Character absolute squares

The absolute squares of the characters in a given row (times the weighting factor for each class if the abbreviated form is used) equals the order of the group. (Character vectors are normalized) This results directly from Eq. (13-2). 

Table I also contains an analysis of the orbital character of these five energy levels. These were determined from the four-component spinors by neglecting the two lower, "small," components, and by assuming that the radial functions depend only upon , i.e. that the radial functions for pi/2 and p3/2> or for da/2 and ds/2> are the same. The orbitals may then be written in "Pauli" form as products of (complex) spherical harmonics and spin functions. Populations are equal to the squares of the absolute magnitudes of the coefficients listed in Table I. [For all but 17e3g, an additional orbital (not shown) is occupied which has the same energy but the opposite spin pattern (i.e. a and 3 are interchanged).]...

The sum of the squares of the absolute values of the characters in any irreducible representation is equal to the order of the group. 

Characters and Tests.—Bight square octohedrons or prisms, colourless and inodorous sparingly soluble in water, but communicating to it an intensely bitter taste soluble in boiling rectified spirit and in chloroform, but not in absolute alcohol or ether. Pure sulphuric acid forms vnth it a colourless solution, which on the addition of solid potassium bichromate acquires a purple hue, changes to yellowish-red, and ultimately leaves a green residue. Should not be coloured by nitric acid if it turns yellow, it shows that brucia is present. Should leave no ash when burned with free excess of air. 

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