Exact Finite-range DWBA Calculations Research Articles

Instabilities of the Conventional Nucleus-Nucleus Interactions for (3H4He) Proton Pickup Cross-Sections

The angular distributions of the 26 Mg, 28 Si, 30 Si( 3 H, 4 He) reactions have been analyzed using the exact finite-range DWBA calculations. The optical model potential is assumed to have the conventional spin-orbit potential. The obtained cross-sections with the spin-orbit potential are not significantly different from those calculated using the phenomenological Woods‐Saxon form factors in the forward angle regions. The inclusion of the spin-orbit potential gives the best fit to the data and greatly improves the large angle cross-sections. Different reasonable spectroscopic factors are found to account well for the cross-section magnitudes.

Effect of Gaussian Potential on the Differential Cross Sections of Alpha Transfer Reactions

The differential cross sections of different alpha transfer reactions have been investigated by using the exact finite-range DWBA calculations. The double-folding density-dependent model is used for the real and imaginary nucleus-nucleus potential in the initial and final channels. The effective nucleon-nucleon interaction is assumed to be the double-Gaussian potential. The Yukawa interaction is found reasonable and exhibits a slight better agreement at energies above the barrier region. The obtained values of the extracted normalization factors are reasonable.

DWBA analyses of the (t,6He) reaction at 38 MeV

New differential cross section data are presented for the (t,6He) reaction on targets of 7Li and 19F at an incident energy of 38 MeV. Existing data for the (t,6He) reaction on 12,13C have been re-extracted and revised values are reported for 12C. Exact finite range DWBA calculations are presented using Woods-Saxon potentials for the projectile and target wavefunctions; the effect of the choice of geometry parameters is examined. The spectroscopic factors are compared with shell-model and microscopic-model calculations.

Structure of 14c studied by the 14c(p,d) 13c reaction

Cross sections for the neutron pickup reaction 14C(p, d) 13C were measured at E p = 35.0 MeV for the states below E = 10 MeV, and at E p = 40.1 MeV for the states between E x = 11 and 18 MeV. Obtained angular distributions were compared with exact finite-range DWBA calculations to extract spectroscopic factors. Second-order DWBA calculations were also made in some cases. Almost full 0p 1 2 strength was found, while the observed 0p 3 2 strength was 80% of the simple sum-rule limit. The main part of the remaining strength was found in the 0d 5 2 orbit, and, in a lesser degree, in the 1s 1 2 and 0d 3 2 orbits. Small fractions of the 0f 5 2 and Og 9 2 strengths were also necessary to explain the angular-distribution shapes and the cross-section magnitudes of the predominantly multistep transitions to the 5− 2 and 5+ 2 states.

Proton-hole states in 57Co studied with the 58Ni(d, 3He) 57Co reaction at 78 MeV

The 58Ni(d, 3He) 57Co reaction was measured at a bombarding energy of 78 MeV. Energy levels up to 7.0 MeV excitation energy in 57Co were studied. Angular distributions of the 3He particles, corresponding to transitions to the ground state and to 42 excited states in 57Co, were analyzed in the range of θ lab = 2.7° to 25°. Exact finite-range DWBA calculations were employed to extract l-values and spectroscopic factors. Shell-model calculations were carried out in an fp-shell model space. In addition, calculations of the energy levels in 57Co were performed in the SU(6) particle-vibration model (PTQM). Satisfactory agreement is observed between the experimental results and both theoretical predictions.

Study of proton-hole states in 61Co using the 62Ni(d, 3He) 61Co reaction at 78 MeV

The 62Ni(d, 3He) 61Co reaction was studied at a bombarding energy of 78 MeV. Angular distributions were measured in the range of θ lab = 4.5° to 25°. Energy levels up to 5.0 MeV excitation energy in 61Co were studied. Exact finite-range DWBA calculations were employed to extract spectroscopic factors. Shell-model calculations were carried out in the truncated fp-model space. Qualitatively good agreement between theory and experiment is observed for the states based on fp components. In addition, calculations of the energy levels in 61Co were performed in the SU(6) particle-vibration model (PTQM). Spectroscopic factors have been calculated by using the PTQM transfer-operator form arising microscopically on the basis of RPA. This operator contains an additional term which has no counterpart in the interaction boson-fermion model (IBFM). Rather good agreement between theory and experiment was obtained.

The ( 7Li, 6Li) reaction on 28Si and 40Ca at [formula omitted

Angular distributions for the ( 7Li, 6Li) reaction on 28Si and 40Ca to ground and excited states of 29Si and 41Ca have been measured at E( 7 Li) = 45 MeV . The shapes of the angular distributions are well described by exact finite-range DWBA calculations. To test the sensitivity of the calculated angular distributions to the exit channel potential, calculations were made using a strongly absorbing 7Li potential for both the entrance and exit channels. This calculation produced as good a fit to the shape of the angular distributions as did calculations with a 6Li potential in the exit channel, even though 7Li and 6Li elastic scattering on these target nuclei are not very similar. However, the magnitudes of the calculated cross sections are sensitive to the choice of potentials, and agreement with light-ion spectroscopic factors is obtained when the more weakly absorbing 6Li potentials are used. The spectroscopic factors obtained from the 40Ca( 7Li, 6Li) reaction study are in good agreement with the extensive light-ion results showing that the absolute magnitude of the reaction is correctly predicted by exact finite-range DWBA calculations that use optical parameters determined from elastic-scattering data.

The DWBA description of the 90Zr(p,d) 89Zr reaction at energies from 20 MeV to 185 MeV

Exact finite range DWBA calculations were performed for the lowest four transitions in the 90Zr(p,d) 89Zr reaction at seven incident energies varying from 22.9 to 185 MeV. The energy dependence of the spectroscopic factors reported recently by other authors was not reproduced. We point out that the use of an effective p-n interaction related to G-matrix techniques in the DWBA amplitude for the transfer reaction cannot be justified so easily as for the case of inelastic nucleon scattering. Our present results show further that there is no need for such an effective interaction in the DWBA description of the (p,d) reaction.

Large-angle enhancements in the 16O( 6Li, α) 18F reaction at 48 MeV

The elastic scattering of 6Li + 16O at 48 MeV has been measured and fitted with an optical model calculation. Measurements have been made of the 16O( 6Li, α)F reaction at 48 MeV populating the 1 + g.s., 3 + 0.927 MeV and 5 + 1.122 MeV states in 18F. The data exhibit cross sections at large angles comparable to those at forward angles, and have been compared with exact finite-range DWBA calculations. Exchange contributions were included for the 1 + g.s. and were unable to account for the large-angle data. Calculated statistical compound nucleus cross sections were approximately a factor of 100 below the data. The same conclusions are reached for previously published data at 34 MeV.

Exact finite range DWBA calculations for heavy-ion induced nuclear reactions

Nuclear cluster radioactivity is investigated using microscopic potentials in the framework of the Wentzel–Kramers–Brillouin approximation of quantum tunneling by considering the Bohr–Sommerfeld quantization condition. The microscopic cluster–daughter potential is numerically constructed in the well-established double-folding model. A realistic M3Y-Paris NN interaction with the finite-range exchange part as well as the ordinary zero-range exchange NN force is considered in the present work. The influence of nuclear deformations on the cluster decay half-lives is investigated. Based on the available experimental data, the cluster preformation factors are extracted from the calculated and the measured half lives of cluster radioactivity. Some useful predictions of cluster emission half-lives are made for emissions of known clusters from possible candidates, which may guide future experiments.

Four-nucleon transfer with the 32S( 16O, 12C) 36Ar reaction

Angular distributions have been measured for the 32S( 16O, 12C) 36Ar reaction at 45.5 MeV leading to excited states between E x, = 0 and 8 MeV. Experimental cross sections are compared with exact finite-range DWBA calculations in combination with extensive shell-model calculations, which include sd- and fp-shell configurations. Transitions to low-energy positive-parity states and bound negative-parity states are well reproduced. The calculations, however, fail to describe some high-energy positive-parity states. Calculations with a complete cluster expansion for the four transferred nucleons give about 50% larger cross sections, but can not explain the observed discrepancies. Possible interference of reaction processes other than direct α-transfer and special structure effects are discussed.

Resonant structures in the 24Mg( 16O, 12C) 28Si reaction

The gross resonant structures observed in excitation functions at forward angles for the 24Mg( 16O, 12C) 28Si (gs) reaction are studied using exact finite-range DWBA calculations in which the entrance channel potential contains both a J-dependent absorptive terms and a parity-dependent real interaction. The gross structures and their previously assigned J π values are well described by the calculations.

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 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.

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.

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.

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.