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.     

Elastic and inelastic pion scattering on C and C at 100 MeV

Angular distributions of π⁺ and π^? at 100 MeV incident energy were measured for elastic and inelastic scattering from ¹²C and ¹³C. Elastic data were obtained between 6° and 180°. Inelastic scattering on the 2⁺ (4.4 MeV), 0⁺ (7.6 MeV), 3^? (9.6 MeV) and 1⁺ (12.7 MeV) states of ¹²C and on the $\text{3}\text{2}{}^{\mathrm{?}}\text{(3.7}\text{MeV}\text{),}\text{5}\text{2}{}^{\mathrm{?}}\text{(7.5}\text{MeV}\text{),}\text{9}\text{2}{}^{\mathrm{+}}\text{(9.5}\text{MeV}\text{)}$ and 11.7 MeV states of ¹³C was mea ¹²C results are compared to a Δ-hole model.     

Elastic scattering at small angles of protons

Differential cross sections and asymmetries are obtained from elastic scattering, between 0° and 7°, of 36.2 MeV polarized protons by C, Al, Fe and Ni natural targets.     

Polarization in the inelastic scattering of 185 MeV protons

The polarizations produced in the inelastic scattering of 185 MeV protons exciting the lowest octupole states in ¹²C and ²⁰⁸Pb are measured. The data together with earlier similar measurements for ⁴⁰Ca and ⁹⁰Zr are compared with existing theoretical models. The inclusion of a deformed spin-dependent interaction of the full Thomas form in the DWBA amplitude is found to considerably improve the theoretical fits to the data. For ¹²C, however, the DWBA fit is found to be inferior to that obtained using DWIA. The strong absorption model is found to give qualitatively good fits to the data for the heavier nuclei but again fails in the ¹²C case.     

Inelastic scattering of 185 MeV protons from Mg and Al

A magnetic spectrometer was used for the energy analysis of protons scattered from targets of magnesium (natural isotopic composition) and aluminium. The mean energy of the incident protons in the targets was 185 MeV. A total energy resolution of 350 keV (FWHM) was achieved, which made possible the observation of the excitation of a large number of discrete levels. Energy spectra were measured in the angular region of 4° to 40° (lab system).

The results are presented partly in the form of tables giving measured excitation energies and maximum cross sections for resolved levels and partly in the form of graphs of angular distributions of the differential cross sections.

A qualitative discussion of the results is given in terms of the multipolarities of the transitions involved and comparisons are made with similar results from other experiments in inelastic scattering and in a few cases with theoretical predictions.     

Elastic and inelastic scattering of 178 MeV protons from 58Ni and 60Ni

The elastic and inelastic scattering of 178 MeV protons from ⁵⁸Ni and ⁶⁰Ni has been studied. Angular distributions were measured for the differential cross sections for elastic scattering as well as inelastic scattering from excited states below about 5 MeV, all with natural parity. For the elastic and for the inelastic scattering from the first excited state (2⁺ in both nuclei, the angular distributions for the polarization were also measured. The measurements extend out to c.m. angles of about 60°, corresponding to a momentum transfer of about 600 MeV/c.The elastic and inelastic scattering data were compared to the results of coupled-channel calculations in the vibrational model using a deformed spin-orbit interaction of the full Thomas form. Good agreement was found in general showing that the main features of the experimental results are well described in this model.     

Elastic and inelastic scattering of neutrons from Fe and Cu : (I). Measurements from 8 to 14 MeV and a spherical optical model analysis

Differential cross sections were measured at 8, 10, 12 and 14 MeV for elastic scattering of neutrons from enriched samples of ⁵⁴Fe, ⁵⁶Fe, ⁶³Cu and ⁶⁵Cu. Inelastic scattering to the first excited state in ^{54, 56}Fe was also observed. For the ^{63, 65}Cu isotopes, the inelastic cross sections for scattering to the combined group of the three (five) states were determined at 8 and 10 MeV (12 and 14 MeV). The elastic scattering data are compared to predictions of earlier global optical models. New spherical optical model representations were obtained. These data were combined with data for nickel, tin and lead to generate a new global parametrization. Comparisons of derived volume integrals for the potentials, total cross sections and potential radii are made to available information.     

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 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).     

The elastic and inelastic scattering of 30.5 MeV protons by24Mg

Measurements of the differential cross sections for the elastic scattering of 30.5 MeV protons by ²⁴Mg and for the inelastic scattering to the 1.37, sum of 4.12 and 4.23, 5.22 and 6.0 MeV states are reported. Optical model fits to the elastic data, a distorted wave calculation for the first excited state, and coupled channel calculations are also presented.     

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 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.     

The deuteron breakup reaction induced by protons of 65, 85 and 100 MeV

Coplanar energy sharing spectra for p + d breakup at 65, 85 and 100 MeV proton bombarding energies were measured using the University of Maryland sectored isochronous cyclotron, by measuring the energies of either two protons or one proton and one neutron in coincidence. The detector angles were chosen to enhance either the p-p or p-n quasifree scattering, or the p-n final state interaction. The energy dependence of the peak cross section at equal symmetric quasifree scattering angle pairs was extracted for the ²H(p, 2p)n and ²H(p, pn)p reactions. Quasifree angular distributions were obtained for the reaction ²H(p, 2p)n at 65 MeV and for the reaction ²H(p, pn)p at 65, 85 and 100 MeV. The plane wave impulse approximation theory can only qualitatively reproduce the shape of the quasifree scattering peak in the energy sharing spectra and the shape of the p-p quasifree angular distribution. The discrepancies observed between the plane wave impulse approximation theory and the experimental data imply that the presence of the spectator particle (i.e., the multiple scattering effects) has a strong influence on the magnitude and the shape of the experimental results. Multiple scattering calculations were carried out in the three-body model of Aaron, Amado and Yam except that the S-wave separable two-body amplitudes were modified to fit two-nucleon elastic scattering data at higher energies. Comparisons of the results of these multiple scattering calculations to the experimental data show excellent quantitative agreement throughout the energy range and the angular region of this experiment, except for a few cases in which this model is inherently insufficient; namely, regions in which the Coulomb interaction is important, or regions for which a Hulthén wave function is inaccurate and the off-shell effects are not properly taken into account.     

Elastic and inelastic scattering of 88 MeV 6Li ions

The elastic scattering of 88 MeV ⁶Li ions has been studied for eleven targets ranging in mass from ²⁴Mg to ²⁰⁸Pb. Angular distributions were measured from about 10° c.m. in steps of 0.5°, mostly out to 60 or 70° c.m. where the elastic cross sections range from 10^?3 to 10^?5 of the Rutherford values. Inelastic data for exciting the lowest 2⁺ states of ^24,26Mg and ⁶⁰Ni were also obtained. The elastic data were analyzed using the optical model, with potentials of both Woods-Saxon and double-folding forms. The analysis confirms that the potentials for ⁶Li obtained from the folding model with the M3Y interaction need renormalizing by about 0.6, in agreement with results obtained at other energies. The inelastic data were compared to distorted-wave calculations. Coupled-channels analyses were also made for ^{24, 26}Mg, ⁶⁰Ni and ⁵⁹Co. Reorientation effects were found to be important to give the correct 2⁺ angular distributions for ^{24, 26}Mg and could also account for the differences between the elastic scattering from the odd-A and adjacent even-A targets.     

Elastic scattering of 56 MeV polarized deuterons on 4He

The differential cross section and the vector and tensor analyzing powers A_y, A_xx, A_yy and A_xz were measured for the d-⁴He elastic scattering at 56 MeV. The measurement of A_xz was performed using a deuteron beam polarized in the horizontal plane. An optical-model analysis of the experimental data was carried out. The magnitude of the tensor analyzing powers could not be reproduced without the tensor potential. By including the T_R type tensor potential, the optical-model calculations give a reasonable reproduction of the experimental data at θ_c.m. < 120°. The obtained T_R tensor potential was much stronger than that predicted by the folding model. The strength of the real T_R potential was roughly in accordance with that obtained from the optical-model analysis of d-⁴He elastic scattering at 20.2 MeV.     

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.