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.     

The (p,d) reaction at 65 MeV

The (p, d) reaction on ¹²C, ¹⁴N, ¹⁶O, ⁴⁰Ca and ⁹⁰Zr has been studied with 65 MeV incident protons. DWBA calculations have been carried out to investigate the importance of finite range and non-locality effects. The experimental angular distributions for the strong transitions have been compared to DWBA calculations to study the effect of the deuteron optical potential. This comparison supports the use of the adiabatic deuteron potential which includes the effect of deuteron breakup.     

Étude des niveaux du noyau 27Al par la réaction 26Mg(d,n)27Al

The ²⁶Mg(d, n)²⁷Al reaction has been studied at 6 and 8 MeV deuteron bombarding energies using the time-of-flight technique for neutron detection. The good neutron energy resolution of the present work permitted the determination of the excitation energy of 70 states populated by the reaction. Angular distributions of neutrons leading to 50 levels in ²⁷Al were measured between 0° and 100°. The experimental cross sections were analysed in the framework of the DWBA and Hauser-Feshbach theories to deduce l_p values and transition strengths. New spin and parity assignments were obtained for 11 levels. The agreement between the DWBA predictions and some of the measured angular distributions was improved by modifying the optical-model radii in both incoming and outgoing channels. The experimental results are compared with the corresponding data from previous studies and with Nilsson-model and recent shell-model calculations.     

Influence of breakup on elastic and α-production channels in the ~6Li+~(116)Sn reaction

The effects of breakup reactions on elastic and α-production channels for the ~6Li+~(116)Sn system have been investigated at energies below and near the Coulomb barrier. The angular distributions of α-particle production differential cross sections have been obtained at several projectile energies between 22 and 40 MeV. The measured breakup α-particle differential cross sections and elastic scattering angular distributions have been compared with the predictions of continuum-discretized coupled channels(CDCC) calculations. The influence of breakup coupling has also been investigated by extracting dynamic polarization potentials(DPP) from the CDCC calculations. From the predictions of CDCC calculations the relative importance of the nuclear, Coulomb, and total breakup contributions have also been investigated. The nuclear breakup couplings are observed to play an important role in comparison to the Coulomb breakup for the direct breakup mechanisms associated in the reaction of ~6Li projectile with ~(116)Sn target nuclei. The influence of strong nuclear breakup coupling exhibits suppression in the Coulomb-nuclear interference peak. The direct breakup cross sections from the CDCC calculations under-predict the measured α-particle differential cross sections at all energies. This suggests that the measured α particles may also have contributions from other possible breakup reaction channels.     

Asymmetric fission of the pre-actinide nuclei

Study of α particles, protons and neutrons emission in reactions induced by¹⁶O on Sn targets. The threshold for direct a emission is found to be v/c?0.04 (v velocity of the projectile at the top of the Coulomb barrier) whereas direct protons and neutrons, if any, would be emitted for beam energies higher than 7.8MeV/n. (v/c>0.092). Atv/c 0.092, 90% of the direct a cross section is shown to be incomplete fusion. On¹¹⁶Sn target, besides the main exit channels α4n and αp4n, we observed 2α4n and α2p4n channels where the direct α is followed by evaporation particles. This implies a lower initial angular momentum than for the main channels.     

Neutron-proton charge-exchange scattering from 8 to 29 GeV/c

The differential cross sections for neutron-proton charge-exchange scattering have been measured for incident neutron momenta between 8 and 29 GeV/c and for four-momentum transfers |t| between 0.002 and 1.0 (GeV/c)². A neutron beam with a broad momentum spectrum was scattered from a liquid hydrogen target. The momenta and scattering angles of the forward-scattered protons were measured by a spark-chamber magnet spectrometer. The flight times and scattering angles of the recoil neutrons were measured by a bank of thick scintillation counters. The efficiencies of the neutron counters were determined in a separate measurement. Absolute normalization of the data was obtained from a measurement of the diffraction dissociation of neutrons from carbon nuclei. Differential cross sections, based on ～ 23 000 events, are presented for 9 different momenta. The shape of the differential cross sections and the momentum dependence are examined in detail.     

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.     

Projectile breakup and total reaction strengths in Li-induced reactions

Spectra and angular distributions have been measured for the light particles emitted from the reactions induced by 36 MeV ⁶Li and ⁷Li ions on targets of ¹²C, ¹³C and ²⁷Al. Some measurements were also performed at beam energies of 28 and 32 MeV. The spectra are dominated by broad peaks centered at energies corresponding to the beam velocity, a characteristic of projectile breakup. A simple breakup model roughly reproduces the shapes of the measured spectra and angular distributions. The total cross sections observed for projectile breakup average about 600 mb and are almost as large as the fusion cross sections. The ⁷Li breakup yields are somewhat larger than those for ⁶Li, the same trend that was previously observed for the Li-induced fusion cross sections on C. As a result the measured total reaction cross sections induced by ⁷Li ions are about 200 mb larger than those of ⁶Li on the same targets. This difference is not predicted by conventional optical model calculations.     

Measurement of the 2H(p,n) Breakup Reaction at 170 MeV and the Three-Nucleon Force Effects

The effects of three nucleon force (3NF) have been actively studied via the nucleon–deuteron (Nd) scattering states. The differential cross sections and the vector analyzing powers A _y of the ²H(p, n) inclusive breakup reaction at 170 MeV were measured for the study of 3NF effects in the intermediate energy region. The polarized proton beam of 170 MeV was injected to the deuterated polyethylene (CD₂) target and the energy of scattered neutrons were measured by using TOF method. The data were compared with the Faddeev calculations based on modern nucleon–nucleon (NN) forces with and without the 3NF. Concerning the differential cross sections, we can see large discrepancies between the data and the calculations in the region of scattered neutron energies are low, which is similar to the results of the ²H(p, p) inclusive breakup reaction at 250 MeV.     

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.     

Interfering transfer processes in heavy-ion reactions

Heavy-ion reactions in which two different transfer processes may interfere are analyzed. Angular distributions of the reactions ¹⁴C(¹⁶O, ¹⁷O)¹³C and ¹⁴C(¹⁶O, ¹⁸O)¹²C were measured at incident energies of 20, 25 and 30 MeV. The strong oscillations observed at the Coulomb barrier together with a backward rise at higher energies are taken as evidence for the superposition of two competing transfer reactions. DWBA calculations for the two single transfer processes were performed using the fixed-range approximation, and the two transition amplitudes were summed coherently. The experimental angular distributions are well reproduced. The DWBA also explains the disappearance of the interference structures for higher transferred angular momenta l. Data on the reaction ¹¹B(¹⁶O, ¹⁵N)¹²C measured earlier are included in the analysis in order to show the systematic dependence on l-values.     

Second-order breakup corrections to elastic deuteron-nickel scattering between 13 and 80 MeV

Breakup corrections to the elastic scattering matrix elements are calculated in the second-order distorted-wave Born approximation at deuteron incident energies of 45 and 85 MeV. The effects of spin are included. The size of the corrections are found to be generally as large as those obtained in a previous study at 13 and 21.6 MeV. The breakup cross section is calculated to first order in the breakup matrix elements by a distorted-wave Born treatment. Comparison with fully coupled calculations shows that the DWBA method overestimates the breakup cross section by a factor of about three.The continuum of breakup states up to a n-p relative momentum 1 fm^?1 is included in the calculations. This continuum is discretized by subdividing it first into two bins, and then into four bins. The finer discretization does not make a large difference in either the elastic cross section or the breakup cross sections. The higher bins give only a small contribution to either quantity.     

Neutron total cross sections on nuclei at Fermilab energies

We have measured total cross sections for neutrons on protons, deuteriom, beryllium, carbon, aluminium, iron, copper, cadmium, tungsten, lead, and uranium for momenta between 30 and 300 GeV/c. The measurements were carried out in a small-angle neutral beam at Fermilab. Typical accuracy of the data is 0.5 to 1%. The cross sections are consistent with an A^0.77±0.01 dependence over the entire momentum range. The cross sections are compared with theoretical predictions. Agreement is found only if inelastic screening is included. Nuclear radii obtained from our data are in good agreement with previous determinations.     

Proton-hole states in 115In observed in the 116Sn(d, 3He) reaction

The ¹¹⁶Sn(d, ³He)¹¹⁵In reaction has been investigated at E_d = 50 MeV. Thirteen transitions to states up to 3 MeV excitation energy were studied. The measured angular distributions were compared with DWBA calculations and transferred angular momenta and spectroscopic factors were deduced. Levels at 1.04, 2.23 and 2.52 MeV were found to be excited most likely by l = 3 angular momentum transfer in contrast to previous investigations at lower incident energies in which no l = 3 transitions have been observed.     

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.     

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.     

High-resolution investigation of the 112Sn(p,d)111Sn reaction

The ¹¹²Sn(p, d)¹¹¹Sn reaction was studied at a proton energy of 27.45 MeV. The outgoing deuterons were momentum analyzed with an Enge split-pole spectrograph and recorded with position-sensitive solid-state detectors with a total resolution between 12 and 16 keV. Angular distributions were compared with DWBA calculations in order to extract l-values, spectroscopic factors, single-quasiparticle energies and occupation probabilities. In the gross structure between 3 and 6 MeV, which was interpreted as being due to the pickup of deeply bound neutrons, several discrete peaks were also found with an angular distribution characteristic for l = 1 or 4 transfer. The excitation of core-coupled states was investigated by performing two-step DWBA calculations. The results of the present experiment are compared with previous experimental results and with number-projected BCS calculations.     

Lifetime of the second excited state of K

Energy distributions of neutrons from the (d, n) reactions on ^12–14C leading to unbound states of ^13–15N have been measured at 6.3 or 6.5 MeV deuteron energy. Angular distributions have been extracted for ^{13, 14}C(d, n) transitions and analysed with DWBA using the extra-polation technique to give l-values and transition strengths for ten unbound states in ¹⁴N and six in ¹⁵N. For the ¹⁵N level at 10.541 MeV it is concluded that J^π is $\text{3}\text{2}$^?. A new ¹⁵N level is observed at 11.44 MeV. The 0° (d, n) cross sections have been set in proportion to (p, p₀) resonance cross sections, and a pronounced l-dependence of the ratio is obtained.