Study of the (p,pn) reaction in light nuclei

The (p, pn) reaction on ²H, ⁶Li, ⁷Li, ⁹Be has been studied at 47 MeV bombarding energy. Excitation energy spectra and energy sharing spectra are presented. Fragmentary information on ¹⁰B, ¹¹B and ¹²C was also obtained. Sequential decay contributions to the ⁶Li(p, pn)⁵Li¹ reaction suggest an admixture of parentage $\text{(α)π(}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)π(}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}$ for the (3^?), 23 MeV excited state of ⁶Be. A possible 15.5 MeV excited state in ⁶Be is reported. An extensive study of the ⁹Be (p, pn)⁸Be reaction for 45 MeV protons was made. Results for θ_p = θ_n = 25°, 30°, 35°, 40°, 45°, 55°, 65°; θ_n = 40°, θ_p = 25°, 30°, 35°, 40°, 45°, 55°, 65°; θ_p/θ_n = 40°/45°, 38.5° are reported and compared to DWIA calculations. Agreement is good when the lower momentum components of the wave function are sampled, and deteriorates as higher momenta are required. Results are in agreement with the Cohen and Kurath spectroscopic factors for ⁹Be.     

Investigation of backward α-particle scattering in 24Mg and 28Si through α-γ angular correlations

Alpha-gamma angular correlations have been measured for the reaction ²⁴Mg(α, α'γ) in the energy range 15.50 to 17.00 MeV in steps of 300 keV and for ²⁸Si(α, α'γ) from 15.00 to 16.20 MeV in steps of 200 keV to provide energy averaged results. The scattered α-particles were detected for lab angles θ_α = 115°–178° in a multidetector arrangement. The coincident γ-rays were observed with a Ge(Li) detector placed at 90° in the reaction plane. Data were obtained for the 1st, 2nd and 3rd excited states of ²⁴Mg and for the 1st, 2nd, 3rd and 4th excited states of ²⁸Si. The absolute doubledifferential cross sections were analysed with Hauser-Feshbach calculations. The analyses show that compound nuclear processes are responsible for the rise of backward α-scattering in ²⁴Mg(α, α'γ)²⁴Mg and ²⁸Si(α, α'γ)²⁸Si at the energy studied.     

Investigation of the 6Li(d, α)4He reaction between 1.5 and 11.5 MeV

The differential cross section σ₀(θ) and the analysing powers T₁₁(θ), T₂₀(θ), T₂₁(θ) and T₂₂(θ) of the reaction ⁶Li(d, α)⁴He have been measured for twelve energies between 1.5 and 11.5 MeV at c.m. angles between 3.5° and 90°. The results were fitted with Legendre polynomials. The energy dependence of the resulting coefficients indicates resonance-like behaviour at several energies corresponding to excitation between 22 and 32 MeV in ⁸Be. The reaction ⁶Li(d, α)⁴He shows excellent features as an analyser for deuteron vector and tensor polarization over the whole energy range investigated.     

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.     

Large angle scattering of α-particles from 32S

The elastic scattering of α-particles from ³²S was studied in the incident energy range between 4 and 8.9 MeV. In order to ascertain whether quasi-molecular states exist, as predicted in the α-³²S system, excitation functions were measured, and angular distribution measurements were carried out using targets with different thicknesses in the angular range from θ_lab = 30° to 175° at each extreme in the excitation functions. The analysis of the angular distribution data at back angles was performed using the Regge-pole method. A resonance with J = 3 was observed at 7.7 MeV in the α-³²S system. Evidence was also found for both a broad resonance which can be characterized by an angular momentum J = 1, and for a narrow J = 2 resonance.     

A study of isobaric analogue resonances in 71Ga

Differential cross-section and analysing-power excitation functions were measured for elastic proton scattering from E_p = 3.6–6.4 MeV at θ_c.m. = 90°, 115.8°, 129.8° and 155.3°. Differential cross-section angular distributions were measured at 3.56, 3.94, 5.78 and 8.98 MeV and analysing-power angular distributions at 5.78 and 8.98 MeV. Optical-model parameters were deduced from these distributions. Resonance parameters were determined for eight analogue resonances in ⁷¹Ga and neutron spectroscopic factors were calculated. These were compared with the results of previous (p, p) cross-section analyses and the results of (d, p) reactions leading to states in ⁷¹Zn.     

Microscopic and macroscopic DWBA analysis of the reactions 28Si(α, d)30P, 32S(d, α)30P and 32S(α, d)34Cl studied at Eα = 50MeV and Ed = 40MeV

The reactions ²⁸Si(α, d)³⁰P, ³²S(d, α)³⁰P and ³²S(α, d)³⁴Cl have been studied at E_α = 50 MeVand E_d = 40 MeV. The angular distributions have been analysed in terms of the single-step, zero-range DWBA with microscopic as well as macroscopic form factors. By requiring an almost identical shape in the microscopic and macroscopic radial form factors for all L-values with L ? 6 the size parameters of the Woods-Saxon well in which the transferred cluster is bound to the nucleus were determined as r₀ = 1.15 fmanda = 0.76 fm. Despite the differences between the two approaches with these parameters the shape of the microscopic angular distribution is well reproduced and the corresponding strengths agree to within 25%. The method has been applied to the three reactions and relative two-nucleon spectroscopic factors have been deduced. A comparison is made with the results of two shell-model calculations.     

High-resolution study of four-nucleon pickup via the (d, 6Li) reaction at Ed = 55 MeV on sd-shell nuclei: (II). odd-A nuclei

The ²⁵Mg(d, ⁶Li)²¹Ne and ²⁷Al(d, ⁶Li)²³Na reactions were studied with a broad-range magnetic spectrograph at E_d = 55 MeV with an energy resolution of ~ 40 keV. Angular distributions were obtained from θ_lab = 10°–37° for some eighty transitions to states up to E_x ? 9.5 MeV. The data were analyzed with zero-range and finite-range DWBA. Experimental spectroscopic factors are compared with those predicted by the SU(3) model and by microscopic shell-model calculations made with the Chung-Wildenthal interaction in the full (1sd)ⁿ space.     

Search for intermediate structure in 36Ar via the 24Mg(12C, α)32S reaction

The ²⁴Mg(¹²C,α)³²S reaction was investigated in the energy range E_c.m. = 11.9–19.4 MeV by measuring excitation functions of the α₀ and α₁ groups. Angular distributions (θ_c.m. = 12–97°) were also measured at a number of energies. The excitation functions were subjected to a statistical analysis by means of evaluating correlation and deviation functions; no statistically significant anomalies were found. The α₀ angular distributions display fairly high angular-momentum selectivity as pairs of Legendre polynomials provide acceptable fits to most of them: however, only one, at E_c.m. = 18.1 MeV, is strongly dominated by a single partial wave, l = 11. Excitation functions as well as angular distributions of both α₀ and α₁ cross sections were found to be in good qualitative agreement with Hauser-Feshbach calculations throughout the energy range studied. Thus, the analysis of the data shows that intermediate resonant structures, if present, are weak and interfere strongly with the statistical compound-nucleus background, which effectively prevents their clear observation and identification in the present study.     

A search for resonant two-step α-exchange in 6Li + 12C scattering

Excitation functions for ¹²C(⁶Li, ⁶Li)¹²C (gs, 4.43 MeV) have been measured at 10 angles (40° ? θ_cm ? 160°) over the energy range 20 MeV < E_lab < 36 MeV. A single anomaly of width Γ ≈ 800 keV is observed at E_lab = 22.8 MeV. The results casts doubts on the resonant two-step α-exchange mechanism suggested to occur in this system.     

12C(7Li,t)16O and stellar helium fusion

The reaction ¹²C(⁷Li, t)¹⁶O has been studied at $\text{E(}{}^7\text{Li}\text{) = 34}\text{MeV}$ with the LASL tandem accelerator and QDDD magnetic spectrometer. Angular distributions to levels with E_x < 11 MeV have been obtained from 0° to 90°, including 0°. The results have been analyzed with finite-range distorted-wave Born approximation theory. The α-particle spectroscopic factors and reduced widths obtained are compared with those calculated with group theory (SU(3)) and other models. The analysis of data for the 7.1 and 9.6 MeV J^π = 1^? levels, which are of great importance in stellar helium buring, yields a ratio, R, of dimensionless reduced α-widths $\text{θ}{}^2{}_{\mathrm{<mtext>a</mtext>}}\text{(7.1}\text{MeV}\text{)}\text{θ}{}^2{}_{\mathrm{<mtext>a</mtext>}}\text{(9.6}\text{MeV}\text{)}\text{= 0.35b ± 0.13}$. The observed line width of the 9.6 MeV level (Γ_c.m. = 390 ± 60 keV) is less than the accepted value (Γ_c.m. = 510 ± 60 keV) and implies θ²_a(9.6 MeV) ≈ 0.6. These results as well as data for the 6.92 MeV J^π = 2⁺ and 10.35 MeV J^π = 4⁺ “α-cluster” states indicate 0.09 < θ²_a(7.1 MeV) < 0.33 with a mean value θ²_a(7.1 MeV) = 0.14 ± 0.04. The implication for stellar helium burning is discussed.     

The 12C(13C, α)21Ne reaction: High-spin states,resonances and coherence widths

Excitation functions were measured for states of ²¹Ne populated by the ${}^{12}\text{C}\text{(}{}^{13}\text{C}\text{, α)}$ reaction over the bombarding energy range E_lab = 18.2–32.0 MeV (18.4–27.0 MeV) at θ_lab = 7°(25°) in in 200 keV steps, and average coherence widths of states and the moment of inertia of the compound nucleus ²⁵Mg were obtained from these excitation functions. A statistical analysis of these data was performed. Angular distributions for states in ²¹Ne to 10 MeV in excitation energy were measured at θ_lab = 7°, 18°, 28° and 43° at bombarding energies from 29.0 to 31.0 MeV in 400 keV steps. These data along with Hauser-Feshbach predictions allow us to suggest spins for some states as well as to suggest possible candidates for rotational bands in ²¹Ne.     

Bremsstrahlung in proton-α scattering

Proton-α bremsstrahlung cross sections have been measured at 45 MeV for θ_p = 91°, θ_α = 30° and θ_p = 70°, θ_α = 39°; at 40 MeV for θ_p = 92°, θ_α = 29°; and at 22 MeV for θ_p = 70°, θ_α = 30°. Calculations for these cross sections have been made using the Feshbach-Yennie model following the methods of Green and Prodon including p-α partial waves up to L = 4. These potential-independent calculations have only the proton-α elastic-scattering phase shifts as input. Good agreement with the experimental cross sectios has been obtained.     

Alpha-heavy-ion angular correlations from 28Si + 12C

Alpha particles have been measured in coincidence with heavy recoil nuclei from the ²⁸Si + ¹²C reaction. At E_lab = 87 MeV angular correlations for alphas between 15° and 55° and heavy ions at angles ?9°, ?12° and ?15° have been taken. An excitation function of coincidence events with θ_α = 30° and θ_HI = ?12° has been measured for 84 MeV < E_lab < 91.5 MeV. The results are well described by a statistical-model calculation for compound nucleus decay. No evidence is found for additional processes.     

The reactions 50,52Cr(d, 6Li) 46,48Ti at Ed = 651 MeV

The ^50,52Cr(d, ⁶Li) ^46,48Ti reactions have been studied at E_d = 65 MeV bombarding energy. Angular distributions of outgoing Li particles were measured for final states in ^46,48Ti nuclei from 15° to 50° (lab). These were compared with zero-range and finite-range DWBA calculations in an α-cluster pick-up approximation to obtain relative α-spectroscopic factors.     

The (d, 6Li) reaction on 12C, 16O, 24Mg, 40Ca and 58Ni at 54.25 MeV

The (d, ⁶Li) reaction was studied at E_d = 54.25 MeV on the target nuclei ¹²C, ¹⁶O, ²⁴Mg, ⁴⁰Ca and ⁵⁸Ni. The data were analyzed with finite-range DWBA calculations. The absolute values of the α-cluster spectroscopic factors and the target mass dependence of the relative S_α were in agreement with those in the (p, pα) reaction at E_p = 100 and 157 MeV. The theoretical calculations of the relative S_α were in better agreement with the experimental data at higher energy than at the lower energies.     

Measurement and MIA analysis of the neutron differential cross section and polarization in the α-D break-up at 33 MeV c.m.

Differential cross sections at 0° and 20° and polarizations at 20° have been measured for the ²H(α, n) αp reaction at E_α = 100 MeV and the ⁴He(d, n) αp reaction at E_d = 50 MeV. Data have been analyzed by the Modified Impulse Approximation (MIA). Satisfactory agreement was obtained but some discrepancy remained in the analysis of polarization data.     

Interference maxima in the backward excitation curve of α-particle elastic scattering on medium-weight nuclei

Excitation functions for the elastic scattering of α-particles from Ni, Co and Cu at θ_lab = 179° were measured in the lab energy range 22.75–28.40 MeV, as well as some angular distributions for Co(α, α). Broad maxima with a width of about 2.5 MeV were found in the excitation functions. It is shown that a simple four-parameter optical model of the interaction is able to reproduce the angular distributions as well as the excitation functions. Examination of the Argand diagrams leads to the conclusion that the maxima in the excitation curves are formed as a result of a coherent superposition of a number of partial waves, none of which behaves in itself in a resonance-like manner.     

Spin and parity assignments for 35Cl levels from the 31P(α, p)34S reaction

³⁵Cl states at excitation energies between 9.9 and 11.8 MeV have been identified through sharp resonances in the ³¹P(α, p_o)³⁴S excitation functions at 25°, 105° and 155° for E_α = 3.25–5.50 MeV. Forty-eight on-resonance angular distributions, normalized to an absolute cross section scale, have been subjected to single-level and two-level analyses resulting in spin and parity assignments for each resonance. Approximately half the resonances were of the pure single-state type, having unique angular distribution shapes. Data from 12 resonances of an earlier experiment ¹) were analyzed with the same theory, extending the diagnostics down to a ³⁵Cl excitation energy of 9.1 MeV. A set of optical potentials consistent in all four reactions that this experimental program encompasses has been incorporated in the present analysis. Validity of the optical potential is demonstrated for α-particles elastically scattered by ³¹P.