Resonant Excitation Stark Ionization Spectroscopy Research Articles

Atomic properties of actinide ions with particle-hole configurations

We study the effects of higher-order electronic correlations in the systems with particle-hole excited states using a relativistic hybrid method that combines configuration interaction and linearized coupled-cluster approaches. We find the configuration interaction part of the calculation sufficiently complete for eight electrons while maintaining good quality of the effective coupled-cluster potential for the core. Excellent agreement with experiment was demonstrated for a test case of La$^{3+}$. We apply our method for homologue actinide ions Th$^{4+}$ and U$^{6+}$ which are of experimental interest due to a puzzle associated with the resonant excitation Stark ionization spectroscopy (RESIS) method. These ions are also of interest to actinide chemistry and this is the first precision calculation of their atomic properties.

Properties of Fr-like Th3+from rf spectroscopy of high-LTh2+Rydberg ions

Relative positions of twenty $n=28$ Rydberg levels of Th${}^{2+}$ with $L=9$, 10, 11, and 12 were determined with sub-MHz precision using the rf-RESIS (resonant excitation Stark ionization spectroscopy) technique. The pattern of binding energies was analyzed with the effective potential model, modified to account for significant nonadiabatic effects. The analysis yielded measurements of several properties of the Fr-like Th${}^{3+}$ core ion, including the quadrupole moment, $Q=0.5931$(14) a.u.; hexadecapole moment, \ensuremath{\Pi} $=$ \ensuremath{-}0.69(28) a.u.; $g$ factor, ${g}_{J}=1.24$(48); scalar and tensor dipole polarizabilities, \ensuremath{\alpha}${}_{D}$${}_{,0}=15.224$(33) a.u. and \ensuremath{\alpha}${}_{D}$${}_{,2}$ $=$ \ensuremath{-}5.30(11) a.u.; scalar quadrupole polarizability, \ensuremath{\alpha}${}_{Q}$${}_{,0}=60$(15) a.u.; and the reduced dipole and octupole matrix elements connecting the ground 5$f$ ${}^{2}$${F}_{5/2}$ level with the low-lying 6$d$ ${}^{2}$${D}_{3/2}$ level, $|{\ensuremath{\langle}}^{2}{F}_{5/2}||{\mathrm{M}}^{[1]}|{|}^{2}{D}_{3/2}\ensuremath{\rangle}|=1.436(2)$ a.u. and $|{\ensuremath{\langle}}^{2}{F}_{5/2}||{\mathrm{M}}^{[3]}|{|}^{2}{D}_{3/2}\ensuremath{\rangle}|=3.3(1.1)$ a.u. The measured properties are compared with theoretical predictions.

Microwave spectroscopy of high-L,n=9Rydberg levels of nickel: Polarizabilities and moments of the Ni+ion

The complete pattern of Rydberg binding energies of the 18 $n=9$ levels of nickel with $L=6$, 7, and 8 was measured using microwave plus resonant-excitation Stark-ionization spectroscopy. The measured pattern is consistent with the form predicted with the effective potential model, showing significant structure proportional to scalar products of tensor operators of order 0--4. The variation of the structure with $L$ separates the various contributing terms and provides determinations of several properties of the Ni${}^{+}$ core ion. These include the quadrupole moment, $Q$ $=$ \ensuremath{-}0.469 78(9) a.u., the hexadecapole moment, \ensuremath{\Pi} $=$ 0.36(5) a.u., the scalar and tensor dipole polarizabilities, ${\ensuremath{\alpha}}_{D,0}=$ 7.949(2) a.u., ${\ensuremath{\alpha}}_{D,2}=0.905$(12) a.u., the scalar quadrupole polarizability, ${\ensuremath{\alpha}}_{Q,0}=55$(8) a.u., the $g$ value, ${g}_{J}=1.257$(14), and the vector hyperpolarizability, ${\ensuremath{\beta}}_{D,1}=0.454$(24) a.u.

Polarizabilities ofSi2+: A benchmark test of theory and experiment

We have calculated electric-dipole polarizabilities of the 3s^2 ^1S_0, 3s3p ^3P_0, and 3s3p ^1P_1 states of the Si^{2+} ion using recently developed configuration interaction + all-order method. Detailed evaluation of the uncertainties of the final results is carried out. Our value for the ground state electric-dipole polarizability 11.670(13) a.u. is in excellent agreement with the resonant excitation Stark ionization spectroscopy value 11.669(9) a.u. [Komara et al., J. Phys. B 38, 87 (2005); Mitroy, Phys. Rev. A 78, 052515 (2008)]. This work represents the most precise benchmark test to date of theory and experiment in divalent atoms. The near cancellation of the ns^2 ^1S_0 ground state and the lowest nsnp ^3P_0 polarizabilities previously observed in B+, Al+, In+, Tl+, and Pb^{2+} is also found in Si^{2+} ion.

Polarizabilities of Rn-like Th4+from rf spectroscopy of Th3+Rydberg levels

High resolution studies of the fine structure pattern in high-L n=37 levels of Th3+ have been carried out using radio-frequency (rf) spectroscopy detected with Resonant Excitation Stark Ionization Spectroscopy (RESIS). Intervals separating L=9 to L=15 levels have been measured, and the results analyzed with the long-range effective potential model. The dipole polarizability of Th4+is determined to be aD= 7.720(7) a.u.. The quadrupole polarizability is found to be 21.5(3.9) a.u. Both measurements represent significant tests of a-priori theoretical descriptions of this highly relativistic ion.

Properties of Fr-like Th3+from spectroscopy of high-LRydberg levels of Th2+

Binding energies of high-L Rydberg states (L^3 7) of Th2+ with n=27-29 were studied using the Resonant Excitation Stark Ionization Spectroscopy (RESIS) method. The core of the Th2+ Rydberg ion is the Fr-like ion Th3+ whose ground state is a 5 2F5/2 level. The large core angular momentum results in a complex Rydberg fine structure pattern consisting of six levels for each value of L that is only partially resolved in the RESIS excitation spectrum. The pattern is further complicated, especially for the relatively low L levels, by strong non-adiabatic effects due to the low-lying 6d levels. Analysis of the observed RESIS spectra leads to determination of five properties of the Th3+ ion: its electric quadrupole moment, Q = 0.54(4), its adiabatic scalar and tensor dipole polarizabilities, ad,0 = 15.42(17) and ad,2 = -3.6(1.3), and the dipole matrix elements connecting the ground 52F5/2 level to the low lying 62D3/2 and 62D5/2 levels, |<52F5/2||D||62D3/2>| = 1.435(10) and |<52F5/2||D||62D5/2>| = 0.414(24). All are in atomic units. These are compared with theoretical calculations.

Polarizability of Rn-like Th4+from spectroscopy of high-LRydberg levels of Th3+

Binding energies of high-$L$ Rydberg levels of Th${}^{3+}$ were measured using the resonant excitation Stark ionization spectroscopy technique. Analysis of the data with the long-range polarization model leads to determination of dipole and quadrupole polarizabilities of the free Th${}^{4+}$ ion, ${\ensuremath{\alpha}}_{\mathrm{d}}$ $=$ 7.61(6) a.u., ${\ensuremath{\alpha}}_{\mathrm{Q}}$ $=$ 47(11) a.u.

Dipole transition strengths in Ba+from Rydberg fine-structure measurements in Ba and Ba+

The fine structure of high-$L$ $n$ $=$ $19$ and $20$ Rydberg states of Ba${}^{+}$ has been measured precisely using the resonant excitation Stark ionization spectroscopy technique, allowing for a determination of the Ba${}^{2+}$ polarizability: ${\ensuremath{\alpha}}_{D}$(Ba${}^{2+}$) $=$ $10.75(10)$ a.u. This result, in combination with an improved model of the $K$ splittings in Ba Rydberg levels, allows for a more precise determination of the Ba${}^{+}$ dipole transition strengths connecting the $6$$ {}^{2}{S}_{1/2}$ ground state to the $6$$ {}^{2}{P}_{1/2}$ and $6$$ {}^{2}{P}_{3/2}$ excited states. The results, in atomic units, are $\ensuremath{\langle}$$6$$ {}^{2}{S}_{1/2} ||D|| 6 {}^{2}{P}_{1/2}\ensuremath{\rangle}$ $=$ $3.3251(21)$ and $\ensuremath{\langle}$6$ {}^{2}{\mathrm{S}}_{1/2} ||D|| 6 {}^{2}{P}_{3/2}\ensuremath{\rangle}$ $=$ $4.7017(27)$.

Polarizabilities of Pb2+and Pb4+and ionization energies of Pb+and Pb3+from spectroscopy of high-LRydberg states of Pb+and Pb3+

The binding energies of high-$L$ Rydberg levels of Pb${}^{+}$ with $n=19$ or 20 and $6\ensuremath{\leqslant}L\ensuremath{\leqslant}10$ were measured with resonant excitation Stark ionization spectroscopy (RESIS). When combined with previous measurements of members of the $\mathit{nh}$ Rydberg series in Pb${}^{+}$, and analyzed with the long-range polarization model, these determined the polarizability of the $5{d}^{10}6{s}^{2}$ ground state of Pb${}^{2+}$ to be ${\ensuremath{\alpha}}_{d}$ $=$ 13.62(8) a.u. This value is substantially larger than the estimate published recently based on the measured lifetime of the $6s6{p}^{1}{P}_{1}$ resonance level of Pb${}^{2+}$, 7.9(6) a.u. The difference is mostly due to the polarizability of Pb${}^{4+}$, the $5{d}^{10}$ core of the Pb${}^{2+}$ ion. This was established by observation of resolved fine structure in the excitation of $n=39$, high-$L$ Rydberg levels of Pb${}^{3+}$, using the same RESIS technique. Analysis of this spectra determined the polarizability of Pb${}^{4+}$ to be ${\ensuremath{\alpha}}_{d}$ $=$ 3.61(4) a.u. Reanalysis of optical spectra of $\mathit{nh}$ and $\mathit{ng}$ levels in Pb${}^{+}$ and Pb${}^{3+}$ in view of the polarizabilities determined in the RESIS studies indicates revised ionization energies of both ions, ${E}_{\mathrm{I}}$(Pb${}^{+}$) $=$ 121245.28(6) cm${}^{\ensuremath{-}1}$ and ${E}_{\mathrm{I}}$(Pb${}^{3+}$) $=$ 341 435.1(8) cm${}^{\ensuremath{-}1}$.

Optical spectroscopy of high-LRydberg states of nickel

Binding energies of 23 Rydberg fine-structure levels of Ni with n $=$ 9 and $L\ensuremath{\geqslant}5$ were measured using resonant excitation Stark ionization spectroscopy. From this spectrum, the quadrupole moment and the scalar and tensor dipole polarizability of the ${}^{2}{D}_{5/2}$ ground state of Ni${}^{+}$ were determined to be $Q=\ensuremath{-}0.474(2)$, ${\ensuremath{\alpha}}_{d,0}=7.92(6)$, and ${\ensuremath{\alpha}}_{d,2}=1.15(14)$ a.u. The electric hexadecapole moment was determined to be $\ensuremath{-}0.33(21)$ a.u.

Polarizability of theSi2+ion

The dipole polarizability of the ${\mathrm{Si}}^{2+}$ ground state has been determined by a large-scale configuration-interaction (CI) calculation using the sum-over-states approach. The CI calculation was used to describe the valence electron dynamics with respect to the Hamiltonian which treats core-valence correlations with a semiempirical approach. Various higher-order polarizabilies were computed, and this permitted a more refined analysis of the energy intervals measured by resonant excitation Stark ionization spectroscopy (RESIS). The polarizability derived from the revised analysis of the RESIS data was $11.669(9)\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$, only 0.03% larger than that reported in Komara et al. [J. Phys. B 38, 87 (2005)]. The CI value of the polarizability, $11.688\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$, was only 0.2% larger than experiment, while the quadrupole polarizability of $35.75\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ was also consistent with experiment. A resonant oscillator strength of 1.621(3) was derived from the experimental dipole polarizability.

Fine-structure measurements in high-Ln=17and 20 Rydberg states of barium

Fine-structure intervals in $n=17$ and 20 barium Rydberg levels with $6\ensuremath{\le}L\ensuremath{\le}11$ have been measured precisely with the resonant excitation Stark ionization spectroscopy microwave technique. The measured intervals were analyzed using the long-range polarization model, including allowance for the large nonadiabatic effects of the ${\text{Ba}}^{+}$ $5d$ level and the contributions of higher-order terms. The analysis determined improved values in atomic units of both dipole and quadrupole polarizabilities of ${\text{Ba}}^{+}$, ${\ensuremath{\alpha}}_{1}=123.88(5)$ and ${\ensuremath{\alpha}}_{2}=4420(250)$.

Polarizability ofKr6+from high-LKr5+fine-structure measurements

The transition between $n=55$ and $n=109$ Rydberg levels of ${\mathrm{Kr}}^{5+}$ has been studied at high resolution using the resonant excitation stark ionization spectroscopy method. Resolved excitation of $L=6$, 7, 8, and 9 levels in $n=55$ lead to a determination of the fine-structure energies of these levels. Interpreted with the long-range polarization model, this leads to a measurement of the dipole polarizabilities of Zn-like ${\mathrm{Kr}}^{6+}$, ${\ensuremath{\alpha}}_{d}=2.69(4){a}_{0}^{3}$. Obtaining a value of the quadrupole polarizability from the data will require additional theoretical input. Factors contributing to the signal and noise levels in measurements of this type are discussed.

Determination of dipole and quadrupole polarizabilities ofBa+by measurement of the fine structure of high-Ln=9and 10 Rydberg states of barium

The fine structure of high-angular-momentum n=9 and 10 Rydberg states of barium has been measured precisely, using the resonant excitation Stark ionization spectroscopy method. Optical transitions corresponding to (n,n{sup '})=(10,30) (9,17), and (9,20) were induced with a Doppler-tuned CO{sub 2} laser, determining the fine-structure energies corresponding to all n=9 and 10 levels with L{>=}6. The pattern of these fine-structure energies conforms closely with an effective potential model, by comparison with which the dipole and quadrupole polarizabilities of Ba{sup +} can be determined. Combining our data with earlier measurements made it possible to deduce, in addition, the portion of {alpha}{sub 2} due to the lowest excited D state of Ba{sup +}. Our best estimates of these three properties are {alpha}{sub 1}=124.30(16)a{sub 0}{sup 3}, {alpha}{sub 2}=2462(361)a{sub 0}{sup 5}, and {alpha}{sub 2}{sup 0}=1828(88)a{sub 0}{sup 5}.