with a median of $\lambda = 0.86$ for the donors (with masses up to $20\,M_\odot$) of a population of 165,000 binaries at the onset of a CE. Note that this does not hold for massive giants, where $0.004 \lesssim \lambda \lesssim 10$ [@Dewi01; @podsi03].

An alternative approach to determine the orbital period after the ejection of the envelope is by considering the other available integral of motion, the angular momentum [@Nelemans00; @Nelemans05]. This is known as the $\gamma$-formalism and can be expressed as:

$$\frac{\Delta J_\mathrm{lost}}{J_\mathrm{i}} 
    = \frac{J_\mathrm{i} - J_\mathrm{f}}{J_\mathrm{i}} 
    = \gamma \frac{m_\mathrm{d, e}} {m_\mathrm{d}+m_\mathrm{a}},
\label{gammaform}$$

where $J_\mathrm{i}$ and $J_\mathrm{f}$ are the angular momenta of the initial and the final binaries. Hence, the $\gamma$-parametrization describes the specific fraction of the initial angular momentum that is carried away by the envelope as it is lost from the system, in terms of a multiplicative factor ($\gamma$) times the fraction of the total mass lost from the system.

It was shown that the $\gamma$-formalism can reproduce the distributions of the orbital periods and mass ratios in the observed DWD systems with a single value of $\gamma=1.5$ for the first mass-transfer event, where the range for possible reconstructed values was found to be between $\sim1.2$ 