Take the tour ×  Reading "Fundamentals of Nuclear Physics" by
Atam P. Arya, I understand that in a nuclear reaction, let say
$x+X \to y+Y$ meaning that "when a particle $x$ strikes a target
nucleus $X$, the outcome of the nuclear reaction is a recoil
nucleus $Y$ and a particle $y$. In many cases more than one type
of particle may be given out." Now, Arya applies the energy
conservation to the nuclear reaction, writing $$E_i=E_f$$ where
$$E_i=K_x+m_xc^2+K_X+M_Xc^2$$ and $$E_f=K_Y+M_Yc^2+K_y+m_yc^2$$
being $K_x, K_X, K_y, K_y$ the kinetic energies of the particle
$x$, the target nucleus (parent), the recoil nucleus (daughter)
and the particle $y$, respectively. And $M$ & $m$ its respective
masses.  Rewriting energy conservation, he defines a quantity
$Q$ (the disintegration energy):
$$Q:=(K_Y+K_y)-(K_X+K_x)=(M_X+m_x)c^2-(M_Y+m_y)c^2 \qquad (1)$$
Now, my question is whether or not the equation (1) (and its
interpretation) can be applied to alpha and beta decay (where
there are no particle colliding with the nucl