Optical-model analysis of elastic scattering of 53.4 MeV helions from Fe

Elastic helion scattering from ⁵⁶Fe at 53.4 MeV was measured over the angular range 12° to 150°. Using the regular optical model, real-potential ambiguities, the shape of the imaginary term and the need for a spin-orbit term were explored. Coupled-channels (SCA) calculations based on the ground state and principal 2⁺ and 3⁻ states indicate that such coupling effects are not as dominant as the inclusion of a spin-orbit potential in the regular optical model. Previously reported helion scattering from ⁵⁹Co and ⁶⁰Ni at 50.1 MeV has been included in an average parameter analysis to generalise the improvements in the helion optical-model parameterization in this energy region.     

Optical-model analysis of the elastic scattering of 100 MeV protons from Mg and Si

Elastic scattering differential cross sections for the interaction of 100 MeV protons with ²⁴Mg and ²⁸Si have been measured using a high-resolution Ge(Li) spectrometer to resolve the inelastic scattering contribution to the elastic peak. The results have been analysed using the conventional optical model, and the experimental differential cross sections and total reaction cross section are excellently reproduced. The results agree with previous analyses of the elastic scattering of 100 MeV protons on 1p shell nuclei in that no set of geometric parameters can provide a quantitative fit to both nuclei. It is observed, however, that the fluctuations of the optical-model parameters for optimum fits are decreased over the fluctuations observed for the 1p shell nuclei. The present results combined with previous optical-model analyses on ²⁴Mg and ²⁸Si at 50 MeV and 40 MeV respectively, are found to be consistent with an energy dependence of dV/dE ≈ −0.3 for the depth of the real central potential in agreement with other, more extensive, investigations of the energy dependence for protons elastically scattered from ¹⁶O and ⁴⁰Ca.     

A global optical-model analysis of neutron elastic scattering data

Differential cross sections for neutron elastic scattering in the energy range 7–26 MeV from ⁴⁰Ca, ⁹⁰Zr, ⁹²Mo, ^{116, 124}Sn and ²⁰⁸Pb are analyzed in terms of a global optical-model potential. A smooth variation of the real radius parameters with mass number is investigated. Otherwise, optical-model geometrical parameters are kept fixed at values obtained by averaging individual best fits. The energy and isospin dependences of potential strengths and volume integrals per nucleon are presented.     

Optical-model analysis of 7Li + 25Mg and 7Li + 27Al elastic scattering at 89 MeV

The elastic scattering angular distributions for ⁷Li + ²⁵Mg and ⁷Li + ²⁷Al were measured at $\text{E(}{}^7\text{Li}\text{) = 89}\text{MeV}$ over angular ranges of 8–55° c.m. and 8–64° c.m. Previously published measurements for ^{24, 26}Mg at 89 MeV and ²⁴Mg at 34 MeV are reanalyzed. The cross sections were analysed using a 6-parameter phenomenological Saxon-Woods potential. No discrete ambiguities were found but the usual continuous ambiguities exist. The data were also analysed with double folded real potentials generated using the M3Y effective interaction. The folded potential must be multiplied by about 0.6 to fit the data. The extent to which ⁷Li optical-model potentials are determined and suggestions for further work on the normalization of the folded potential are discussed.     

Large-angle 6Li + 28Si elastic and inelastic scattering at 27 and 34 MeV

Elastic and inelastic scattering data extending to θ_c.m ≈ 175° are reported for ⁶Li + ²⁸Si at 27 and 34 MeV. Optical model analyses of the elastic data were made using a variety of real potential forms. The large-angle data cannot be fitted with a Woods-Saxon real potential, but are well described by Woods-Saxon squared, double-folded or Fourier-Bessel potentials. The real potential is the same at both energies, but the imaginary potential is weaker at 27 MeV. The inelastic data were analyzed using the DWBA and coupled channels techniques with folded real form factors and deformed Woods-Saxon imaginary potentials, with the deformations taken from electron scattering. The 2⁺ state was fitted well at both energies with the DWBA, while the prediction decreased too rapidly at large angles for the 4⁺ state. The large-angle 4⁺ data were better described when two-step excitations were included in the coupled-channels calculations. The forward-angle 2⁺ data are sensitive to the interference between Coulomb and nuclear scattering and show that the nuclear and Coulomb deformation parameters β₂ are equal for this transition.     

Phase-shift analysis of d-α elastic scattering between 3 and 43 MeV

Phase shifts for the d-α elastic scattering have been extracted from differential cross sections and the vector and tensor analyzing powers of ${}^4\text{He(}\text{d}\text{, d)}{}^4$He scattering in the energy range from 3 to 43 MeV. The analysis includes spin-orbit splitting, mixing of states and absorption to reaction channels. A new parametrization of two-channel scattering matrices is given and compared. Excellent fits have been obtained with a new phase-shift code ONEZERO, which is capable of taking into account all degrees of freedom in strong interactions. The Argand-plot method has been used for resonance analysis of the excited ⁶Li system. Five new broad T = 0 resonances above 15 MeV deuteron energy have been found in ⁶Li, corresponding to D₃, F₂, F₃, G₃ and G₄ resonant states. Problems from phase-shift ambiguities are pointed out.     

Alpha-nucleus elastic scattering at intermediate energies

Elastic scattering of 288,340,480 and 699 MeV Alpha-particles was measured on ²⁰⁸Pb, ¹¹⁶Sn and ⁵⁸Ni. The data were analysed in terms of a phenomenological optical model. The optical potentials obtained were found to vary consistently with the target nucleus and the incident energy. The radial zone where the potentials are well determined was studied in detail. The data for ²⁰⁸Pb were also analysed with a folding model. The energy dependence of the strong-absorption radius and of the reaction cross section shows that the nuclear surface becomes slightly transparent for incident energies above 150 MeV per nucleon.     

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.     

Proton-nucleus elastic scattering at 156 MeV

Cross sections for the elastic scattering of 156 MeV protons on eleven targets ranging from ¹²C to ²⁰⁹Bi were measured and an optical model analysis has been performed. The effect of different optical potentials in DWIA inelastic scattering calculations is shown by some examples.     

Optical model analysis of proton elastic scattering excitation functions around A = 90

Excitation functions of protons elastically scattered from ⁸⁸Sr, ⁸⁹Y, ⁹⁰Zr and ⁹²Mo over an energy range from 8 to 15 MeV were analysed with the optical model. The deep minima exhibited by these excitation functions especially at extreme backward angles can be described by an imaginary potential which is smaller than that of Becchetti and Greenlees. Compound nucleus contributions were taken into account by appropriate weighting of the data. The magnitude of these contributions in the minima could thus be estimated.     

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.     

p-4He elastic scattering at 2.68 GeV

The p-⁴He elastic differential cross section has been measured at a kinetic energy of 2.68 GeV. The momentum transfer region studied is t = 0.15–0.66 (GeV/c)². The cross section displays a shallow first minimum and shape very similar to recent data at 1 GeV.     

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.     

The time evolution of compound elastic scattering measured by crystal blocking

Using the crystal blocking technique, we have measured the emission distributions of protons near the 〈110〉 axis elastically scattered from a 7000 Å thick single nickel crystal, at 5.65 and 6.50 MeV. These distributions are fitted by an analytic multiple string calculation of the blocking process which yields the time-dependent compound-nucleus decay probability curve. Shape- and compound-elastic cross sections are simultaneously determined in a reaction-model-independent way, as is the mean compound nucleus lifetime. The resulting decay curves for the delayed component are consistent with a single exponential at both energies and show no indication of the presence of level-level correlations. Use of such data in testing recent statistical theories is discussed.     

Microscopic analysis of the elastic scattering of 11Li neutron-rich nuclei on protons

Amicroscopic optical potential is used to calculate cross sections for elastic ¹¹Li +p scattering at the energies of 62, 68.4, and 75 MeV per nucleon, and the results are compared with available experimental data. The potential used does not involve free parameters, but the depths of its real and imaginary parts are renormalized. The known trend in the energy dependence of the volume integrals of the optical potential is taken into account in analyzing experimental data. The role of spin-orbit interaction is studied, and the total reaction cross sections that are proposed to be measured in future experiments are calculated.