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Register a new userProton-nucleus total reaction cross sections in the optical limit Glauber theory: Subtle dependence on the equation of state of nuclear matter
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We calculate the proton-nucleus total reaction cross sections at different energies of incident protons within the optical limit approximation of the Glauber theory. The isospin effect has been taken into account. The nucleon distribution is obtained in the framework of macroscopic nuclear models in a way depending on the equation of state of uniform nuclear matter near the saturation density. We find that at an energy of order 40 MeV, the reaction cross section calculated for neutron- rich isotopes significantly increases as the parameter L characterizing the density dependence of the symmetry energy increases, while at energies of order 300 and 800 MeV, it is almost independent of L. This is a feature of the optical limit Glauber theory in which an exponential dependence of the reaction cross section on the neutron skin thickness remains when the total proton-neutron cross section is small enough.
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We systematically calculate the total reaction cross sections of oxygen isotopes, $^{15-24}$O, on a $^{12}$C target at high energies using the Glauber theory. The oxygen isotopes are described with Slater determinants generated from a phenomenological mean-field potential. The agreement between theory and experiment is generally good, but a sharp increase of the reaction cross sections from ^{21}O to ^{23}O remains unresolved. To examine the sensitivity of the diffraction pattern of elastic scattering to the nuclear surface, we study the differential elastic-scattering cross sections of proton-^{20,21,23}O at the incident energy of 300 MeV by calculating the full Glauber amplitude.
A simple functional form has been found that gives a good representation of the total reaction cross sections for the scattering of protons from (15) nuclei spanning the mass range ${}^{9}$Be to ${}^{238}$U and for proton energies ranging from 20 to 300 MeV.
We perform a parameter-free calculation for the high-energy proton-nucleus scattering based on the Glauber theory. A complete evaluation of the so-called Glauber amplitude is made by using the factorization of the single-particle wave functions. The multiple-scattering or multistep processes are fully taken into account within the Glauber theory. We demonstrate that proton- $^{12}$C, $^{20}$Ne, and $^{28}$Si elastic and inelastic scattering ($J^pi=0^+ to 2^+$ and $0^+ to 4^+$) processes are very well described in a wide range of the incident energies from $sim$50 MeV to $sim$ 1 GeV. We evaluate the validity of a simple one-step approximation andfind that the approximation works fairly well for the inelastic $0^+ to 2^+$ processes but not for $0^+ to 4^+$ where the multistep processes become more important. As an application, we quantify the difference between the total reaction and interaction cross sections of proton-$^{12}$C, $^{20}$Ne, and $^{28}$Si collisions.
Total reaction cross sections of deuteron, $sigma_d^{rm R}$, are calculated by a microscopic three-body reaction model. The reaction model has no free adjustable parameter and applicable to reactions at various deuteron incident energies $E_d$ and with both stable and unstable nuclei. The predicted $sigma_d^{rm R}$ are consistent with those evaluated by a phenomenological optical potential for $E_dleq 200$ MeV in which the potential has been parametrized. A simple formula of $sigma_d^{rm R}$ up to $E_d=1$ GeV, as a function of $E_d$, the target mass number $A$ and its atomic number $Z$, is given.
A simple functional form has been found that gives a good representation of the total reaction cross sections for the scattering from ${}^{208}$Pb of protons with energies in the range 30 to 300 MeV.
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