Charge asymmetry and rovibrational excitations of HD+

Average values of the interparticle distances for rovibrationally excited HD⁺ are calculated using a method where the Born–Oppenheimer (BO) approximation is not assumed. The difference between the proton–electron and deuteron–electron distances is used to describe the charge asymmetry in the system. All-particle one-centre explicitly correlated Gaussian functions are used in the calculations of the HD⁺ rovibrational states. In this work, the non-BO method is extended to calculate the rovibrational states corresponding to the total rotational quantum number of two (N = 2). The algorithms for calculating the Hamiltonian and overlap matrix elements, and the matrix elements of the analytical energy gradient determined with respect to the exponential parameters of the Gaussians, are presented. The gradient is employed in the variational optimisation of the parameters, which is key in obtaining very accurate rovibrational energies in the calculations. The algorithm for calculating the average interparticle distances is also shown. The charge asymmetry of HD⁺ near the dissociation limit occurs, as expected, with the electron preferentially being near to the deuteron. The asymmetry for a particular vibrational level increases with rotational excitations. The rovibrational transition energies are also calculated and compared with available experimental data.     

Wave-particle duality of solitons and solitonic analog of the Ramsauer-Townsend effect

We study the interaction of light beams carrying angular momentum with a single, trapped and well localized ion. We provide a detailed calculation of selection rules and excitation probabilities for quadrupole transitions. The results show the dependencies on the angular momentum and polarization of the laser beam as well as the direction of the quantization magnetic field. In order to optimally observe the specific effects, focusing the angular momentum beam close to the diffraction limit is required. We discuss a protocol for examining experimentally the effects on the S_1/2 to D_5/2 transition using a ⁴⁰Ca⁺ ion. Various applications and advantages are expected when using light carrying angular momentum: in quantum information processing, where qubit states of ion crystals are controlled, parasitic light shifts could be avoided as the ion is excited in the dark zone of the beam at zero electric field amplitude. Such interactions also open the door to high dimensional entanglement between light and matter. In spectroscopy one might access transitions which have escaped excitation so far due to vanishing transition dipole moments.     

High sensitivity ICLAS of H2O in the region of the second decade (11 520-12 810 cm)

The high resolution absorption spectrum of the H₂¹⁸O isotopologue of water has been recorded by Intracavity Laser Absorption Spectroscopy (ICLAS) with a sensitivity on the order of α_min ∼ 10⁻⁹ cm⁻¹. The 11 520-12 810 cm⁻¹ spectral region corresponding to the 3ν + δ decade of vibrational states, was explored with an ICLAS spectrometer based on a Ti:Sapphire laser. It allowed detecting transitions with an intensity down to 10⁻²⁷ cm/molecule which is about 100 times lower than the weaker line intensities available in the literature, in particular in the HITRAN database.The rovibrational assignment was performed on the basis of the results of variational calculations and allowed for assigning 3659 lines to the H₂¹⁶O, H₂¹⁸O, H₂¹⁷O, HD¹⁶O and HD¹⁸O species, leaving only 1.7% unassigned transitions. A line list including 1712 transitions of H₂¹⁸O has been generated and assigned leading to the determination of 692 rovibrational energy levels belonging to a total of 16 vibrational states, 386 being newly observed. A deviation on the order of 25% has been evidenced for the average intensity values given by HITRAN and the results of variational calculations. Ninety two transitions of the HD¹⁸O isotopologue could also be assigned and the corresponding upper rovibrational levels are given.     

Determination of Г3 valence band in CuCl by two-photon absorption

We present the first two-photon measurements of higher band to band transitions in CuCl far beyond the well-known exciton transitions. Our measurements allow to locate the Г^v₃ valence band. This band cannot be observed in one-photon absorption in a transition to the lowest conduction band of Г^c₁ symmetry. Our assignment, which we confirm by the observed polarization dependence, should be used to reinterpret recent one-photon data.     

Techniques to Treat the Continuum Applied to Electromagnetic Transitions in 8Be

Bremsstrahlung emission in collisions between charged nuclei is equivalent to nuclear gamma decay between continuum states. The way the continuum spectrum can be treated is not unique, and efficiency and accuracy of cross section calculations depend on the chosen method. In this work we describe, relate, and compare three different methods in practical calculations of inelastic cross sections, that is, by (i) treating the initial and final states as pure continuum states on the real energy axis, (ii) discretizing the continuum states on the real energy axis with a box boundary condition, and (iii) complex rotation of the hamiltonian (complex scaling method). The electric quadrupole transitions, 2⁺ → 0⁺ and 4⁺ → 2⁺, in α + α scattering are taken as an illustration.     

Atomic and molecular ions in intense ultra-fast laser fields

The interaction of a 60 fs 790 nm laser pulse with beams of Ar⁺, C⁺, H₂ ⁺, HD⁺ and D₂ ⁺ are discussed. Intensities up to 10¹⁶ Wcm^-2 are employed. An experimental z-scanning technique is used to resolve the intensity dependent processes in the confocal volume.Received: 6 January 2003, Published online: 15 July 2003PACS: 32.80.Fb Photoionization of atoms and ions - 33.80.Rv Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states) - 42.50.Hz Strong-field excitation of optical transitions in quantum systems; multiphoton processes; dynamic Stark shift     

Hyperfine structure and isotope shifts in the 5d6s2 a2D3/2--5d6s(a3D)6p z4F5/2 ° transition of Hf II

The hyperfine structure and isotope shifts of the transition between the 5d6s² a²D_3/2 ground state and the 5d6s(a³D)6p z⁴F_5/2 ^° excited state of singly ionized hafnium at \lambda=340 nm have been investigated by laser spectroscopy using a radio-frequency quadrupole ion trap. The magnetic dipole coupling constant A and electric quadrupole coupling constant B of the two atomic levels for both stable isotopes ¹⁷⁷Hf and ¹⁷⁹Hf are determined. The changes of mean square nuclear charge radii \delta[ r²] of the stable Hf isotopes and the radioactive isotope ¹⁷²Hf (T_1/2=1.87a) have been extracted from the data. This revised version was published online in August 2006 with corrections to the Cover Date.     

High harmonic generation in \textbf{H}_{{2}}^{{+}} and HD + by intense femtosecond laser pulses: A wave packet approach with nonadiabatic interaction in HD +

We have theoretically investigated the high harmonic generation (HHG) spectra of $\textrm{H}_2^+ $ and HD^?+? using a time-dependent wave packet approach for the nuclear motion with pulsed lasers of peak intensities (I ₀) of 3.5 ×10¹⁴ and 4.5 ×10¹⁴ W/cm², wavelengths (λ_L) of 800 and 1064 nm, and pulse durations (T) of 40 and 50 fs, for initial vibrational levels v ₀?=?0 and 1. We have argued that for these conditions the harmonic generation due to the transitions in the electronic continuum by tunnelling or multiphoton ionization will not be important. Thus, the characteristic features of HHG spectra in our model arise only due to the nuclear motions on the two lowest field-coupled electronic states between which both interelectronic and intraelectronic (due to intrinsic dipole moments, for HD^?+?) radiative transitions can take place. For HD^?+?, the effect of nonadiabatic (NA) interaction between the two lowest Born–Oppenheimer (BO) electronic states has been taken into account and comparison has been made with the HHG spectra of HD^?+? obtained in the BO approximation. Even harmonics and a second plateau in the HHG spectra of HD^?+? with the NA interaction and hyper-Raman lines in the spectra of both $\textrm{H}_2^+ $ and HD^?+? for v ₀?=?1 have been observed for higher value of I ₀ or λ_L. Our calculations indicate reasonable efficiencies of harmonic generation even without involving the electronic continuum.     

Structure and optical properties of silicon implanted by high doses of 70 and 310 keV carbon ions

Two-photon excitation spectrum of the luminescence emitted in the A _T -band has been observed in KBr:In⁺ and NaBr:Tl⁺. The nonlinear excitation follows the A-band lineshape but reveals a feature, not present in one-photon spectrum, that may be interpreted as due to the forbidden ¹ A_Ig →³A_Iu transition. The cross section of the process indicates that the two-photon transitions are indirect ones, allowed by phonons. The dependence of the emitted light intensity upon the direction of polarization of the exciting photons, makes it possible to identify the symmetry of the transitions.     

Rovibrational transition properties of the X1Σ+ and A1Π states of carbon monosulfide

Carbon monosulfide was detected in outer space by rovibrational spectroscopy of the X ¹Σ⁺ state and A ¹Π – X ¹Σ⁺ system. This work calculated the potential energy curves and dipole moment functions of the X ¹Σ⁺ ₀₊ and A ¹Π₁ states, and computed the transition dipole moments between the two states employing the CASSCF method, followed by the valence icMRCI approach. Core-valence correlation and scalar relativistic corrections were included. The extrapolation of potential energies to the complete basis set limit was performed. The spin-orbit coupling effect was included. The Einstein A coefficients, band origins, and oscillator strengths were calculated for the rovibrational transitions when J?≤?150. The rovibrational transitions of the X ¹Σ⁺ ₀₊ and A ¹Π₁ states became very weak when Δυ?≥?6. The Einstein A coefficients of vibronic emissions of the A ¹Π₁ – X ¹Σ⁺ ₀₊ system were large, indicating that the emissions were able to be measured easily through spectroscopy. Several rovibrational transitions of the A ¹Π₁ – X ¹Σ⁺ ₀₊ system were analysed in detail. The distribution of radiative lifetime varying as rotational quantum number was calculated. The results obtained in this work agree well with the available experimental values.     

Rovibrational constants for the ground state and ν8 = 1 state of ethylene-d3 (C2HD3) by high-resolution FTIR spectroscopy

The Fourier transform infrared (FTIR) spectrum of the ν₈ fundamental band of ethylene-d₃ (C₂HD₃) was recorded with a unapodized resolution of 0.0063 cm⁻¹ in the wavenumber region of 840–980 cm⁻¹. By assigning and fitting a total of 738 infrared transitions using a Watson’s A-reduced Hamiltonian in the I^r representation, rovibrational constants for the upper state (ν₈ = 1) up to all five quartic centrifugal distortion terms were derived for the first time. The root-mean-square (rms) deviation of the fit was 0.00076 cm⁻¹. The ground state rovibrational constants of C₂HD₃ were also determined for the first time by a fit of 450 combination-differences from the present infrared measurements, with rms deviation of 0.00075 cm⁻¹. Local frequency perturbations were not detected in the C-type ν₈ band of C₂HD₃ which is centred at 918.73199 ± 0.00007 cm⁻¹.     

The dipole polarizability of the hydrogen molecular cation HD+ and other isotopomers

Fully non-adiabatic calculations are reported of the electric dipole polarizabilities for the N = 0 and N = 1 levels of the ground electronic states of H⁺ ₂ (ν ≤ 16), D⁺ ₂ (ν ≤ 24) and HD⁺ (ν ≤ 20). For H⁺ ₂ (ν = 0, N = 0) the calculated value still differs from the experimental value; this difference cannot be explained by the inclusion of higher order contributions.     

Doppler-free two-photon laser spectroscopy of barium I: Hyperfine splitting and isotope shift of high lying levels

The Doppler-free two-photon absorption method performed with a narrowbandc w dye laser permitted high resolution measurements of transitions from the Ba I ground state 6s ^{2 1} S ₀ to several highly excited states. The lifetimes and hyperfine splittings of these states as well as the isotope shifts of the transitions have been determined accurately. The lifetime values are in agreement with transition probability data; the hyperfine splitting results show considerable configuration interaction effects. A detailed discussion of the isotope shifts is given.     

The Infrared Spectrum of C2D2: The Bending States up to v4+v5=2

The vibration-rotation spectrum of ¹³C₂D₂ has been recorded in the infrared region between 420 and 1100 cm⁻¹ with an effective resolution ranging from 0.004 to 0.006 cm⁻¹, and in the millimeter-wave region between 68 and 518 GHz. A total of about 1400 rovibrational transitions (66 of which have been measured in the millimeter-wave region) have been assigned to 8 bands with 15 l-vibrational components involving the bending states up to v_t=v₄+v₅=2. The ground state and nine vibrationally excited states have been characterized. All the measured transitions have been analyzed simultaneously by adopting a model Hamiltonian which takes into account the usual vibration and rotation l-type resonances, together with the Darling-Dennison coupling between the v₄=2 and v₅=2 bending states. The derived spectroscopic parameters reproduce the transition wavenumbers with a standard deviation of the fit of the order of the experimental uncertainty.     

Ab initio nonadiabatic vibrational energies of the hydrogen molecule ion

Nonadiabatic corrections to the four lowest vibrational energy levels of H₂⁺ and HD⁺ are computed by a variational-perturbational method. The results increase the disagreement with experiment of the theoretical 2-1 and 3-2 vibrational transitions and improve the theoretical energy of the 1-0 transition.     

Polarisation-dependent optical pumping for interrogation of a magnetic-field-independent “clock” transition in laser-cooled trapped 87Sr+

We discuss the prospect of using the ⁸⁷Sr⁺ ion as an optical frequency standard. The ion offers a narrow electric quadrupole clock transition which has no first-order Zeeman shifts, and the required wavelengths can be generated with convenient solid-state laser systems. We describe how to cool and probe the ion in zero magnetic field by employing polarisation modulation of the cooling light to avoid coherent population trapping in dark states. The polarisation modulation scheme also provides optical pumping of the ion into the initial state of the narrow clock transition.     

Die Hyperfeinstruktur des 32P3/2-Zustands von Natrium im starken Magnetfeld

The hyperfine structure of the 3²P_3/2 State of Na²³has been measured by the optical double resonance technique in a magnetic field of 3.1 kG sufficiently strong to decouple completelyI andJ. In the case of π or (σ⁺+σ^?) excitation the double resonance signal represents the superposition curve of eight unresolved radio-frequency transitions. The dependence of the signal on the pressure of sodium vapour and the radio-frequency field strength has been studied. The analysis of the experimental curves yields for the hyperfine coupling constants the valuesa=(18.7±0.4) Mc/s andb=(3.4±0.4) Mc/s. The nuclear electric quadrupole moment derived from the ratio ofb/a isQ=(0.146±0.02) · 10^?24cm². The Lande factor and the lifetime for the 3²P_3/2state are g_J=1.3344±0.0004 and τ=(1.61±0.07) · 10^?8 sec.     

The Infrared Spectrum of CCH2: The Bending States up to v4+v5=4

The vibration-rotation spectra of ¹³C monosubstituted acetylene, ¹²C¹³CH₂, have been recorded in the region between 450 and 3200 cm⁻¹ with an effective resolution ranging from 0.004 to 0.006 cm⁻¹. A total of about 5300 rovibrational transitions have been assigned to 53 bands involving the bending states up to v_t=v₄+v₅=4, allowing the characterization of the ground state and of 30 vibrationally excited states. All the bands involving states up to v_t=3 have been analyzed simultaneously by adopting a model Hamiltonian which takes into account the vibration and rotation l-type resonances. The derived spectroscopic parameters reproduce the transition wavenumbers with a RMS value of the order of the experimental uncertainty. Using the same model larger discrepancies between observed and calculated values have been obtained for transitions involving states with v_t=4. These could be satisfactorily reproduced by only adopting, in addition to the previously determined parameters which were constrained in the analysis, a set of effective constants for each vibrational manifold.     

The infrared spectrum of DCCF in the 320–850 cm−1 region: bending states up to υ4+υ5 = 3

Infrared spectra of deuterated monofluoroacetylene, DCCF, have been recorded in the region between 320 and 850 cm^?1 at an effective resolution ranging from 0.0024 to 0.0031 cm^?1. In total, 6650 rotation vibration transitions were assigned to 37 bands involving the bending states with v₄ + v₅ and |l₄+l₅|, respectively, up to 3, allowing the characterisation of the ground state and of 18 vibrationally excited states. The vν₅ bending fundamental has been studied for the first time. In addition, the difference band v₃ ← v₄ has been detected and analysed. All the assigned transitions have been fitted simultaneously by adopting a model Hamiltonian that takes into account the vibration and rotation l?type resonances. Rotational transitions in the ground and in bending excited states reported in the literature have been included in the global analysis. The set of 57 derived spectroscopic parameters reproduces 6130 infrared and 90 microwave and millimetre?wave transitions satisfactorily with root mean square values of 5.3 × 10^?4 cm^?1 and 77 kHz, respectively.     

Dark resonances for ground-state transfer of molecular quantum gases

One possible way to produce ultra-cold, high-phase-space-density quantum gases of molecules in the rovibronic ground state is given by molecule association from quantum-degenerate atomic gases on a Feshbach resonance and subsequent coherent optical multi-photon transfer into the rovibronic ground state. In ultra-cold samples of Cs₂ molecules, we observe two-photon dark resonances that connect the intermediate rovibrational level |v=73,J=2〉 with the rovibrational ground state |v=0,J=0〉 of the singlet X ¹ Σ _g ⁺ ground-state potential. For precise dark resonance spectroscopy we exploit the fact that it is possible to efficiently populate the level |v=73,J=2〉 by two-photon transfer from the dissociation threshold with the stimulated Raman adiabatic passage (STIRAP) technique. We find that at least one of the two-photon resonances is sufficiently strong to allow future implementation of coherent STIRAP transfer of a molecular quantum gas to the rovibrational ground state |v=0,J=0〉.