1. Introduction
2. Theoretical method
2.1. Method of solving the three-dimensional time-dependent Schrödinger equation
2.2. The DFT method
2.2.1. Construction of one-electron potentials for atoms and ions
2.2.2. Creation of wave functions with correct asymptotic tail for atoms or ions
2.3. The PPT and ADK models
3. Results and discussion
Figure 1. (a) The effective charge of He, Ne+, H−, and F−, where potentials are calculated by using the density-functional theory; (b) the structure parameter Cl of He is extracted from the electronic wave function in the asymptotic region by the fitting method. |
Figure 2. Radial functions of Xe in the (a) small-r region; (b) large-r region. |
Table 1. Direct comparison of the calculated IPs using the LBα model and the experimental values from the NIST database [43]. The optimized α parameters used in LBα model are also listed. |
Atom/ion | LBα (eV) | Ip (eV) | α | Atom/ion | LBα (eV) | Ip (eV) | α |
---|---|---|---|---|---|---|---|
H(1s) | 13.60 | 13.60 | — | He(1s) | 24.59 | 24.59 | 1.34 |
Li(2s) | 5.41 | 5.39 | 1.24 | Be(2s) | 9.33 | 9.32 | 1.26 |
B(2p) | 8.27 | 8.30 | 1.20 | C(2p) | 11.23 | 11.26 | 1.21 |
N(2p) | 14.47 | 14.53 | 1.22 | O(2p) | 13.58 | 13.62 | 1.03 |
F(2p) | 17.38 | 17.42 | 1.11 | Ne(2p) | 21.65 | 21.56 | 1.20 |
Na(3s) | 5.12 | 5.14 | 0.87 | Mg(3s) | 7.78 | 7.65 | 0.75 |
Al(3p) | 5.96 | 5.99 | 1.19 | Si(3p) | 8.16 | 8.15 | 1.20 |
P(3p) | 10.44 | 10.49 | 1.22 | S(3p) | 10.36 | 10.36 | 1.07 |
Cl(3p) | 12.84 | 12.97 | 1.13 | Ar(3p) | 15.75 | 15.76 | 1.22 |
K(4s) | 4.35 | 4.34 | 0.54 | Ca(4s) | 6.12 | 6.11 | 0.41 |
Br(4p) | 11.83 | 11.81 | 0.98 | Kr(4p) | 13.98 | 14.00 | 0.99 |
Rb(5s) | 4.13 | 4.18 | 0.50 | I(5p) | 10.55 | 10.45 | 0.85 |
Xe(5p) | 12.16 | 12.13 | 0.95 | He+(1s) | 54.48 | 54.42 | — |
Li+(1s) | 75.67 | 75.64 | 1.31 | Be+(2s) | 18.24 | 18.21 | 1.22 |
B+(2s) | 25.18 | 25.16 | 1.21 | C+(2p) | 24.37 | 24.38 | 1.25 |
N+(2p) | 29.44 | 29.60 | 1.24 | O+(2p) | 35.23 | 35.12 | 1.26 |
F+(2p) | 35.03 | 34.97 | 1.21 | Ne+(2p) | 40.95 | 40.96 | 1.14 |
Na+(2p) | 47.17 | 47.29 | 1.23 | Mg+(3s) | 15.06 | 15.04 | 0.72 |
Al+(3s) | 18.82 | 18.83 | 0.56 | Si+(3p) | 16.36 | 16.35 | 1.23 |
P+(3p) | 19.74 | 19.77 | 1.22 | S+(3p) | 23.35 | 23.34 | 1.25 |
Cl+(3p) | 23.75 | 23.81 | 1.09 | Ar+(3p) | 27.94 | 27.63 | 1.19 |
K+(3p) | 31.63 | 31.63 | 1.20 | Ca+(4s) | 11.86 | 11.87 | 0.39 |
Br+(4p) | 21.60 | 21.59 | 1.08 | Kr+(4p) | 24.30 | 24.36 | 0.95 |
Rb+(4p) | 27.35 | 27.29 | 1.15 | I+(5p) | 19.10 | 19.13 | 1.04 |
Xe+(5p) | 21.15 | 20.98 | 0.92 | H−(1s) | 0.76 | 0.75 | 1.17 |
Li−(2s) | 0.62 | 0.62 | 1.13 | C−(2p) | 1.26 | 1.26 | 1.15 |
O−(2p) | 1.46 | 1.46 | 1.05 | F−(2p) | 3.40 | 3.40 | 1.14 |
Na−(3s) | 0.54 | 0.55 | 0.72 | Al−(3p) | 0.44 | 0.44 | 1.11 |
Si−(3p) | 1.39 | 1.39 | 1.17 | P−(3p) | 0.75 | 0.75 | 1.01 |
Cl−(3p) | 3.61 | 3.62 | 1.17 | K−(4s) | 0.50 | 0.50 | 0.48 |
Br−(4p) | 3.38 | 3.37 | 1.00 | Rb−(5s) | 0.49 | 0.49 | 0.43 |
Atom/ion | Cl | Atom/ion | Cl | Atom/ion | Cl | |||
---|---|---|---|---|---|---|---|---|
H(1s) | 2.00 | He(1s) | 2.42 | Ne(2p) | 1.47 | |||
2.00 | [7] | 2.98 | [7] | 2.77 | [7] | |||
3.13 | [8] | 2.10 | [8] | |||||
2.87 | [24] | 1.75 | [24] | |||||
2.96a | 1.95a | |||||||
Ar(3p) | 1.85 | Kr(4p) | 2.17 | Xe(5p) | 4.39 | |||
2.25 | [7] | 2.05 | [7] | 1.80 | [7] | |||
2.44 | [8] | 2.49 | [8] | 2.57 | [8] | |||
2.11 | [24] | 2.22 | [24] | 2.40 | [24] | |||
2.51 | [44] | 2.59 | [44] | 2.72 | [44] | |||
2.44a | 2.01a | 2.55a | ||||||
Li(2s) | 0.56 | Be(2s) | 1.44 | B(2p) | 0.66 | |||
0.59 | [7] | 1.36 | [7] | 1.17 | [7] | |||
0.82 | [24] | 1.62 | [24] | 0.88 | [24] | |||
C(2p) | 0.92 | N(2p) | 1.21 | O(2p) | 0.95 | |||
1.67 | [7] | 2.11 | [7] | 2.00 | [7] | |||
1.30 | [24] | 1.50 | [24] | 1.30 | [24] | |||
F(2p) | 1.19 | Na(3s) | 0.32 | Mg(3s) | 0.79 | |||
2.42 | [7] | 0.54 | [7] | 1.05 | [7] | |||
1.59 | [24] | 0.74 | [24] | 1.32 | [24] | |||
Al(3p) | 0.46 | Si(3p) | 0.98 | P(3p) | 1.48 | |||
0.71 | [7] | 1.15 | [7] | 1.55 | [7] | |||
0.61 | [24] | 1.10 | [24] | 1.65 | [24] | |||
S(3p) | 1.16 | Cl(3p) | 1.53 | K(4s) | 0.26 | |||
1.53 | [7] | 1.92 | [7] | 0.38 | [7] | |||
1.11 | [24] | 1.78 | [24] | 0.52 | [24] | |||
Ca(4s) | 0.61 | Br(4p) | 1.71 | Rb(5s) | 0.31 | |||
0.74 | [7] | 1.76 | [7] | 0.34 | [7] | |||
0.95 | [24] | 1.83 | [24] | 0.48 | [24] | |||
I(5p) | 3.72 | He+(1s) | 5.66 | Li+(1s) | 6.03 | |||
1.55 | [7] | 5.66 | [7] | 6.52 | [7] | |||
1.94 | [24] | 6.50 | [24] | |||||
Be+(2s) | 2.21 | B+(2s) | 3.71 | C+(2p) | 2.17 | |||
1.96 | [7] | 3.04 | [7] | 2.93 | [7] | |||
2.67 | [24] | 6.70 | [24] | 2.53 | [24] | |||
N+(2p) | 2.43 | O+(2p) | 2.88 | F+(2p) | 2.40 | |||
3.62 | [7] | 4.23 | [7] | 4.21 | [7] | |||
2.90 | [24] | 3.30 | [24] | 3.10 | [24] | |||
Ne+(2p) | 2.67 | Na+(2p) | 2.74 | Mg+(3s) | 1.33 | |||
4.76 | [7] | 5.23 | [7] | 1.41 | [7] | |||
3.40 | [24] | 3.70 | [24] | 2.31 | [24] | |||
3.43a | ||||||||
Al+(3s) | 2.14 | Si+(3p) | 1.58 | P+(3p) | 2.55 | |||
2.06 | [7] | 1.64 | [7] | 2.22 | [7] | |||
3.10 | [24] | 1.80 | [24] | 2.50 | [24] | |||
S+(3p) | 2.86 | Cl+(3p) | 2.96 | Ar+(3p) | 3.47 | |||
2.78 | [7] | 2.85 | [7] | 3.37 | [7] | |||
3.20 | [24] | 3.10 | [24] | 3.40 | [24] | |||
3.81a | ||||||||
K+(3p) | 3.59 | Ca+(4s) | 0.79 | Br+(4p) | 2.74 | |||
3.86 | [7] | 0.86 | [7] | 2.51 | [7] | |||
3.90 | [24] | 1.62 | [24] | 2.50 | [24] | |||
Kr+(4p) | 3.55 | Rb+(4p) | 3.58 | I+(5p) | 3.60 | |||
2.93 | [7] | 3.33 | [7] | 2.11 | [7] | |||
3.70 | [24] | 3.82 | [24] | 2.90 | [24] | |||
Xe+(5p) | 4.97 | H−(1s) | 0.47 | Li−(2s) | 0.78 | |||
2.42 | [7] | 1.12a | 1.00 | [24] | ||||
3.20 | [24] | |||||||
C−(2p) | 0.45 | O−(2p) | 0.38 | F−(2p) | 0.65 | |||
0.74 | [24] | 0.65 | [24] | 0.84 | [24] | |||
0.76a | ||||||||
Na−(3s) | 0.42 | Al−(3p) | 0.57 | Si−(3p) | 1.02 | |||
1.00 | [24] | 0.51 | [24] | 1.10 | [24] | |||
P−(3p) | 0.55 | Cl−(3p) | 1.20 | K−(4s) | 0.57 | |||
0.90 | [24] | 1.34 | [24] | 0.90 | [24] | |||
Br−(4p) | 1.41 | Rb−(5s) | 0.78 | |||||
1.49 | [24] | 0.80 | [24] |
Figure 3. Comparison of ionization probabilities obtained from three different methods: (a) He+, (b) Ar+, (c) H− and (d) F−. We take the laser field to be a Gaussian pulse with pulse duration (full width at half maximum, FWHM) of 15 fs. |
Figure 4. Comparison of ionization yields at several different laser wavelengths: (a) Ar, (b) Kr, (c) Mg and (d) K. The volume effect of a focused laser pulse with FWHM of 90 fs is considered. The Experimental data are from [45]. |