高精度测量$^{12}$ C（p，p '）质子角分布确定Hoyle态$E0$衰变分支比
High precision proton angular distribution measurements of $^{12}$C(p,p') for determination of the $E0$ decay branching ratio of the Hoyle state
摘要：
工作背景：在恒星中，碳只通过$3α$过程产生，其中三个$α$粒子融合形成处于激发态的$^{12}$ C，然后可以衰变到基态。恒星产生碳的速率取决于霍伊尔态的辐射宽度。辐射宽度可以通过结合三个单独测量的量来推导，其中之一是$E0$衰变分支比。$E0$分支比可以通过激发$^{12}$ C $(p,p')$反应中的Hoyle态并测量其Hoyle态和第一$2^+$态的对衰变来测量。目的：通过测量10.20和10.70 MeV之间$^{12}$ C中$(p,p')$反应中霍伊尔态（$0^+_2$）和$2^+_1$态粒子数的一组质子角分布，减少宇宙中碳生成率的不确定性，用于测定霍伊尔态的$E0$分支比。方法：在$^{12}$ C（p，p '）反应中，用硅探测器阵列覆盖$22^\circ<θ<158^\circ$，在10.20和10.70 MeV之间的14个能量阶跃中，用薄的（$60\ μ$ g/cm $^2$）$^{nat}$ C靶，测量了$^{12}$ C（p，p'）中基态、第一$2^+$和Hoyle态的质子角分布。结果如下：提取每个状态的总截面，并在每个能量步骤确定$2^+_1$和Hoyle状态之间的布居比。通过适当地平均这些横截面并取它们的比率，可以提取适用于在配对转换测量中使用的任何厚$^{12}$ C靶的等效群体比率。结论：我们提出了一个高精度的$^{12}$ C $(p,p')$截面的一般数据集，使得由质子非弹性散射引起的$2^+_1$和$0^+_2$态的布居产生的不确定性对于$^{12}$ C中的$E0$分支比的任何未来测量都可以忽略不计。
英文摘要：
Background: In stars, carbon is produced exclusively via the $3α$ process, where three $α$ particles fuse to form $^{12}$C in the excited Hoyle state, which can then decay to the ground state. The rate of carbon production in stars depends on the radiative width of the Hoyle state. The radiative width can be deduced by combining three separately measured quantities, one of which is the $E0$ decay branching ratio. The $E0$ branching ratio can be measured by exciting the Hoyle state in the $^{12}$C$(p,p')$ reaction and measuring the pair decay of its Hoyle state and first $2^+$ state. Purpose: To reduce the uncertainties in the carbon production rate in the universe by measuring a set of proton angular distributions for the population of the Hoyle state ($0^+_2$) and $2^+_1$ state in $^{12}$C in $^{12}$C$(p,p')$ reactions between 10.20 and 10.70 MeV, used in the determination of the $E0$ branching ratio of the Hoyle state. Method: Proton angular distributions populating the ground, first $2^+$, and the Hoyle states in $^{12}$C were measured in $^{12}$C(p,p') reactions with a silicon detector array covering $22^\circ<θ<158^\circ$ in 14 energy steps between 10.20 and 10.70 MeV with a thin ($60\ μ$g/cm$^2$) $^{nat}$C target. Results: Total cross-sections for each state were extracted and the population ratio between the $2^+_1$ and Hoyle state determined at each energy step. By appropriately averaging these cross-sections and taking their ratio, the equivalent population ratio can be extracted applicable for any thick $^{12}$C target used in pair-conversion measurements. Conclusions: We present a general data set of high-precision $^{12}$C$(p,p')$ cross-sections that make uncertainties resulting from the population of the $2^+_1$ and $0^+_2$ states by proton inelastic scattering negligible for any future measurements of the $E0$ branching ratio in $^{12}$C.
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