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.     

Elastic proton scattering from He in the forward direction at 200, 350 and 500 MeV

The differential cross section for the elastic scattering of protons from ⁴He has been measured at 200, 350, and 500 MeV over an angular range from 3.5° to 15° in the lab system. In addition, the analyzing power was measured in the same angular range at 350 and 500 MeV. The experiment makes use of a tenuous gas target in which the recoil -energy is measured with solid-state detectors. The proton scattering angle is measured outside the target by a system of multi-wire proportional counters. The differential cross sections have a nearly exponential dependence on momentum transfer in this kinematic range and grow with increasing energy. The analyzing power shows strong positive asymmetry.     

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 scattering of 32S on 24Mg, 27Al and 40Ca and the effect of nuclear forces on the grazing collision

Elastic scattering of ³²S ions on ²⁴Mg, ²⁷Al and ⁴⁰Ca has been measured at energies between 67 MeV and 120 MeV. Angular distributions were analyzed with the optical model with Woods-Saxon potentials. Strong absorption radii are extracted with and without consideration of the nuclear interaction at the surface. The nuclear potential decreases the otherwise anomalously large strong absorption radii which can then be described by a radius parameter of r₀ = 1.41 fm.     

Inelastic electron scattering from He

The spectra of electrons scattered inelastically from ⁴He have been measured at incident energies from 150 MeV to 400 MeV for scattering angles from 38° to 90°. Through the use of a liquid ⁴He target, a high momentum resolution (≈0.25%) was obtained, and the 20 MeV 0⁺ state of the -particle was observed for the first time in electron scattering. The excitation energy and the total width of this state were determined and are in good agreement with the results from other experimental methods. It was found that the total disintegration cross section appears be smaller than 2(σ_p+σ_n) by more than an order of magnitude at the lowest q²(≈ 0.33 fm⁻²). In earlier work the assumption of a total cross section of 2(σ_p+σ_n) was found to be quite accurate for higher q². As a new result, the partial radiative width for the 0⁺ state is determined to be Γ_rad = 1.1±0.3 meV.     

Elastic scattering of B on B in the energy range from 4 to 15 MeV

Angular distributions (at E_c.m. = 4, 6.5 and 10.5 MeV) and excitation functions (at 30°, 60° and 90°) are given for the elastic scattering of ¹⁰B on ¹⁰B. The results of an optical model (OM) analysis are presented and discussed. In the energy range covered the Sommerfeld parameter η varies from 4.4 to 2.3.     

Neutron scattering from 26Mg

Elastic and inelastic cross sections have been measured for 24 MeV neutrons incident on ²⁶Mg using the time-of-flight technique. These cross sections and existing proton data were analyzed in terms of a Lane-consistent optical potential. Distorted-wave and coupled-channel calculations are presented. Deformation parameters for the first 2⁺ state (1.81 MeV) and the second 2⁺ state (2.94 MeV) derived from both the (n, n') and (p, p') data are used to obtain the ratio of neutron and proton transition matrix elements M_n(E2) and M_p(E2) for these states. Comparison of results for $\text{M}{}_{\mathrm{<mtext>n</mtext>}}\text{(}\text{E}\text{2)}\text{M}{}_{\mathrm{<mtext>p</mtext>}}\text{(}\text{E}\text{2)}$ with those obtained from pion work, from electromagnetic (EM) rates and theoretical evaluations are presented.     

Elastic electron scattering from C and O

Electron scattering cross sections for carbon and oxygen between q = 1 fm⁻¹ and 4 fm⁻¹ are given. The data are analysed in terms of a phenomenological charge distribution and new information concerning the tail and the center of the charge distribution are obtained. The presence of dispersion effects appears to be necessary to explain the cross sections in the first diffraction minimum. The effect of a finite potential and short range correlations on the form factor are discussed.     

Elastic and inelastic scattering of 79.5 MeV 11B and 87.5 MeV 10B ions

The elastic scattering of 79.5 MeV ¹¹B ions has been studied for seven targets ranging in mass from ²⁴Mg to ¹⁹⁷Au and of 87.5 MeV ¹⁰B ions for three of these targets (^{24, 25}Mg, ⁶⁰Ni). Angular distributions were measured from ~10° c.m. in steps of 0.5°, to angles beyond 40° c.m. where the elastic cross sections are ? 10^?3 of the Rutherford values (except for ¹⁹⁷Au). Inelastic data for exciting the lowest 2⁺ states of ^24,26Mg and ⁶⁰Ni were also obtained. Important odd-A-even-A differences are observed in the ¹¹B elastic angular distributions for the Mg and Al targets; for ¹⁰B scattering these are obscured by projectile quadrupole moment effects on the elastic scattering. The elastic data were analyzed using the optical model with potentials of both Woods-Saxon and double-folding form. The data for both ¹⁰B and ¹¹B are consistent with the potential obtained in the folding model with the M3Y interaction without renormalization. The inelastic data were analyzed by the distorted-waves method.     

Magnetic elastic electron scattering from 3Be and 13C

Elastic scattering through 180° from ⁹Be, ¹²C and ¹³C targets has been observed for electrons of 35 to 90 MeV. Magnetic scattering cross sections for ⁹Be and ¹³C have been obtained by subtracting charge scattering as deduced from the scattering from the spin-zero nucleus ¹²C. Theoretical shell model predictions for the magnetic cross sections are derived for (1s)⁴(1p)^A?4 configurations and various coupling schemes. Both harmonic oscillator and Woods-Saxon radial wave functions are used. A comparison of our results with magnetic cross sections calculated in DWBA yields magnetic rms radii $\text{〈r}{}^2\text{〉}{}_{\mathrm{<mtext>M</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 3.2 ± 0.3}\text{fm}$ and $\text{〈r}{}^2\text{〉}{}_{\mathrm{<mtext>M</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 3.3 ± 0.3}\text{fm}$ for ⁹Be and ¹³C. For ¹³C a combined flt to our low-q data and to earlier high-q data, yields $\text{〈r}{}^2\text{〉}{}_{\mathrm{<mtext>M</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 3.4 ± 0.1}\text{fm}$ and a strong preference for intermediate coupling (IC) wave functions. Magnetic dipole scattering from ⁹Be is also close to the IC prediction, as deduced from a fit to our data and earlier high-q data. The fitted value of the octupole moment $\text{Ω = 5±1 μ}{}_{\mathrm{<mtext>N</mtext><mtext>fm</mtext>}}{}^1$ can only be explained by a deformation of the average nuclear potential. The radial size $\text{〈r}{}^2\text{〉}{}_{\mathrm{<mtext>1</mtext><mtext>p</mtext>}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 2.85 ± 0.05}\text{fm}$ for the 1p radial wave function is in agreement with both the ⁹Be and ¹³C data.     

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 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.     

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 at small angles of protons

Differential cross sections and asymmetries are obtained from elastic scattering, between 0° and 7°, of 36.2 MeV polarized protons by C, Al, Fe and Ni natural targets.     

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.