There is a translation. If you look at reference #172 in this article then that's given as
G. M. Zhislin, A.G. Sigalov. The spectrum of the energy operator
for atoms with ﬁxed nuclei on subspaces corresponding to irreducible
representations of the group of permutations. (Russian) Izv. Akad. Nauk
SSSR Ser. Mat. 29 (1965), p. 835–860. Transl. A.M.S. Ser. 2 91,
p. 263–296 (English translation).
So as you can see, an English translation has been published by the AMS. This is the book you're looking for:
Eighteen Papers on Analysis and Quantum Mechanics
L. I. Barklon, B. G. Gabdulhaev, V. P. Gačok, K. K. Kolovkin,
A. A. Gončar, R. G. Mamedov, V. A. Matveev, H. S. Muhtarov,
A. A. Privalov, A. G. Sigalov, Ju. L. Šmul'jan, M. S. Stavskiĭ,
B. M. Stepanov, S. A. Teljakovskiĭ, V. R. Vinokurov, and G. M. Žislin
The Russian article is available free of charge in PDF form btw. This PDF contains copy-and-paste'able text; in particular, you can feed it to google translate if you're very much in a hurry.