Electric ring currents $I_{nlm}$ and corresponding magnetic fields ${\mathbf{B}}_{nlm}$ exist in atomic orbitals ${\psi }_{nlm}$ $(m\ne 0)$. Simple expressions are derived for $I_{nlm}$ and for ${\mathbf{B}}_{nlm}(\mathbf{r}=\mathbf{0})$ at the nucleus. The magnitude of $I_{nlm}$ depends only on $n$ and decreases with increasing quantum number $n$. In contrast, ${\mathbf{B}}_{nlm}(\mathbf{r}=\mathbf{0})$ decreases with increasing quantum numbers $n$ and $l$ but increases with $m$. The largest magnitudes of the electric ring currents and induced magnetic fields are thus obtained for $2p_{\pm 1}$ orbitals. Moreover, $I_{nlm}$ and ${\mathbf{B}}_{nlm}(\mathbf{r}=\mathbf{0})$ increase with the nuclear charge $Z$ as $Z^2$ and $Z^3$, respectively. Simple circularly polarized $\pi$ laser pulses are designed for complete population transfers from $1s$ to target $2p_{\pm 1}$ orbitals. The corresponding solutions of the time-dependent Schrödinger equation for the hydrogen atom H $(Z=1)$ imply equivalent solutions for arbitrary $Z$, by means of simple scaling laws for the time $(1∕Z^2)$, frequency $\left(Z^2\right)$, and field strength $\left(Z^3\right)$ or intensity $\left(Z^6\right)$. For example, the parameters of the $\pi$ pulse for H (pulse duration $\tau =115\mathrm{fs}$, maximum intensity ${\mathcal{I}}_{\max }=1.47\times {10}^{10}\mathrm{W}{\mathrm{cm}}^{-2}$) are scaled to values $\tau =679$ as and ${\mathcal{I}}_{\max }=7.09\times {10}^{16}\mathrm{W}{\mathrm{cm}}^{-2}$ for ${\mathrm{Al}}^{12+}$, inducing the giant magnetic field $\mid {\mathbf{B}}_{21\pm 1}(\mathbf{r}=\mathbf{0})\mid =1146\mathrm{T}$. The results for hydrogenlike atoms allow corresponding estimates of electric ring currents and magnetic fields in molecules, where molecular orbitals are expressed as linear combinations of atomic orbitals.

• Received 19 October 2006

DOI:https://doi.org/10.1103/PhysRevA.75.012510