Deuteron stripping to the single particle states of 17O

Angular distributions for deuteron-¹⁶O elastic scattering and the ¹⁶O(d, p)¹⁷O reaction leading to levels with E_x = 0.0, 0.87, and 5.08 MeV have been measured at energies of 25.4, 36.0 and 63.2 MeV. The elastic deuteron data have been fit with a standard spin one optical model potential to obtain parameters for use in a DWBA analysis of the (d, p) data. The potential found in the search is shown to be consistent with other data taken in the range from 25 to 82 MeV. In addition to this deuteron optical potential, an adiabatic deuteron potential, which includes the effects of deuteron breakup, was used in the DWBA analysis. The neutron form factor was selected independent of the width of any state. The mean square radius, a single particle property, is used to find the well parameters and it determines the width of the single particle state. The spectroscopic factors obtained for the ground and first excited states are between 0.8 and 1.0 and are consistent with a large single particle parentage for these states and lower energy data. The width extracted from the DWBA analysis of the 5.08 MeV unbound state was 20% less than that obtained from elastic neutron scattering to the same state, possibly pointing up some difficulties with DWBA procedures commonly used. The adiabatic deuteron potential yields spectroscopic factors that are energy independent to 20% and gives satisfactory calculated angular distribution shapes for angles less than 40°. The conventional deuteron potential gives less satisfactory calculated shapes with the consequent introduction of some ambiguity in the derived spectroscopic factors.     

Observation of deuteron D-state and compound nucleus effects in (d,p) reactions on 46Ti and 52Cr with a polarized deuteron beam

The cross section and the vector and tensor analyzing powers have been measured for ⁴⁶Ti(d, p)⁴⁷Ti at deuteron energies of 6 and 10 MeV and ⁵²Cr(d, p)⁵³Cr at 6 MeV. Transitions were observed to the states at E_x=0.159, 1.549 and 1.793 MeV in ⁴⁷Ti and the states at E_x=0.0, 0.564, 1.006 and 2.321 MeV in ⁵³Cr. In addition, the cross sections and vector analyzing powers for deuteron elastic scattering were measured for the same targets and deuteron energies and compared to optical model calculations. The choice of optical parameters for the DWBA analysis of the (d, p) reactions is discussed. Calculations made with the DWBA method show that the deuteron D-state must be included to reproduce even qualitatively the (d, p) tensor analyzing power measurements. The j-dependence of the tensor analyzing power T₂₂ is discussed. The validity of the local energy approximation (which was used to incorporate the deuteron D-state into the DWBA calculations) is evaluated by comparison to finite range calculations. The contribution of compound nucleus reactions to the measured cross sections and analyzing powers was investigated. In order to determine the compound cross section, the Ericson fluctuations in excitation functions of cross section and vector analyzing power were measured from 5 to 7 MeV on each target. The formulas used to calculate the polarization observables from the Hauser-Feshbach theory are presented.     

Study of low-lying levels in 47Ca with the 48Ca(d, t)47Ca reaction

Angular distributions of cross sections [α(θ)] and vector analyzing powers [iT₁₁(γ)] have been measured for seven low-lying states or groups of states excited by the ⁴⁸Ca($\text{d}$, t)⁴⁷Ca reaction with 13.5 MeV deuterons and analyzed by the DWBA. On the basis of comparison of vector analyzing powers with DWBA calculations, spin-parity assignments have been made or confirmed for several states. Spectroscopic factors have been extracted. Angular distributions for weak states at 3.30 and 3.57 MeV excitation in ⁴⁷Ca could not be reproduced by DWBA calculations. Investigations of compound nucleus and multi-step contributions to the cross sections and analyzing powers for these states have been made by means of Hauser-Feshbach and CCBA calculations. Optical model parameters were obtained from analysis of 13.5 MeV deuteron elastic scattering cross sections and analyzing powers.     

Vector analysing power and cross section for 90Zr(d, p)91Zr at 11 and 12 MeV

Angular distributions of the vector analysing power and the cross section were measured for ⁹⁰Zr($\text{d}$, p)⁹¹Zr. Measurements were made on two transitions at a deuteron energy of 11 MeV and on 20 transitions at 12 MeV. The observed j-dependence of the vector analysing power provided unambiguous spin assignments for most final states. Measurements of the cross section and vector analysing power were also made for deuteron elastic scattering at 11 MeV in order to determine the potential parameters for DWBA calculations. The DWBA predictions are in good agreement with the measured (d, p) cross sections and in qualitative agreement with the analysing powers. Enriched targets.     

A study of the reactions208Pb(d,d)208Pb and208Pb(d,p)209Pb at energies above and below the Coulomb barrier

The reactions²⁰⁸Pb(d, d)²⁰⁸Pb and²⁰⁸Pb(d, p)²⁰⁹Pb have been studied in the energy region from below to above the Coulomb barrier. An optical-model analysis of the elastic scattering results has been performed to obtain parameters for a DWBA analysis. Distorted wave calculations for the direct transitions leading to single-particle states in²⁰⁹Pb have been used to extract spectroscopic factors. Only two deuteron potential sets give a good account of the stripping data throughout the energy region studied.     

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.     

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.     

The16O(d,n)17F reaction at deuteron energies from 2.5 to 5.5 MeV

The¹⁶O(d, n)¹⁷F transitions to the ground state and to the first excited state were studied in the deuteron energy range 2.5–5.5 MeV. Time-of-flight techniques and gas targets were used. Differential cross sections in the angular range 0–160? at deuteron energies from 3.0 to 5.5 MeV in steps of 0.5 MeV were recorded as well as yield curves at 0 and 30? from 2.5 to 5.5 MeV in steps of 100 keV. DWBA calculations using seven different deuteron optical potentials were performed. It is found that the spectroscopic factors depend strongly on the choice of deuteron optical potential. The ratio between the spectroscopic factors for the ground state and for the first excited state varies between 0.9 and 1.7 for various choices. The most straightforward choice gives the ratio 1.4. Similar studies at higher deuteron energies have yielded ratios close to unity.     

Studies of single-neutron holes in the transitional nuclei N = 83–89: The 142Ce(d,t)141Ce and 142Ce(3He, α)141Ce pick-up reactions

The level structure of ¹⁴¹Ce up to 3.7 MeV excitation energy has been investigated by the (d, t) and (³He, α) reactions using 17 MeV deuteron and 24 MeV ³He beams respectively. The angular distributions have been analyzed with standard DWBA calculations and spectroscopic factors are deduced. The experimental information is compared to unified model calculations involving both one-particle and two-particle one-hole configurations with quadrupole and octupole vibrations of the underlying N = 82 and N = 84 core.     

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.     

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.     

Finite-range DWBA analyses of (dt) and (d3He) reactions on 64Zn at Ed = 13 MeV

Exact finite-range DWBA analyses of ($\text{d}\text{, t}\text{)}$ and $\text{(}\text{d}\text{d}$, ³He) reactions have been performed for an ⁶⁴Zr target at an incident deuteron energy of 13.0 MeV, leading to the ground states of the residual nuclei. The microscopic overlap functions for (d, t) and (d, ³He) systems obtained by using the Phillips triton wavefunctions have been used as projectile form factors into the calculation. The results are compared with zero-range DWBA calculations taking the finite-range effects into account by means of a local energy approximation. The results obtained by finite-range and zero-range calculations for differential cross sections as well as vector and tensor analysing powers are compared with the experimental data. The range of validity of the local energy approximation is discussed.     

Spins and parities of low-lying states in 81Kr from the 80kr(d̄, p)81kr reaction and implications for a 81Br solar neutrino detector

The structure of ⁸¹Kr has been investigated via the ⁸⁰Kr(d?, p)⁸¹Kr reaction using an 11.0 MeV vector-polarized deuteron beam. Differential cross sections σ and vector analyzing powers A_y have been measured from 20° to 90° for 17 excited states below 3.0 MeV excitation energy. Comparisons of these distributions to DWBA calculations and empirical shapes were made to extract spectroscopic factors and values of spin and parity for these states. The significance of these measurements to the design of a bromine solar neutrino detector is discussed.     

Spins and parities of low-lying states in 79Kr from the 78Kr(d,p)79Kr reaction

The structure of Kr has been investigated via the ⁷⁸Kr($\text{d}$, p)⁷⁹ Kr reaction using an isotopically enriched gas target and an 11.0 MeV vector-polarized deuteron beam. Differential cross sections, σ, and vector analyzing powers, A_y, have been measured from 25° to 95° for 10 proton groups below 2.5 MeV excitation energy. Comparisons of these distributions to DWBA calculations and empirical shapes were made to extract spectroscopic factors and values of spin and parity for these states.     

Deuteron elastic scattering and (d,p) reactions on 208Pb at Ed = 22 MeV and j-dependence of T20 in (d,p) reaction

An experimental study of deuteron elastic scattering and (d,p) reactions at E_d = 22 MeV was made for ²⁰⁸Pb target. A new j-dependence of T₂₀ for (d,p) reaction at backward angles was observed. A “model independent” optical potential method was applied to analyze deuteron elastic scattering in the 10–22 MeV energy range. A continuum discretized coupled channels (CDCC) analysis was performed for deuteron elastic scattering at 22 MeV and the deuteron breakup effect was elucidated. DWBA and CDCC (d,p) analyses were made for (d,p) reactions.     

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

The polarization of protons from the ⁹Be(d,p)¹⁰Be 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.     

DWBA Analysis of Polarization of Protons from the 9Be(d,p1)10Bex Reaction at Ed = 5.5, 15.0, and 20.5 MeV

The polarization of protons from the ⁹Be(d, p₁)¹⁰Be^x reaction has been analyzed in terms of the DWBA theory at deuteron energies 5.5, 15.0 and 20.5 MeV. Good fits were obtained which show the usefulness of the DWBA theory for describing polarization by using the optimum optical model parameters.