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.     

Neutron elastic scattering from 116,118,120,122,124Sn

Accurate measurements of neutron differential elastic cross sections have been obtained from even isotopes of Sn. Data are presented for the elastic scattering of 11 MeV neutrons from ^{116, 118, 120, 122, 124}Sn, the elastic scattering for 24 MeV neutrons from ^{116, 118, 124}Sn and the neutron total cross section from ^{118, 120, 122, 124}Sn in the energy ranges 5.0–10.6 MeV and 20.0–26.0 MeV. The elastic scattering data are analyzed in terms of an empirical optical-model potential. The obtained optical-potential parameters are analyzed in terms of energy and isospin dependence and compared with those obtained from proton elastic scattering on even Sn isotopes.     

Neutron scattering from Bismuth,Strontium and Sodium at 14.8 MeV

Differential cross sections for the elastic and inelastic scattering of 14.8 MeV neutrons from Bi, Sr and Na have been measured with four neutron detectors participating in a time-of-flight system which had an energy resolution of 900 keV for the incident neutrons. The whole procedure was checked by scattering from carbon. For the elastic scattering of Bi, Sr and Na satisfactory optical-model fits were obtained. The absolute cross sections for excitation of collective states are compared to the distorted-wave theory for direct reactions, and a reasonable agreement has been found. The nuclear deformation parameters are extracted and compared to the values from other experiments.     

The 208Pb(α, 3He)209Pb reaction at 58 MeV

The ²⁰⁸Pb(α, ³He)²⁰⁹Pb reaction at 58 MeV has been used to search for high-spin states in ²⁰⁹Pb. Only three levels are excited with appreciable intensity: the ground state $\text{(2}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}$ and levels at $\text{0.781 (}\text{li}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{)}\text{and}\text{1.426}\text{MeV}\text{(}\text{lj}{}_{\mathrm{<mtext>15</mtext><mtext>2</mtext>}}\text{)}$. The angular distributions for these levels have been measured and analyzed using standard DWBA calculations to obtain spectroscopic strengths. The ²⁰⁸Pb(α, α) elastic scattering was measured and optical parameters deduced from the data. A normalization value N = 50 yields spectroscopic values which are close to the values measured in the (d, p) reaction. The (α, ³He) reaction should easily pick out any appreciable components of the $\text{j}{}_{\mathrm{<mtext>15</mtext><mtext>2</mtext>}}$ shell model state, which weak-coupling calculations predict should be fragmented. However only three weak transitions previously seen in a (d, p) experiment are observed.     

Angular correlations from 6Li break-up near the Coulomb barrier of 118Sn and 208Pb

Absolute coincidence cross sections for three-particle final states have been measured inplane in the ⁶Li + ¹¹⁸Sn and ⁶Li +²⁰⁸Pb reactions at incident energies of 22.2 and 23.0 MeV, respectively. Most strongly populated is the α + d branch, proceeding sequentially through the first excited state (E_x = 2.18 MeV, J^π = 3⁺) of ⁶Li. The angular distributions are fitted by DWBA calculations including Coulomb interaction in the excitation of the projectile. The main competing reaction channels above and at the Coulomb barrier (¹¹⁸Sn: E/E_c ≈ 1.3; ²⁰⁸Pb: E/E_c ≈ 0.9) are: neutron transfer (⁶Li, αp) and the non-sequential α + d break-up of ⁶Li. The latter spectra are consistent with a quasi-free break-up mechanism. No ³He or tritons have been found in the coincidence spectra, as well as no evidence for a three-particle dissociation of ⁶Li into α + p + n.     

Neutron elastic scattering on T = 0 nuclei

Neutron elastic scattering on Si, S and Ca has been measured at 11, 20 and 26 MeV using the Ohio University 11 MeV Tandem Van de Graaff. A time-of-flight technique was used and the angular distributions covered an angular range from 15° through 155°. The measured cross sections were corrected for dead time, source anisotropy, detector efficiency, finite geometry, neutron flux attenuation and multiple scattering. Individual as well as global fits to the data using an optical-model search code are presented. The comparison of the optical-model analysis to the neutron and proton elastic scattering data in the case of ⁴⁰Ca, allows an empirical determination of the Coulomb correction term which may be parametrized as $\text{0.46 Z/A}\text{1}\text{3}$. It is also shown that the elastic scattering and inelastic scattering to the first 2⁺ states in ²⁸Si and ³²S may be fitted using the same optical-model parameters obtained for ⁴⁰Ca using the coupled-channel formalism.     

Search for giant spin-flip transitions in 90Zr and 208Pb

We have searched for the giant magnetic dipole resonance in ⁹⁰Zr and an associated state in ²⁰⁸Pb. Among the experimental techniques employed in this search was the detection of inelastically scattered protons in coincidence with ground-state de-excitation γ-rays, No state in ⁹⁰Zr up to an excitation of 10.5 MeV or in ²⁰⁸Pb between 5.0 to 6.0 MeV was observed with the desired characteristics. In ⁹⁰Zr, heretofore unidentified levels at 5.51, 5.89 and 6.42 MeV were determined to have J^π = 1^?. In ²⁰⁸Pb J^π = 1^? states were observed at 5.29, 5.51 and 5.94 MeV. The implications of our observations are discussed.     

Neutron inelastic scattering to octupole states in single-closed-shell nuclei

Differential cross sections for the excitation of the first octupole-vibrational state in the closed- neutron-shell nuclides ⁸⁸Sr and ⁹⁰Zr and in the closed-proton shell-nuclei ^{116, 118, 120, 124}Sn by 11 MeV neutrons are presented. The distorted-wave Born approximation is used to obtain deformation lengths, σ(3^?), for each state. Results are compared with earlier measurements of inelastic proton scattering to the same states. Although limited resolution in the neutron time- of-flight spectrometer complicates the interpretation of the Sn data, the overall conclusion that σ_nn′(3^?) ≈ σ_pp′(3^?) is supported by all of the measurements.     

Small-angle neutron scattering from Pb and 238U between 0.6 and 2.2 MeV

Differential cross sections for neutrons scattered from natural Pb and 99.9 % isotopically pure ²³⁸U have been measured at 0.5°, 1.0°, and 1.5°. A neutron energy continuum was produced by bombarding a thick natural lithium target with a 4 MeV, nanosecond-pulsed proton beam. Neutron energies were determined by time-of-flight techniques. Flight paths from the neutron source to the scatterer and from the scatterer to the detector were each about 5 m. For the 0.5° measurements an annular detector geometry with an angular resolution of ± 0.1° was developed to maximize detection solid angle. Data were averaged over 100 keV intervals from 0.6 to 2.2 MeV and were corrected for backgrounds, multiple scattering and inelastic scattering. Measured cross sections were compared to optical-model calculations which included electromagnetic interactions of neutrons with the nuclear Coulomb field. Inclusion of an induced neutron electric dipole moment interaction was not warranted by the data. The angular dependence of the cross section was fitted with a function $\text{A + B}\text{cot}{}^2\text{case1}\text{2}$θ at each energy. Mean values of B for ²³⁸U are in agreement with theoretical predictions. Values of B for Pb are apparently 15 % too low.     

The determination of the nuclear charge distribution of 208Pb from elastic electron scattering and muonic X-rays

An iterative procedure is presented for determining a static nuclear charge distribution from experimental electron scattering cross sections and muonie atom X-ray transition energies. The errors and error correlations implied by the independent statistical errors in the experimental data are expressed in coordinate space, and kernels are derived which specify the linear constraints imposed on the charge density by the experimental data. Pseudo-experimental data for ²⁰⁸Pb, generated from a known charge distribution, are used to demonstrate the validity of the procedure. A detailed analysis of experimental data for ²⁰⁸Pb is presented, utilizing electron scattering data at five different energies and six muonic energy levels. The theoretical implications of this work concerning quantum density fluctuations and the possible existence of a central depression are discussed.     

Neutron particle-hole electric dipole states in 206, 207, 208Pb

Inelastic proton scattering on ²⁰⁶Pb, ²⁰⁷Pb and ²⁰⁸Pb through isobaric analog resonances has been used to study neutron particle-hole excitations with large ground-state γ-branches in these Pb isotopes. Relative (p, p′) cross sections at 90° are extracted for structures selectively excited on the $\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{,}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{and d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{?}\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ resonances. Interpretation of excitations is ²⁰⁶Pb and ²⁰⁷ Pb in terms of coupling to states in ²⁰⁸Pb is discussed. Branching ratios for 1^?states in ²⁰⁸Pb at 4.84, 5.29, 5.94 and 6.31 MeV and the $\text{1}\text{2}{}^{\mathrm{+}}$ state in ²⁰⁷Pb at 4.63 MeV are deduced.     

201 MeV proton excitation of giant resonances in 208Pb: Macroscopic and microscopic analysis

The region of the giant resonances in ²⁰⁸Pb has been investigated by inelastic scattering of 201 MeV protons. To test the analysis, angular distributions were measured for the low-lying 3^?, 5^?, 2⁺ and 4⁺ collective states. The giant isoscalar quadrupole resonance (ISGQR) is split into two structures, one at 9.0 MeV with a full width at half-maximum Γ = 1.0 MeV, the other one at 10.6 MeV (Γ = 2.0 MeV), with fine structures at 8.9, 9.3, 10.1, 10.6 and 11 MeV. A macroscopic analysis using the distorted-wave Born approximation (DWBA) leads for the low-lying collective levels, as well as for the ISGQR, to transition probabilities too small by a factor of two, compared with those obtained in other reactions. Microscopic analysis using the distorted-wave impulse approximation (DWIA), with three different sets of random phase approximation (RPA) transition densities, is in very good agreement with the data. At forward angles, in the 12 to 16 MeV excitation energy region, a strong resonance at 13.5 MeV (Γ = 3.6 MeV) is accounted for by the Coulomb excitation of the isovector giant dipole resonance (IVGDR); at larger angles the results are compatible with the excitation of the isoscalar monopole resonance (ISGMR) located at 13.9 MeV (Γ = 2.6 MeV).A resonance located at 21.5 MeV (Γ = 5.7 MeV) appears as the superposition of an isovector quadrupole resonance (IVGQR) excited by Coulomb interaction and a resonance of multipolarity L = 1 ΔT = 0 (ISGDR “squeezing mode”).     

The charge-distribution differences of 209Bi, 208, 207, 206, 204Pb and 205, 203Tl investigated by elastic electron scattering and muonic X-ray data

Elastic electron scattering cross sections and cross-section ratios have been measured for the stable Bi, Pb and T1 isotopes. The data are analysed with the Fourier-Bessel method and the charge-distribution differences of the isotonic and isotopic pairs are presented as well as the Fourier-Bessel coefficients of the seven single nuclei. To improve the accuracy of the results, muonic X-ray data are incorporated into the analysis. The measured Δρ(r) are compared with the simple shell model, where the stretching due to the additional nucleons is taken into account, and with more sophisticated HF calculations.     

Proton polarization observables for the elastic and inelastic scattering of 500 MeV protons from Ca and Pb

Measurements for the elastic and inelastic scattering of 500 MeV protons from ⁴⁰Ca and ²⁰⁸Pb at small momentum transfers are reported. The induced proton polarization P and the spin rotation parameter Q were measured for the elastic scattering. The spin rotation parameters D_SS′, D_SL′, D_LL′, d_LS′ and the induced polarization P were measured for transitions to the 3⁻(3.37 MeV) and 5⁻(4.48 MeV) states in ⁴⁰Ca and the 3⁻(2.61 MeV) state in ²⁰⁸Pb. Comparisons of the data with the theoretical calculations were carried out in the framework of nonrelativistic and relativistic approaches. We extracted the spin-up and spin-down channels for the elastic scattering cross sections and found that predictions of the relativistic and nonrelativistic approaches agree well with the spin-up channel data and differ considerably in the spin-down channel.     

Neutron total and scattering cross sections of 6Li in the low-MeV range

Neutron total cross sections of ⁶Li are measured at intervals of ? 10 keV from ≈ 0.1 to 4.8 MeV with precisions of ≈ 1 to 3 %. Differential elastic scattering cross sections are measured at intervals of ? 100 keV from 1.5 to 4.0 MeV at 10 or more scattering angles distributed between ≈ 20 and 160 deg. Differential inelastic scattering cross sections are measured at selected angles in the energy range 3.5 to 4.0 MeV. The experimental results are analyzed in terms of R-matrix theory and the model parameters used to deduce the ${}^6\text{Li(n}\text{,α)}$ cross sections. The implications of the measurements and their interpretation on the level structure of ⁷Li and the reaction mechanisms are discussed.     

Neutron total and scattering cross sections of some even Mo isotopes and the optical model

Neutron total cross sections of ⁹²Mo, ⁹⁶Mo, ⁹⁸Mo and ¹⁰⁰Mo were measured at intervals of ? 10 keV from 1.6 to 5.5 MeV with resolutions of ≈ 10 keV. Neutron elastic and inelastic scattering cross sections of these isotopes were measured from 1.8 to 4.0 MeV at intervals of 0.2 MeV. Neutron groups corresponding to the excitation of forty states were identified. The experimental results were examined in the context of optical and statistical nuclear models. It was concluded that the real part of the optical potential includes a term proportional to [(N-Z)/A] and suggested that the imaginary part of the potential was shell dependent with decreasing magnitude as N = 50 is approached. Comparison of measured and calculated inelastic neutron excitation cross sections suggested a number of J^π assignments extending previous knowledge.     

Angular distributions of photoprotons from 208Pb

Angular distributions of photoprotons following the (e, e′p) reaction in ²⁰⁸Pb have been measured at incident energies of 25.0 MeV and 40.0 MeV. The proton energy distributions were measured at several angles and the angular distributions were obtained for several proton energy ranges. Proton groups at around 11.0 MeV and 15.3 MeV are separated for the angular distributions and the results show almost isotropic distributions, which indicate that these proton groups are emitted through IAR. The angular distributions for other slowly varying parts of the proton spectra proved strongly asymmetrical, indicative of interference between E1 and E2 transition.     

6Li elastic scattering ON 12C, 16O, 40Ca, 58Ni, 74Ge, 124Sn, 166Er and 208Pb at E(6Li) = 50.6 MeV

The elastic scattering of ⁶Li ions from a variety of targets, A = 12 to 208, has been measured at a bombarding energy of 50.6 MeV. The angular distributions are characteristic of strongly absorbed particles, such as ³He and heavy ions, and less diffractive than for ⁴He. A simple optical model with Woods-Saxon real and imaginary volume potentials is adequate to fit the data. Spin-orbit effects are not apparent in the data.