Mathieu Laroche,
Jean-Louis Doualan,
Sylvain Girard,
Jean Margerie,
and Richard Moncorgé
Centre Interdisciplinaire de Recherche Ions Lasers, Unité Mixte de Recherche 6637, Centre National de la Recherche Scientifique/Commissariat à l’Energie Atomique/Institut des Sciences de la Matière et du Rayonnement, 6, Boulevard Maréchal Juin, 14050 Caen Cedex 4, France
Mathieu Laroche, Jean-Louis Doualan, Sylvain Girard, Jean Margerie, and Richard Moncorgé, "Experimental and theoretical investigations of the 4f2 → 4f5d ground-state and excited-state absorption spectra of Pr3+ in LiYF4," J. Opt. Soc. Am. B 17, 1291-1303 (2000)
Near-UV excited-state absorption spectra obtained with a pulsed pump–probe technique were recorded in at 77 and at 8 K and revealed a detailed structure of the and optical transitions. These experimental results, together with those previously obtained at room temperature, are compared with the numerical predictions of a full calculation of the sublevels and of the electric dipole transitions toward these sublevels from different states of the configuration. The agreement is good, provided that the four adjustable parameters of the theory are taken as
and Å. The level structure of the configuration of is shown to be dominated, as expected, by the crystal field coupling of the electron but also, to a noticeable extent, by the spin–orbit coupling of the electron and the Coulomb repulsion of both electrons. The former of these two interactions is somewhat more efficient than the latter in the low-energy part of the configuration, i.e., in the spectral region where the largest amount of experimental data is currently available.
Mathieu Laroche, Alain Braud, Sylvain Girard, Jean Louis Doualan, Richard Moncorge, Michel Thuau, and Larry D. Merkle J. Opt. Soc. Am. B 16(12) 2269-2277 (1999)
Annabelle Collombet, Yannick Guyot, Marie-France Joubert, Jean Margerie, Richard Moncorgé, and Alexandra Tkachuk J. Opt. Soc. Am. B 21(11) 2053-2057 (2004)
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Energies of Some Stark Sublevels of the Configurationa
Level
Energy (cm-1)
Symmetry
0
2
79
±1
210*
0
220
0
⋮
16740
2
16810
0
17083
±1
17406
2
20860
0
21076*
2
21077*
2
⋮
Values of energies (column 2) are from Table VII of Ref. 9. Experimental values are listed whenever they are known; when they are not, calculated values (minus 7 cm-1, the calculated energy of the ground Stark sublevel) are listed and marked with asterisks. The symmetries of column 3 are crystallographic quantum numbers μ.13
Column 1 obtained from ESA at 8 K; column 2 obtained from ESA at 8 K. For these two columns the wavenumbers above the space are zero-phonon line positions and those under the space are broadband maxima. Column 3, crystallographic quantum number μ. Columns 4 and 5, respectively, d and (see Fig. 7 below). An asterisk in column 5 indicates a value obtained by a procedure involving a hot line (see Section 2). Column 6, sublevel energies calculated with the parameters of Table 3 below. Column 7, i of the sublevel in a list ranked by increasing calculated energies within the configuration.
All values are in inverse centimeters, except that is in angstroms.
From Ref. 18; see Subsection 3.C.
Adjusted in the present calculation; see Subsection 4.A.
From Ref. 9.
Obtained from through Eq. (7).
Adjusted in the present calculation; see Subsection 4.C.
Table 4
Calculated and Observed ESA Spectra at 295 K from the and Levels of a
Initial Level, Polarization
Position
Absorption Cross Section
Calculated
Observed
Difference
Calculated
Observed
Ratio
Identification
From
σ Polarized
30 420
30 460
-40
0.48
0.53
0.91
∼31 200
31 440
∼-240
0.45
0.48
0.94
33 550
33 400
150
0.40
0.40
1.00
37 240
36 650
590
2.88
2.31
1.25
∼40 900
40 430
∼470
0.71
0.81
0.88
π Polarized
30 070
30 110
-40
0.42
0.78
0.54
33 010
32 770
240
0.32
0.63
0.51
38 350
38 120
230
2.83
2.13
1.33
41 180
40 460
720
3.32
2.10
1.58
From and
σ Polarized
27 590
27 630
-40
0.66
0.86
0.77
33 050
32 260
790
1.20
1.14
1.05
34 780
34 810
-30
0.68
0.59
1.15
38 370
?
0.48
?
π Polarized
27 250
27 330
-80
0.29
0.61
0.48
30 110
30 160
-50
0.12
0.19
0.63
35 360
35 020
340
0.73
0.78
0.94
37 930
∼37 630
∼300
0.16
0.29
0.55
Positions are in inverse centimeters; cross sections are in units of Calculated values have been obtained with the parameters of Table 3. In the rightmost column, represents the first excited Stark sublevel of the final level of the transition, which makes the main contribution to the maximum, is represented by the values of quantum numbers and whenever a given accounts for more than 60% of the wave function. is a sublevel whose wave function consists of 42.4% and 36.4% |5/2, 0〉, together with minor contributions; is a sublevel with 44.6% |5/2, ±1〉, 25.8% |7/2, 0〉, and a number of minor contributions.
Positions are in inverse centimeters; cross sections are in units of Three top rows, values calculated with the parameters of Table 3; three bottom rows; values calculated with and The calculated positions and absorption cross sections were arbitrarily taken to be the unweighted means of the corresponding values for π and σ polarizations. In the rightmost column the final states in the immediate vicinity of band maxima are represented by the and quantum numbers that correspond to the largest-by-far contribution to the excited wave functions.
Table 6
Percentages of Pure Coupling States in Pure Ones for an Configuration
Pure LS State
(%)
(%)
(%)
74.8
21.8
3.4
36.7
12.2
51.0
57.1
–
42.9
–
85.7
14.3
Tables (6)
Table 1
Energies of Some Stark Sublevels of the Configurationa
Level
Energy (cm-1)
Symmetry
0
2
79
±1
210*
0
220
0
⋮
16740
2
16810
0
17083
±1
17406
2
20860
0
21076*
2
21077*
2
⋮
Values of energies (column 2) are from Table VII of Ref. 9. Experimental values are listed whenever they are known; when they are not, calculated values (minus 7 cm-1, the calculated energy of the ground Stark sublevel) are listed and marked with asterisks. The symmetries of column 3 are crystallographic quantum numbers μ.13
Column 1 obtained from ESA at 8 K; column 2 obtained from ESA at 8 K. For these two columns the wavenumbers above the space are zero-phonon line positions and those under the space are broadband maxima. Column 3, crystallographic quantum number μ. Columns 4 and 5, respectively, d and (see Fig. 7 below). An asterisk in column 5 indicates a value obtained by a procedure involving a hot line (see Section 2). Column 6, sublevel energies calculated with the parameters of Table 3 below. Column 7, i of the sublevel in a list ranked by increasing calculated energies within the configuration.
All values are in inverse centimeters, except that is in angstroms.
From Ref. 18; see Subsection 3.C.
Adjusted in the present calculation; see Subsection 4.A.
From Ref. 9.
Obtained from through Eq. (7).
Adjusted in the present calculation; see Subsection 4.C.
Table 4
Calculated and Observed ESA Spectra at 295 K from the and Levels of a
Initial Level, Polarization
Position
Absorption Cross Section
Calculated
Observed
Difference
Calculated
Observed
Ratio
Identification
From
σ Polarized
30 420
30 460
-40
0.48
0.53
0.91
∼31 200
31 440
∼-240
0.45
0.48
0.94
33 550
33 400
150
0.40
0.40
1.00
37 240
36 650
590
2.88
2.31
1.25
∼40 900
40 430
∼470
0.71
0.81
0.88
π Polarized
30 070
30 110
-40
0.42
0.78
0.54
33 010
32 770
240
0.32
0.63
0.51
38 350
38 120
230
2.83
2.13
1.33
41 180
40 460
720
3.32
2.10
1.58
From and
σ Polarized
27 590
27 630
-40
0.66
0.86
0.77
33 050
32 260
790
1.20
1.14
1.05
34 780
34 810
-30
0.68
0.59
1.15
38 370
?
0.48
?
π Polarized
27 250
27 330
-80
0.29
0.61
0.48
30 110
30 160
-50
0.12
0.19
0.63
35 360
35 020
340
0.73
0.78
0.94
37 930
∼37 630
∼300
0.16
0.29
0.55
Positions are in inverse centimeters; cross sections are in units of Calculated values have been obtained with the parameters of Table 3. In the rightmost column, represents the first excited Stark sublevel of the final level of the transition, which makes the main contribution to the maximum, is represented by the values of quantum numbers and whenever a given accounts for more than 60% of the wave function. is a sublevel whose wave function consists of 42.4% and 36.4% |5/2, 0〉, together with minor contributions; is a sublevel with 44.6% |5/2, ±1〉, 25.8% |7/2, 0〉, and a number of minor contributions.
Positions are in inverse centimeters; cross sections are in units of Three top rows, values calculated with the parameters of Table 3; three bottom rows; values calculated with and The calculated positions and absorption cross sections were arbitrarily taken to be the unweighted means of the corresponding values for π and σ polarizations. In the rightmost column the final states in the immediate vicinity of band maxima are represented by the and quantum numbers that correspond to the largest-by-far contribution to the excited wave functions.
Table 6
Percentages of Pure Coupling States in Pure Ones for an Configuration
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