We systematically analyze total reaction cross sections of carbon isotopes with N = 6-16 on a 12 C target for wide range of incident energy. The intrinsic structure of the carbon isotope is described by a Slater determinant generated from a phenomenological mean-field potential, which reasonably well reproduces the ground state properties for most of the even N isotopes. We need separate studies not only for odd nuclei but also for 16 C and 22 C. The density of the carbon isotope is constructed by eliminating the effect of the center of mass motion. For the calculations of the cross sections, we take two schemes: one is the Glauber approximation, and the other is the eikonal model using a global optical potential. We find that both of the schemes successfully reproduce low and high incident energy data on the cross sections of 12 C, 13 C and 16 C on 12 C. The calculated reaction cross sections of 15 C are found to be considerably smaller than the empirical values observed at low energy. We find a consistent parameterization of the nucleon-nucleon scattering amplitude, differently from previous ones. Finally, we predict the total reaction cross section of 22 C on 12 C.

We systematically study total reaction cross sections of carbon isotopes with N = 6-16 on a proton target for wide range of incident energies, putting an emphasis on the difference from the case of a carbon target. The analysis includes the reaction cross sections of 19,20,22 C at 40 AMeV, the data of which have recently been measured at RIKEN. The Glauber theory is used to calculate the reaction cross sections. To describe the intrinsic structure of the carbon isotopes, we use a Slater determinant generated from a phenomenological mean-field potential, and construct the density distributions. To go beyond the simple mean-field model, we adopt two types of dynamical models: One is a core+n model for odd-neutron nuclei, and the other is a core+n+n model for 16 C and 22 C. We propose empirical formulas which are useful in predicting unknown cross sections.

with a conversion error in Table I. The last numbers of the sixth column should read as −0.24, −0.35, −0.38, −0.2, and −0.46. The table has been corrected as of December 28, 2009. The table is incorrect in the printed version of the journal.

We find a new method to deduce nuclear radii from proton-nucleus elastic scattering data. In this method a nucleus is viewed as a "black" sphere. A diffraction pattern of protons by this sphere is equivalent to that of the Fraunhofer diffraction by a circular hole of the same radius embedded in a screen. We determine the black sphere radius in such a way as to reproduce the empirical value of the angle of the observed first diffraction peak. It is useful to identify this radius multiplied by 3/5 with the root-mean-square matter radius of the target nucleus. For most of stable isotopes of masses heavier than 50, it agrees, within the error bars, with the values that were deduced in previous elaborate analyses from the data obtained at proton incident energies higher than ∼ 800 MeV.PACS numbers: 21.10. Gv, 24.10.Ht, 25.40.Cm Size of atomic nuclei, one of the most fundamental nuclear properties, remains to be determined precisely. Most popularly, the size is deduced from electron and proton elastic scattering off nuclei [1,2,3,4,5]. The charge radii are well determined due to our full understanding of the underlying electromagnetic interactions [5,6,7], while deduction of the matter radii from the proton-nucleus scattering data depends on the scattering theory, which is more or less approximate in the sense that the nucleon-nucleon interactions involved are not fully understood. During the past three decades there have been many efforts of deducing the matter density distributions, which are based on various scattering theories incorporating empirical nucleon-nucleon scattering amplitudes, such as Glauber theory [1,3] and nonrelativistic and relativistic optical potential methods [8,9,10,11]. A systematic analysis of the data for a large number of nuclides, however, is still missing. In this paper we propose a method to deduce the root-mean-square (rms) matter radii, which is powerful enough to allow us to perform such a systematic analysis. This method, in which we assume that the target nucleus is completely absorptive to the incident proton and hence acts like a "black" sphere, is far simpler than the conventional methods. This approximation was originally used by Placzek and Bethe [12] in describing the elastic scattering of fast neutrons.The present method is useful for heavy stable nuclei for which the proton elastic scattering data are present, as we shall see. In the conventional framework to deduce the rms radius, one tries to reproduce empirical data for the differential cross section for scattering angles covering several diffraction maxima [1,4,13], whereas, in the present method, one has only to analyze the data around a maximum in the small angle regime. Remarkably, these two methods turn out to be similar in the deducibility of the radius.Elastic scattering data for more neutron-rich unstable nuclei are expected to be provided by radioactive ion beam facilities, such as GSI and Radioactive Ion Beam Factory in RIKEN. In a possible scheme, a beam of unstable nuclei, such as Ni and Sn isotopes, creat...

We identify a length scale that simultaneously accounts for the observed proton-nucleus reaction cross section and diffraction peak in the proton elastic differential cross section. This scale is the nuclear radius, a, deduced from proton elastic scattering data of incident energies higher than ∼ 800 MeV, by assuming that the target nucleus is a "black" sphere. The values of a are determined so as to reproduce the angle of the first diffraction maximum in the scattering data for stable nuclei. We find that the absorption cross section, πa 2 , agrees with the empirical total reaction cross section for C, Sn, and Pb to within error bars. This agreement persists in the case of the interaction cross section measured for a carbon target. We also find that 3/5a systematically deviates from the empirically deduced values of the root-mean-square matter radius for nuclei having mass less than about 50, while it almost completely agrees with the deduced values for A > ∼ 50. This tendency suggests a significant change of the nuclear matter distribution from a rectangular one for A < ∼ 50, which is consistent with the behavior of the empirical charge distribution. The size of atomic nuclei is considered to be well deduced from empirical data for the proton-nucleus elastic differential cross section, dσ el /dΩ, and the total reaction cross section, σ R ≡ σ T − σ el , where σ T is the total cross section. So far, the analysis that respects both data in deducing the nuclear size has not been completed in particular for proton incident energies, T p , higher than 800 MeV. Various approximate theories based on optical potentials have been proposed to reproduce the elastic scattering data, while they usually tend to overestimate the reaction cross section for 800 MeV < ∼ T p < ∼ 1000 MeV (e.g., Ref.[1] and references therein).In Ref.[2], we constructed a method for deducing the nuclear size by focusing on the peak angle in the proton-nucleus elastic differential cross section measured at T p > ∼ 800 MeV, where the corresponding optical potential is strongly absorptive. In this method, we regard a nucleus as a "black" (i.e., purely absorptive) sphere of radius a, and determine a in such a way as to reproduce the angle of the observed first diffraction peak. If we multiply a by 3/5, a ratio between the root-mean-square and squared off radii for a rectangular distribution, the result for stable nuclei of A > ∼ 50 shows an excellent agreement with the root-mean-square radius, r m , of the matter density distribution as determined from conventional scattering theories so as to reproduce the overall diffraction pattern and analyzing power in the proton elastic scattering.In this paper, we extend such a previous analysis to the case of A < ∼ 50, and find out a systematic deviation between 3/5a and r m . We next show that the present method is effective at explaining the observed reaction cross sections for stable nuclei ranging from light to heavy ones. In the black sphere approximation of a nucleus, where the geometrical cross section ...