Microwave spectroscopy of S, P, and D states of sodium Rydberg atoms.

Abstract

The transition frequencies of the nS\ensuremath{\rightarrow}nP and nD\ensuremath{\rightarrow}(n+1)P sodium atom series were measured within the 53--350-GHz range for the main quantum number n=22--32. More precise values of ls splitting and quantum defects for ${\mathit{P}}_{1/2,3/2}$ and ${\mathit{D}}_{3/2,5/2}$ terms were determined. The frequencies were measured with an accuracy of better than 50 kHz. The results were treated using the Rydberg formula E(n,l,j)=-${\mathit{R}}_{\mathrm{Na}}$/(n-${\mathrm{\ensuremath{\delta}}}_{\mathit{n}\mathit{l}\mathit{j}}$${)}^{2}$. The quantum defect was calculated by using the expression ${\mathrm{\ensuremath{\delta}}}_{\mathit{n}\mathit{j}}$=${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{l}\mathit{j}}$+${\mathrm{\ensuremath{\alpha}}}_{\mathit{l}\mathit{j}}$/${\mathit{n}}^{\mathrm{*}2}$. The constants ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{l}\mathit{j}}$ and ${\mathrm{\ensuremath{\alpha}}}_{\mathit{l}\mathit{j}}$ that result from this work are ${\mathrm{\ensuremath{\varepsilon}}}_{1/2}$=0.855 444 58(14), ${\mathrm{\ensuremath{\alpha}}}_{1/2}$=0.112 668 (90), ${\mathrm{\ensuremath{\varepsilon}}}_{3/2}$=0.854 625 83(12), and ${\mathit{a}}_{3/2}$=0.112 878(81) for the P term and ${\mathrm{\ensuremath{\varepsilon}}}_{3/2}$=0.014 909 19(38), ${\mathit{a}}_{3/2}$=-0.042 19(25), ${\mathrm{\ensuremath{\varepsilon}}}_{5/2}$=0.014 925 82(55), and ${\mathit{a}}_{5/2}$=-0.043 33(35) for the D term. The ls-splitting constants determined from the expression \ensuremath{\Delta}${\ensuremath{\nu}}_{\mathit{l}}$=${\mathit{A}}_{\mathit{l}}$/${\mathit{n}}^{\mathrm{*}3}$ are ${\mathit{A}}_{\mathit{p}}$=5 384 790(420) MHz for the P term and ${\mathit{A}}_{\mathit{d}}$=97 340(680) MHz for the D term.