设 $X_1, X_2, \cdots, X_n$ 为来自总体 $X \sim N\left(0, \sigma^2\right)$ 的简单随机样本, 样本均值与样本方差分别为 $\bar{X}=\frac{1}{n} \sum_{i=1}^n X_i, S^2=\frac{1}{n-1} \sum_{i=1}^n\left(X_i-\bar{X}\right)^2$, 则 $D\left(\sqrt{n} \bar{X}^2-S^2\right)=(\quad)$
A
$2\left(\frac{1}{n}-\frac{1}{n-1}\right) \sigma^4$
B
$(n-1) \sigma^2$
C
$\left(\frac{1}{n}+\frac{1}{n-1}\right) \sigma^2$
D
$2\left(\frac{1}{n}+\frac{1}{n-1}\right) \sigma^4$
E
F