Elastic scattering of He from Be,B, B,Mg, Mg,Mg and Al

Elastic scattering angular distributions of ³He particles from ⁹Be, ¹⁰B, ¹¹B, ²⁴Mg, ²⁵Mg, ²⁶Mg and ²⁷A1 at E(³He) ≈ 13 to 27 MeV have been measured and some of the representative results are reported. In most cases the angular range of the measured cross sections was from 8° to 150° (lab). The results have been analyzed in terms of a six-parameter optical model and are compared with previous work.     

Elastic scattering of 40Ar on 40Ca at Elab = 191, 236 and 272 MeV

Cross sections for elastic scattering of ⁴⁰Ar on ⁴⁰Ca have been measured at energies E_lab = 191, 236 and 272 MeV employing position-sensitive detectors and the method of kinematical coincidences. The experimental data are first compared with the ordinary and the generalized Fresnel models. Only the generalized Fresnel model describes the experimental data well. An optical model analysis with a Woods-Saxon potential yields an energy independent set of parameters (V_R = ?21.76 MeV, r_OR = 1.37 fm, a_R = 0.45 fm; W₁ = ?13.69 MeV, r₀₁ = 1.40 fm, a₁ = 0.36 fm) very similar to the one found in ⁴⁰Ca-⁴⁰Ca scattering at corresponding energies. Values deduced for the total reaction cross sections for the three energies are in good agreement with those predicted by the generalized Fresnel model. The data are also compared with optical model calculations with the real part of the potential replaced by various microscopically determined potentials. The proximity, Fleckner-Mosel and the Krappe-Nix-Sierk potentials like the phenomenological optical model potential reproduce the measured data fairly well over several orders of magnitude.     

Folding model analysis of 10, 11B, 12C + 27Al, 39K and 40Ca

Elastic scattering angular distributions for ^{10, 11}B + ⁴⁰Ca at E_lab = 46.6 and 51.5 MeV and¹²C+³⁹K at E_lab = 54 and 63 MeV have been measured and compared with Woods-Saxon and double-folding optical models. The oscillatory structure observed previously for ¹²C + ⁴⁰Ca disappears when the projectile is changed to ^10,11B or the target is changed to ³⁹K. The angular distributions are adequately reproduced by a double-folding analysis, which employs the nucleon-nucleon potential of Bertsch et al., with a range of real normalizations N_R = 1.0–1.38. This same range of real normalizations was also able to describe previously measured ^10,11B, ¹²C + ²⁷A1 data. The double-folding analysis of ¹²C + ⁴⁰Ca scattering indicates that this system behaves differently from neighboring systems.     

Inelastic scattering of 185 MeV protons from Mg and Al

A magnetic spectrometer was used for the energy analysis of protons scattered from targets of magnesium (natural isotopic composition) and aluminium. The mean energy of the incident protons in the targets was 185 MeV. A total energy resolution of 350 keV (FWHM) was achieved, which made possible the observation of the excitation of a large number of discrete levels. Energy spectra were measured in the angular region of 4° to 40° (lab system).

The results are presented partly in the form of tables giving measured excitation energies and maximum cross sections for resolved levels and partly in the form of graphs of angular distributions of the differential cross sections.

A qualitative discussion of the results is given in terms of the multipolarities of the transitions involved and comparisons are made with similar results from other experiments in inelastic scattering and in a few cases with theoretical predictions.     

Phenomenological analysis of the 24Mg(12C, α)32S resonant reaction studied at low incident energy

The ²⁴Mg(¹²C, α)³²S reaction has been studied in the region of the Coulomb barrier. Three angular distributions for the α-particle groups populating the ground and first-excited 2⁺ state of ³²S have been measured spanning the apparent resonant structure observed at E_c.m = 14.20 MeV. Regge-pole and phase-shift analyses suggest a spin assignment of 8 for the corresponding resonance at E_x = 30.51 MeV in ³⁶Ar.     

Direct capture in the 24Mg(p, γ)25Al reaction

Excitation functions for the ²⁴Mg(p, γ)²⁵Al capture reaction have been obtained for the beam energy range E_p = 0.2–2.3 MeV. The analysis of these data revealed the presence of the direct capture process to the low-lying states in ²⁵Al at , $\text{945(}\text{3}\text{2}{}^{\mathrm{+}}\text{), 2485(}\text{1}\text{2}{}^{\mathrm{+}}\text{)}\text{and}\text{3062}\text{keV}\text{(}\text{3}\text{2}{}^{\mathrm{?}}\text{)}$. The presence of the weaker direct capture transitions is manifested through interference effects on the tails of the two broad resonances at E_p = 823 and 1623 keV. The deduced spectroscopic factors for these final states in ²⁵Al are compared with the corresponding values from stripping data as well as model calculations. An astrophysical S-factor of S(0) ≈ 30 keV· b for this reaction has been obtained.     

The study of the width for intermediate resonances in the 27Al(d,p)28Al, 27Al(d, α)25Mg, 31P(d,p)32P and 31(d, α)29Si reactions

The protons and α-particles from the reactions ²⁷Al(d, p)²⁸Al(d, α)²⁵Mg, ³¹P(d, p)³²P and ³¹P(d, α)²⁹Si were measured and analyzed with the channel cross correlation function and auto-correlation function to determine the correlating numbers N_d and average width 〈Γ_μ〉. With these values, the theoretical intermediate widths were calculated to be 119 ± 30 keV in the ²⁹Si nucleus and 249 ± 46 keV in the ³³S nucleus, which were in good agreement, within the errors, with the present experimental results of 185 ± 37 keV in ²⁹Si and 204 ± 24 keV in ³³S.     

Elastic scattering of polarized deuterons from Al, Si and Ni between 7 and 11 MeV

Polarization parameters have been determined for deuteron elastic scattering from ²⁷Al, Si and ⁶⁰Ni at energies between 7 and 11 MeV and laboratory scattering angles from 30° to 135°. The vector polarization, iT₁₁, and two tensor parameters T₂₀ and T₂₂, were measured by scattering polarized and unpolarized deuterons which were obtained from a tandem accelerator. The largest polarization was |iT₁₁| ≈ 0.3 and |T₂₀| ≈ 0.2 for ²⁷Al at 11 MeV. For ⁶⁰Ni, the observed polarizations were substantially smaller. Angular distributions of the unpolarized cross section were also measured for ²⁷Al and Si. An optical-model analysis of the polarization and cross-section data was performed. The vector polarization was reproduced reasonably well by a vector spin-orbit coupling of similar strength as found for nucleon scattering. A tensor interaction appears to be needed to account for the observed tensor polarizations.     

Elastic electron scattering from the magnetization distribution of 27Al

Cross sections have been measured for the scattering of electrons through 180° from Mg, Al and Si targets in the energy range 35 to 95 MeV. Scattering from the magnetization distribution of ²⁷Al is observed as the difference of the scattering from ²⁷Al and from the neighbouring doubly even nuclei Mg and Si. Corrections have been applied for differences in instrumental effects and in rms charge radii. Theoretical magnetic cross sections have been computed with a single-particle wave function and with a shell-model wave function involving configuration mixing. If the distorted-wave Born approximation is used, good agreement with experiment is obtained. In both cases the best fit to the data yields a value of the oscillator range parameter b = 1.71 ± 0.06 fm. Using the q-dependence of the single-particle model a value $\text{Ω = 18.7 ± 3.5 μ}{}_{\mathrm{<mtext>N</mtext>}}\text{·}\text{fm}{}^2$ for the magnetic octupole moment of ²⁷Al is found. The present low-energy (E < 100 MeV) data are in good agreement with the results obtained from the scattering of high-energy (E = 500 MeV) electrons from ²⁷Al through “normal” angles.     

Elastic scattering of protons and neutrons on 40Ca by the density-dependent Hartree-Fock field

We use the self-consistent density-dependent Hartree-Fock field as the real part of the optical model potential. Introducing a phenomenological imaginary potential, we describe elastic scattering of protons and neutrons on ⁴⁰Ca at several incident energies. Results show that the density-dependent Hartree-Fock field, including the rearrangement potential, well reproduces differential cross sections and polarizations simultaneously. This calculation explicitly shows a unified way to understand the ground-state properties and the scattering problem. Detailed study is given the properties of the non-local Hartree-Fock field, via the WKB equivalent local potential.     

Elastic and inelastic scattering of 11.8 MEV polarized deuterons from 34S

The elastic and inelastic scattering of 11.8 MeV vector polarized deuterons from ³⁴S has been studied. Angular distributions of the cross section σ(θ) and vector analyzing power iT₁₁(θ) have been measured for the ground state and the first three excited states in ³⁴S. Optical model parameters were first obtained by fitting the elastic deuteron scattering data alone. DWBA calculations with a collective model form factor were performed for the inelastic scattering to the excited states. Coupled-channels calculations were also done both for the one-phonon and the two-phonon excited states. The optical model parameters were suitably modified to obtain simultaneous fit to elastic and inelastic data when channel coupling was introduced. The values of the vibrational parameter β₂ for one- and two-phonon states are discussed and compared with those obtained from γ-decay width studies.     

Elastic and inelastic scattering of 15 MeV polarized deuterons from isotopes of Ca,Cu, Sr,Zr, and Mo

The elastic and inelastic scattering of 15 MeV polarized deuterons from ⁴⁸Ca, ⁶³Cu, ⁸⁸Sr, ⁹⁰Zr, ⁹²Zr, and ⁹²Mo has been investigated. Angular distributions of the cross section and vector analyzing power iT₁₁ have been measured for all these nuclei; the tensor analyzing powers T₂₀ and T₂₂ have been studied for ⁹²Zr. Cross sections and vector analyzing powers are generally well explained by the optical model for elastic scattering and by the DWBA with a macroscopic form factor for the inelastic scattering; this is consistent with previous work. Distributions for ⁴⁸Ca, however, are poorly fitted. Anomalous behavior of the N = 50 nuclei found in the inelastic scattering of polarized protons is not present for deuterons. Tensor analyzing powers are not well explained by standard procedures: use of approximate folding model optical parameters did not improve the fits. The distribution of iT₁₁ for the $\text{1}\text{2}$^? state in ⁶³Cu is significantly different from the distributions for the $\text{5}\text{2}$^? and $\text{7}\text{2}$^? states.     

Elastic scattering of positive pions from 12C at 30, 40 and 50 MeV

We have measured the angular distribution of π⁺ elastically scattered from ${}^{12}\text{C at}\text{E}\text{?}{}_{\mathrm{\pi }}\text{= 28.4, 38.6}\text{and}\text{48.9}\text{MeV}$. The angular range was between 13° and 165° lab. Scattered pions were detected with two counter telescopes which required pion identification through the observation of the decay muon. Data agree well with calculations derived from the free πn scattering amplitudes when absorption effects have been included.     

Elastic electron scattering on Zr and Mo

Elastic electron scattering on ⁹⁰Zr and ⁹²Mo has been measured at 200 and 300 MeV up to 2 fm⁻¹ momentum transfer. Data analysis led us to adopt the parabolic Gaussian shape as a valuable charge distribution for these nuclei. For ⁹⁰Zr, we have compared this model with charge distributions given by recent Hartree-Fock calculations.     

Study of 16O, 20Ne, 22Ne, 28Si and 32S by inelastic scattering of polarized protons

Analyzing powers and cross sections have been measured for elastic and inelastic scattering of 24.5 MeV protons from ²⁰Ne and ²²Ne, and for ¹⁶O, ²⁸Si and ³²S at 30.3 MeV. The experimental results were analyzed in terms of the coupled-channels formalism using the rotational model and (for ³²S and ¹⁶O) the vibrational model. The results for ²⁰Ne, ²²Ne and ²⁸Si show a systematic trend of the hexadecapole deformation. Prolate shapes for ²⁰Ne and ²²Ne and an oblate shape for ²⁸Si are confirmed. The results for ³²S are almost equally well-reproduced by the vibrational or rotational model, and there is a slight preference for the prolate shape for this nucleus. The best fits for the analyzing power for all the nuclei were obtained by using the full Thomas form for the spin-orbit potential     

The (3He,t) reaction on 24Mg and 28Si

The (³He, t) charge exchange reaction on ²⁴Mg and ²⁸Si has been studied at 38.5 MeV. The angular distributions provide a number of new spin assignments in ²⁴Al and ²⁸P. A two-step excitation through intermediate α-particle channels was used to predict the ²⁴Al cross sections. The fits are fair in shape, but about a factor of three too large when a perfect overlap of initial and final shapes is assumed. The data to three 1⁺ states of ²⁸P are compared to the known electromagnetic reduced transition rate B(M1) to the analog states in ²⁸Si.     

Elastic and inelastic pion scattering on C and C at 100 MeV

Angular distributions of π⁺ and π^? at 100 MeV incident energy were measured for elastic and inelastic scattering from ¹²C and ¹³C. Elastic data were obtained between 6° and 180°. Inelastic scattering on the 2⁺ (4.4 MeV), 0⁺ (7.6 MeV), 3^? (9.6 MeV) and 1⁺ (12.7 MeV) states of ¹²C and on the $\text{3}\text{2}{}^{\mathrm{?}}\text{(3.7}\text{MeV}\text{),}\text{5}\text{2}{}^{\mathrm{?}}\text{(7.5}\text{MeV}\text{),}\text{9}\text{2}{}^{\mathrm{+}}\text{(9.5}\text{MeV}\text{)}$ and 11.7 MeV states of ¹³C was mea ¹²C results are compared to a Δ-hole model.     

Study of electric monopole transitions between the ground state and the first excited 0+ state in 40, 42, 44, 48Ca with high resolution inelastic electron scattering

Monopole transitions from the 0₁⁺ ground states to 0₂⁺ excited states at 3.353 MeV (⁴⁰Ca), 1.837 MeV (⁴²Ca), 1.884 MeV (⁴⁴Ca) and 4.272 MeV (⁴⁸Ca) have been investigated with high resolution inelastic electron scattering (FWHM ≈ 30 keV) at low momentum transfer (0.29 ≦ q ≦ 0.53 fm^?1). The respective monopole matrix elements are 2.53 ± 0.41 fm², 5.24 ± 0.39 fm², 5.45 ± 0.41 fm² and 2.28 ± 0.49 fm². These results are used together with known ground state charge radii and the average number of holes in the sd shell in the ground state to estimate the number of particle-hole excitations in the wave functions of the excited 0⁺ states.