Coulomb explosions and stopping of molecular ions channeled through carbon nanotubes

We study Coulomb explosions of fast $\mathrm{H}_2{}^{+}$ molecules under the channeling conditions through a single-wall carbon nanotube by solving the classical equations of motion for the fragment ions, involving both the repulsive continuum potential of the nanotube wall and the dynamically screened Coulomb repulsion between the two ions. Dynamic polarization of the nanotube electrons, described by a two-dimensional hydrodynamic model, gives rise to the correlated energy losses, a wakelike interaction between the fragment ions, as well as the dynamical image force on each ion. The explosion dynamics is dominated by the bare Coulomb repulsion and it mostly proceeds in the longitudinal direction, accompanied with the radially constrained oscillations of the fragment ions. Strong vicinage effects are found in both the molecule self-energy and its stopping power in the early stages of explosions, but they quickly diminish with the increasing dwell time in a manner which depends on the impact molecule speed and its axis orientation.

Figure 1

Internuclear distance $R$ (in a.u.) as a function of the penetration time $t$ during the Coulomb explosion of $\mathrm{H}_2{}^{+}$ ion channeled in a SWNT of radius $a=20\mathrm{a.u.}$ with the initial radial position of the center of mass ${\rho }_{m0}=10\mathrm{a.u.}$ Results are shown for the fixed incident alignment angle ${\alpha }_0=30°$, and for several incident speeds: (a) $v_0=2$, 3, 4, and (b) $v_0=5,6,7\mathrm{a.u.}$

Figure 2

The dependence of the radial position (in a.u.) of (a) the leading ion ${\rho }_1$, and (b) the trailing ion ${\rho }_2$ on the penetration time $t$ during the Coulomb explosion of $\mathrm{H}_2{}^{+}$ ion channeled in a SWNT of radius $a=20\mathrm{a.u.}$ with the initial radial position of the center of mass ${\rho }_{m0}=10\mathrm{a.u.}$ Results are shown for the fixed incident alignment angle ${\alpha }_0=30°$, and for several incident speeds: $v_0=2,5,7\mathrm{a.u.}$

Figure 3

(a) Radial component, $\Delta \rho ={\rho }_1-{\rho }_2$, and the longitudinal component, $\Delta z=z_1-z_2$, of the internuclear separation (in a.u.) as functions of the penetration time $t$ during the Coulomb explosion of $\mathrm{H}_2{}^{+}$ ion channeled in a SWNT of radius $a=20\mathrm{a.u.}$ with the initial radial position of the center of mass ${\rho }_{m0}=10\mathrm{a.u.}$ Results are shown for the fixed incident speed $v_0=5\mathrm{a.u.}$, and for several incident alignment angles: ${\alpha }_0=0°,30°,45°$.

Figure 4

The dependence of the radial position (in a.u.) of (a) the leading ion ${\rho }_1$ and (b) the trailing ion ${\rho }_2$ on the penetration time $t$ during the Coulomb explosion of $\mathrm{H}_2{}^{+}$ ion channeled in a SWNT of radius $a=20\mathrm{a.u.}$ with the initial radial position of the center of mass ${\rho }_{m0}=10\mathrm{a.u.}$ Results are shown for the same parameters as those in Fig. 3 [fixed incident speed $v_0=5\mathrm{a.u.}$ and several incident alignment angles: ${\alpha }_0=0°$ (solid line), 30° (dashed line), and 45° (dotted line)].

Figure 5

The dependences of (a) the total self-energy $E_T$ (in a.u.) and (b) the sum $E_1+E_2$ (in a.u.) of the self-energies of two uncorrelated protons on the penetration time $t$ during the Coulomb explosion of $\mathrm{H}_2{}^{+}$ ion channeled in a SWNT of radius $a=20\mathrm{a.u.}$ with the initial radial position of the center of mass ${\rho }_{m0}=10\mathrm{a.u.}$ Results are shown for the same parameters as those in Fig. 1a (fixed incident alignment angle ${\alpha }_0=30°$ and several incident speeds: $v_0=2,3,4\mathrm{a.u.}$).

Figure 6

The dependences of (a) the total self-energy $E_T$ (in a.u.) and (b) the sum $E_1+E_2$ (in a.u.) of the self-energies of two uncorrelated protons on the penetration time $t$ during the Coulomb explosion of $\mathrm{H}_2{}^{+}$ ion channeled in a SWNT of radius $a=20\mathrm{a.u.}$ with the initial radial position of the center of mass ${\rho }_{m0}=10\mathrm{a.u.}$ Results are shown for the same parameters as those in Fig. 1b (fixed incident alignment angle ${\alpha }_0=30°$ and several incident speeds: $v_0=5,6,7\mathrm{a.u.}$).

Figure 7

The dependences of (a) the total stopping power $S_T$ (in a.u.) and (b) the sum $S_1+S_2$ (in a.u.) of the stopping powers of two uncorrelated protons on the penetration time $t$ during the Coulomb explosion of $\mathrm{H}_2{}^{+}$ ion channeled in a SWNT of radius $a=20\mathrm{a.u.}$ with the initial radial position of the center of mass ${\rho }_{m0}=10\mathrm{a.u.}$ Results are shown for the same parameters as those in Fig. 1a (fixed incident alignment angle ${\alpha }_0=30°$ and several incident speeds: $v_0=2,3,4\mathrm{a.u.}$).

Figure 8

The dependences of (a) the total stopping power $S_T$ (in a.u.) and (b) the sum $S_1+S_2$ (in a.u.) of the stopping powers of two uncorrelated protons on the penetration time $t$ during the Coulomb explosion of $\mathrm{H}_2{}^{+}$ ion channeled in a SWNT of radius $a=20\mathrm{a.u.}$ with the initial radial position of the center of mass ${\rho }_{m0}=10\mathrm{a.u.}$ Results are shown for the same parameters as those in Fig. 1b (fixed incident alignment angle ${\alpha }_0=30°$ and several incident speeds: $v_0=5,6,7\mathrm{a.u.}$).

Figure 9

The dependences of (a) the total self-energy $E_T$ (in a.u.) and (b) the sum $E_1+E_2$ (in a.u.) of the self-energies of two uncorrelated protons on the penetration time $t$ during the Coulomb explosion of $\mathrm{H}_2{}^{+}$ ion channeled in a SWNT of radius $a=20\mathrm{a.u.}$ with the initial radial position of the center of mass ${\rho }_{m0}=10\mathrm{a.u.}$ Results are shown for the same parameters as those in Fig. 3 (fixed incident speed $v_0=5\mathrm{a.u.}$ and several incident alignment angles: ${\alpha }_0=0°,30°,45°$).

Figure 10

The dependences of (a) the total stopping power $S_T$ (in a.u.) and (b) the sum $S_1+S_2$ (in a.u.) of the stopping powers of two uncorrelated protons on the penetration time $t$ during the Coulomb explosion of $\mathrm{H}_2{}^{+}$ ion channeled in a SWNT of radius $a=20\mathrm{a.u.}$ with the initial radial position of the center of mass ${\rho }_{m0}=10\mathrm{a.u.}$ Results are shown for the same parameters as those in Fig. 3 (fixed incident speed $v_0=5\mathrm{a.u.}$ and several incident alignment angles: ${\alpha }_0=0°,30°,45°$).

Figure 11

(a) The self-energy ratio $R_E$ and (b) the stopping-power ratio $R_S$ as composite functions of the penetration time $t$ during the Coulomb explosion of $\mathrm{H}_2{}^{+}$ ion channeled in a SWNT of radius $a=20\mathrm{a.u.}$ with the initial radial position of the center of mass ${\rho }_{m0}=10\mathrm{a.u.}$ Results are shown for the same parameters as those in Fig. 2 (fixed incident alignment angle ${\alpha }_0=30°$ and several incident speeds: $v_0=2,5,7\mathrm{a.u.}$).

Figure 12

(a) The self-energy ratio $R_E$ and (b) the stopping-power ratio $R_S$ as composite functions of the penetration time $t$ during the Coulomb explosion of $\mathrm{H}_2{}^{+}$ ion channeled in a SWNT of radius $a=20\mathrm{a.u.}$ with the initial radial position of the center of mass ${\rho }_{m0}=10\mathrm{a.u.}$ Results are shown for the same parameters as those in Fig. 3 (fixed incident speed $v_0=5\mathrm{a.u.}$ and several incident alignment angles: ${\alpha }_0=0°,30°,45°$).