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替代比率法[5]是在替代法基础上发展起来的一种新方法,与替代法相比该方法的主要优点是不需要测量复合核数目,不依赖理论计算。根据Hauser-Feshbach复合核理论[6]和Weisskopf-Ewing近似[7],假定γ衰变概率不明显依赖于复合核的自旋宇称,则A(n, γ)B截面可写为
$$ {\sigma _{A({{{\rm{n}},\;\gamma }})B}}({E_{\text{n}}}) = \sigma _{{\text{n}} + A}^{{\text{CN}}}({E_{\text{n}}}) \times G_{B^{*} \to \gamma + B}^{{\text{CN}}}({E_{\text{n}}})\begin{array}{*{20}{c}} , \end{array} $$ (1) 其中:$\sigma _{{\text{n + }}A}^{{\text{CN}}}({E_{\text{n}}})$为复合核形成的截面; $G_{B^{*} \to \gamma + B}^{{\text{CN}}}({E_{\text{n}}})$为复合核衰变到γ道的概率(或中子俘获概率);${E_{\text{n}}}$为中子入射能。在替代比率法中,一个截面已知的参照反应A2(n, γ)B2将用于目标反应A1(n, γ)B1的推导。基于等式(1),两个反应截面的比率可写为
$$ \begin{split} \frac{{{\sigma _{A1({ {{\rm{n}},\;\gamma }})B1}}({E_{\text{n}}})}}{{{\sigma _{A2({{{\rm{n}},\; }\gamma })B2}}({E_{\text{n}}})}} = & \frac{{\sigma _{{\text{n}} + A1}^{{\text{CN}}}({E_{\text{n}}}) \times G_{B1^{*} \to \gamma + B1}^{{\text{CN}}}({E_{\text{n}}})}}{{\sigma _{{\text{n}} + A2}^{{\text{CN}}}({E_{\text{n}}}) \times G_{B2^{*} \to \gamma + B2}^{{\text{CN}}}({E_{\text{n}}})}} \\ \approx & \frac{{G_{B1^{*} \to \gamma + B1}^{{\text{CN}}}({E_{\text{n}}})}}{{G_{B2^{*} \to \gamma + B2}^{{\text{CN}}}({E_{\text{n}}})}}。 \end{split} $$ (2) 如果选择的参照反应与目标反应相似,可以使得$\sigma _{{\text{n}} + A1}^{\rm{CN} }({E_{\text{n}}})/\sigma _{{\text{n}} + A2}^{{\text{CN}}}({E_{\text{n}}}) \approx 1$,则两个中子俘获截面之比可以简化为复合核衰变到γ道的概率之比。实验测量时,我们采用实验室易于实现的替代反应d1+D1→b1+B1*与d2+D2→b2+B2*生成复合核B1*和B2*,并测量其衰变到γ道的概率比。利用该比值和截面的已知的参照反应A2(n, γ)B2 截面可以得到目标反应A1(n, γ)B1 截面。如验证实验利用90Zr(18O, 16O)92Zr*代替91Zr+n合成复合核92Zr*,利用92Zr(18O, 16O)94Zr*代替93Zr+n合成复合核94Zr*,并测量94Zr*和92Zr*衰变到γ道的衰变概率比,结合91Zr(n, γ)92Zr直接测量截面则可以推导出93Zr(n, γ)94Zr截面。
在该实验测量中,我们利用加速器加速117 MeV的18O轰击90Zr、92Zr高富集同位素金属自撑靶,用ΔE-E硅望远镜(碗形ΔE阵列和Micron公司的S1型环形探测器组成)覆盖22~39度出射角(望远镜角度分辨好于1度),探测和鉴别出射的轻粒子,粒子鉴别谱如图1。通过90, 92Zr(18O, 16O)92, 94Zr*双中子转移后出射的16O的能量和出射角度,利用两体运动学可以重构92Zr*或94Zr*激发态能量。92Zr*或94Zr*发射的特征γ用溴化镧探测器探测,并与硅探测器鉴别的16O符合。实验设置详见参考文献[2]。实验中我们确定了92Zr*或94Zr*的激发态能量,并探测到了92Zr*或94Zr*发射的特征γ射线,经靶、束流归一,以及探测器效率等实验参数修正后,即可得到通过双中子转移反应生成的复合核92Zr*和94Zr*的γ道衰变概率比。实验确定了92Zr*和94Zr*的γ道衰变概率比, 即可结合91Zr(n, γ)92Zr直接测量截面推导出93Zr(n, γ)94Zr截面。我们还在同样的实验设置下测量94Zr(18O, 16O)96Zr*反应,用于推导95Zr的中子俘获截面。
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摘要: 不稳定核中子俘获截面对于恒星核合成及恒星内部中子密度研究有重要意义,但由于难以制靶,直接测量极其困难。在前期工作验证了替代比率法可以可靠推导不稳定核的中子俘获截面的基础上,本工作主要讨论了复合核自旋宇称态分布差异对复合核γ衰变概率比的影响。本工作计算了不同自旋宇称态下94Zr*和92Zr*衰变到γ道的衰变概率比,计算结果显示在中子入射能较高的区域复合核自旋宇称态分布差异对γ衰变概率比影响较小。同时,理论计算结果与实验数据比较显示,在低能区域(18O, 16O)的替代反应生成的复合核倾向布居与中子俘获反应生成的复合核相近的低自旋宇称态。本工作的计算和讨论进一步证明了替代比率法推导(n, γ)截面的可靠性。Abstract: The neutron capture cross sections of unstable nuclei are important to the study of the stellar nucleosynthesis and the neutron densities in massive stars. Due to the difficulties of the target fabrication, it is very hard to measure the neutron capture cross section of unstable nuclei directly. Therefore, the surrogate ratio method had been employed in (n, γ) determination and proved valid previously. In this work, the difference of the spin-parity distribution in compound nuclei that formed by surrogate reaction or neutron capture was discussed in (n, γ) determination with surrogate ratio method. The γ-decay probabilities ratio of 92Zr* and 94Zr* were calculated in various spin-parities, and the calculation showed the ratio is insensitive to their spin-parity distribution in high incident neutron energies. The measured γ-decay probabilities ratios of 92Zr* and 94Zr* were compared to the theoretical calculations, it imply that the spin-parity distributions of compound nuclei formed by (18O, 16O) reactions are similar to the one formed by neutron captures, and the validity of the surrogate ratio method was further proved in this work.
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Key words:
- surrogate ratio method /
- neutron capture cross section /
- unstable nuclei
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