Flavor Symmetry and Scale Invariance Properties of Singly Ionized Helium Ions

Hydrogen atoms possess flavor symmetry (as shown in our previous paper) and scale invariance symmetry (as shown in our other previous paper). The existence of the second flavor of hydrogen atoms (SFHA) is evidenced by three different types of atomic experiments: the SFHA-based explanations eliminated huge discrepancies—up to several orders of magnitude—between the experiments and the corresponding previous theories, while alternative explanations were never provided. The existence of the SFHA is also evidenced by the SFHA-based explanation of the long-standing neutron lifetime puzzle, while alternative explanations were off by several orders of magnitude. The SFHA has only the S-states, so that due to the selection rules of quantum mechanics, the SFHA does not interact with electromagnetic radiation: it remains dark. Theoretically, the SFHA is based on the second solution of the Dirac equation for hydrogen atoms, which becomes legitimate after allowing for experimental charge density distribution inside protons. In the present paper, we bring to the attention of the research community that the experimental charge density distribution in alpha-particles satisfies the conditions under which the second solution of the Dirac equation for He+ ions becomes legitimate for the S-states. This constitutes the theoretical basis of the proposed existence of the second flavor of He+ ions (SFHeI), analogous to the existence of the SFHA; therefore, He+ ions have flavor symmetry. We also show that the second exterior solution (i.e., outside the He nucleus) and the matching interior solution are scale-invariant with respect to the change in the boundary R between them. In addition, we demonstrate that there is experimental evidence for the existence of the SFHeI from the experiments on the excitation of the 2S state of He+ ions by electron impact. It is the existence of the SFHeI that removes the 2.4-times discrepancy between the experimental and theoretical cross-sections for this process, while alternative explanations were never provided. The primary feature of the SFHeI is the same as for the SFHA: due to the quantum selection rules for atoms/ions having only the S-states, both the SFHeI and SFHA do not interact with the electromagnetic radiation as they remain dark. The engagement of the SFHA previously explained the observed anomalous absorption (both qualitatively and quantitatively) in the 21 cm line from the early Universe and made the SFHA a candidate for baryonic dark matter. It was previously shown that the SFHA constitutes most of baryonic dark matter. Now, since the experimental ratio of the SFHeI to the usual He+ ions turned out to be of the same order as the experimental ratio of the SFHA to the usual hydrogen atoms, and given that the combined abundance of hydrogen and helium is about 98%, the combination of the SFHA with the SFHeI could possibly constitute an even larger share of baryonic dark matter than just the SFHA.