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.     

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.     

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.     

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.     

Microscopic description of low-energy neutron scattering by nuclei

The Bloch and Gillet shell-model formalism extended to continuum states is applied to lowenergy neutron scattering by nuclei. It is shown that complete antisymmetrization leads in the r-representation to corrective terms which yield important corrections to the scattering lengths. Calculations are performed within a model restricted configuration space for the target nuclei ¹²C, ¹³C, ¹⁶O, ¹⁷O and ⁴⁰Ca. We predict values for the spin-dependent scattering amplitude for ¹³C and ¹⁷O. The antisymmetrization problem in the case of a large configuration mixing is studied for the ¹⁹F target nucleus. The resonant effects of the compound nucleus are then very important and the results become very sensitive to the configuration space and the interaction parameters.     

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.     

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.     

Direct neutron scattering from 182W and 184W

Differential elastic and inelastic neutron scattering cross sections for ¹⁸²W and ¹⁸⁴W have been measured at incident energies 4.87 and 6.00 MeV. Cross sections for the first (0⁺, 2⁺, 4⁺, 6⁺), second (0⁺, 2⁺), and some higher excitations are presented. Angular distributions exhibit direct reaction characteristics, suggesting that compound cross sections for these states are small. This is supported by statistical-model calculations. Coupled-channel calculations of cross sections are made using a phenomenological deformed optical potential. Quadrupole and hexadecapole deformations have been searched to optimize fits. The necessity of introducing a β₆ deformation is investigated. Electric multipole transition matrix elements, used in the coupled-channel analysis, are obtained from the rotation-vibration model and the dynamic-deformation theory.     

Intermediate structure in the neutron scattering cross sections of iron

Differential cross sections for the Fe(n, n), (n, n′), (n, n′γ) reactions were measured at incident energies between 1.43 and 2.15 MeV. Structure with intermediate widths was observed. The result was analysed by the doorway-state model, and the widths of the assumed doorway states were obtained. Spin and parity assignment of $\text{3}\text{2}$(⁺) was made to a doorway-state resonance at about 2.0 MeV.     

Effective interactions in the proton optical-model potential

A six-parameter optical model is developed in which the real central part is calculated by folding several effective nucleon-nucleon interactions into matter distributions which reproduce single-particle binding energies and electron scattering data. A simple local approximation is made to take into account the exchange term. It is concluded that the density-dependent effective interactions derived from nuclear-structure calculations are also appropriate for nucleon-nucleus scattering. Off-shell effects are apparent from the worsening of the quality of fit for light nuclei.     

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.     

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.     

A systematic semi-microscopic analysis of the scattering of oxygen isotopes

A semi-microscopic theory for the scattering of nuclei near closed shells is discussed in detail and applied to the bulk of the presently available experimental data. The results generally indicate that the single-folding model can be used to extrapolate the effective interactions for heavy-ion scattering away from closed-shell systems. We particularly discuss the importance of the imaginary part of the valence interaction and the effects of higher-order reorientation and two-step transfer processes.     

Optical model analysis of the elastic scattering of 45 MeV 3He particles on 1p shell nuclei

Angular distributions of elastically scattered ³He particles from the 1p shell nuclei ⁶Li, ⁷Li, ⁹Be, ¹⁰B, ¹¹B, ¹²C and ¹⁶O were measured by using a 45 MeV ³He beam. The absolute differential cross section data obtained were analysed in terms of the standard optical model. Using the fact that the rms radius of the 1p shell nuclei is nearly constant a simple folding model allows finding an optical potential family whose real potential depth varies linearly with the target mass. The best fits exhibit a normalized volume integral of about 400 MeV · fm³ for the real potential. From the best-fit parameters a mean parameter set is deduced which varies smoothly with the target mass A_T. The average parameter set compares well with the systematics found for heavier nuclei.