Isotope effects in the harmonic response from hydrogenlike muonic atoms in strong laser fields

High-order harmonic generation from hydrogenlike muonic atoms exposed to ultraintense high-frequency laser fields is studied. Systems of low nuclear-charge number $Z$ are considered where a nonrelativistic description applies. By comparing the radiative response for different isotopes, we demonstrate characteristic signatures of the finite nuclear mass and size in the harmonic spectra. In particular, for $Z>1$, an effective muon charge appears in the Schrödinger equation for the relative particle motion, which influences the position of the harmonic cutoff. Cutoff energies in the million-electron-volt domain can be achieved, offering prospects for the generation of ultrashort coherent $\gamma$-ray pulses.

Figure 1

HHG spectra for muonic hydrogen (dashed black line) and deuterium [solid grey (red) line], respectively. The laser parameters are $I=1.05\times {10}^{23}$ W/cm${}^2$ and $\hslash \omega =118$ eV, corresponding to $\xi \approx 0.02$. The calculation was performed in one spatial dimension using the soft-core potential (14).

Figure 2

HHG spectra for muonic ${}^3\mathrm{He}$ (dashed black line) and ${}^4\mathrm{He}$ [solid grey (red) line], respectively, at the laser parameters $I=8\times {10}^{24}$ W/cm${}^2$ and $\hslash \omega =347$ eV. The inset shows an enlargement of the cutoff region.

Figure 3

HHG spectra calculated with the hard-core potential (15). The dashed black line represents the spectrum for muonic hydrogen at the laser parameters $I^{(\mathrm{H})}=1.05\times {10}^{23}$ W/cm${}^2$ and $\hslash {\omega }^{(\mathrm{H})}=177$ eV. The solid grey (red) line represents the spectrum for muonic deuterium at the appropriatly scaled laser parameters $I^{(\mathrm{D})}=1.30\times {10}^{23}$ W/cm${}^2$ and $\hslash {\omega }^{(\mathrm{D})}=186$ eV in order to compensate for the nuclear-mass effect. The inset shows an enlargement of the cutoff region on a linear scale.

Figure 4

Inner region of the hardcore potentials generated by a proton in muonic H (dashed black line) and by a deuteron in muonic D [solid grey (red) line], according to Eq. (15).

Figure 5

HHG spectra calculated with the hard-core potential (15). (a) The dashed black line shows the spectrum for muonic ${}^4\mathrm{He}$ at the laser parameters $I^{({}^4\mathrm{He})}=8.7\times {10}^{24}$ W/cm${}^2$ and $\hslash {\omega }^{({}^4\mathrm{He})}=255$ eV. The solid grey (red) line represents the spectrum for muonic ${}^3\mathrm{He}$ at the accordingly scaled values $I^{({}^3\mathrm{He})}=8.3\times {10}^{24}$ W/cm${}^2$ and $\hslash {\omega }^{({}^3\mathrm{He})}=253$ eV. (b) Same as (a) but for muonic ${}^9\mathrm{Li}$ at $I^{({}^9\mathrm{Li})}=1.06\times {10}^{26}$ W/cm${}^2$, $\hslash {\omega }^{({}^9\mathrm{Li})}=583$ eV (dashed black line) and muonic ${}^6\mathrm{Li}$ at $I^{({}^6\mathrm{Li})}=1.01\times {10}^{26}$ W/cm${}^2$, $\hslash {\omega }^{({}^6\mathrm{Li})}=580$ eV [solid grey (red) line].