}^{+}$ state can be well described using coupled-channel Born approximation calculations that take into account the important indirect processes. Furthermore, the relative intensities among various states are better reproduced by coupled-channel Born approximation calculations than by distorted-wave Born approximation calculations.NUCLEAR REACTIONS $^{64}\mathrm{Ni}$($^{16}\mathrm{O}$, $^{14}\mathrm{C}$) and $^{100}\mathrm{Mo}$($^{12}\mathrm{C}$, $^{10}\mathrm{Be}$), ${E}_{{16}_{0}}=56$ MeV and ${E}_{{12}_{\mathrm{C}}}=48$ MeV. Angular distribution measured between 13\ifmmode^\circ\else\textdegree\fi{} and 70\ifmmode^\circ\else\textdegree\fi{} lab. DWBA and CCBA analyses performed with Saturn-mars-i and ii.

Inelastic processes and form factor effects in the 162, 164Dy( 3He, d) reactions at 46.5 MeV

The 162, 164Dy( 3He, d) reactions at E 3He = 46.5 MeV are analyzed using the coupled channels Born approximation (CCBA) and improved form factors derived from a deformed Woods-Saxon potential. The latter are generated using the coupled channels procedure of Rost. The transitions considered populate the 7 2 −[523], 1 2 +[411], 3 2 +[411], 1 2 −[541] and 5 2 + orbitals in 163, 165Ho. Indirect processes induced by inelastic scattering are found to have an influence on the cross sections comparable to that deduced for neutron transfer reactions on rare earth nuclei at lower energies. Considered alone, these can alter the cross sections even of strong transitions by a factor of two and of weaker ones by an order of magnitude. For the weaker transitions equally large changes can result when the improved form factors, rather than conventional spherical Woods-Saxon functions, are used in the calculations. In the examples considered these two effects tend to cancel, often, but not always, resulting in predicted cross sections similar in magnitude to the results of conventional DWBA calculations made with spherical Woods-Saxon form factors. The CCBA angular distributions are generally similar in shape to DWBA predictions, which usually give good fits to the experimental angular distributions over the 0–35° range of the data. Compared with DWBA predictions which use (he same optical parameters, but spherical Woods-Saxon form factors, the CCBA with deformed Woods-Saxon form factors is in better overall agreement with the experimental cross-section magnitudes. However there are a number of cases in which the CCBA, although usually predicting larger cross sections than the DWBA, still underestimates the experimental cross sections by nearly factor of two. These cases all occur in the 71 2 −[541] band or in the strongly Coriolis mixed 1 2 +[411] and 3 2 +[411] bands, and include the majority of transitions populating these orbitals. Since both nuclear structure and reaction mechanism effects are interwoven m the calculations, further data would be most useful in probing the origin of the discrepancy.

Exact finite-range CCBA calculations for the reactionO16(d,Li6)C12atEd=35MeV

The reaction /sup 16/O(d, /sup 6/Li)/sup 12/C at 35 MeV has been analyzed with a finite-range coupled channel Born approximation code. Agreement in shape and normalization is found if the interaction radius for the cluster system /sup 12/C + ..cap alpha.. is taken to be R = 1.27(12/sup 1///sup 3/ + 4/sup 1///sup 3/) fm. (AIP)

A coupled-channel born approximation analysis of 22Ne(p, t) 20Ne and 24Mg(p, t) 22Mg using shell-model wave functions

Coupled-channel Born approximation calculations for the reactions 22Ne(p, t) 20Ne and 24Mg(p, t) 22Mg to the 0 +, 2 + and 4 + members of the ground-state rotational bands have been carried out. The two-nucleon transfer spectroscopic amplitudes were determined from shell-model wave functions, the calculation of inelastic excitations was based on the collective model, and the reaction space was limited to the first 0 +, 2 +and 4 +states in each nucleus. The measured cross sections in the case of 22Ne(p, t) are reasonably well described by this model. However, significant deviations were observed between the calculated cross sections and the experimental data for the 24Mg(p, t) transitions to the 2 + and 4 + states. These discrepancies are possibly attributable to multistep processes involving higher-lying states in 24Mg not included in the reaction space. The effects on the calculations of other possible inadequacies of the reaction model and uncertainties in the parameters of this model are discussed.

Positive-parity levels inCa41populated in theCa40(d→,p)Ca41(J+)reaction

Differential cross sections and vector analyzing powers for the /sup 40/Ca(d, p) reaction are presented as a test of the particle-core coupling model for high-spin positive parity levels at 2.88, 3.20, 3.37, and 3.83 MeV in /sup 41/Ca. The data representations by the coupled-channels Born approximation support the model. In contrast, the distorted-wave Born approximation fails completely to represent the analyzing power data for some levels. (AIP)

Excitation of three isospin modes of the giant magnetic dipole resonance in mass 24 isobars

All three isospin modes of two T = 1, 1/sup +/ states in mass 24 have been studied by (/sup 3/He, t), (/sup 3/He, /sup 3/He'), and (t, /sup 3/He) reactions on /sup 24/Mg. The relative strengths of the two 1/sup +/ states in each reaction agree with the relative strengths of the electromagnetic transitions, but the shapes and magnitudes of the charge-exchange data are not as predicted by a one-step interaction with a central force. It is necessary to perform a two-step coupled-channel Born-approximation calculation via intermediate /sup 4/He channels using mixed wave functions to account for the results. (AIP)

Alpha-transfer reactions in light nuclei. II. (He3,Be7) pickup reactions

The ($^{3}\mathrm{He}$, $^{7}\mathrm{Be}$) reaction has been studied at a laboratory energy of 25.5 MeV for $^{16}\mathrm{O}$ and $^{24}\mathrm{Mg}$ targets and at energies of 25.5, 27.0, and 29.0 MeV for a $^{12}\mathrm{C}$ target. Angular distributions have been measured from ${\ensuremath{\theta}}_{\mathrm{lab}}=15\ifmmode^\circ\else\textdegree\fi{} \mathrm{to} 160\ifmmode^\circ\else\textdegree\fi{}$ for transitions to low-lying states in the residual nuclei. The resulting angular distributions have been analyzed (1) using an exact-finite-range distorted-wave Born-approximation formalism including multistep processes and (2) using a Hauser-Feshbach compound-nuclear model. In general, the shapes of the forward angle ($^{3}\mathrm{He}$, $^{7}\mathrm{Be}$) data are well described by the finite-range distorted-wave Born-approximation and finite-range coupled-channels Born-approximation calculations. The magnitude of the measured transition to the 1.63-MeV (${2}^{+}$) state in $^{20}\mathrm{Ne}$ is approximately 100 times larger than predicted by an ${\mathrm{SU}}_{3}$ theory for a simple one-step transition, and this transition is shown to be an example in which a finite-range coupled-channels Born-approximation analysis is required. Arguments concerning the direct nature of the reaction process populating these states are discussed, and spectroscopic information is extracted.NUCLEAR REACTIONS $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{24}\mathrm{Mg}$($^{3}\mathrm{He}$, $^{7}\mathrm{Be}$), ${E}_{(^{3}\mathrm{He})}=25.5, 27.0, 29.0$ MeV, measured $\ensuremath{\sigma}(E,\ensuremath{\theta})$ Hauser-Feshbach and finite-range CCBA analysis, spectroscopic factors.

Multistep processes in theF19(O16,N15)Ne20reaction

An exact-finite-range coupled-channels Born-approximation analysis, which takes into account multistep processes, was made of the reaction $^{19}\mathrm{F}$($^{16}\mathrm{O}$, $^{15}\mathrm{N}$)$^{20}\mathrm{Ne}$ (${0}^{+}$, ${2}^{+}$, ${4}^{+}$). Good fits to data were obtained not only for the ${0}^{+}$ and ${2}^{+}$ state cross sections, but also for the ${4}^{+}$ state which is forbidden in a one-step process. Deviation of the distorted-wave Born-approximation result from the coupled-channel Born-approximation result was observed even for the allowed transition to the ${0}^{+}$ and ${2}^{+}$ states.NUCLEAR REACTIONS $^{19}\mathrm{F}$($^{16}\mathrm{O}$, $^{15}\mathrm{N}$), $E=68$ MeV calculated $\ensuremath{\sigma}(\ensuremath{\theta})$ with CCBA and DWBA.

Exact finite-range coupled-channels Born approximation analysis ofC13-induced reactions

Different descriptions of the reaction $^{28}\mathrm{Si}$ ($^{13}\mathrm{C}$, $^{12}\mathrm{C}$) $^{29}\mathrm{Si}$ at 36 MeV leading to the ground and first excited states of $^{29}\mathrm{Si}$ are examined. Sensitivity of the reaction cross section to various families of optical parameters is investigated and the so-called "surface transparent potential" is used as an alternate treatment. Exact finite-range distorted-wave Born approximation and coupled-channels Born approximation analyses of the reaction are performed, showing that the coupled-channels Born approximation analysis, even in its presently restricted form, leads to an improvement over the distorted-wave Born approximation predictions.NUCLEAR REACTIONS $^{28}\mathrm{Si}$ ($^{13}\mathrm{C}$, $^{12}\mathrm{C}$) calculated cross sections using exact finiterange CCBA with "surface transparent potential."

Multistep inelastic processes in the reactionSi28(He3,d)P29leading to bound and unbound states

We analyze the stripping reaction $^{28}\mathrm{Si}(^{3}\mathrm{He},d)^{29}\mathrm{P}$ at an incident $^{3}\mathrm{He}$ energy of 35.3 MeV, considering seven residual states. These extend in excitation energy to 4.8 MeV with the highest four being unbound to proton emission and described via complex energy eigenstates. The results of a distorted-wave Born-approximation analysis are rather disappointing. Through a coupled-channel Born approximation analysis, inelastic excitation in both the entrance and exit channels is shown in several cases to be important in accounting for the detailed shape of the angular distributions. Additional data obtained at 20 and 40 MeV are included in the analysis as a check of the optical potentials and spectroscopic amplitudes adopted. The spectroscopic amplitudes used are consistent with results of large-basis shell-model calculations. Good fits to the ($^{3}\mathrm{He},d$) data are obtained in both shape and magnitude, suggesting that the coupled-channel Born approximation should replace the distorted-wave Born approximation in the analysis of experimental data for single-nucleon transfer reactions in this mass region.

Finite-range coupled-channels Born approximation

The formalism for calculating finite-range coupled-channels Born approximation differential cross sections is developed using the plane wave expansion method. A discussion of the computer code OUKID which was developed using this formalism is presented. A test of the reliability of this code is also presented and the effect of multistep processes on an $alpha$ transfer reaction is shown. (AIP)

Neutron Number Dependence of Interference in Two-Neutron Transfer Reactions and the Nuclear Deformation

By making use of a simple model for the nuclear deformation, the number dependence of the form factors for inelastic scattering and two-neutron transfer processes are discussed for even-even deformed nuclei in the rare earth region. The form factor amplitudes are expressed in terms of the Legendre polynomials, whose argument is a func­ tion of the number. It is easy to understand, in the perturbative sense, a number dependence of the interference between the direct and two-step processes observed in (p, t) reactions leading to the 0, + and 2, + states. The interference for the 2, + state in deformed nuclei shows a striking parallelism with that for the quadrupole vibrational state in spherical nuclei. It has been shown that the two-neutron transfer reactions on deformed nuclei 1l can be well described in terms of the coupled-channel Born approximation (CCBA), 2l which includes the effect of multi-step processes via inelastic scattering. It has also been dezywnstrated that the same is ;true in the case of the two-neutron transfer reactions leading to the collective vibrational state in spherical nuclei. 3l~sl The purpose of the present paper is to explain,. in the perturbative sense, the neutron number dependence of the interference between direct and two-step processes in the (p, t) and ( t, p) reactions leading to the ground band members in even-even deformed nuclei in the rare earth region. The explanation applies equally well to other deformed nuclei. The interference observed in the (p, t) reactions, leading to the 2 1 + state in the spherical vibrational nuclei has been treated by Udagawa and coworkers. 3l· 5l· 6l They have pointed.ouel.al in the frame­ work of the quasiparticle RPA that a number dependence of the form factor amplitudes originates from the dynamical role of the ground state correlations and the gross number dependence of the occupation coefficients vv and uu, and that the number dependence of the form factor amplitudes provides .an explanation to the sign change of the interference observed in the middle of a major shell. In § 2, the transition amplitude for the A(p, t)B reaction is given in a second­ order perturbative form of the CCBA description. In this procedure, it is shown that the amplitude of the core-excitation model studied by Kozlowsky et aFl is

D−γAngular Correlations as a Test for the Importance of Multistep Processes in the ReactionMg24(d, d′)

The in-plane $^{24}\mathrm{Mg}(d, {d}_{1}\ensuremath{\gamma})$ angular correlation has been measured at an incident energy of 10 MeV. Analyses of the experimental data with distorted-wave and coupled-channel Born-approximation calculations show that multistep processes are important to describe this reaction although the distorted-wave Born approximation reproduces quite well the differential cross section.

One- and Multi-Step Processes in the ReactionNd144(C12,C14)

Two very different types of angular distributions, one having a normal bell shape and the other being much more constant with angle were observed in the reaction $^{144}\mathrm{Nd}$($^{12}\mathrm{C}$, $^{14}\mathrm{C}$) for two well-known ${2}^{+}$ states of $^{142}\mathrm{Nd}$. The fits to these angular distributions using the distorted-wave Born approximation and/or coupled-channel Born approximation confirms the conclusion that the data give definite evidence for the importance of multistep processes. A comparison with the reaction $^{144}\mathrm{Nd}(p, t)$ is also discussed.