A relativistic description of the structure of heavy alkali-metal atoms and alkali-like ions using S-spinors and L-spinors is developed. The core wave function is defined by a Dirac-Fock calculation using an S-spinor basis. The S-spinor basis is then supplemented with a large set of L-spinors for calculation of the valence wave function in a frozen-core model. The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a

Z = 60

hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the

5 s, 4 d

, and

5 p

states of

{Sr}^{+}

. The magic wavelengths at which the Stark shifts between different pairs of transitions are 0 are computed. Determination of the magic wavelengths for the

5 s \to 4 d_{\frac{3}{2}}

and

5 s \to 4 d_{\frac{5}{2}}

transitions near 417 nm (near the wavelength for the

5 s \to 5 p_{j}

transitions) would allow determination of the oscillator strength ratio for the

5 s \to 5 p_{\frac{1}{2}}

and

5 s \to 5 p_{\frac{3}{2}}

transitions.

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