proposed for searching permanent electric dipole moments [7; 8]. In more recent times, much theoretical research as well as new experimental proposals have been devoted to investigate new physics beyond the Standard Model (SM) exploiting atoms and molecules trapped through this technique [9; 10; 11; 12]. In particular, searches for time-reversal or CP symmetry violations, electric dipole moment of standard-model particles, or DM candidates have been carried out through MIS (for reviews on these subjects, see for example [13; 14; 15; 16]. Cosmological axions are supposed to be one of the possible constituents of the DM [17], whose composition is still unknown [18]. Axions were initially introduced by [PERSON] and [PERSON] in order to solve the strong CP problem in quantum chromodynamics [19; 20; 21; 22], and are assumed to interact very weakly with ordinary matter. Successively, [PERSON] proposed that they could induce magnetic-type transitions between atomic Zeeman sub-levels, yielding the possibility of their indirect detection in atomic structures [23]. It is thus of fundamental importance to envisage possible mechanisms and relative experiments to detect these particles. Several possibilities have been recently proposed; for a review, see for example [17; 24; 25; 26; 27; 28; 29; 30]. Recently, possible detection schemes for cosmological axions in the meV energy range, based on electron transitions between Zeeman-shifted levels of dilute alkali or oxygen atoms [12], or their ionization [11], embedded in a solid matrix of inert gases at cryogenic temperatures [31], have been proposed. The basic idea is illustrated in Figure 1: \(a\) and \(b\) denote two Zeeman sublevels of the guest atom, with energy \(E_{a}\) and \(E_{b}\), respectively; \(\Delta E=E_{b}-E_{a}\) is their energy separation, that can be varied through the external magnetic field \(B\). \(\Delta E\) is tuned to the axion mass \(m_{a}\), that is unknown, but supposed to be of the order of some meV. The absorption of the axion by the guest atom induces a transition from the Zeeman sublevel \(a\) to the sublevel \(b\). The two Zeeman sublevels involved have the same electronic structure, so this transition does not induce any change of the electronic configuration, and possible linewidths due to electronic rearrangement or interatomic interactions or vibrational effects are absent. Then, the atomic excitation can be detected, exploiting a laser field that brings the atomic electron from \(b\) to the conduction band of the solid matrix where the atom is embedded, or, with an alternative scheme, to an electronic excited state [12]. Detection of the atomic excitation is thus a signature of the absorption of the axion. In order that this detection mechanism works efficiently, it is necessary that the two sublevels \(a\) and \(b\) can be sharply resolved as much as possible: this requires that the linewidth of the atomic levels involved be smaller than their energy separation. In the case of excitation to a higher discrete state of the atom, the linewidth of the excited level \(c\) should be minimized too. It is therefore necessary to make as small as possible all possible effects and interactions leading to the broadening of the spectral lines; this is particularly important in our case, due to the very small energy separation of the two Zeeman sublevels, assumed of the order of the meV. Some specific properties of the guest atoms or molecules are required, such as enough sensitivity to the external magnetic field, spherical symmetry of the wavefunction in order to have a vanishing electric dipole moment, and easy accomodation in the solid matrix, in order to minimize its deformation. In [12], an oxygen molecule, \({}^{16}\)O\({}_{2}\), was used; in this paper we will consider alkali atoms, initially Rubidium, from both the experimental and theoretical point of view, and then Lithium (only a theoretical analysis). Alkali atoms are very sensitive to magnetic fields, have a spherically symmetric structure, and, for Lithium in particular, can have a small size.