... universal¹

The adjective 'universal' refers to the fact that the three parameters of the central potential, viz. depth $\bar{V}$, radius $r_0$, and diffusivity $a$, and the corresponding parameters of the spin-orbit potential can be chosen once for all nuclei of the Periodic Table providing a very good description, on average, of the single-particle spectra from light to heaviest nuclei. For more details see below.

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... improper²

Let us remind the reader that the operations called improper rotations about a certain axis $\hat{\mathcal{O}}$ through an angle are composed of the usual, i.e., proper rotations followed by a reflection in a plane perpendicular with respect to $\hat{\mathcal{O}}$. According to the terminology used in nuclear physics literature, those improper rotations are sometimes called simplex operations.

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... ourselves³

In principle one may expect that under some circumstances (specific choice of the symmetry group $\mathbf{G}$ and of the multipolarity of the class of shapes) there exist degenerate solutions to our problem in (10). In such a case we should be able to construct the same symmetry surfaces by taking arbitrary linear combinations of the degenerate eigen-vectors. This type of situation, however, was not encountered so far in the applications of interest in this article and will not be treated further here.

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... found⁴

The final evidence is expected from comparison of the unique features of the branching ratios of the corresponding electromagnetic transitions. A dedicated study is in progress.

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