Elastic scattering of 119 MeV 3He particles and energy and mass-number dependence of optical potential parameters

The elastic scattering of 119 MeV ³He particles by ¹²C, ²⁷Al, ^58,60,62,64Ni, ⁵⁹Co, ^90,92Zr and ⁸⁹Y has been investigated over a wide angular range in order to study the mass-number dependence of the optical potential and odd-even differences in the elastic scattering. The elastic scattering cross sections have been analyzed in terms of the optimal model. The data, except for ¹²C, ²⁷Al and ⁵⁹Co, were fitted with r_R = 1.21 fm, a_R = 0.76 fm and r_I = 1.17 fm, fixed at the average values. The following formulae were obtained for the three remaining parameters by combining with the energy dependence of the parameters (90–120 MeV) obtained previously:

$\text{V=111.4?0.173E+}\text{Z}\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{+14.9}\text{N?Z}\text{A}\text{(}\text{MeV}\text{)}$

$\text{W}{}_{\mathrm{<mtext>D</mtext>}}\text{=24.8?0.028E (}\text{MeV}\text{)}$

,

$\text{a}{}_{\mathrm{I}}\text{=0.754+0.78}\text{N?Z}\text{A}\text{(}\text{fm}\text{)}$

The depths of the valleys of the angular distribution in the case of ${}^{59}\text{Co}\text{(I =}\text{7}\text{2}\text{)}$ are considerably shallower than those for Ni isotopes, while the depths in the case of ${}^{89}\text{Y}\text{(I =}\text{1}\text{2}\text{)}$ are nearly the same as those for Zr isotopes. Thus it may be concluded that the odd-even differences are attributed to the scattering from the quadrupole moment of the odd-A nucleus (if $\text{I >}\text{1}\text{2}$).     

Elastic scattering of 100 MeV protons and systematic optical model analysis

Using a Ge(Li) total energy detector the elastic scattering of 100 MeV protons from ⁵⁸Ni, ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸Pb has been measured. Optical model fits with $\text{x}{}^2\text{N}$ of order unity have been made. The parameters of these fits varied systematically with A enabling the isospin dependence of the real part of the potential and its volume integral to be deduced. The limitations of the conventional optical model analysis in the case of ⁵⁸Ni are illustrated and discussed.     

Elastic scattering of tritons by 16O

Angular distributions and excitation functions have been measured for the ¹⁶O(t, t) reaction from 1.4 to 3.7 MeV triton energy using a differentially pumped gas target. The observed resonances have been analysed with the Humblet-Rosenfeld theory. It appears that the 13–15 MeV excitation range of the compound system of ¹⁹F is dominated by several levels of large triton partial width. Levels populated in the three-particle transfer reaction (⁷Li, α) on ¹⁶O are compared with the resonances.     

Elastic scattering of 217 MeV 3He particles

Differential cross sections have been measured for the elastic scattering of 217 MeV ³He particles from ⁶Li, ⁹Be, ¹²C, ²⁸Si, ⁴⁰Ca, ⁵⁸Ni, ⁸⁹Y, ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸pb. The data have been analysed with an optical potential. The ambiguities found at lower energies (discrete families of real potential well depths) disappear. An optical potential is also calculated with an effective ³He-N interaction and a matter distribution. The agreement with experiment is good. Some comparisons are made with 166 MeV α-particle elastic scattering data.     

Evidence for energy dependence in the isospin dependent part of the nuclear optical model potential

Angular distributions and the excitation function of the total cross section for the ²⁰⁸Pb(p, n) charge exchange reaction are fitted with DWBA calculations. Isospin potentials which have the relative real volume and surface imaginary strengths found in the optical model studies of Becchetti and Greenlees provide adequate fits to the angular distributions. The excitation function indicates a strong energy dependence in the strength of the isospin potential.     

Elastic scattering of 2.76 MeV neutrons by Ca40

The elastic scattering of 2.76 MeV neutrons by calcium has been studied using the nuclear emulsion technique. The angular distribution of the elastically scattered neutrons has been compared with optical-model calculations. A satisfactory agreement with the theory has been obtained. In addition, the total cross section for 2.76 MeV neutrons on calcium has been measured by the transmission technique.     

Elastic scattering of 13.6 MeV deuterons by light nuclei

Measurements were made of the differential cross section or elastic scattering of 13.6 MeV deuterons by 19 nuclei, from beryllium to iron, and of the cross sections for inelastic scattering corresponding to the excitation of the lower excited levels of beryllium, carbon, titanium-46, and titanium-48. Several features found in the angular distributions are attributed to the interference of Coulomb and nuclear scattering. All the angular distributions are analyzed on the basis of the optical model; a quite good agreement is found between theory and experiment. A calculation is carried out for scattering by titanium-48 by the method of complex angular momenta. This model satisfactorily describes inelastic scattering of deuterons.Translated from Izvestiya VUZ. Fizika, No. 8, pp. 105–113, August, 1970.The authors thank the staff at the cyclotron of the Scientific-Research Institute of Nuclear Physics, Electronics, and Automation, Tomsk Polytechnical Instutute, for the reliable operation of the accelerator; and L. S. Sokolov and K. O. Terenetskii for assistance in the calculations.     

Elastic scattering of 3He nuclei on 13C nuclei at 50 and 60 MeV and V-W ambiguity in choosing optical potentials

At energies of 50 and 60 MeV, the elastic scattering of ³He nuclei on ¹³C nuclei is investigated at laboratory angles in the range 10°–170°. The measured differential cross sections are analyzed on the basis of the optical model of the nucleus by using Woods-Saxon potentials, including both volume and surface absorption. The potential parameters are determined by fitting the computed cross sections to experimental data. It is found that, even in the region of sensitivity, the values of the real and imaginary parts of the potentials (V and W, respectively) show considerable scatter, with extreme values differing by a factor greater than two. This scatter is explained by the existence of a V-W ambiguity in choosing optical potentials.     

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.     

Elastic scattering of 86 MeV9Li and 55 MeV6He on208Pb

The cross sections of elastically scattered⁹Li and⁶He on²⁰⁸Pb were measured. The scattered particles were detected by an annular CR-39 solid state nuclear track detector and the monitoring was done with a triple telescope of silicon detectors. The classical and optical model analyses of the measured elastic cross sections have been carried out. It was shown that the peripheral⁹Li interaction region has a rather high transparency. Strong dynamical polarization of⁹Li ions in the process of scattering is suggested.     

Elastic and inelastic scattering of 185 MeV protons from 12C

The polarization of 185 MeV protons in elastic scattering and in the excitation of the 2⁺ state at 4.44 MeV and the 0⁺ state at 7.65 MeV in ¹²C has been measured in the angular region 2°–60°. Optical model calculations are performed for the elastic scattering. Angular distributions for the inelastic scattering from the 2⁺ state at 4.44 MeV and the 3^? state at 9.64 MeV are calculated in the distorted-wave impulse approximation (DWIA) as well as in the distorted-wave Born approximation (DWBA).     

Elastic scattering of 0.5 MeV gamma rays by heavy elements

The absolute differential cross sections for the elastic scattering of 0.511 MeV gamma rays were measured in the angular range 0.5? to 10? for the elements withZ=72 toZ=92. The experimental method, employing annihilation radiation in coincidence, permits the investigation at very small momentum transfer. In general the results obtained are in very good agreement with the predictionZ ² r ₀ ² for the differential Rayleigh cross section atθ=0? and with the form factor theory, using Hartree-Fock-Slater wave functions, for the investigated angular range. However, for the elements lead, bismuth and thorium we found marked deviations from the form factor predictions, occurring at very small scattering angles. This is attributed to an outer atomic charge distribution different from the other investigated elements, which is also indicated by considerably greater metallic radii. Also effects due to the crystalline structure cannot be excluded. — Further, an elastic, resonance-like andZ-dependent scattering effect by bound electrons is discussed which is due to the formation of an intermediate, bound positronium state by electron-positron pairs.     

On the energy dependence of the real central optical potential for proton-nucleus scattering

The energy dependence of the real central optical potential in the energy range 25–1000 MeV has been determined from optical model analyses of p+¹²C, p+¹⁶O, p+²⁷Al, p+⁴⁰Ca and p+²⁰⁸Pb elastic scattering data. The volume integral and the strength can be represented by a relation linear in the incident energy only if a limited energy range is chosen. When the energy range 25–1000 MeV is considered a logarithmic energy dependence gives a better representation of the phenomenological results, especially for the light nuclei.     

Elastic scattering of positive pions by O between 80 and 340 MeV

Angular distributions of cross sections for π⁺ elastic scattering by ¹⁶O have been measured between 14° and 138° at five energies (79, 114, 163, 240 and 343 MeV). They are compared to calculations using a first-order static model and an isobar doorway model. Phase-shift analyses have been done using the theoretical inputs as guidelines. The validity of these models is discussed.