Spin-orbit and Pauli-correlation effects in intermediate-energy proton-nucleus inelastic scattering

The excitation of the 3^? (6.13 MeV) state of ¹⁶O by 0.8 GeV protons is studied using Glauber theory with a spin-orbit NN amplitude. Two previously suggested approaches for handling the z-ordered non-commuting NN profile functions, γ, are compared and found to give nearly identical results for the usual observables. Transitions to certain LM substates which are forbidden in one approach are allowed in the other, but their cross sections are proportional to the fourth power of the strength of the NN spin-orbit amplitude and thus quite small. It is also shown that, in this energy region, an expansion in powers of the strength of the spin-orbit interaction converges rapidly and consequently any convenient ordering of the γ's can be used without serious errors. Using this result an estimate of the effects of Pauli correlations on the cross section and the polarization is given.     

Asymmetry in polarized e-d inelastic scattering

The parity violating asymmetry is calculated for polarized electron-deuteron inelastic scattering in the closure approximation for the outgoing nucleons. The results are applicable in the intermediate-energy region of the incident electron where asymmetries are found to be in the range accessible to the present experiments.     

Coupled-channels effects for inelastic scattering of 15 MeV polarized deuterons from Ti and Sm isotopes

Cross sections and analyzing powers have been measured for elastic and inelastic scattering of 15 MeV deuterons from ¹⁴⁸'Sm and ¹⁵²Sm. These data, as well as previous data for the ${}^{\mathrm{48,\; 50}}\text{Ti}\text{(}\text{d}\text{, d'}\text{)}$ reaction have been analyzed in the coupled-channels approximation. Data for ⁴⁸Ti and ¹⁵²Sm are better described by the rotational model than by the vibrational model but the quality of the fits is not sufficiently good to establish ($\text{d}\text{, d'}$) reactions as a sensitive method of discriminating between these two models.     

Evidence from inelastic proton scattering for a giant quadrupole vibration in spherical nuclei

A systematic study of inelastic proton continuum spectra produced at small angles by bombardment of ²⁷Al, ⁵⁴Fe, ¹²⁰Sn and ²⁰⁹Bi with 62 MeV protons suggests the existence of a collective region in the continuum with properties of a giant quadrupole vibration.     

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.     

High resolution proton scattering from 42Ca

Differential cross sections were measured for ⁴²Ca(p, p) at four angles between E_p = 1.2 and 3.0 MeV, with an overall energy resolution of 325 eV. Spins, parities and proton widths were extracted for 170 resonances. Two analogue states were identified and spectroscopic factors determined. The nearest neighbor spacing distributions were analyzed. Proton strength functions were determined for $\text{1}\text{2}$⁺, $\text{1}\text{2}$^? and $\text{3}\text{2}$^? resonances.     

Excitation of low-lying levels and giant resonances in 90Zr via 57.5 MeV polarized proton inelastic scattering

Differential cross section and analyzing power angular distributions have been measured for transitions to low-lying bound states with J^π = 2⁺, 3^?, 4⁺ and 5^?, and the giant resonance region from 6 to 27 MeV excitation energy. Collective model calculations using a full Thomas form factor reproduce the data fairly well. The so-called LEOR turns out not to be seen as pure E3 in (p, p′). In the giant resonance region the data do not reveal the presence of a sizeable monopole strength, 10–20% of the energy-weighted sum rule at most. There is strong indication for a mixture of E2 (18% of the EWSR) and E4 (16% of the EWSR). Calculations were also carried out using RPA (1p1h) wave functions. They reproduce the experimental data rather poorly, except for the general behaviour of the cross-section angular distributions.     

High resolution proton inelastic scattering from 50Cr

Resonances in the ⁵⁰Cr(p, p′γ) reaction were investigated with the TUNL high resolution system. All previously observed p-wave resonances between Ep = 2.00 and 3.03 MeV were studied. Measurement of the p' and the γ-ray angular distributions provides sufficient information to determine unambiguously the J-value of the resonance and the magnitude and relative phase of the inelastic decay amplitudes. Expressions are given for the appropriate angular distributions and for the transformation between the channel spin and the total angular momentum representation. Experimental results are presented for 24 p-wave resonances in ⁵¹Mn including decay amplitudes and relative phases for $\text{16}\text{3}\text{2}{}^{\mathrm{?}}$ resonances. Six resonances formerly assigned $\text{1}\text{2}{}^{\mathrm{?}}$ are reassigned $\text{3}\text{2}{}^{\mathrm{?}}$. Inelastic spectroscopic factors were determined for two analogue states. Proton strength functions were evaluated from both the elastic and inelastic data.     

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.     

A study of deuteron quadrupole moment effects in sub-coulomb scattering of tensor polarized deuterons

Measurements of the tensor analyzing power T₂₀ are presented for deuteron elastic scattering from ²⁰⁸Pb at energies below the Coulomb barrier. It is found that, for energies below about 7 MeV, T₂₀ arises primarily from the interaction of the deuteron quadrupole moment with the nuclear electric field gradient. Contributions to T₂₀ from nuclear interactions with the target are shown to be very small for E_d ? 5 MeV. Measurements of T₂₀ at E_d = 4 MeV, accurate to ± 8 × 10^?5, are presented. After correcting for deuteron stretching and a number of additional small effects, the data are used to make a new determination of the quadrupole moment. The result, Q = 0.282 ± 0.019 fm², is in good agreement with the conventional value deduced from molecular hyperfine structure data.     

Elastic and inelastic scattering of vector polarized deuterons from even samarium isotopes at 56 MeV

Differential cross sections and vector analyzing powers of deuteron elastic and inelastic scattering have been measured at 56 MeV over the whole range of the even samarium isotopes. Comprehensive analyses were performed with the optical model and the coupled-channels formalism. In the optical model analysis, calculations with a global parameter set could reproduce the experimental data only for the vibrational nuclei. The strong coupling approximation was applied assuming the ^{144, 148, 150}Sm to be harmonic vibrators and the ^152,154Sm symmetric rotators. The 2^λ (λ = 2, 3, 4, 6) pole deformation parameters were deduced from a systematic coupled-channels analysis. The transition strengths were extracted from the deformed optical potentials and compared with the corresponding electromagnetic ones. The transition rates for the rotational nuclei agreed with the electro-magnetic ones, but those for the vibrational nuclei gave the systematically smaller values. The latter fact was attributed to the difference between the proton and neutron transition matrix elements near the neutron-closed-shell nuclei. The ratios of the two matrix elements were obtained.     

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.     

Isobaric analogue resonances in proton scattering on Ba

Extensive experimental data for the resonance scatttering of protons to the ground state and first excited state in ¹³⁸Ba are presented. A Breit Wigner analysis with a background term of the form Σ_n(a_n/Eⁿ) is performed and the extracted background function is compared with optical-model calculations using the parameters given in a detailed investigation by Perey. Neutron spectroscopic factors calculated in different ways from this data are compared with the corresponding factors from (d, p). An accurate determination of resonance energies for the first two resonances reveals a deviation from a constant Coulomb shift of the order of 10 keV.     

Inelastic electron scattering at 180° from 14C

Inelastic scattering of 37, 50, and 60 MeV electrons at 180° from ¹⁴C has been studied. Cross sections for the excitation of eight states in ¹⁴C with excitation energy less than 16 MeV have been observed. Most of the strength is observed to be concentrated in one transition at 11.31 MeV which is assigned a spin and parity of 1⁺. The total width of this state is observed to be 207 ± 13 keV, while the electromagnetic transition width is determined to be 6.8 ± 1.4 eV.     

Theoretical investigation of giant resonances by inelastic proton scattering

A fully microscopic, antisymmetrized DWBA analysis of (p, p') spectra in the giant resonance region of ¹⁶O, ⁴⁰Ca and ²⁰⁸Pb is presented. The nuclear structure information is derived from RPA wave functions calculated in large configuration spaces. The theoretical spectra are in general in agreement with the experimental results. A new interpretation follows from our. investigation for the spectrum of the giant dipole region in the heavy nuclei: This resonance structure is mainly due to the breathing mode, whereas the electric dipole contribution is much smaller.     

Excitation of isobaric analogue resonances by inelastic scattering of polarized protons from 126Te

An experimental study of inelastic scattering of polarized protons from ¹²⁶Te, leaving this nucleus in its first excited state, is presented. The scattering proceeds through isobaric analogue resonances in ¹²⁷I.A method has been developed and applied to extract partial width amplitudes from measured cross sections and analyzing powers. From these amplitudes coefficients of fractional parentage are deduced, characterizing the relation between five negative parity parent states in ¹²⁷Te and the first excited state of ¹²⁶Te.     

Microscopic and macroscopic aspects of 135 MeV proton scattering from 16O

Differential cross sections have been measured for the scattering of 135 MeV protons from ¹⁶O and data from the transitions to 13 states (up to 19.5 MeV excitation) have been analysed using microscopic and macroscopic nuclear reaction models. Extensive collective model calculations have been made of the transitions to all natural-parity states. The deformation parameters for the 4p4h rotational band are in good agreement with theoretical models. The inelastic scattering data from the excitation of the negative-parity states have also been analysed in the distorted-wave approximation using microscopic (shell and RPA) models of nuclear structure and with density-dependent two-nucleon t-matrices. For positive-parity states, we report the first shell-model calculation using the complete 2?ω basis space and find that the triplet of 2p2h states (4⁺, 2⁺, 0⁺) around 11 MeV excitation is quite well described by this model, as may be a 1⁺ state which is observed for the first time by proton scattering from ¹⁶O.     

A study of the elastic scattering of polarized deuterons from 60Ni and 90Zr nuclei

Five quantities, σ₀, iT₁₁, T₂₀, T₂₁ and T₂₂, have been measured for the elastic ($\text{d}$, d) scattering from ⁶⁰Ni at 9 and 12 MeV and from ⁹⁰Zr at 10, 11 and 12 MeV over a wide angular range. Excitation functions for σ₀ and T₂₀ have been also measured at an angle of 175°(lab) in the approximate energy range of 6–13 MeV for both target isotopes. The experimental results, together with similar data published earlier for 15 MeV have now been analysed using the optical model with the complex central, spin-orbit and tensor T_R potentials. Excellent fits are obtained for the angular distributions for all five measured quantities. The main features of the excitation functions are also well reproduced. Five of the optical-model parameters can be fixed. Three other parameters can be constrained by simple mass dependence functions. Further evidence for the presence of an imaginary component of the spin-orbit potential is supplied by the analysis of the present data.