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Physica Scripta

Hyperfine Interaction, Zeeman and Stark Effects for Excited States in Rubidium

G Belin, Lennarth Holmgren, Sune R. Svanberg

Published Jun 1, 1976• 35 citations
Publisher

Abstract

Highly excitedPandDstates in87Rb were examined using a two-step excitation procedure. A conventional rf lamp and a CW dye laser were used for the first and second step, respectively. The following results for the magnetic dipole interaction constanta, the electric quadrupole interaction constantb, the LandégJfactor, and the tensor polarizability α2were obtained in level-crossing and optical-double-resonance experiments: 92P3/2:a= 4.05(3) MHz,b=0.55(3) MHz,gJ= 1.3335(15) 102P3/2:a= 2.60(8) MHz,gJ= 1.3332(20) 82D3/2:a= 2.840(15) MHz,b= 0.17(2) MHz 82D5/2:a= -1.20(15) MHz,gJ= 1.1998(15) 92D3/2:a= 1.900(10) MHz,b= 0.11(3) MHz 92D5/2:a= (-)0.80(15) MHz,gJ= 1.1995(15), α2= 180.3(9.0) MHz/(kV/cm)2 Many-body calculations of the hyperfine structure of Rb have been performed. The polarization effect is included to all orders, whereas the correlation effect is omitted. The negativeafactors for the2D5/2states, indicating large perturbations, are explained by the polarization contribution. A review of experimental hyperfine interaction constants, LandégJfactors and tensor polarizabilities for rubidium is given together with theoretical values of theafactors. The quadrupole moment for87Rb is obtained from thebfactors for the2P3/2and2D3/2states, using quadrupole parameters from the many-body calculations. The correlation effect is included in a semi-empirical way.

DOI
10.1088/0031-8949/13/6/004

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Hyperfine-structure investigation of highly excited D2 levels in Rb87 and Cs133 using a cw tunable dye laser in a two-step excitation scheme

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The hyperfine structure of several highly excited $^{2}D$ states in $^{87}\mathrm{Rb}$ and $^{133}\mathrm{Cs}$ has been measured. The $D$-state atoms were produced in a two-step-excitation process. In the first step, multiple scattering of the strong alkali-metal ${D}_{1}$ and ${D}_{2}$ lines from an rf lamp was used to excite atoms into the first excited $^{2}P$ levels. The intense tunable radiation from a cw dye laser was used in the second step to transfer $P$-state atoms into highly excited $D$ states. Level-crossing and optical-double-resonance techniques were used for the determination of the absolute values of the hyperfine-interaction constants. The following results (in MHz) were obtained for the magnetic dipole and the electric quadrupole interaction constants $a$ and $b$: For $^{87}\mathrm{Rb}$, $|a(6^{2}D_{\frac{3}{2}})|=7.84(5)$, $|b(6^{2}D_{\frac{3}{2}})|=0.53(6)$ ($\frac{b}{a}>0$), $|a(^{2}D_{\frac{5}{2}})|=3.6(7)$, $|a(7^{2}D_{\frac{3}{2}})|=4.53(3)$, $|b(7^{2}D_{\frac{3}{2}})|=0.26(4)$ ($\frac{b}{a}>0$), $|a(7^{2}D_{\frac{5}{2}})|=2.2(5)$. For $^{133}\mathrm{Cs}$, $|a(8^{2}D_{\frac{3}{2}})|=3.98(8)$, $|a(8^{2}D_{\frac{5}{2}})|=0.9(4)$, $|a(9^{2}D_{\frac{3}{2}})|=2.37(3)$, $|a(9^{2}D_{\frac{5}{2}})|=0.5(2)$, $|a(10^{2}D_{\frac{3}{2}})|=1.52(3)$, $|a(10^{2}D_{\frac{5}{2}})|=0.4(2)$. The $a$ factors generally deviate strongly from the values expected in a one-electron picture of the alkali-metal atom indicating the importance of polarization and correlation effects for these states. For $^{87}\mathrm{Rb}$ a comparison with a recent calculation including polarization effects is made. The $b$ factors for $^{87}\mathrm{Rb}$ are the first significant values allowing a calculation of an alkali-metal-atom nuclear quadrupole moment from non-$P$-state data.

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Measurements of magnetic-dipole and electric-quadrupole interaction constants of the 11, 12 and 132D5/2states in87Rb by the quantum-beat method

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Hyperfine structure in three n 2 D 5/2 states (n=11, 12 and 13) of 87 Rb was investigated by the quantum-beat method in zero magnetic field. The states of interest were excited by two-photon absorption from a single hyperfine substate (with F=1) of the ground state. The magnetic-dipole interaction constant A and the electric-quadrupole interaction constant B were obtained by analysis of the modulation frequencies of the fluorescence signals (transition n 2 D 5/2 -5 2 P 3/2 ). The results (MHz) are as follows: mod A(11 2 D 5/2 ) mod =0.361(7), mod B(11 2 D 5/2 ) mod =0.071(11), mod A(12 2 D 5/2 ) mod =0.266(9), mod B(12 2 D 5/2 ) mod =0.063(14), mod A(13 2 D 5/2 ) mod =0.20(1), mod B(13 2 D 5/2 ) mod =0.05(2). For all the states, A and B differ in sign. The effective lifetimes obtained as a by-product of the experiment are also presented.

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The Stark effect of the 5 s 2 S 1/2 –5 p 2 P 3/2 transition ( D 2 line) of Rb has been studied by high-resolution atomic-beam laser spectroscopy. The splittings of magnetic sublevels of 5 p 2 P 3/2 have been resolved, and the Stark shifts and splittings of the D 2 line have been measured at various electric fields. The scalar polarizability of the D 2 line and the tensor polarizability of the 5 p 2 P 3/2 level have been determined to be α s (5 p 2 P 3/2 ) - α s (5 s 2 S 1/2 ) = 136.95(89) kHz/(kV/cm) 2 and α t (5 p 2 P 3/2 ) = -40.91(38) kHz/(kV/cm) 2 , respectively, by considering the mixing between hyperfine structure levels of 5 p 2 P 3/2 . The precision of α t (5 p 2 P 3/2 ) has been improved by a factor of 2 compared with the previously reported values.

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Stark Effect Investigation of the Third Excited2P3/2Levels in the First Spectra of Rb87and Cs133

Sune R. Svanberg

Using the level crossing technique with parallel magnetic and electric fields the tensor polarizability of the 7 p 2 P 3/2 level in Rb 87 and the 8 p 2 P 3/2 level in Cs 133 was measured with the results α 2 (7 p 2 P 3/2 Rb 87 ) = -3.2 (2) MHz (kV/cm) 2 and α 2 (8 p 2 P 3/2 Rb 133 ) = -7.6 (3) MHz (kV/cm) 2 Theoretical values, calculated with the Coulomb approximation of Bates and Damgaard, agree very well with the experimental results.

Physica Scripta•Mar 1, 1972•14 citations
Highly excitedPandDstates in87Rb were examined using a two-step excitation procedure. A conventional rf lamp and a CW dye laser were used for the first and second step, respectively. The following results for the magnetic dipole interaction constanta, the electric quadrupole interaction constantb, the LandégJfactor, and the tensor polarizability α2were obtained in level-crossing and optical-double-resonance experiments: 92P3/2:a= 4.05(3) MHz,b=0.55(3) MHz,gJ= 1.3335(15) 102P3/2:a= 2.60(8) MHz,gJ= 1.3332(20) 82D3/2:a= 2.840(15) MHz,b= 0.17(2) MHz 82D5/2:a= -1.20(15) MHz,gJ= 1.1998(15) 92D3/2:a= 1.900(10) MHz,b= 0.11(3) MHz 92D5/2:a= (-)0.80(15) MHz,gJ= 1.1995(15), α2= 180.3(9.0) MHz/(kV/cm)2 Many-body calculations of the hyperfine structure of Rb have been performed. The polarization effect is included to all orders, whereas the correlation effect is omitted. The negativeafactors for the2D5/2states, indicating large perturbations, are explained by the polarization contribution. A review of experimental hyperfine interaction constants, LandégJfactors and tensor polarizabilities for rubidium is given together with theoretical values of theafactors. The quadrupole moment for87Rb is obtained from thebfactors for the2P3/2and2D3/2states, using quadrupole parameters from the many-body calculations. The correlation effect is included in a semi-empirical way.
The hyperfine structure of several highly excited 2D^{2}D2D states in 87Rb^{87}\mathrm{Rb}87Rb and 133Cs^{133}\mathrm{Cs}133Cs has been measured. The DDD-state atoms were produced in a two-step-excitation process. In the first step, multiple scattering of the strong alkali-metal D1{D}_{1}D1​ and D2{D}_{2}D2​ lines from an rf lamp was used to excite atoms into the first excited 2P^{2}P2P levels. The intense tunable radiation from a cw dye laser was used in the second step to transfer PPP-state atoms into highly excited DDD states. Level-crossing and optical-double-resonance techniques were used for the determination of the absolute values of the hyperfine-interaction constants. The following results (in MHz) were obtained for the magnetic dipole and the electric quadrupole interaction constants aaa and bbb: For 87Rb^{87}\mathrm{Rb}87Rb, ∣a(62D32)∣=7.84(5)|a(6^{2}D_{\frac{3}{2}})|=7.84(5)∣a(62D23​​)∣=7.84(5), ∣b(62D32)∣=0.53(6)|b(6^{2}D_{\frac{3}{2}})|=0.53(6)∣b(62D23​​)∣=0.53(6) (ba>0\frac{b}{a}>0ab​>0), ∣a(2D52)∣=3.6(7)|a(^{2}D_{\frac{5}{2}})|=3.6(7)∣a(2D25​​)∣=3.6(7), ∣a(72D32)∣=4.53(3)|a(7^{2}D_{\frac{3}{2}})|=4.53(3)∣a(72D23​​)∣=4.53(3), ∣b(72D32)∣=0.26(4)|b(7^{2}D_{\frac{3}{2}})|=0.26(4)∣b(72D23​​)∣=0.26(4) (ba>0\frac{b}{a}>0ab​>0), ∣a(72D52)∣=2.2(5)|a(7^{2}D_{\frac{5}{2}})|=2.2(5)∣a(72D25​​)∣=2.2(5). For 133Cs^{133}\mathrm{Cs}133Cs, ∣a(82D32)∣=3.98(8)|a(8^{2}D_{\frac{3}{2}})|=3.98(8)∣a(82D23​​)∣=3.98(8), ∣a(82D52)∣=0.9(4)|a(8^{2}D_{\frac{5}{2}})|=0.9(4)∣a(82D25​​)∣=0.9(4), ∣a(92D32)∣=2.37(3)|a(9^{2}D_{\frac{3}{2}})|=2.37(3)∣a(92D23​​)∣=2.37(3), ∣a(92D52)∣=0.5(2)|a(9^{2}D_{\frac{5}{2}})|=0.5(2)∣a(92D25​​)∣=0.5(2), ∣a(102D32)∣=1.52(3)|a(10^{2}D_{\frac{3}{2}})|=1.52(3)∣a(102D23​​)∣=1.52(3), ∣a(102D52)∣=0.4(2)|a(10^{2}D_{\frac{5}{2}})|=0.4(2)∣a(102D25​​)∣=0.4(2). The aaa factors generally deviate strongly from the values expected in a one-electron picture of the alkali-metal atom indicating the importance of polarization and correlation effects for these states. For 87Rb^{87}\mathrm{Rb}87Rb a comparison with a recent calculation including polarization effects is made. The bbb factors for 87Rb^{87}\mathrm{Rb}87Rb are the first significant values allowing a calculation of an alkali-metal-atom nuclear quadrupole moment from non-PPP-state data.
Hyperfine structure in three n 2 D 5/2 states (n=11, 12 and 13) of 87 Rb was investigated by the quantum-beat method in zero magnetic field. The states of interest were excited by two-photon absorption from a single hyperfine substate (with F=1) of the ground state. The magnetic-dipole interaction constant A and the electric-quadrupole interaction constant B were obtained by analysis of the modulation frequencies of the fluorescence signals (transition n 2 D 5/2 -5 2 P 3/2 ). The results (MHz) are as follows: mod A(11 2 D 5/2 ) mod =0.361(7), mod B(11 2 D 5/2 ) mod =0.071(11), mod A(12 2 D 5/2 ) mod =0.266(9), mod B(12 2 D 5/2 ) mod =0.063(14), mod A(13 2 D 5/2 ) mod =0.20(1), mod B(13 2 D 5/2 ) mod =0.05(2). For all the states, A and B differ in sign. The effective lifetimes obtained as a by-product of the experiment are also presented.
Stark effect investigations in the 6, 7 and 82D3/2,5/2levels of85Rb and the 8, 9 and 102D3/2,5/2levels of133Cs were performed with the level crossing technique. The levels were populated in a two-step excitation process, involving a CW tunable dye laser. The tensor polarizability of all states was measured and a good agreement with theoretical values, obtained with the Coulomb approximation, is found. Furthermore, the signs of the dipole interaction constants, determined to absolute value in earlier experiments, could be inferred. The sign was found to be positive for the2D3/2states and negative for the2D5/2states, indicating strong polarization effects in the magnetic hyperfine interaction.
The Stark effect of the 5 s 2 S 1/2 –5 p 2 P 3/2 transition ( D 2 line) of Rb has been studied by high-resolution atomic-beam laser spectroscopy. The splittings of magnetic sublevels of 5 p 2 P 3/2 have been resolved, and the Stark shifts and splittings of the D 2 line have been measured at various electric fields. The scalar polarizability of the D 2 line and the tensor polarizability of the 5 p 2 P 3/2 level have been determined to be α s (5 p 2 P 3/2 ) - α s (5 s 2 S 1/2 ) = 136.95(89) kHz/(kV/cm) 2 and α t (5 p 2 P 3/2 ) = -40.91(38) kHz/(kV/cm) 2 , respectively, by considering the mixing between hyperfine structure levels of 5 p 2 P 3/2 . The precision of α t (5 p 2 P 3/2 ) has been improved by a factor of 2 compared with the previously reported values.