binary configuration for these particular companion masses. *By coincidence*, the $\gamma\approx 1.5$ solution crosses the final binary configuration at approximately the location mandated by energy consideration. However, we will show below that this is no longer the case for a giant of the same mass but with a different core mass. The self-consistent solutions in this example are those with $\gamma \approx 1.43-1.47$ (dotted black lines), where for some core masses values between 1.38 and 1.505 could also give physically valid solutions (thick solid black lines). Note that the change in $\gamma$ by $\pm0.05$ around $\gamma=1.45$, for the same core mass, results in final orbits being different by a factor of 10, while a bigger change in $\gamma$ leads to either merger, or to an unphysical energy generation. As such, it is not possible for one system to have a large range of $\gamma$ giving physically valid solutions, such as from 1.2 to 3, as in [@Nelemans05].

![ Orbital angular momentum and energy for a $2\,M_\odot + 0.5\,M_\odot$ binary ($r_\mathrm{d}=86\,R_\odot$ and $m_\mathrm{d,X}=0.38\,M_\odot$). Thick and thin solid red lines show the only possible final binary configurations for various adopted core masses, for the comparison we also show the the minimum energy 