Program - Brookhaven National Laboratory

sections (SACS) based on the assumption that cross section excitation curves for all targets have a similar
shape shifted by differences in Q-value, and that their properties, such as σmax, Emax and width at the half
maximum ∆ 1/2, have a pronounced smooth trend as a function of A or the asymmetry s=(N-Z)/A. The
reduced χ 2 were given by means of a comparison between some typical reaction excitation functions and
available experimental data. The σmax(s) of all reactions were plotted and the confidence intervals were
given not only for whole library but also for each of its components from different libraries or calculated
with TALYS. In order to give the error factor of the library comprehensively, the reduced χ 2 were converted
into the equivalent confidence interval to SACS. As a result, the error factors were given for all reactions
in the libraries except for (n, γ) reaction at thermal energy.
DC 4 4:40 PM
The Covariance Evaluation for the 12 C- 208 Pb (n,tot) Cross Sections from the Microscopic
Optical Model
Ruirui Xu, Tinjin Liu, Yue Zhang, Zhigang Ge, Zhongyu Ma, Zhixiang Zhao
China Institute of Atomic Energy
It is known that the fundamental microscopic theory is more powerful in the predictions of nuclear data of
unstable nuclei and the nuclei lack of measurements than the phenomenlogical model. The corresponding
uncertainty evaluations are also important and valuable to the applications of these theoretical data. In this
work, we propose to employ the deterministic least square approach (LS) to evaluate the covariance of the
microscopic theoretical calculation, and the (n, tot) cross sections based on the microscopic optical model
are taken as an example to illuminate it. A microscopic optical model potential (OMP) is successfully
constructed based on the relativistic Dirac-Brueckner-Hartree-Fock (DBHF) theory in our previous study
Ref.[1]. Here, this OMP is utilized to reproduce the (n,tot) cross sections of 12C-208Pb blow 200 MeV.
All of the calculations are compared with experimental data and the calculations based on the empirical
phenomenological potentials Ref.[2] and good agreement are achieved. Then, we respectively evaluate the
sensitivities of theory and the covariance of experimental data (Vexp) for LS approach according to the
characteristic of the present microscopic OMP. At first, in the sensitivity evaluation, the treatments in
constructing the microscopic OMP are analyzed and the existing uncertain elements are parameterized.
In the energy region 5-200 MeV, the sensitivities of this OMP to (n, tot) cross sections are systematically
calculated for 12 C- 208 Pb, 77 nuclei in total. Additioanlly, instead of Vexp, we introduce the definition
of ”equivalent covariance of experimental data” (EVexp) in the present study to describe the systematic
deviation between experimental data and OMP results of 12 C- 208 Pb (77 nuclei also) as well as the errors
of experimental data, and during this procedure, the statistic Gaussian function is adopted to estimate the
systematic errors of EVexp. Finally, the derived 12 C- 208 Pb(n, tot) cross sections and relevant covariance
(DCOV) are output by LS. The DCOV can be adopted as the covariance of the theoretical results when the
LS output cross sections are very close to the theoretical calculations. Besides, a method named ”selection
of effective points” is proposed to avoid the Peelle’s Pertinent Puzzle(PPP) problem in the present work,
and a satisfactory result is obtained. In addition, the covariance of parameter(Vc) is obtained through
global analysis for 12 C- 208 Pb(n,tot) cross sections, therefore, it is very helpful to generate the covariance
of (n,tot) cross sections by this microscopic OMP for unstable nuclei. Meanwhile, it should be metioned
that, up to now, LS is not utilized to evaluate theoretical (n,tot) cross sections in the energy below 5 MeV
yet due to its basic assumption of linear function.
[1] Ruirui Xu, and Zhongyu Ma, E. N. E. van Dalen and H. Müther, Phys. Rev.C 85, 034613 (2012); [2]
A.J.Koning and J.P.Delaroche, Nucl. Phys. A 713, 231(2003).
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