Three-Dimensional Resonant Coherent Excitation of Nonchanneling Ions in a Crystal

We have observed resonant coherent excitation (RCE) of H-like ${\mathrm{Ar}}^{17+}$ ions traveling through a $1\mu \mathrm{m}$-thick Si crystal at an energy of $391\mathrm{MeV}/\mathrm{u}$ in the nonchanneling condition. A three-dimensional periodic array of atomic planes induces RCE of the nonchanneling ions. The high energy heavy ions together with the thin crystal allow us to observe this new RCE through the measurements of the charge-state distribution of the emerging ions. The observed resonances are much narrower than those of planar-channeling ions due to the absence of the large Stark shift caused by the planar potential.

Figure 1

Configurations of the ion velocity $\mathbf{v}$ in a Si crystal. Three kinds of periodic arrays are shown: (a) atoms in an atomic string (1D) in the [$\overline{1}10$] axial-channeling condition; (b) atomic strings on an atomic plane (2D) in the (220) planar-channeling condition; (c) atomic planes in the crystal (3D) in the nonchanneling condition. $\mathbf{A}$, $\mathbf{B}$, and $\mathbf{C}$ represent the base lattice vectors. The (220) atomic plane is spanned by $\mathbf{A}$ and $\mathbf{B}$, and the (004) atomic plane by $\mathbf{A}$ and $\mathbf{C}$. $\overrightarrow{\mathrm{SP}}$ and $\overrightarrow{\mathrm{SR}}$ are the projections of $\mathbf{v}(\overrightarrow{\mathrm{SV}})$ on the (004) and (220) atomic planes. $\overrightarrow{\mathrm{SQ}}$ is the projection of $\overrightarrow{\mathrm{SP}}$ on the [$\overline{1}10$] axis. $\theta$ is the angle between $\overrightarrow{\mathrm{SV}}$ and $\overrightarrow{\mathrm{SP}}$, $\varphi$ between $\overrightarrow{\mathrm{SP}}$ and $\overrightarrow{\mathrm{SQ}}$.

Figure 2

Bottom—the resonance conditions of $1s\mathrm{\text{−}}2p_{1/2}$ (dashed line) and $1s\mathrm{\text{−}}2p_{3/2}$ (solid line) transitions of the $391.07\mathrm{MeV}/\mathrm{u}$ H-like ${\mathrm{Ar}}^{17+}$ ion for $(k,l,m)=(1,1,m)$ ($m=-4,-2,0,2,4$). The horizontal arrows indicate the scanned regions in the present experiment. The survived fraction of H-like ${\mathrm{Ar}}^{17+}$ ions measured as a function of $\theta$ keeping (a) $\varphi =0.000°$, the (220) planar-channeling condition, and (b) $\varphi =0.080°$, (c) $\varphi =0.100°$, the nonchanneling conditions. The survived fraction is normalized to the value in the non-RCE condition. The vertical arrows on the lower axes indicate the resonance conditions for $1s\mathrm{\text{−}}2p_{1/2}$ and $1s\mathrm{\text{−}}2p_{3/2}$. The additional scale in (c) is the transition energy calculated with Eq. (1) for $(k,l,m)=(1,1,0)$.

Figure 3

Schematic cross section of the crystal at the plane SVR defined in Fig. 1. The trajectories of the nonchanneling ion at $\varphi =0.100°$ and the (220) planar-channeling ion are shown. The enlarged sketch shows the atomic strings of $(k,l)=(1,1)$ and the atomic planes of $(k,l,m)=(1,1,0)$ and (1,1,2). When $\theta$ is small, $\varphi$ is nearly equal to the incident angle of the ions with respect to the (220) atomic plane.