Because of weak (neutral-current) interactions there is a parity-violating potential between the atomic electron and the nucleus as follows: v = ? [?⁽³⁾(x) S ? p + S ? p ?⁽³⁾(x)], where S and p are the spin and momentum operators of the electron, and the nucleus is assumed to be situated at the origin. As a result, the ground state of an alkali atom, usually characterized by | n, l, j, rn) actually contains very tiny contributions from other eigenstates as follows:

On the basis of symmetry considerations alone, what can you say about (n?, l?, j? m?), which give rise to non-vanishing contributions? Suppose the radial wave function s and the energy levels are all known. Indicate hot you may calculate C_n?l;j;m?. Do we get further restrictions on (n?, l?, j? m?),

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|n, 1, j, m) In, I, j, m) + Cwrim|n', l', j', m'). n'tj'm' 2