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Physical Review Letters

Cascade Anticrossing Measurement of the Anomalous Hyperfine Structure of the 4D2 State of Rubidium

K. H. Liao, L. K. Lam, R. Gupta, W. Happer

Published Jun 17, 1974• 50 citations
Publisher

Abstract

A new technique, cascade anticrossing spectroscopy, has been developed to determine the effective values of $〈{r}^{\ensuremath{-}3}〉$ for the spin-dipole, orbital, contact, and quadrupole hyperfine interaction terms for the $4^{2}D$ state of Rb. They are, in units of ${10}^{24}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, ${〈{r}^{\ensuremath{-}3}〉}_{d}=\ensuremath{-}0.36(8)$, ${〈{r}^{\ensuremath{-}3}〉}_{l}=+0.20(2)$, ${〈{r}^{\ensuremath{-}3}〉}_{c}=\ensuremath{-}4.3(1)$, and ${〈{r}^{\ensuremath{-}3}〉}_{q}=+0.79(66)$, respectively. The negative value of ${〈{r}^{\ensuremath{-}3}〉}_{d}$ and the unexpectedly large value of ${〈{r}^{\ensuremath{-}3}〉}_{c}$ are surprising. The fine-structure splitting has been measured to be - 13 360.9(8) MHz.

DOI
10.1103/physrevlett.32.1340

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Cascade Radio-Frequency Spectroscopy of Excited S and D States of Rubidium; Anomalous D -State Hyperfine Structure

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Measurement of hyperfine structure of the 8S122 and 9S122 states of rubidium, and 12S122 state of cesium by stepwise dye-laser spectroscopy

Pericles G. Tsekeris, R. Gupta

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Physical Review A•Feb 1, 1975•20 citations

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

Sune R. Svanberg, Pericles G. Tsekeris

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.

Physical Review A•Apr 1, 1975•46 citations
A new technique, cascade anticrossing spectroscopy, has been developed to determine the effective values of 〈r\ensuremath−3〉〈{r}^{\ensuremath{-}3}〉〈r\ensuremath−3〉 for the spin-dipole, orbital, contact, and quadrupole hyperfine interaction terms for the 42D4^{2}D42D state of Rb. They are, in units of 1024{10}^{24}1024 cm\ensuremath−3{\mathrm{cm}}^{\ensuremath{-}3}cm\ensuremath−3, 〈r\ensuremath−3〉d=\ensuremath−0.36(8){〈{r}^{\ensuremath{-}3}〉}_{d}=\ensuremath{-}0.36(8)〈r\ensuremath−3〉d​=\ensuremath−0.36(8), 〈r\ensuremath−3〉l=+0.20(2){〈{r}^{\ensuremath{-}3}〉}_{l}=+0.20(2)〈r\ensuremath−3〉l​=+0.20(2), 〈r\ensuremath−3〉c=\ensuremath−4.3(1){〈{r}^{\ensuremath{-}3}〉}_{c}=\ensuremath{-}4.3(1)〈r\ensuremath−3〉c​=\ensuremath−4.3(1), and 〈r\ensuremath−3〉q=+0.79(66){〈{r}^{\ensuremath{-}3}〉}_{q}=+0.79(66)〈r\ensuremath−3〉q​=+0.79(66), respectively. The negative value of 〈r\ensuremath−3〉d{〈{r}^{\ensuremath{-}3}〉}_{d}〈r\ensuremath−3〉d​ and the unexpectedly large value of 〈r\ensuremath−3〉c{〈{r}^{\ensuremath{-}3}〉}_{c}〈r\ensuremath−3〉c​ are surprising. The fine-structure splitting has been measured to be - 13 360.9(8) MHz.
We report the first successful measurements by cascade radio-frequency spectroscopy of the hyperfine structures of excited SSS and DDD states of rubidium. We obtain the following magnetic dipole coupling constants (in MHz): for Rb87{\mathrm{Rb}}^{87}Rb87, $A(7^{2}S_{\frac{1}{2}})=312.5\ifmmode\pm\else\textpm\fi{}3.5$, $A(5^{2}D_{\frac{3}{2}})=14.1\ifmmode\pm\else\textpm\fi{}0.5$, $A(5^{2}D_{\frac{5}{2}})=\ensuremath{-}8.0\ifmmode\pm\else\textpm\fi{}1.5$; for Rb85{\mathrm{Rb}}^{85}Rb85, $A(7^{2}S_{\frac{1}{2}})=92.6\ifmmode\pm\else\textpm\fi{}1.0$, $A(5^{2}D_{\frac{3}{2}})=4.1\ifmmode\pm\else\textpm\fi{}0.5$. The anomalous, negative value of AAA for the 52D525^{2}D_{\frac{5}{2}}52D25​​ state may be related to the anomalously small fine-structure interval of the 5D5D5D state of rubidium.
The hyperfine structure of the second-excited DDD states of 85Rb^{85}\mathrm{Rb}85Rb, 85Rb^{85}\mathrm{Rb}85Rb, and 133Cs^{133}\mathrm{Cs}133Cs has been measured by the method of cascade-radio-frequency spectroscopy and cascade-level crossing. The sign of the magnetic-dipole coupling constant AAA is determined by the method of cascade-decoupling and cascade-radio-frequency spectroscopy with narrow-band excitation. Lifetimes $\ensuremath{\tau}$ of some of these states are measured by the cascade-Hanle effect. We find that for 87Rb^{87}\mathrm{Rb}87Rb, $A(5^{2}D_{\frac{3}{2}})=14.43\ifmmode\pm\else\textpm\fi{}0.23$ MHz, $A(5^{2}D_{\frac{5}{2}})=\ensuremath{-}7.44\ifmmode\pm\else\textpm\fi{}0.10$ MHz, $\ensuremath{\tau}(5^{2}D_{\frac{3}{2}})=205\ifmmode\pm\else\textpm\fi{}40$ nsec; for 85Rb^{85}\mathrm{Rb}85Rb, $A(5^{2}D_{\frac{3}{2}})=4.18\ifmmode\pm\else\textpm\fi{}0.20$ MHz, $A(5^{2}D_{\frac{5}{2}})=\ensuremath{-}2.12\ifmmode\pm\else\textpm\fi{}0.20$ MHz; for 133Cs^{133}\mathrm{Cs}133Cs, $A(6^{2}D_{\frac{3}{2}})=16.30\ifmmode\pm\else\textpm\fi{}0.15$ MHz, $A(6^{2}D_{\frac{5}{2}})=\ensuremath{-}3.6\ifmmode\pm\else\textpm\fi{}1.0$ MHz, $\ensuremath{\tau}(6^{2}D_{\frac{3}{2}})=57\ifmmode\pm\else\textpm\fi{}15$ nsec.
In a recent paper Lee, Rodgers, Das, and Sternheimer have reported on the evaluation of the fine and hyperfine structure of the 42D4^{2}D42D state of the rubidium atom by considering the first-order polarization of the electron core. By means of more extensive calculations we have shown that the first-order results can be quite unreliable for such strongly perturbed systems. By including polarization effects to all orders and the most important correlation effects, we have been able to reproduce the experimental results for this state quite well. The good agreement obtained by Lee et al. for the spin-dipole parameter is in our opinion largely fortuitous.
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 structures of the 82S128^{2}S_{\frac{1}{2}}82S21​​ and 92S129^{2}S_{\frac{1}{2}}92S21​​ states of 87Rb^{87}\mathrm{Rb}87Rb and of the 122S1212^{2}S_{\frac{1}{2}}122S21​​ state of 133Cs^{133}\mathrm{Cs}133Cs have been measured by the method of stepwise excitation spectroscopy using a cw dye laser. We measure the magnetic dipole coupling constants to be $A(8^{2}S_{\frac{1}{2}}, ^{87}\mathrm{Rb})=159.2\ifmmode\pm\else\textpm\fi{}1.5$ MHz, $A(9^{2}S_{\frac{1}{2}}, ^{87}\mathrm{Rb})=90.9\ifmmode\pm\else\textpm\fi{}0.8$ MHz, and $A(12^{2}S_{\frac{1}{2}}, ^{133}\mathrm{Cs})=26.31\ifmmode\pm\else\textpm\fi{}0.10$ MHz.
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.