  We calculate the nuclear structure orbital entanglement entropy of short
range correlations (SRC) based on the nuclear scale separation. Specifically,
the entanglement between the SRC orbitals and the rest of the system. It should
be stressed that this is a single nucleon not a pair entanglement entropy
between the proton and neutron. The entanglement arises from the probability
for a nucleon to occupy a momentum state above the Fermi momentum. We separate
the momentum space of the nucleus into two parts such that nucleons can occupy
the meanfield part of the wave function, i.e. Fermi sea (FS) and separately the
high-momentum SRC part. The orbital entropy we obtain is between these two
parts where we essentially define two momentum subspaces, one containing all
the low momentum FS states and the other the high-momentum part as a SRC
"orbital" state. For the calculation we employ the decoupling of low and
high-momenta which was established by the similarity normalization group the
SRC is viewed as a further "orbital" which can be multiply occupied. Since the
probability of the occupation of a single SRC is given by the nuclear contact
we are able to obtain a simple general expression of the orbital entanglement
entropy for SRC by employing the generalized contact formalism. This general
formula for the SRC orbital entanglement entropy of a nuclear structure in
terms of the nuclear contact, allows us to obtain the scaling of the entropy in
terms the mass number, $A$. We find that, unlike the entanglement entropy of
many quantum systems which scales with the surface area, the orbital
entanglement entropy associated with the SRC in large nuclei is linearly
dependent on $A$, i.e., it is shown to be extensive.
