中子辐照量指数分布函数式中比例系数和平均中子辐照量的计算公式

Calculating Formulas of Coefficient and Mean Neutron Exposure in the Exponential Expression of Neutron Exposure Distribution

已有的研究表明,在AGB(Asymptotic Giant Branch)星s-过程核合成模型发展演化的3个典型阶段中,其核合成区域中子辐照量分布在有效取值范围内都可视为指数分布,即ρ_(AGB)(τ)=C/τ_0 exp(-τ/τ_0),但式中比例系数C和平均中子辐照量τ_0的具体表达式相关文献中并未全部给定.通过深入剖析中子辐照量指数分布函数的基本求解方法,并系统梳理不同恒星模型中子辐照量分布函数的求解过程,得到了C和τ_0的计算通式及其辅助关系式.只要确定了恒星模型中子辐照量的分立分布函数,就可以据此组公式确定出C和τ_0与模型参量之间的关系式.所得结果有效地解决了利用解析方法求解目前流行的^(13)C壳层(^(13)C pocket)辐射燃烧AGB星s-过程核合成模型中子辐照量分布问题.

Present studies have shown that, in the main stages of the development and evolution of asymptotic giant branch （AGB） star s-process models, the distributions of neutron exposures in the nucleosynthesis regions can all be expressed by an exponential function PAGB（T） = C/7oexp（-τ/τo） in the effective range of values. However, the specific expressions of the proportional coefficient C and the mean neutron exposure To in the formula for different models are not completely determined in the related literatures. Through dissecting the basic solving method of the exponential distribution of neutron exposures, and systematically combing the solution procedure of exposure distribution for different stellar models, the general calculating formulas as well as their auxiliary equations for calculating C and T0 are reduced. Given the discrete distribution of neutron exposures Pk, i.e. the mass ratio of the materials which have exposed to neutrons for k （k - 0, 1, 2...） times when reaching the final distribution with respect to the materials of the He intershell, C = -P1/In R, and TO = --AT/In R can be obtained. Here, R expresses the probability that the materials can successively experience neutron irradiation for two times in the He intershell. For the convective nucleosynthesis model （including the Ulrich model and the 13C-pocket convective burning model）, R is just the overlap factor r, namely the mass ratio of the materials which can undergo two successive thermal pulses in the He intershell. And for the 13C-pocket radiative burning model, R =This set of formulas practically give the corresponding relationshipbetween C or τo and the model parameters. The results of this study effectively solve the problem of analytically calculating the distribution of neutron exposures in the low-mass AGB star s-process nucleosynthesis model of 13C-pocket radiative burning.