DWBA Theory Research Articles

Potential energy calculations of the rotational barriers in molecular solids: I: Polycyclic aromatics

Neutron time-of-flight spectra from the 23Na(d, n)24Mg reaction have been measured at Ed = 5.5MeV. Angular distributions of transitions to 20 states in 24Mg up to 12.7 MeV excitation energy have been analysed with DWBA and Hauser-Feshbach theory to yield lp values and absolute spectroscopic factors. The spins and parities of the 24Mg states at 7.75 and 8.86 MeV were found to be 1+ and 2−, respectively. The T = 1 isobaric analogue states were identified at 9.52, 10.07, 10.74, 11.22, 12.53 and 12.67 MeV, the latter two being the previously un-observed analogues of the 24Na states at 3.41 and 3.37 MeV, respectively. From the isobaric analogue identification, probable spins and parities of several 24Na states were deduced. The experimental spectroscopic factors for stripping to the six lowest-lying 24Mg states show rather poor agreement with the Nilsson model predictions.

Spin-dependence and coherent summations in two-nucleon transfer reactions

Abstract The differential cross sections of the 19 F(p, 3 He) 17 O and 19 F(p, t) 17 F reactions leading to the ground and first three excited states have been measured at an incident energy of 42.4 MeV. The polarization analysing powers of two of the (p, 3 He) reactions have been measured at a higher energy of 49.5 MeV with a polarized incident beam. The experimental results have been analysed in terms of conventional DWBA theory, and the importance of interference terms arising from the proper coherent summations contained in the definition of the differential cross section and analysing power, have been investigated. It is found that the interference term arising from the coherent summation over the transferred spin S is significant and should not normally be neglected.

DWBA with charge exchange and isospin

The DWBA theory is examined under the assumption that both the form factors and distorted waves are functions of isospin. The formalism is developed and presented in both the coupled (isospin) and uncoupled (neutron-proton) representations. Applications are made in the areas of inelastic scattering and rearrangement phenomena. A model involving the t · T operator and the conservation of isospin for the strong interaction is introduced. The relation between this model and antisymmetry is discussed. A set of generalized Lane equations, the solutions of which describe both elastic and quasi-elastic scattering, are derived. This approach allows the charge exchange process to be explicitly incorporated into the transition amplitude. Numerical calculations are performed and partial success is attained in explaining certain spectroscopic anomalies deduced previously by conventional theory.

A study of the (d, α) reaction in 56Fe at 12 MeV

The (d, α) reaction in 56Fe is studied at E d = 12 MeV and angular distributions of the α-particles are obtained over the angular range 13°–83° (c.m.s.); the results are analysed in terms of the DWBA theory of direct reactions using the two-nucleon pick-up mechanism of Glendenning. Spectroscopic information on 54Mn levels up to 4.3 MeV excitation is obtained.

Study of (d, p) reactions to unbound states of 13C AND 17O

Cross-section and vector-analysing-power measurements have been made for (d, p) reactions on 12C and 16O leading to the unbound fourth, eighth, ninth, tenth, and eleventh excited states in 13C and to the unbound fourth, fifth and eighth excited states in 17O. The results are compared to predictions of the DWBA theory using (i) a form factor for a weakly bound particle, and (ii) a resonance form factor, following the approach of Vincent and Fortune. For the transitions in which the stripping mechanism dominates, the two approaches give results of comparable quality, except that the measured cross sections at forward angles are better reproduced using resonance form factors. Resonance widths obtained from the analysis generally agree with those obtained from neutron scattering measurements. Results are also presented for 16O(d, p 3) 17O ∗ and for the transitions to the bound states of 13C.

A study of nuclear structure in 59Ni from the (d, p) reaction on 58Ni

Level structure in 59Ni is studied from the (d, p) reaction in 58Ni using the Aldermaston tandem Van de Graaff accelerator and the multichannel magnetic spectrograph. Angular distributions of protons are measured over the angular range 5°–175° up to an excitation of ≈ 8 MeV and absolute cross sections are measured. The data are analysed in terms of the finite-range DWBA theory of direct reactions and spins, parities and spectroscopic factors are deduced for various levels. The summed spectroscopic factors and the single-quasiparticle energies of the shell-model states are obtained. Properties of the low-lying levels in 59Ni are compared with predictions based on exact shell-model calculations.

The Elastic and Inelastic Scatterings of 3He from 12C at 24.0, 29.2, 34.7 and 39.6 MeV

The measurements were made at angles of the center of mass extending from 14° to 128° or 172°. The yield of inelastic scattering at most angles was of the same order in the elastic scattering. A Thomas type spin-orbit coupling of the optical potential is useful for the elastic scattering at backward angles. Discrete and continuous ambiguities in the optical model parameters appeared in the analysis. The experimental values of inelastic scattering were predicted fairly well by the DWBA theory, and the deformation parameters β 2 were about 0.5. In the coupled channel analysis, the predicted values of elastic scattering were much different from the results of optical model analyses by coupling to the inelastic channel, and the potential whose imaginary part was shallower than that given by the optical model analysis gave better fit. The value of β must be -0.5 for 39.6 and 34.7 MeV.

Analysis of (d, p?) Reactions

The reactions 24Mg(d, py)25Mg via the 3 �40 MeV state, 4�Ca(d,py)41Ca via the 1�95 MeV state, and 28Si(d,py)29Si via the 2�03 MeV state are analysed using the stripping theory developed by Butler, Hewitt, McKellar, and May. The theory is in reasonable agreement with the experimental data. It is pointed out that a study of the correlation as a function of the proton scattering angle is necessary to obtain a test of this theory vis-it-vis the standard DWBA theory of stripping reactions.

Coulomb (d, p) stripping to states in 117,123,125Sn

Angular distributions were measured for the reactions 116Sn(d, p) 117Sn(d, p) 123Sn and 124Sn(d, p) 125Sn at several incident deuteron energies between 4.55 and 5.55 MeV. Below 5.2 MeV excitation energy, 52 levels are observed in 117Sn, 49 in 123Sn, and 49 in 125Sn. Many of the upper levels in all three nuclei are previously unreported, as is the 0.859 MeV level in 125Sn. Spectroscopic factors and reduced widths for many states of interest were extracted using the DWBA theory. Comparison with Spectroscopic factors from other experiments and with results from pairing theory calculations reveals general agreement, although not within the accuracy expected for the present results.

Polarization of protons from the 9Be(d, p)10Be reaction at Ed = 12.0 MeV

Abstract The polarization of protons from the 9 Be(d,p) 10 Be reaction at E d = 12.0 MeV was measured for the ground state and first excited state transitions. The results obtained are compared with the predictions of DWBA theory. It was found that better fits to the experimental data can be obtained using volume absorption in the distorting potential of the deuteron elastic channel. A comparison of the present polarization data with the vector analysing power for the same reaction and the same incident deuteron energy has also been made.

Elastic and inelastic proton scattering from 86Sr

Angular distributions of elastically and inelastically scattered 12 MeV protons from 86Sr have been measured for angles between 24° and 165°. Inelastic scattering to 20 levels in 86Sr were observed, and angular distributions measured for the ground state and excited states at 1076, 1854, 2482 and 2997 keV. The 2482 keV level appears to be the octupole state, rather than the 2997 keV level which also has spin-parity 3 −. Quadrupole and octupole deformation parameters β 2 = 0.130 and β 3 = 0.153 were extracted from the experimental cross sections for inelastic scattering to the 2 + and 3 − states at 1076 and 2482 keV, respectively, by means of DWBA theory and coupled-channel calculations. The coupled-channel calculation for the differential cross section for the possible two-phonon 2 + state at 1854 keV indicates that this state has a limited phonon-like character.

A study of the 46, 48Ti( 3He, t) and 58, 60Ni( 3He, t) reactions to isobaric analogue states

The ( 3He, t) reaction populating 0 + and 2 + states in 58, 60Cu and 46, 48V which are isobaric analogue states (IAS) of the 0 + ground states and 2 + first excited states in 58, 60Ni and 46, 48Ti have been studied at an incident 3He energy of 24.6 MeV. Triton spectra were measured for the targets 46,48Ti, natNi and 58Ni and angular distributions for the 0 + and 2 + IAS of 46, 48Ti and 58, 60Ni determined. The data were obtained using a magnetic spectrometer and position-sensitive detectors. The results have been analysed using DWBA theory. The 0 + → 0 + transitions to analogue states are described quite well using a microscopic form factor derived from a nucleon-nucleon interaction. However, with a Gaussian form, the m.s. radius of this interaction is only limited to the region 0–9 fm 2. Comparisons with data at other incident energies indicate that the strength of the effective interaction is strongly energy dependent. The Coulomb energies and ( 3He, t) angular distributions of the states assigned as the 2 + analogues in 48V and 58,60Cu are not described well by the models investigated. The 46V 2 + IAS angular distribution is reproduced by a microscopic calculation, however. The ratios of the 0 + → 2 + IAS to the 0 + → 0 + IAS transitions are used to deduce a quadrupole deformation for the valence neutrons. The difference in the quadrupole deformations of the matter and proton distributions, as determined by other means, is found to be correlated with those of the valence neutrons. Several transitions to non-analogue states are also investigated.

Inelastic scattering of 12.8 MeV deuterons from 39K nuclei

The cross sections for the elastic and inelastic scattering of 12.8 MeV deuterons by 39K have been measured by means of a broad-range magnetic spectrograph. Angular distributions from 20° to 145° were obtained for deuterons inelastically scattered to the 2.53, 2.82, 3.02, 3.60, 3.88, 3.94, 4.08 + 4.09, 4.12, 4.51 and 5.17 MeV states in 39K. These cross sections are analysed with the DWBA theory, and the angular momentum transfer and dynamical deformation parameters are determined. A discussion of the structure of the 39K levels in terms of the excited core model is given.

Features of core polarization knock-out exchange contributions to inelastic nucleon scattering

The collective virtual core excitation model is employed in the description of core polarization exchange contributions and the antisymmetrized microscopic DWBA theory of inelastic nucleon scattering. These numerical investigations extend the widely used direct core polarization corrections to include exchange terms arising from antisymmetrization of projectile and target nucleons. Several results are discussed in terms of angular momentum transfer and interaction multipolarity for scattering to low-lying states in 89Y.

Reactions induced by 30 MeV α-particles on 7Li

A 7Li target was bombarded with α-particles of 30 MeV. Angular distributions of emitted protons, deuterons and tritons were measured simultaneously. The results are analysed in terms of DWBA and PWBAE theories. Better fits are obtained for PWBAE calculations. Validity of a DWBA theory is discussed and cluster reduced widths concerned are deduced.

Elastic and inelastic proton scattering from 116Cd

The differential cross sections for elastically and inelastically scattered 12 MeV protons from 116Cd have been measured for 18 groups to levels below ≈ 2.8 MeV. The elastic scattering was fitted by searching for the best parameters of an optical model. The observed cross sections for excitation of the one-phonon 2 + and 3 − states were compared to the predictions of both the DWBA and coupled-channel theories. Distortion parameters were extracted and compared to those determined from E2 transition probabilities. The coupled-channel theory was used to calculate cross sections for the one-octupole-one-quadrupole and two-quadrupole phonon states. States at 2.041, 2.115 and 2.296 MeV were fitted by means of the 1 −, 3 − or 5 −, and 3 − octupole-quadrupole coupled-channel calculations, respectively. Fits to the two-quadrupole phonon-like states were obtained by assuming an admixture of the one-phonon state in their description. The amplitudes of these admixed wave functions were calculated from both the proton scattering and Coulomb excitation experimental results and it was found that the onephonon amplitudes, especially for the second 2 + states, are large. The results for 116Cd are compared with those obtained from inelastic proton scattering and Coulomb excitation of other nuclei in this mass region to determine systematic trends.

Finite-range DWBA analysis of (p, α) reactions on 9Be and 11B

The ground state angular distributions of the reactions 9 Be(p, α) 6 Li and 11 B(p, α) 8 Be are analyzed by means of the DWBA theory. One-step direct mechanisms only are considered, but for both reactions the inclusion of the heavy-particle pick-up is found to be essential. DWBA fits to the data are obtained (a) in the zero-range approximation, (b) in the “fixed-range” approximation and (c) by an exact finite-range calculation. Only the latter method yields both an acceptable fit and reasonable values for the spectroscopic factors.

The (3He, 6Li) reaction on several nuclei in the region A = 10 to 27

Abstract Angular distributions for the (3He, 6Li) reaction were measured on the targets 12C, 16O, 19F, 23Na and 27Al at a 3He bombarding energy of 40.7 MeV, on 10B, 12C, 16O and 19F at 30.0 MeV and on 19F at 22.4 MeV. The reaction was described within the framework of the zero-range DWBA theory, and triton reduced widths for the target nuclei were extracted. These experimental widths are compared with the theoretical triton reduced widths predicted by j−j coupling.

The 9Be(p, d) 8Be reaction

The 9Be(p, d) 8Be reaction at 46 and 100 MeV have been analysed using the DWBA theory with a local-energy approximation. The deuteron optical potentials were obtained by fitting the angular distribution of the ground state transition. Reasonably good fits to the experimental data have been achieved. Spectroscopic factors were extracted from experiment using both the pure isospin wave functions and mixed isospin wave functions for the states in the 16 to 20 MeV region in 8Be, and the results were compared with various shell-model predictions. It has been found that the agreement between theory and experiment was significantly better with the isospin-mixed wave functions than without isospin mixing.

The (α, t) reaction on medium-weight odd-mass nuclei (II). 59Co

Angular distributions have been measured from 15° to 55°(lab) for the 59Co(α, t) 60Ni reaction at 29.0 MeV and analysed by the DWBA theory. Zero-range DWBA calculations gave better fits to the l p = 3fs and l p = 1 transitions with the depths of the real pans of the α-particle and triton potentials equal to 204.0 and 142.0 MeV, respectively. The results gave information about 1p-1h states of the 60Ni nucleus containing the particular ( 1 f 7 2 −1 - one particle ) components.