Finite-range DWBA Calculations Research Articles

Analyzing powers and cross sections for (p, d) reactions on nuclei of N = 50–82

Vector analyzing powers A( θ) and cross sections σ(θ) have been measured, with the use of a polarized proton beam of 22.0 MeV and a magnetic spectrograph, for (p, d) reactions leading to the following final states, the excitation energy being given in MeV: 91 Zr( g.s., 5 2 +), 91 Zr(1.21, 1 2 +), 91 Zr(1.47, 5 2 +), 91 Zr(1.88, 7 2 +), 91 Zr(2.04, 3 2 +), 101 Ru( g.s., 5 2 +), 105 Pd( g.s., 5 2 +), 107 Pd( g.s., 5 2 +), 107 Pd(0.12, 1 2 +), 107 Pd(0.21, 11 2 −), 111 Cd( g.s., 1 2 +), 113 Cd( g.s., 1 2 +), 117 Sn( g.s., 1 2 +), 117 Sn(0.16, 3 2 +), and 117 Sn(0.32, 11 2 −) . Angular distributions of A( θ) and σ(θ), resulting from neutron transfers of l = 0, 2, 4, 5 and thus j = 1 2 , 3 2 , 5 2 , 7 2 , 11 2 , have been measured from 5° to 65° in 5° or 2.5° steps. The analysis was carried out with finite-range and zero-range DWBA calculations. Spectroscopic factors were extracted. A comparison of the predictions of the deuteron adiabatic theory with conventional DWBA theory predictions was made. The effect of the two-step (p, p')(p', d) processes was studied by taking into account a strong excitation of the first 2 + state in the proton inelastic channel. Also the effect of the deuteron D-state on A( θ) and σ(θ) was investigated. A phenomenological treatment was provided so as to remedy a large discrepancy between the experimental σ(θ) and A( θ) and the theoretical ones observed in the case of the large angular momentum transfers.

7Li + 54Fe Single-nucleon stripping reactions at E = 48 MeV

Angular distributions have been measured for the 54Fe( 7Li, 6Li/ 6He) 55Fe, 55Co reactions at E( 7Li) = 48 MeV . Exact finite-range DWBA calculations for both reactions, employing Woods-Saxon real and imaginary potentials to generate the distorted waves, reproduce the shape of the f-state angular distributions but not the rate of fall-off with increasing angle for p-states. Using real potentials constructed by double-folding a microscopic nucleon-nucleon potential with a Woods-Saxon shaped imaginary potential to generate the distorted waves did not change the calculations. The forward angle ( 7Li, 6He) data allowed the 2 p 1 2 states in 55Co to be located and the determination of the single-particle centroid energies. The 55Co spectroscopic factors are in good agreement with those from the (d, n) reaction but are generally 25 % lower than those from average ( 3He, d) results. The 55Fe spectroscopic factors are in good agreement with (d, p) results.

Excitation of high-spin particle-hole states in A = 28 nuclei by 27Al(α, t) and (α, 3He) reactions

Abstract The 27 Al(α, t) and (α, 3 He) reactions have been measured at E α = 64.5 MeV. The experimental angular distributions were analyzed by the exact finite-range DWBA calculations assuming a nucleon stripping mechanism. The distributions of spectroscopic strengths for the single-particle transitions with transferred angular momenta l = 0, 1, 2, 3 and 4 have been obtained. The strengths for the transitions to the stretched 6 − states in 28 Si and 28 Al are compared to those obtained from inelastic scattering on 28 Si. The present results show no distinctive differences in the structures for 6 − T = 0 and 1 states in 28 Si such as are observed in proton and pion inelastic scattering on 28 Si.

The reactions 50,52Cr(d, 6Li) 46,48Ti at Ed = 651 MeV

The 50,52Cr(d, 6Li) 46,48Ti reactions have been studied at E d = 65 MeV bombarding energy. Angular distributions of outgoing Li particles were measured for final states in 46,48Ti nuclei from 15° to 50° (lab). These were compared with zero-range and finite-range DWBA calculations in an α-cluster pick-up approximation to obtain relative α-spectroscopic factors.

The effects of finite range and channel coupling in the [formula omitted] reaction

Comparisons of exact finite-range (EFR) DWBA calculations and zero-range (ZR) calculations are presented for the cross sections and analysing powers of the 32 S( 3 He , 4 He) 31 S reaction to the ground state ( 1 2 + ), 1.25 MeV ( 3 2 +) and 2.23 MeV ( 5 2 +) states. The data for the 3 2 + and 5 2 + states are quite well fitted and show the characteristic j-dependence of the analysing powers. Only small differences between the EFR and ZR calculations are seen. The analysing power data for the 1 2 ± state are poorly fitted by the EFR or ZR calculations but better agreement is obtained when the coupling to other levels is included in a coupled channel Born approximation (CCBA) calculation.

DWBA calculation of the cross section of the12C(6Li, d)16O* [O 2 + , 6.05 MeV] reaction

Exact finite range DWBA calculation performed for the reaction12C(6Li, d)16O* [6.05] reproduces satisfactorily the 18 MeV experimental cross section and yields a value of 0.17 for the product of the spectroscopic factors. A comparison of the results with two approximate descriptions shows that the finite range effects induce more oscillations in the angular distribution and depress the maxima at medium and backward angles. A finite range correction calculation with 1.5 fm for the finite range parameter is acceptable for describing the experimental data.

The reaction 16O( 6Li, d) 20Ne at 75 MeV

The angular distributions of the reaction 16O( 6Li, d) 20Ne at 75 MeV for transitions to members of the ground state band are well fitted by exact finite-range DWBA calculations assuming a direct α-cluster transfer and yield spectroscopic factors in good agreement with shell-model predictions.

The [formula omitted] proton orbit size in 209Bi

Angular distributions of α-particles from the reaction 209Bi(t, α) 208Pb (ground state) have been measured at bombarding energies E t = 8.5 MeV and E t = 9.0 MeV. Zero-range (ZR) DWBA analyses of the data are used to determine the radial extent of the wave function of the lh 9 2 orbit in which the transferred proton is bound in 209Bi. The applicability of the sub-Coulomb ZR DWBA treatment is investigated by comparison of ZR and exact finite-range DWBA calculations. A value of the (t, α) normalization constant of (20.8 ± 3.1) × 10 4 MeV 2 · fm 3, based on forward dispersion relations, has been obtained from this comparison. The asymptotic amplitude of the wave function is measured directly and the rms radius is extracted via a Woods-Saxon model. A value of √〈 r 2〉 = 6.10 −0.08 +0.12 fm, corresponding to a point proton and to a local Woods-Saxon potential, is obtained. The rms radius and radial wave function of the 1 h 9 2 proton are compared with the results of electron scattering and muonic atom data on targets of 209Bi and 208Pb and with the results of Hartree-Fock calculations.

Final-state spins of 49Sc from the 48Ca( 7Li, 6He) reaction

The forward-angle j-dependence of the 48Ca( 7Li, 6He) reaction has been used to determine the spins of the states populated. Spectroscopic factors are in good agreement with previous ( 3He, d) values when the new spin values are used. The centroid energies obtained show that the 1 f 5 2 and 2 p 1 2 states are nearly degenerate in 49Sc. The value obtained for the 1 f 7 2 strength shows that the calculated magnitude of the ( 7Li, 6He) reaction is correct to within 10 % when Cohen and Kurath Spectroscopic factors are used in the exact finite-range DWBA calculations.

15N excitation contribution to 48Ca( 16O, 15N) 49Sc reaction

The effect of 15N excitation process is studied in the reaction 48Ca( 16O, 15N) 49Sc. The excitation process is included into a generalized non-local optical potential for a scattersing 15N- 49Sc and is found to be responsible for a shift of a grazing peak in the exact finite-range DWBA calculation.

The (d, 6Li) reaction on 12C, 16O, 24Mg, 40Ca and 58Ni at 54.25 MeV

The (d, 6Li) reaction was studied at Ed = 54.25 MeV on the target nuclei 12C, 16O, 24Mg, 40Ca and 58Ni. The data were analyzed with finite-range DWBA calculations. The absolute values of the α-cluster spectroscopic factors and the target mass dependence of the relative Sα were in agreement with those in the (p, pα) reaction at Ep = 100 and 157 MeV. The theoretical calculations of the relative Sα were in better agreement with the experimental data at higher energy than at the lower energies.

α-Transfer reactions between light nuclei

Alpha-transfer reactions between light nuclei, namely 10B, 12C, 14N, 16O and 20Ne, were studied at incident energies of 5–7 MeV/ A. Conventional exact finite range DWBA calculations were performed on them and spectroscopic factors were extracted for several α-core systems. These values are consistent among all the α-transfer reactions studied in the present experiment, but are different from the theoretical values. A DWBA calculation using the cluster model wave functions was performed on the 20Ne( 16O, 20Ne) 16O reaction, and gave better results than the conventional analysis for the absolute magnitude.

Study of the energy dependence of the 16O(d, 6Li) 12C reaction

16O(d, 6Li) 12C reaction cross sections have been measured at incident deuteron energies of 80, 65, 60 and 50 MeV. The experimental angular distributions for the ground state transitions have been analyzed by finite range DWBA calculations, employing different values for the potential depths of the 6Li optical potential. Alpha-transfer spectroscopic factors for the 0 + ground state, for the 2 + first excited and for the 4 + state at 14.08 MeV in 12C have been extracted. The variations of these spectroscopic factors are discussed in terms of an energy dependent optical model parametrization.

Four-nucleon pickup fromN14

Spectroscopic factors for four-nucleon transfer have been extracted for states in $^{10}\mathrm{B}$ populated via the $^{14}\mathrm{N}$($d$,$^{6}\mathrm{Li}$) reaction, at an incident energy of 80 MeV. The experimental angular distributions were analyzed in the framework of finite-range distorted wave Born approximation calculations. The results are compared to theoretical shell model predictions.NUCLEAR REACTIONS $^{14}\mathrm{N}$($d$,$^{6}\mathrm{Li}$) $^{10}\mathrm{B}$; ${E}_{d}=80$ MeV measured $\ensuremath{\sigma}({E}_{^{6}\mathrm{Li}},\ensuremath{\theta})$. Gas target. Finite-range DWBA calculations.

Study of 60Zn and 61Zn

The (12C, 10Be) and (12C, 9Be) reactions on 58Ni were studied at 77 MeV. New levels were determined for both residual nuclei, 60Zn and 61Zn. For 61Zn, levels and a new ground state mass were also measured with the 64Zn(3He, 6He) reaction. A mass excess for 61Zn of −56333±23 keV was obtained. Angular distributions for the 12C induced reactions are compared with finite range DWBA calculations and found to be insensitive to L− and J-transfer.

The 18O(18O, 16O)20O reaction at 52 MeV

Abstract The structure of the 20 O nucleus was studied by the 18 O( 18 O, 16 O) 20 O reaction at E 1ab = 52 MeV. Angular distributions for the transitions to the lowest four states in 20 O were obtained and analyzed with finite-range DWBA calculations. Optical potential sets were used which fit the experimental elastic scattering differential cross sections over almost the whole angular range. The two L = 0 transitions to the ground state and the 4.45 MeV state of 20 O populated by the 18 O( 18 O, 16 O) reaction were analyzed with exact finite-range DWBA calculations using microscopic form factors. These calculations underestimate the absolute cross sections by a factor of 11. The relative strength of the two L = 0 transitions is well reproduced in the 18 O( 18 O, 16 O) reaction. However, DWBA calculations for the 18 O(t, p) 20 O reaction overestimated the relative cross sections for the excited 0 + state by a factor of 6. Several model wave functions were tested for the ground-state transition. It was found that the absolute cross sections of the ( 18 O, 16 O) reaction are very sensitive to the mixing of shell-model configurations. The angular distribution shapes are also slightly dependent on the mixing.

Scattering and transfer reactions for 6, 7Li + 90, 91Zr

Abstract Elastic scattering data have been measured for the 7Li + 90Zr, 6Li + 90Zr, and 6Li + 91Zr systems at E(Li) = 34 MeV. Inelastic scattering data for the 7Li + 90Zr and 6Li + 90Zr systems were also measured for the 2+(2.18 MeV) and 3−(2.75 MeV) states in 90Zr and the 1 2 − (0.48 MeV ) state in 7Li. Optical model analyses of the elastic scattering data and DWBA analyses for the states in 90Zr were performed. The deduced deformation lengths for the 2+ state agreed with those extracted in other studies but the deformation length for the 3− state was smaller. The 90Zr(7Li, 6Li)91Zr angular distributions were measured for the 1.21 and 2.03 MeV states and the 2.19 MeV doublet in 91Zr. Also, 90Zr(7Li, 6He)91Nb angular distributions were measured for the ground states, 0.10, 3.41 and 4.82 MeV states in 91Nb. The transitions well matched in angular momentum were described by finite-range DWBA calculations, while other transitions displayed the same phase problems seen with heavier ions. The extracted spectroscopic information was consistent with the results of other reaction studies. At the present energy, it was not possible to determine whether the l = 1 phase problem that occurs for heavy-ion single-nucleon transfer reactions on 2s-1d shell nuclei occurs in 91Zr also.

A DWBA analysis of heavy ion α-transfer reactions on 16O

Abstract Alpha transfer reactions on 16O have been measured using beams of 7Li at 50 and 68 MeV, 11B at 115 MeV and 13C at 105 MeV. Angular distributions have been obtained and the data analysed using exact finite range DWBA calculations incorporating all the Coulomb and nuclear interactions. Cluster wave functions for the states populated in 20Ne incorporating the Gamow formalism for states unbound to α-decay have been used in the form-factor calculations. Spectroscopic amplitudes are deduced both from the α-widths and from the reaction cross sections for the unbound states. We find, in common with previous results, that spectroscopic factors deduced from the 7Li induced reactions even at 68 MeV are in disagreement with the structure calculations. Results for the 11B induced reaction are inconclusive, but for the 13C induced reaction, which is the best matched kinematically, the deduced spectroscopic amplitudes are in excellent agreement with theoretical predictions. On this basis the 9− at 21.0 MeV in 20Ne is assigned to the Kπ = 0− band.

Investigation of the (d, 6Li) reaction on 16O at Ed = 80 MeV

The (d, 6Li) reaction on 16O has been investigated with the 80 MeV deuteron beam of the Jülich Isochronous Cyclotron. Angular distributions were obtained between 10° and 55° lab. Experimentally an excitation energy range up to 40 MeV was observed. Single states and level groups with E x < 22 MeV show up clearly in the present data. These were analysed by both zero-range and finite-range DWBA calculations. Spectroscopic factors have been obtained and compared to theoretical predictions. Evidence for other than direct transfer mechanism is discussed phenomenologically.

A test of DWBA for (p,t) reactions

Presents exact finite-range DWBA calculations using a realistic triton wavefunction for a series of (p,t) reactions on nuclei for which reliable spectroscopic factors are available. The theory predicts both the absolute magnitude and the shape of angular distributions and thus, for the cases studied, provides a test of the DWBA. The results obtained indicate that finite-range DWBA analysis of (p,t) reactions can probably provide additional information on the structure of nuclear wavefunctions.