Active Ions

Before proceeding to a discussion of the active laser ions, we will review briefly the nomenclature of atomic energy levels.
Different energy states of electrons are expressed by different quantum numbers. The electrons in an atom are characterized by a principal quantum number n, an orbital angular momentum l, the orientation of the angular momentum vector m, and a spin quantum number s. A tradition from the early days of line-series allocation has established the following method of designating individual electronic orbits: a number followed by a letter symbolizes the principal quantum number n and the angular momentum number l, respectively. The letters s, p, d, f stand for l = 0, 1, 2, 3, respectively. For example, a 3d electron is in an orbit with n = 3 and l = 2.
To designate an atomic energy term one uses by convention capital letters with a system of subscripts and superscripts. The symbol characterizing the term is of the form ^2S+1L J , where the orbital quantum numbers L = 0, 1, 2, 3, 4, 5, are expressed by the capital letters S, P, D, F, G, H, I . A superscript to the left of the letter indicates the value (2S + 1), that is, the multiplicity of the term due to possible orientation of the resultant spin S. Thus a one-electron system (S = 1/2) has a multiplicity 2. L and S can combine to a total angular momentum J , indicated by a subscript to the right of the letter. Thus the symbol ²P_3/2 shows an energy level with an orbital quantum number L = 1, a spin of S = 1/2, and a total angular momentum of J = 3/2. The complete term description must include the configuration of the excited electron, which precedes the letter symbol. Thus the ground state of lithium has the symbol 2s ²S_1/2.
When an atom contains many electrons, the electrons that form a closed shell may be disregarded and the energy differences associated with transitions in the atom may be calculated by considering only the electrons outside the closed shell. In describing the state of a multielectron atom, the orbital angular momenta and the spin angular momenta are added separately. The sum of the orbital angular momenta are designated by the letter L, and the total spin is characterized by S. The total angular momentum J of the atom may then be obtained by vector addition of L and S. The collection of energy states with common values of J , L, and S is called a term.
In the following section, a qualitative description is given of some of the prominent features of the most important rare earth, actinide, and transition metal ions.