Concept

Lambda and T12 衰变概率 衰变常数可以用于描述原子核的衰变几率，表示单位时间内发生衰变的概率。 半衰期与衰变常数关系 根据半衰期的定义： $$ N_t = N_0 \cdot 2^{-\frac{t}{T_{\frac 1 2}}} $$ $$ \lambda = \frac{\mathrm{ln}(2)}{T_{\frac12}} $$ 活度与不稳定核数量 $$ A=-\frac{\mathrm d N}{\mathrm d t} = \lambda N $$ 数量计算 衰变常数: $\lambda$ 0 时刻活度为 $A_0$ 分支比为 $\epsilon$ ，能量为 $E$ 的伽玛测量计数为 $n$ 测量时间为$t_1$ ~ $t_2$ 活度积分 $t$ 时刻活度 $A$ 为： $$ A = A_0 \cdot e ^ {- \lambda t} $$ 测量时间$t_1$ ~ $t_2$目标核衰变数量 $N_{measured}$ 为： $$ N_{measured} = \int_{t_1} ^{t_2} A \mathrm dt,\\ N_{measured} = \int_{t_1} ^{t_2} A_0 \cdot e ^ {- \lambda t} \mathrm dt,\\ N_{measured} = \frac {A_0} {\lambda} \left (e ^{-\lambda t_1} - e ^{-\lambda t_2} \right ) $$ ...

Number density is a useful concept for thinking about macroscopic samples in a microscopic way. Number density can be thought of as the number of particles that are present in a particular volume. The number density (symbol: n or ρN) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number density, two-dimensional areal number density, or one-dimensional linear number density. ...

Least Significant Bit, 模数转换， 主要参考以下内容 What is an LSB? The LSB is the smallest level that an ADC can convert, or is the smallest increment a DAC outputs. The ADC needs a voltage reference to convert an analog signal into a digital word. Depending on the number of bits it has, the ADC divides the voltage reference in small levels called counts. For example, if this is an 8-bit ADC, the counts will look like those in Figure 1. In an 8-bit ADC there are 28 = 256 counts. ...

$$ r_{1,2}=N_{1} N_{2} \int_{0}^{\infty} v \sigma(E) P(E) \mathrm{d} E $$ where N1 and N1 are the number densities of the two reacting particles in the plasma, v and E are, respectively, the relative velocity and energy of the particles, P (E)is the energy distribution and σ(E) is the cross section of the reaction as a function of the interaction energy. At typical stellar conditions the energy distribution of the interacting particles can be well approximated by a Maxwell-Boltzmann distribution. So: $$r_{1,2}=N_{1} N_{2}\left(\frac{8}{\pi \mu}\right)^{1 / 2} \frac{1}{k T^{3 / 2}} \int_{0}^{\infty} E \sigma(E) e^{-E / k T} \mathrm{~d} E$$ Here T is the plasma temperature and μ is the reduced mass of the reacting particles. 在核天体物理中是联系微观和宏观的重要物理量，其截面(库仑势垒穿透系数)和粒子能量(麦克斯韦分布)分布预示着[[Gamow window]]，可以直接用于进行下一步天体环境发展的计算。 ...