Semiquantum versus quantum methods for grazing-incidence fast-atom diffraction: Influence of the wave-packet size

To take full advantage of the capabilities of grazing-incidence fast-atom diffraction (GIFAD) as an experimental technique for analyzing surfaces and phenomena that occur on them, versatile theoretical tools are needed that accurately describe the experiments while allowing a simple but meaningful interpretation at a reasonable computational cost. During the last years, the semiquantum method named surface initial value representation (SIVR) has been postulated to fill this room. However, to date, SIVR has not yet been validated using full quantum calculations as a reference. Here, we have contrasted GIFAD simulations performed with the SIVR approach with those obtained with the full quantum method known as multiconfiguration time-dependent Hartree (MCTDH), taking into account the influence of the size of the initial wave packet. Our comparative study, using GIFAD for the He-LiF(001) system as a benchmark, shows a very good agreement, both qualitative and quantitative, between SIVR and MCTDH simulated diffraction spectra, under different incidence conditions. These findings support the use of SIVR as a versatile theoretical tool to extract as much accurate information as possible from GIFAD experiments.

Figure 1

MCTDH spectra, as a function of the azimuthal angle ${\phi }_f$, for different initial wave functions: Black circles display MCTDH results for $N_{\mathrm{ch}}=+\infty$ [Eq. (6)], while solid lines show MCTDH results considering a finite transverse coherence length [Eq. (7)], with $N_{\mathrm{ch}}$ denoting the number of coherently illuminated channels, as given by Eq. (8). The dashed lines represent the spectra obtained from the Gaussianized-MCTDH method (see text for explanation). The vertical dashed lines indicate the positions ${\phi }_f^{\left(B\right)}$ of the Bragg peaks. The inset depicts intrachannel and interchannel interference.

Figure 2

Intrachannel spectra, as a function of the azimuthal angle ${\phi }_f$, for ${}^4\mathrm{He}$ incidence with $E=1.25$ keV and $E_{\perp }=0.1$ eV. Solid lines, SIVR distributions derived from Eq. (19) for different $\gamma$ values; blue dashed line, projectile distribution obtained by using the SIVR coordinate form, as given by Eq. (9) of Ref. [33].

Figure 3

Analogous to Fig. 2 for $E_{\perp }=0.5$ eV.

Figure 4

Two-dimensional diffraction charts, in terms of the normal energy $E_{\perp }$ and the azimuthal angle ${\phi }_f$, for ${}^4\mathrm{He}$ impact along the $\langle 110\rangle$ channel with energy $E=1.25$ keV. (a) Gaussianized-MCTDH results, with ${\sigma }_G=0.{01}^{\circ }$. (b) SIVR simulations for $N_{\mathrm{ch}}=2$.

Figure 5

Azimuthal projectile distributions, as a function of the azimuthal angle ${\phi }_f$, for the case of Fig. 4 considering four different normal energies: (a) $E_{\perp }=0.1$ eV, (b) $E_{\perp }=0.3$ eV, (c) $E_{\perp }=0.5$ eV, and (d) $E_{\perp }=1$ eV. In all panels, the red solid line displays the SIVR distribution for $N_{\mathrm{ch}}=2$; black solid line, MCTDH distribution Gaussianized with ${\sigma }_G=0.{01}^{\circ }$, as explained in the text; green dashed line, MCTDH simulations with a finite transverse coherence length corresponding to $N_{\mathrm{ch}}=2$. The vertical dashed lines indicate the Bragg-peak positions.

Figure 6

Projectile distribution, as a function of the deflection angle $\mathrm{\Theta }$, for ${}^4\mathrm{He}$ impact along the $\langle 110\rangle$ channel with energy $E=5$ keV and $E_{\perp }=1.45$ eV. Experiments were extracted from Fig. 17 of Ref. [4]. Simulations: red solid line, SIVR approximation for $N_{\mathrm{ch}}=1$; black dashed and solid lines, Gaussianized-MCTDH results with different ${\sigma }_G$ values, as indicated. The vertical dashed lines indicate the Bragg-peak positions.

Figure 7

Analogous to Fig. 6 for ${}^3\mathrm{He}$ impact with energy $E=3$ keV and $E_{\perp }=0.99$ eV. Experiments were extracted from Fig. 3 of Ref. [25].

Figure 8

Projectile distribution, as a function of the azimuthal angle, for ${}^4\mathrm{He}$ impact along the $\langle 110\rangle$ channel with energy $E=5$ keV and $E_{\perp }=0.365$ eV. Experiments were extracted from Fig. 18 of Ref. [4]. Simulations: red solid line, SIVR approximation for $N_{\mathrm{ch}}=2$; black solid line, Gaussianized-MCTDH results with ${\sigma }_G=0.{01}^{\circ }$. The vertical dashed lines indicate the Bragg-peak positions.

Figure 9

Analogous to Fig. 6. Simulations: red solid line, SIVR approximation for $N_{\mathrm{ch}}=1$ with a constant background addition; solid black line, Gaussianized-MCTDH with ${\sigma }_G=2.0^{\circ }$.

Figure 10

Analogous to Fig. 7. Simulations: red solid line, SIVR approximation for $N_{\mathrm{ch}}=1$ with a constant background addition; solid black line, Gaussianized-MCTDH with ${\sigma }_G=2.2^{\circ }$.