Finite-range DWBA Calculations Research Articles

Nucleon transfer in heavy-ion reactions: energy dependence of the cross section

The authors derive an analytical formula for the transfer cross section in a heavy-ion reaction at high incident energy (>or=20 MeV/u). A semiclassical transfer amplitude and a sharp cut-off approximation for the absorption from the elastic channel are used. Two reactions are studied and the results compared with finite-range DWBA calculations.

Tensor polarisation of [formula omitted] in the [formula omitted] reaction at Ep = 41.3 MeV

Angular correlation measurements have been made between the deuterons and the 12C g.s. product nuclei in the reaction 13 C( p,d) 12 C ∗(15.11 MeV, 1 +)(→ 120 C g.s. + γ) at deuteron scattering angles of 40°, 50°, 60°, and 75°, and a proton bombarding energy of 41.3 MeV. These measurements yield information concerning the k = 2 polarisation tensors ( t 2q) of the excited 12C nucleus produced in the direct (p, d) reaction. Cross-section angular distributions to the strongly excited g.s., 4.43, 12.71, 15.11 and 16.11 MeV states are also reported. Monte Carlo simulations of the laboratory distribution functions associated with the individual t kq were performed, incorporating the effects of finite geometry (beam spot and detector sizes), beam divergence, energy loss and multiple scattering of the 12C nuclei in the target. Finite range DWBA calculations were performed describing the polarisation tensors and cross sections, assuming a 1p neutron pickup. DWBA calculations for both conventional (elastic) and adiabatic d + 12C potentials were performed. Also, the effects of spin-orbit and the T r and T ℓ tensor potential were studied. The results confirmed that the “standard” DWBA formalism using an elastic d + 12C potential is inadequate for describing the recoil nucleus polarization. The use of adiabatic potentials, which arise from three-body effects, produced an improvement in the description of the extracted data. The DWBA calculations showed only a modest sensitivity to inclusion of spin-orbit and the T r or T ℓ tensor terms in the deuteron optical potential.

The 18O(p, α) 15N reaction at 40.9 MeV

The 18O(p, α) 15N reaction has been studied at a proton energy of 40.9 MeV with an overall energy resolution of about 100keV. Differential cross sections for levels with excitation energies up to about 12 MeV were measured. Finite-range DWBA calculations were performed using cluster form factors, and the deduced spectroscopic factors compared with the shell-model calculations of Millener. Numerous states show considerably greater strength than predicted by the shell model.

Elastic scattering and single nucleon transfer reactions for 7+ 11B and 7Li+ 13C at 34MeV

Elastic scattering cross sections for 10–170° c.m. have been measured for 7Li+ 11B and 7Li + 13C at 34 MeV. These data have been analyzed with the optical model using Woods-Saxon potentials, or potentials with a double-folded real part. The double-folded potentials were found to fit the data better, and quadrupole contributions were required to fit the large angle 7Li+ 11B data. In addition angular distributions for the ( 7Li, 8Li), ( 7Li, 6Li) and ( 7Li, 6He) reactions were measured. The transfer data were analyzed with finite-range DWBA calculations which were able to describe the shape of the data well and produced spectroscopic factors in agreement with theoretical and other experimental values. A phase shift of about 3° between the calculations and the data was found for the ( 7Li, 6Li) and ( 7Li, 6He) reactions.

Energy dependence of the 28Si( 32S, 36Ar) 24Mg reaction between 90 and 103 MeV incident energy

Angular distributions for the 28Si( 32S, 36Ar) 24Mg reaction have been measured from 90 to 103 MeV of incident lab energy, in steps of 0.5 MeV. The ground state, the 2 1 + level in each nucleus and the mutual excitation of both 2 1 + states have been resolved. The data have been analysed in the frame of finite range DWBA calculations. The deduced relative spectroscopic factors show good agreement with those predicted by the model of Chung and Wildenthal but are smaller than those deduced in other experiments.

Detailed test of distorting potentials for the transfer reactions 40Ca( 7Li, 6Li/ 6He)

Angular distributions for the transfer reactions 40Ca( 7Li, 6Li) 41Ca and 40Ca( 7Li, 6He) 41Sc have been measured at 34 MeV, in small angular increments out to angles where the cross section has fallen by four orders of magnitude. Finite range DWBA calculations show a high sensitivity to different distorting potentials at the largest angle cross sections. It is found that a combination of Woods-Saxon and double-folded potentials does the best job of reproducing the data over the whole angular range.

Alpha-particle D-state and configuration-mixing effects in the 89Y(d, α) 87Sr reaction

Angular distributions of cross sections and vector and tensor analyzing powers have been measured for low-lying levels populated by 89Y(d, α) 87Sr reaction at 9.0, 12.0, and 16.0 MeV. Full finite-range DWBA calculations that include the effects of an α-particle D-state component and ( L, J) mixing have been performed. The ground-state transition indicates that the D-state parameter D 2 = −0.30 ± 0.1 fm 2. The angular distributions of the tensor analyzing powers are very sensitive to the magnitude and sign of the mixing amplitudes and can be used to determine the neutron-proton configurations transferred. The mixing amplitudes for the 0.388 MeV and 0.873 MeV states in 87Sr are established from the analysis.

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.

Four-nucleon pickup reaction on 12 ⩽ A ⩽ 94 nuclei

The differential cross sections for the (d, 6Li) reaction on targets of 12C, 16O, 24Mg, 40Ca, 58Ni and 94Mo have been measured at E d = 54.2 MeV. The measured angular distributions have been analyzed by finite-range DWBA calculations, and spectroscopic factors for an α-cluster transfer have been extracted. In the DWBA analysis using an optical model with a phenomenological Woods-Saxon potential, the spin-orbit part of the deuteron optical potential played a significant role in reproducing the measured angular distributions but the spin-orbit part of the 6Li optical potential had a minor effect. Relative spectroscopic factors extracted from the present data were compared with theoretical predictions together with the results from the (p, pα) reaction. The relative spectroscopic factors for 1p-shell nuclei were in quantitative agreement with theoretical predictions. However, there were certain discrepancies between the spectroscopic factors extracted from the (d, 6Li) reaction and those from the (p, pα) reaction, and the discrepancies increased with target mass number.

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.

A microscopic cluster form factor for 6Li → α + d and its application to the ( 6Li, d) and (d, 6Li) reactions

A microscopic form factor for the process 6Li → α + d is derived by summing a realistic nucleon-nucleon interaction between the nucleons in the alpha and deuteron clusters within a fully antisymmetrized 6Li wave function and integrating over the internal coordinates of the clusters. The form factor is employed in finite-range DWBA calculations of the ( 6Li, d) and (d, 6Li) reactions and in general provides a good description of the shapes of the angular distributions. However, the spectroscopic factors for ( 6Li, d), (d, 6Li), and those calculated from the shell model are in poor agreement.

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.

Spectroscopy of A = 16 from 13C( 6Li, t) 16O

The 13C( 6Li, t) 16O reaction has been studied at 34 MeV. Selective population of narrow states is observed up to 21 MeV excitation in 16O. This reaction populates strongly both unnatural-and natural-parity states that have little or no 12C + α 0 width. The measured angular distributions are compared with Hauser-Feshbach and finite-range DWBA calculations. Reasonable agreement with the DWBA calculations is found for most of the states strongly populated. The widths of the narrow states populated in the 16–20 MeV excitation region are presented. Comparison of the present data with that from medium-energy inelastic scattering and other multiparticle transfer reactions is made.

Finite-range DWBA calculations of the ( 6Li,d) reaction using an antisymmetrized 6Li wavefunction

The ( 6Li,d) reaction is well described by finite-range DWBA calculations that use 6Li and deuteron optical model parameters that fit elastic scattering when an antisymmetrized 6Li wavefunction is used.

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.

Heavy-ion reactions with nucleon transfer using Skyrme-type potential

Nuclear reactions between two heavy interacting ions with nucleon transfer have been reconsidered. The direct nuclear reaction mechanism is considered. Different reaction processes are considered for single neutron or proton stripping and pickup reactions. The interacting nuclear potential of the transferred nucleon is taken to have the form of the Skyrme-type potential. With this representation for the nuclear potential of the transferred nucleon, an expression for the differential cross section is obtained by using the distorted-wave Born approximation. This expression is applied and considered for the heavy ion reactions with incident heavy ion projectiles $^{10}\mathrm{B}$, $^{13}\mathrm{C}$, $^{16}\mathrm{O}$, $^{18}\mathrm{O}$, and $^{32}\mathrm{S}$ bombarding the heavy targets $^{27}\mathrm{Al}$, $^{28}\mathrm{Si}$, $^{29}\mathrm{Si}$, $^{30}\mathrm{Si}$, and $^{32}\mathrm{S}$. The energies of the incident heavy ions have values in the range between 36.0 and 100.0 MeV. Numerical calculations of the differential cross sections are carried out. The theoretically calculated angular distributions are in good agreements with the experimental measurements. Reasonable spectroscopic factors are extracted from the present calculations.NUCLEAR REACTIONS Nucleon stripping and nucleon pickup induced by 36.0-100.0 MeV $^{10}\mathrm{B}$, $^{13}\mathrm{C}$, $^{16}\mathrm{O}$, $^{18}\mathrm{O}$, and $^{32}\mathrm{S}$ on $^{27}\mathrm{Al}$, $^{28}\mathrm{Si}$, $^{29}\mathrm{Si}$, $^{30}\mathrm{Si}$, and $^{32}\mathrm{S}$; calculated $\ensuremath{\sigma}(\ensuremath{\theta})$. Finite range DWBA calculations, extracted spectroscopic factors.