Elastic and inelastic scattering of 6Li and 7Li by 54Fe at E = 36–50 MeV

Detailed angular distributions for the elastic and inelastic scattering of ⁷Li at E = 36, 42, and 48 MeV and of ⁶Li at E = 38, 44, and 50 MeV by ⁵⁴Fe have been measured. It is not possible to describe both sets of data with the same set of optical-model parameters. The ratio of $\text{U}\text{W}$ is 0.8 for ⁷Li and 1.4 for ⁶Li at the strong absorption radius, implying stronger absorption for ⁷Li than for ⁶Li. No energy dependence in the optical-model parameters was necessary for either ⁶Li or ⁷Li. The inelastic scattering from the ⁵⁴Fe 2⁺, 1.41 MeV state was well described by the DWBA and the extracted deformation length (βR = 0.62) was the same for both ⁶Li and ⁷Li scattering. It was not possible to describe the ⁷Li projectile excitation data with collective-model DWBA calculations showing that more detailed calculations for the projectile excitation are necessary.     

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 the (d, α) reaction applied to 50Cr and 52Cr

The reactions ⁵⁰Cr(d, α)⁴⁸V and ⁵²Cr(d, α)⁵⁰V have been carried out at an incident deuteron energy of 15 MeV to investigate the structure of the low-lying levels of ⁴⁸V and ⁵⁰V in the light of shell model expectations. Excitation energies and angular distributions have been measured for states up to about 1.5 MeV. For all resolved and strongly excited levels angular momentum transfers could be assigned by comparison with DWBA calculations. For ⁵⁰V spectroscopic factors have been extracted in relative units assuming pure configurations for the transferred pair of nucleons. The results indicate the existence of seniority and configuration mixing in the level structure of the ⁴⁸V and ⁵⁰V isotopes. In both reactions some transitions show characteristic deviations from the direct reaction mechanism. These deviations cannot be reproduced by the DWBA calculations.     

Interfering proton and neutron transfer in the reaction C(N, N)C

Elastic scattering and one-nucleon transfer reactions induced by ¹⁶O have been investigated in the energy region 45–60 MeV on targets of ²⁶Mg, ²⁷Al, ³⁰Si and ⁴⁸Ca. Angular distributions were measured in the angular range 4°–40°. Optical model parameters were derived from the elastic scattering data and the transfer reaction data were analysed using both no-recoil and full-recoil DWBA codes. In the case of proton transfer reactions on ⁴⁸Ca, good agreement was obtained between the data and the DWBA calculations while the data for the lighter targets could not be satisfactorily reproduced. The oscillatory pattern of the angular distributions is discussed in terms of the three-parameter model of Kahana, and it is found that the model qualitatively explains the observed transition from smooth to oscillatory angular distributions.     

Proton-neutron correlation in the deuteron breakup at 56 MeV and prior-form DWBA analysis

Proton-neutron angular correlations in the ¹²C, ⁵¹V and ¹¹⁸Sn(d, pn) reactions have been measured at 56 MeV to investigate the deuteron breakup process. The elastic breakup which leaves the target nucleus in its ground state dominates the coincident spectra. The elastic breakup cross sections are estimated to be 36–48% of the inclusive breakup yields at 15° or 17.5°. In the angular correlations the protons are emitted predominantly on the side of the beam opposite to the neutrons. The experimental data have been analyzed using the prior-form DWBA. For both nuclear and Coulomb breakup, sufficient convergence of the calculations is obtained by including the pn angular momenta up to l = 2. For the nuclear breakup calculations, the l = 0 and 2 contributions dominate the cross sections. For the Coulomb breakup the l = 1 contribution is predominant. In the calculations the effect of the Coulomb breakup is seen at forward angles of the angular correlation. The DWBA calculations reproduce fairly well the coincident energy spectra and the angular correlations in the angular region where the protons are emitted on the side of the beam opposite to the neutrons. On the other hand the calculations overestimate the break-up cross sections by a factor of 2 to 10 in the angular region where the protons are emitted on the same side of the beam as the neutrons. The distributions of deuteron c.m. angular momenta that contribute to the breakup amplitude are examined to obtain information on the region of space in which the breakup reactions takes place.     

The 54Fe(p, d)53Fe and 140Ced(p, d)139Ce reactions at 122 MeVag

The ⁵⁴Fe($\text{p}$, d)⁵³Fe and ¹⁴⁰Ce($\text{p}$, d)¹³⁹Ce reactions have been studied at a proton energy of 122 MeV. Analyzing powers and angular distributions were obtained for outgoing deuterons to the strong low-lying single-particle states in both nuclei. These data along with the data of others at 26, 29, 41, 52 and 24, 35, 55 MeV for ⁵⁴Fe and ¹⁴⁰Ce respectively, have been compared with exact-finite-range DWBA calculations carried out in a consistent fashion to determine the energy dependence of the spectroscopic factors. A strong energy dependence was noticed for the spectroscopic factors when the l-values were large.     

Coulomb-nuclear interference for inelastic deuteron scattering

The interference between Coulomb excitation and nuclear excitation has been observed for ^{54, 56}Fe, ⁶⁰Ni, ¹¹⁴Cd, ¹⁵²Sm, and ¹⁹²Os by measuring excitation functions of elastic and inelastic deuteron scattering at back angles. The interference is strongly constructive, indicating a predominantly imaginary nuclear form factor. DWBA calculations using the collective model, although predicting constructive interference, are unable to predict the magnitude of the observed effect.     

Giant resonances in f-p shell nuclei studied by inelastic scattering of 80 MeV 3He ions

Spectra of ⁴⁸Ti, ⁵⁶Fe, ⁵⁹Co and ⁶⁰Ni have been investigated for excitation energies of 10–20 MeV by inelastic scattering of 80 MeV ³He particles. Broad peaks with excitation energies of about $\text{63±1 A}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}\text{MeV}$ and FWHM of 6 MeV have been observed. Much narrower satellite peaks occur at excitation energies about $\text{51±1 A}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}\text{MeV}$. The angular distributions of the sum of these peaks were compared to extended optical model DWBA calculations which confirm the predominant L = 2 character of the GR. A tentative assignment of L = 2 or 4 was made for the 13.5 MeV satellite peak in ⁵⁶Fe. We see no definite evidence for the presence of an L = 1 GR component.     

The (p,t) reaction on 12C, 54Fe and 208Pb at 80 MeV

Angular distributions have been measured for the low-lying levels of the residual nuclei for the ¹²C, ⁵⁴Fe and ²⁰⁸Pb(p, t) reactions at E_p = 80 MeV. The shapes of these angular distributions are generally well reproduced by the zero-range distorted-wave Born approximation (DWBA). Enhancement factors extracted from the data show that the DWBA predicts relative strengths consistent with those observed at lower bombarding energies. However, the overall empirical DWBA normalization at E_p = 80 MeV is observed to be $\text{1}\text{12}$ ($\text{1}\text{4}$) of that required at 40 MeV for ²⁰⁸Pb (⁵⁴Fe).     

DWBA analysis of (3He,d) reactions at 90MeV and contributions from the nuclear interior

Differential cross sections of ³He elastic scatterings and (³He, d) reactions have been measured at 90 MeV for ²⁸Si, ⁵⁴Fe, ⁵⁸Ni, ⁹⁰Zr and ¹²⁴Sn. From the optical-model analysis of the elastic scattering, both shallow ($\text{V ? 105}\text{MeV}$) and deep ($\text{V ? 150}\text{MeV}$) potentials of ³He were obtained. The shallow potentials correspond to the ones which were determined uniquely from other measurements extended to more backward angles. The (³He, d) reactions have been analyzed with the DWBA using the shallow and deep potentials for ³He. The calculations using the deep potentials reproduced the data well, but those using the shallow ones did not. The contributions from the nuclear interior were investigated through the radial cutoff in the DWBA. The calculations using the shallow potentials reproduced the data well when the radial cutoffs were introduced. The effects of the radial cutoff were very small when the deep potentials were used. It was found that a much greater reduction of the contributions from the nuclear interior was needed when the shallow potentials were used in the DWBA calculations.     

Scattering of polarized protons by iron and nickel isotopes

Elastic and inelastic scattering of polarized protons (E = 17.2, 20.4, 24.6 MeV) by ^{54, 56}Fe and ^{58, 60, 62} Ni have been investigated. Most data can be readily accommodated by standard optical-model and DWBA procedures, including full Thomas coupling. The 2⁺₁ state (1.41 MeV) in ⁵⁴Fe is peculiar because the inelastic scattering data require deformation parameters for the central and spin-orbit parts of the nuclear potential that differ by a factor 2 to 3; moreover, this anomaly shows a marked energy dependence.     

Investigation of two- and three-nucleon transfer reactions in12C +56Fe

Multi-nucleon transfer reactions⁵⁶Fe(¹²C, X) have been studied at an incident¹²C energy of 60 MeV. Angular distributions of¹⁰Be and⁹Be corresponding to 2p and 2p 1n transfer reactions in transition to low-lying states in the residual nuclei have been measured. The angular distribution data for 2p transfer have been analysed in terms of finite range DWBA calculations assuming a one-step transfer of two protons. The spectroscopic factors for three low-lying transitions observed in⁵⁶Fe(¹²C,¹⁰Be)⁵⁸Ni have been extracted. Transfer probabilities for the ground state transition in two- and three-nucleon stripping channels have been obtained and compared with the corresponding sequential transfer probabilities in order to emphasise the role of direct transfer of nucleons vis-a-vis sequential transfer.     

High resolution study of the reactions 54, 56, 58Fe(16O, 12C)58, 60, 62Ni and a comparison with (6Li,d) α-transfer spectroscopy

Spectra and angular distributions for the reactions ^{54, 56, 58}Fe(¹⁶O, ¹²C)^{58, 60, 62}Ni (E_x = 0.0–4.5 MeV) have been measured at 50 MeV with an energy resolution of 45–80 keV using a Q3D spectrograph. The selectivity of the (¹⁶O, ¹²C) reaction is found to be very similar to the (⁶Li, d) reaction. The close correspondence recently noted between the (⁶Li, d) spectra and levels strongly excited in (t, p) and (³He, n) two-nucleon transfer reactions is also observed to be present for the (¹⁶O, ¹²C) reaction. Relative α spectroscopic factors for (¹⁶O, ¹²C) and (⁶Li, d) obtained in a DWBA analysis assuming direct one-step α-cluster transfer are in very good quantitative agreement. Unnatural parity states, whose excitation is forbidden in the DWBA α-cluster approximation, are observed to be very weakly populated. These results, together with previous work on s-d shell and Ni targets, strongly suggest that the spectroscopic information provided by the (¹⁶O, ¹²C) and (⁶Li, d) reactions is essentially the same and that this information may be reliably extracted by DWBA analysis.     

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 $\text{E(}{}^7\text{Li) = 48}\text{MeV}$. 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 $\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ 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.     

A study of the odd isotopes of copper using the 58, 60, 62, 64Ni(τ, d) 59, 61, 63, 65Cu and 48Ca(τ, d)49Sc reactions

Experimental measurements are reported for the ^{58, 60, 62, 64}Ni(τ, d) ^{59, 61, 63, 65}Cu and ⁴⁸Ca(τ, d)⁴⁹Sc reactions and for the elastic scattering of ³He particles from ^{58, 60, 62, 64}Ni and ⁴⁸Ca targets at an incident energy of 18 MeV. The (τ, d) angular distributions cover the angular range from approximately θ_c.m. = 5° to 90° and the elastic scattering angular distributions range from θ_c.m. = 12° to 172°. In the (τ, d) reactions several weakly excited states, not previously seen in stripping reactions, have been identified and assignments of the transferred angular momentum made. The ⁴⁸Ca(τ, d)⁴⁹Sc reaction data are used in conjunction with the theoretical sum rules of MacFarlane and French to determine the normalization factors to be used with DWBA calculations for different sets of optical potentials. These normalization factors are used to extract spectroscopic strengths and centroid energies from the Ni(τ, d)Cu data which are compared with published model calculations for the odd copper isotopes. It is concluded that these calculations invariably fail to give a consistent picture of the odd copper isotopes mainly due to the use of centroid energies as variable parameters in the model calculations.     

Exact finite-range DWBA description of the60Ni(160,12C)64Zn reaction at 60 MeV incident energy

Cross section angular distributions of⁶⁰Ni(¹⁶O,¹²C)⁶⁴Zn reactions leading to three strongly excited states at 60 MeV incident energy and the¹⁶O+⁶⁰Ni and¹²C+⁶⁴Zn elastic scattering at 60 MeV respectively 45 MeV and 54 MeV have been measured using aQ3D magnetic spectrograph. EFR-DWBA calculations assuming the transfer of anα-cluster in its 0s ground state are able to describe the general features of the strongly oscillating experimental angular distributions using a surface transparent optical model potential. The optical model parameters used in the DWBA calculations are obtained from fits of the elastic scattering data of incident and exit channels. The importance of “correct” optical model parameters in the exit channels for relative spectroscopic factors will be discussed and the extracted relative spectroscopic factors will be compared to previous (⁶Li,d) results.     

Shell structure studies in the titanium region with 52 mev deuterons

The (d,³He)-reactions on the target nuclei^48,50Ti and⁵¹V have been studied with 52 MeV deuterons. The data were analyzed by means of the DWBA which is shown to be applicable at this energy. All our results agree well with the assumption of pure (f _7/2)ⁿ proton configurations for these nuclei. The inelastic scattering of 52 MeV deuterons from the lowest 2⁺ state in⁴⁸Ti has been described in terms of the collective model as well as of the microscopic shell model. Good fits to the measured angular distributions have been obtained with reasonable values for the deformation parameters and the basic nucleon-nucleon interaction.     

Prior-form DWBA analysis of (3He,pd) elastic breakup at 90 MeV

Proton-deuteron coincident cross sections in ¹²C,⁵¹V,⁹⁰Zr(³He,pd) elastic breakup at 90 MeV have been calculated within the framework of the prior-form distorted-wave Born approximation (DWBA). Sufficient convergence of the calculations was obtained by including the pd relative angular momenta up to l = 4. The calculations reproduced the general trend of the coincident energy spectra and the angular correlation data, though deficiencies of the calculations were seen at some angles. The peripheral feature of the (³He, pd) elastic breakup is discussed from the angular momentum dependence of the transition amplitude.