Reference request for symmetry breaking Hartree-Fock Stationary mean-field solutions break symmetries of the many-body Hamiltonian in favour of lowering the energy, e.g. translational or rotational symmetry, despite $[H,P]=0$, or $[H,L_z]=0$, respectively. This is equally true for bosons - where the Hartree ansatz leads to the Gross-Pitaevskii equation - as it is for fermions.
I can trace back symmetry breaking Hartree ansatz solutions for bosons to 
Comparison between the exact and Hartree solutions of a one-dimensional many-body problem, F. Calogero and A. Degasperis, Phys. Rev. A 11, 265 (1975). I am also well aware that the symmetry breaking GP solutions in that work were known before. But I am sure that there must be references from  a lot earlier, say about 1930 for electrons in molecules, because Hartree-Fock was invented in 1927.
So, since when has it been known in atomic/molecular physics that Hartree-Fock breaks (continuous or discrete) symmetries? Anyone knows a reference?
 A: It appears that the first explicit statement about the symmetry-breaking of  Unrestricted Hartree-Fock (UHF) was by P. O. Löwdin in Discussion on The Hartree-Fock Approximation, P. Lykos and G. W. Pratt,
Rev. Mod. Phys. 35, 496 – Published 1 July 1963. 
Löwdin writes:
"I would like to comment on some peculiarities with respect to the symmetry properties. ... 
Confusion may arise from the fact that the exact eigenfunction $\Psi$ and the approximate eigenfunction in the form of a Slater determinant may have rather different properties. For instance,
if $\Lambda$ is a normal constant of motion satisying the relation $H\Lambda = \Lambda H$, 
then every eigenfunction
to $H$ is automatically an eigenfunction to $\Lambda$ or (in the case of a degenerate energy level) may be
chosen in that way, so that
$H\Psi = E\Psi$
$\Lambda\Psi = \lambda\Psi$
... On the other hand, if one drops the symmetry constraint and considers only the relation
$\delta \langle D\vert H\vert D\rangle=0$
one obtains a, nonrestricted Hartree Fock scheme, and the solution $D$ corresponding to the
absolute minimum has now usually lost its eigenvalue property with respect to $\Lambda$, i.e., the corresponding Hartree-Fock functions are no longer symmetry-adapted....
In my opinion, the Hartree-Fock scheme based on a single Slater determinant $D$ is in a dilemma
with respect to the symmetry properties and the normal constants of motion $\Lambda$. The assumption
that $D$ should be symmetry-adapted or an eigenfunction to $H$ leads to an energy $\langle H\rangle $ high above
the absolute minimum, and the energy difference amounts to at least 1eV per electron pair and
more. In the sense of Eckart's criterion [C. Eckart, Phys. Rev. 36, 877 (1930); B. A. Lengyel,
J. Math. Analysis Appl. 5, 451 (1962)], the absolute minimum of $\langle D\vert H\vert D\rangle$ leads certainly to a
better wave function $D$, but the symmetry properties are now lost and the determinant is a
"mixture" of components of various symmetry types."
