Standard notation for the set of children of a node in a rooted tree

Question

In graph theory, given a rooted tree $T$ and a node $a \in V(T)$, is there a standard way to refer to the set of all children of $a$? I have seen $CHILDREN_T(a)$ being used, but this seem quite clumsy to me, especially when used several times on the same line, e.g. $S = \bigcup_{b \in CHILDREN_T(a)} CHILDREN_T(b)$. In contrast, the common notation for the neighbourhood of $a$ is denoted $N_T(a)$, which is very nice and short. Is there a similar nice/common way to refer to the children of the node $a$ in a rooted tree?