deletions | additions       diff --git a/Photoemission.tex b/Photoemission.tex  index 93ddeb4..dc2c22b 100644  --- a/Photoemission.tex  +++ b/Photoemission.tex 
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Electron photoemission or simply photoemission embraces all the processes where an   atom, a molecule or a bulks surface is ionized under the effect of an external electromagnetic field.  In experiments, the ejected electrons are measured with detectors that are capable   to characterize of characterizing  their kinetic properties. Energy-resolved $P(E)$ and momentum-resolved $P(\vec{k})$ photoemission probabilities are quite   interesting observables since they carry important informations, for instance, on the parent   ion~\cite{Puschnig:2009ho,Wiessner:2014kq} or on the ionization process itself~\cite{Huismans:2011kh}.  
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evaluation of the total wavefunction in an extremely large portion of space (in principle a macroscopic one)   that would be impractical to represent in real space.   We have developed a scheme to calculate photoemission based on real-time TDDFT that is currently implemented in Octopus. We use a mixed real real-  and momentum space momentum-space  approach to solve the problem. Each Kohn-Sham orbital is propagated in real space on a restricted simulation box and then matched at the boundary with a momentum space representation on infinitely extended plane waves.   The matching is made with the help of a mask function $M(\vec{r})$, like the one shown   in Fig.~\ref{fig:pes_sheme}, that separates each orbital into a bounded $\phi_i^A(\vec{r})$   and an unbounded component $\phi_i^B(\vec{r})$ as follows  \begin{equation}\label{eq:mask_split}  \phi_i(\vec{r},t) = M(\vec{r})\,\phi_i(\vec{r},t)+\left[1-M(\vec{r})\right]\phi_i(\vec{r},t) \\ \nonumber  =\phi_i^A(\vec{r},t)+\phi_i^B(\vec{r},t)\, .  \end{equation}