Effective Quantum Number Research Articles

Lifetime measurements of highly excited Rydberg states of strontium I

Lifetimes of Rydberg states of the triplet-series 5s ns3S1 withn = 19–23, 35 and 5s nd3D3 withn = 18–20, 23–28 in the spectrum of neutral strontium have been determined. Observation of the exponential decay after excitation by a pulsed laser in a fast atomic beam and subsequent state-selective field ionization was employed. The lifetimes of the states of the3S1-series show the expectedn*3 dependence on the effective principal quantum number, while the3D3-series is disturbed by configuration mixing. Furthermore, state re-populations induced by black-body radiation have been observed.

Photoionisation of S VII from four lowest 1Se, 3Po, 1Po and 3Se states using R-matrix method

The R-matrix method is used to obtain cross-sections for the photoionization of the ground 1s22s22p6 1Se and first three excited 1s22s22p53s3, 1Po, 1s22s2 2p5 3p3Se states of S VII, for photon energies ranging from first ionization threshold to just above second threshold 2s2p62Se of the residual ion S VIII. The positions and effective quantum numbers for the Rydberg series corresponding to 2s2p62Se arising in the photoionization cross-sections are predicted.

Ionization of Rydberg atoms by subpicosecond half-cycle electromagnetic pulses

We have ionized Rydberg atoms using subpicosecond half-cycle electromagnetic pulses. The threshold electric field required to ionize a Rydberg state with effective quantum number ${\mathit{n}}^{\mathrm{*}}$ is found to scale as ${\mathit{n}}^{\mathrm{*}\mathrm{\ensuremath{-}}2}$ for states with ${\mathit{n}}^{\mathrm{*}}$>13 in contradistinction to the ${\mathit{n}}^{\mathrm{*}\mathrm{\ensuremath{-}}4}$ threshold scaling for static field ionization and high order multiphoton ionization. This novel result is explained using a classical model.

Prequark-antilepton-symmetric electroweak model

We present an electroweak theory based on a composite model in which electroweak and color charges are effective low-energy quantum numbers and the pre-states of quarks and leptons of the first generation are the fundamental particles, with an underlying dynamics being prequark-antilepton symmetric. The three generations of physical states, however, are put on an equal footing as elementary and composite («generation democracy»). All the features of the standard model are accounted for except that one Higgs doublet for each basic fermion and a mixed spin-0 field are included, which break a high-energy extended electroweak symmetry and give rise to an additional set of heavier left-handed weak bosons, having equal mass and no universality. The model provides a deep unification of strong and electroweak interactions,i.e. color and flavor, and also an intimate relation between the number of quark colors and flavor generations.

Photoelectron studies of the resonant excitation and ionization of the Kr 3d inner subshell in the low kinetic energy region

Photoexcitation of the Kr 3d to np resonances and photoionization of the 3d inner shell have been studied by measuring the emitted electrons with energies from 0 to 3 eV and from 0 to 12 eV, respectively. Intense discrete structure due to the Kr+ to Kr2+ transitions has been observed in photoelectron spectra. Assignments are proposed based on the spectator shake model and by analysis of effective quantum numbers of proposed Kr+ states. The observed energy shift and asymmetric line broadening, related to the post-collision interaction, of the Kr+ 3d-1(2D512.3) ionic states have been compared with previous experimental results and with theoretical predictions.

Observation of the Stark effect in autoionizing Rydberg states of Ar with a multichannel quantum-defect analysis

The Stark spectra of autoionizing Rydberg states of Ar converging to the second ionization limit 3p5 2P1/2 have been investigated, experimentally and theoretically, as a function of electric field strength, in the range 15-2000 V cm-1. The levels with effective principal quantum number v=12-19, are excited by single-photon absorption from the ground state using a coherent extreme ultraviolet laser source (bandwidth approximately 1.0 cm-1) generated by four-wave sum-frequency mixing of the outputs of two pulsed dye lasers; a detailed Stark map is obtained for the first time. A multichannel quantum-defect-theory analysis of the field-induced-state mixing is carried out, reproducing positions, widths and shapes of the experimentally observed features. In addition, this analysis provides new insight into the dynamical decay of the autoionizing states.

On theJ-dependence of the odd (ns?,J=0,1) autoionization resonances of the rare gases Ne, Ar, Kr, and Xe

Using resonant two-photon ionization of metastable rare gas atoms Rg(mp5(m + 1)s3P2,0) in a collimated beam by two transverse cw dye lasers, we have performed a comprehensive high resolution study of the odd Rg(ns′,J=0,1) autoionization resonances of all the heavier rare gases Rg=Ne, Ar, Kr and Xe. In this way, we have determined the variation of the nearlyn-independent reduced resonance widths Γr=n*3 · Γn (n*=effective quantum number) with atomic size and — for the first time — with the angular momentumJ for all Rg. The reduced widths for the Rg(ns′,J=1) resonances vary by about a factor of three, being lowest for Ne(371 cm−1) and largest for Kr(1185 cm−1). Compared toJ=1, the Rg(ns′,J=0) resonances are three times narrower for Ne, but up to two times broader for Ar, Kr, and Xe. The results of ab initio calculations for the widths are reported, in which the relevant transition matrix elements are carefully evaluated. Good overall agreement of the calculated widths with the experimental data is achieved. For Rg(ns′,J=0), the first orders′−d coupling amplitude provides a satisfactory description only for Rg=Ne, whereas for Rg=Ar−Xe, correlation effects are important. For Rg(ns′,J=1), the additional amplitudes due tos′−d exchange coupling and due tos′−s decay are found to be of varying importance with atomic number. Destructive interference between the different amplitudes and the influence of Rg(ns′,J=1)−Rg(nd′,J=1) coupling are responsible for the fact that the (ns′,J=1) resonances are narrower than the (ns′,J=0) resonances for Ar, Kr, and Xe.

Atomic data for opacity calculations. XV. Fe I-IV

Photoexcitation and photoionization processes are examined for ground and excited terms of Fe I, Fe II, Fe III and Fe IV. An LS coupling R-matrix approach is used in a seventeen target term expansion for Fe I, including 3d7, 3d6(5D)4S, 3d6(5D)4p and 3d5(6S)4s2 configurations; and sixteen term expansions for Fe II, Fe III and Fe IV, including 3d6, 3d5 and 3d4 configurations respectively. Data for even and odd LS terms having S<or=3; L<or=7 and effective principal quantum numbers up to 10 are calculated. Over six thousand term energies and nearly half a million dipole oscillator strengths are calculated. The photoionization cross section is tabulated for all bound terms over a fine mesh of photon energies to elucidate the low-energy resonance structure.

Highly excited vibrational states of the KCN molecule

Vibrational (J= 0) states for the KCN molecule are calculated in Jacobi coordinates, employing a discrete variable representation (DVR) for the angular internal coordinate. The power of the DVR method is once again illustrated in that some 800 vibrational (J= 0) states are converged for a two-dimensional potential-energy surface. The energy region studied is that where the classical dynamics of the system are known to be chaotic. Most of the states are found to be irregular, although there are classes which appear to be regular and can be assigned effective quantum numbers corresponding to excitation in particular ‘separable’ modes of the system. Phenomenological aspects of the wavefunctions are discovered via graphical analysis, in particular many linearly localised states are identified where the potential-energy surface actually has a saddle point. The statistical behaviour of the level spacings is also investigated. Comparison with a similar study on LiCN (J. R. Henderson and J. Tennyson, Mol. Phys., 1990, 69, 639) is made.

Quantum defects and the 1/n dependence of Rydberg energies: Second-order polarization effects.

The principal result of this paper is a general expression for the second-order dipole polarization energy of a Rydberg electron resulting from the term -${\mathrm{\ensuremath{\alpha}}}_{1}$/${\mathit{r}}^{4}$ in the asymptotic potential, where ${\mathrm{\ensuremath{\alpha}}}_{1}$ is the core polarizability. It is shown that the second-order term contributes even as well as odd powers of 1/n in a 1/n expansion of the energies for Rydberg states. The results are used to extend the interpretation of the terms in a quantum-defect expansion. It is shown that the Ritz expansion for the quantum defect, which contains only even inverse powers of the effective quantum number ${\mathit{n}}^{\mathrm{*}}$, provides a powerful method for deducing the even-order terms in the second-order energy. Least-squares fits to high-precision variational calculations for the Rydberg states of helium, using 1/n and quantum-defect expansions, are presented. The results reveal well-defined ``Ritz defects,'' which represent the degree to which the data cannot be represented by a Ritz expansion for the quantum defect. The implications for extrapolations of quantum defects are discussed. Finally, it is shown that the second-order polarization energy plays a significant role in understanding the quantum defects for the alkali metals.

Semiclassical formula for radial integrals of bound-bound dipole transitions

For the calculation of radial integrals of dipole transitions between nu l and nu 'l' Rydberg states of a non-hydrogenic atom or positive ion a general formula for any Delta nu (0( Delta nu ( infinity ) is developed using the semiclassical and Coulomb approximations. In the limiting case Delta nu << nu the formula is equivalent to the known one. The main point of this paper is the choice of the mean value of the effective principal quantum number as nu c=(2 nu 2v'2/( nu + nu '))13/. This choice ensures the correct behaviour in the region near the continuum threshold. The conditions of validity are examined. The criterion of applicability of the Coulomb approximation is obtained. Comparison with the results of the previous papers is made.

New approach of level-fitting calculations in multiconfiguration approximation. a test on the silicon atom

We report a new method of level-fitting calculations (FS-fit, fine structure fit) in a large multiconfiguration basis. This method allows inclusion of all electrostatic and spin-orbit interactions predicted for the system under study. This has been achieved without accruing interaction parameters faster than level data by relating interaction parameters to the ratios determined on the basis of their effective quantum numbers. The method has been tested for the system consisting of 33 configurations of Si I and a very good FS-fit has been achieved with a mean deviation of 4 cm−1. The method proposed should also yield eigenvectors that can be used to calculate other physical observables with a comparable precision. Moreover, we are able to predict a destructive interference effect on the line strength due to the relative phases of eigenvectors. An example of the absence of some transitions in the silicon spectrum is discussed.

Recurrence relations for multipole radial integrals in the semiclassical Coulomb approximation.

It is shown that in the semiclassical (WKB) Coulomb approximation the radial integrals for multipole transitions in nonhydrogenic atoms obey simple recurrence relations. As a result, any such integral can be analytically expressed in terms of Anger functions plus an algebraic part proportional to sin\ensuremath{\pi}s, where s=\ensuremath{\nu}'-\ensuremath{\nu} is the difference between the effective principal quantum numbers of the states involved. We retrieve, in particular, various formulas established previously for dipole, quadrupole, and octupole transitions.

Resonant scattering of low-energy electrons by Be+ and Mg+ ions

The electron impact excitation cross section for resonance transitions of Be+ and Mg+ is calculated by the diagonalisation method. The energies, effective quantum numbers, total and partial widths of resonances in cross sections are obtained. The partial and differential cross sections were also obtained. The total cross sections were compared with experiment and other calculations.

Isotope-dependent rate constants for CS−2 formation in Cs (n s,n d)+CS2 collisions

Negative ion formation during collisions between Cs (ns,nd) Rydberg atoms and CS2 molecules has been studied for intermediate values of the effective principal quantum number (n*=10–26). Rate constants for CS−2 formation are found to be different for the two isotopes C32S34S and C32S32S for a narrow range of n* near n*=17, with the rate constant for 12C32S34S− production being up to 4.5 times larger than that for 12C32S32S−.

Spectrum and energy levels of six-times-ionized molybdenum (Mo vii)

The spectrum of the kryptonlike ion Mo vii was observed from 140 to 2274 A with sliding-spark discharges on 10.7-m normal- and grazing-incidence spectrographs. Experimental energies were determined for all levels of the 4s24p6, 4s24p54d, 4f, 5s, 5p, 5d, 5f, 5g, and 4s4p64d configurations. A few levels of the 4s24p44 4d2 configuration were also found. A total of 399 lines were classified as transitions between 86 observed levels. The observed configurations were theoretically interpreted. The energy parameters determined by least-squares fits to the observed levels are compared with Hartree–Fock calculations. A revised value of the ionization energy was obtained by using the energy of the 4p55g configuration together with an isoelectronically extrapolated value of the effective quantum number n*(5g). The adopted limit is 1 013 340 ± 200 cm−1 (125.64 ± 0.02 eV).

Laser spectroscopy measurement of radiative lifetimes of highly excited thulium Rydberg states

The radiative lifetimes τrad of the highly excited 4f7/2136s1/2(4)np3/2[11/2](n=21−31) Rydberg Tm states have been measured with the method of multistep laser excitation and electric field ionization. The lifetime values have been obtained with an accuracy of better than 15%. The influence of blackbody radiation on the states with n ≥ 27 has been observed. The experimental results are in good agreement with our previously calculated values obtained by relativistic perturbation theory with a zero-order model approximation. It has been shown that the τrad-versus-n* dependence (n* is the effective principal quantum number) is best described by the relation τrad = 0.0022.(n*)2.46 (μsec). This property may be attributed to the strongly expressed nonhydrogenlike behavior of the investigated states, which is caused by the essentially non-Coulombic core potential acting on the Rydberg electron.

Magnetic quadrupole transition rates and Rydberg states of the magnesium isoelectronic sequence

Excitation energies for the spin-forbidden transitions 3 1S to n3P (n = 3-8) have been calculated for the isoelectronic series of magnesium up to Z = 18, and analytic representations of the singly excited Rydberg states are obtained using the time-dependent linear response theory. The magnetic quadrupole (M2) transition rates have been estimated using the excited state wavefunctions, and the effective quantum numbers for the Rydberg orbitals are evaluated using the complete screening model. Results are compared with existing data wherever available. Satisfactory agreement is observed throughout. 37 refs.

Scaling of radiative collisions between Rydberg atoms.

We have measured the n dependence of the microwave field required to make the single-photon radiatively assisted collision process Na(ns)+Na(ns)+kh\ensuremath{\nu}\ensuremath{\rightarrow}Na(np)+Na ((n-1)p)+(k+m)h\ensuremath{\nu}, m=1, 10% as likely as the resonant collision process in which no photons are absorbed, m=0. Experimentally we find an ${n}^{\mathrm{*}}$ dependence of [2.06(15)\ifmmode\times\else\texttimes\fi{}${10}^{3}$]${n}^{\mathrm{*}\mathrm{\ensuremath{-}}2.0}$ (V/cm), where ${n}^{\mathrm{*}}$ is the effective quantum number of the Na ns state. Over the range of n studied, 16\ensuremath{\le}n\ensuremath{\le}24, this field is within 20% of the field calculated using a theory based on resonant dipole-dipole collisional energy transfer of microwave dressed atoms.

Two-electron Rydberg law for the ns2 1S0 Wannier states of alkaline-earth atoms

The first quantitative calculations on ns2 1S0 Wannier states of alkaline-earth atoms Be through Ba are presented. The two-electron Hamiltonian built on a discrete basis is diagonalised to give the energy positions of the seven lowest members of each Wannier sequence. For each element, the energies are found to obey a two-electron Rydberg law depending on two parameters, a screening constant sigma ' and a quantum defect correction mu ' to the effective quantum number of the parent state ns. The parameters sigma ' and mu ' are nearly the same for each alkaline earth and, moreover, close to those obtained for helium. Treating each ns2 1S0 Wannier state as the lowest member of a Rydberg series converging to the parent state ns, quantum defects are calculated for each ns ms 1S0 series; the linear n dependence of the computed quantum defects accurately reproduces that observed experimentally in several nsms core-excited Rydberg series of Ca and Ba.