Quadrupole Shielding and Antishielding Factors for Atomic States

The atomic shielding (or antishielding) factor

R

for the quadrupole hyperfine structure has been evaluated for several excited atomic states. The values of

R

were determined by means of the perturbed wave functions

v_{1}^{'} (n l \to l^{'})

as obtained by solving the inhomogeneous Schrödinger equation for each type of excitation of the core electrons by the nuclear quadrupole moment

Q

. For the case of copper, the calculations provide a quantitative explanation of the fact that the values of

Q ({Cu}^{65})

obtained from two different excited configurations (

3 d^{9} 4 s^{2}

and

3 d^{10} 4 p

) differ considerably from each other (by ≳40%), when the correction factor

\frac{1}{(1 - R)}

is not applied. The calculated values of

R

, namely

R_{3 d} = + 0.178

(shielding) and

R_{4 p} = - 0.175

(antishielding), bring the two corrected values of

Q

into very good agreement. We thus obtain

Q ({Cu}^{65}) = (- 0.195 \pm 0.004) \times 10^{- 24}

{cm}^{2}

. Besides the work on Cu

3 d

and

4 p

, the following calculations have also been carried out: (1)

R_{5 d}

for the

5 d

states of Pr and Tm; (2)

R_{2 p}

and

R_{3 p}

for the

2 p

and

3 p

states of Li; (3)

R_{2 p}

for the

2 s 2 p {}^{3}P

excited state of beryllium.

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