Effective Two-Body Force Inferred from the (p,n) Reaction onO17,O18,Al27, and Other Light Nuclei

Abstract

Using the Livermore variable-energy cyclotron time-of-flight facility, the angular distribution of the neutrons from the ($p,n$) reaction on ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ has been measured in 15° steps from 0° to 135° for 13 proton energies between 7 and 13.5 MeV. The persistence of a rather large ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}\mathrm{}(p,n)\mathrm{}{}_{}{}^{18}{}_{}{}^{}\mathrm{F}$ ground-state reaction ($\Delta T=1,\Delta J=1\mathrm{}$) over the entire energy region studied clearly indicates the operation of a spin-flip mechanism in the effective two-body force. The ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}\mathrm{}(p,n)\mathrm{}$ isobaric cross sections ($\Delta T=0,\Delta J=0\mathrm{}$) are experimentally observed to be roughly equal, while optical-model calculations (including the isospin potential) predict ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ cross sections to be twice as large as those for ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$. This disagreement can be qualitatively explained by the presence of a large spin-flip term in the effective two-body force. The ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}(p,n_1){}_{}{}^{17}{}_{}{}^{}\mathrm{F}_{}^{*}{}_{}{}^{} (J_i={\frac{5}{2}}^{+},J_f={\frac{1}{2}}^{+})$ and the ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}\mathrm{}(p,n)\mathrm{}{}_{}{}^{18}{}_{}{}^{}\mathrm{F}_{}^{*}{}_{}{}^{} (\Delta T=0,J_i=0^{+},J_f=2^{+})$ cross sections indicate a sizeable value for the quadrupole term in the multipole expansion of the effective two-body force. These data and other light-nucleus data are analyzed using the distorted-wave Born approximation to yield an estimate of the effective central two-body interaction. For an assumed Yukawa force with a range of 1.4 fm, this analysis yields

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