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Precision measurements of transitions between singlet ($S=0$) Rydberg states of H$_2$ belonging to series converging on the $\mathrm{X}^+\,^2\Sigma_g^+(v^+=0,N^+=0)$ state of H$_2^+$ have been carried out by millimetre-wave spectroscopy under field-free conditions and in the presence of weak static electric fields. The Stark effect mixes states with different values of the orbital-angular-momentum quantum number $\ell$ and leads to quadratic Stark shifts of low-$\ell$ states and to linear Stark shifts of the nearly degenerate manifold of high-$\ell$ states. Transitions to the Stark manifold were observed for the principal numbers 50 and 70, at fields below 50 mV/cm, with linewidths below 500~kHz. The energy-level structure was calculated using a matrix-diagonalisation approach, in which the zero-field positions of the $\ell\leq 3$ Rydberg states were obtained either from multichannel-quantum-defect-theory calculations or experiment, and those of the $\ell\geq 4$ Rydberg states from a long-range core-polarisation model. This approach offers the advantage of including rovibronic channel interactions through the MQDT treatment while retaining the advantages of a spherical basis for the determination of the off-diagonal elements of the Stark operator. Comparison of experimental and calculated transition frequencies enabled the quantitative description of the Stark manifolds, with residuals typically below 50 kHz. We demonstrate how the procedure leads to quantum defects and binding energies of high Rydberg states with unprecedented accuracy, opening up new prospects for the determination of ionisation energies in molecules., Comment: 18 pages, 12 figures

We report on the measurement and analysis of photoionisation, mass-analysed-threshold-ionisation and pulsed-field-ionisation zero-kinetic-energy photoelectron spectra of HD in the vicinity of the dissociative-ionisation thresholds H$^+$ + D(1s) + e$^-$ and H(1s) + D$^+$ + e$^-$. The spectra were recorded via the $v=11$-13 vibrational levels of the $\bar{\rm H}$ and $\bar{\rm B}$ outer wells of the H$\bar{\rm H}$~$^1\Sigma_g^+$ and B$^{\prime\prime}\bar{\rm B}$~$^1\Sigma_u^+$ states and provide information on the weakly bound levels of the X$^+$ $^2\Sigma_g^+$ ground state of HD$^+$ with vibrational quantum numbers $v^+=16$-21 and rotational angular-momentum quantum numbers $N^+=0$-10. The spectra also reveal for the first time shape and Feshbach resonances of HD$^+$ located energetically above the H$^+$ + D(1s) dissociation limit. The structure and dissociation dynamics of the $\bar{\rm H}$ and $\bar{\rm B}$ states of HD and of the X$^+$ $^2\Sigma_g^+$ and A$^+$ $^2\Sigma_u^+$ states of HD$^+$ near the dissociation thresholds are strongly influenced by the g/u-symmetry breaking caused by the nuclear-mass asymmetry., Comment: 21 pages, 10 figures

A compact frequency-doubled diode-pumped Nd:YAG master-oscillator power-amplifier laser system with programmable microsecond pulse length has been developed. Analog pulse shaping of the output from a single-frequency continuous-wave Nd:YAG oscillator, and subsequent amplification, allowed the generation of rectangular pulses with pulse lengths on the order of the Nd:YAG fluorescence lifetime. Temporally flat-top pulses of 1064 nm light with 520 mJ pulse energy, 2.6 kW peak power, and 200 $\mu$s duration, with linewidth below 10 kHz, were obtained at a repetition rate of 2 Hz. Second harmonic generation in a LBO crystal yielded pulses of 262 mJ and 1.3 kW peak power at 532 nm. The peak power can be maintained within 2.9% over the duration of the laser pulse, and long-term intensity stability of 1.1% was observed. The spatially flat-top beam at 1064 nm used in the amplifier is converted to a Gaussian beam at 532 nm with beam quality factor $M^2=1.41(14)$ during the second harmonic generation. This system has potential as a pump source for Ti:sapphire, dye, or optical parametric amplifiers to generate tunable high-power single-frequency radiation for applications in precision measurements and laser slowing., Comment: 9 pages, 5 figures

The dissociation energy of H$_2$ represents a benchmark quantity to test the accuracy of first-principles calculations. We present a new measurement of the energy interval between the EF $^1\Sigma_g^+(v=0,N=1)$ state and the 54p1$_1$ Rydberg state of H$_2$. When combined with previously determined intervals, this new measurement leads to an improved value of the dissociation energy $D_0^{N=1}$ of ortho-H$_2$ that has, for the first time, reached a level of uncertainty that is three times smaller than the contribution of about 1 MHz resulting from the finite size of the proton. The new result of 35999.582834(11) cm$^{-1}$ is in remarkable agreement with the theoretical result of 35999.582820(26) cm$^{-1}$ obtained in calculations including high-order relativistic and quantum electrodynamics corrections, as reported in the companion article (M. Puchalski, J. Komasa, P. Czachorowski and K. Pachucki, submitted). This agreement resolves a recent discrepancy between experiment and theory that had hindered a possible use of the dissociation energy of H$_2$ in the context of the current controversy on the charge radius of the proton.

Although the existence of quasi-bound rotational levels of the $X^+ \ ^2\Sigma_g^+$ ground state of H$_2^+$ has been predicted a long time ago, these states have never been observed. Calculated positions and widths of quasi-bound rotational levels located close to the top of the centrifugal barriers have not been reported either. Given the role that such states play in the recombination of H(1s) and H$^+$ to form H$_2^+$, this lack of data may be regarded as one of the largest unknown aspects of this otherwise accurately known fundamental molecular cation. We present measurements of the positions and widths of the lowest-lying quasi-bound rotational levels of H$_2^+$ and compare the experimental results with the positions and widths we calculate using a potential model for the $X^+$ state of H$_2^+$ which includes adiabatic, nonadiabatic, relativistic and radiative corrections to the Born-Oppenheimer approximation., Comment: 5 pages, 3 figures

The pulsed-field-ionization zero-kinetic-energy photoelectron spectrum of H$_2$ has been recorded in the vicinity of the dissociative-ionization threshold following three-photon excitation via selected rotational levels of the B $^1\Sigma_u^+$ ($v=19$) and $\bar{\rm H}$ $^1\Sigma_g^+$ ($v=11$) intermediate states. The spectra consist of transitions to bound levels of the X$^+$ $^2\Sigma_g^+$ state of H$_2^+$ with $v^+$ in the range 14-19 and $N^+$ in the range 0-9, of the A$^+$ $^2\Sigma_u^+$ state with $v^+=0$ and $N^+=0-2$, and of shape resonances corresponding to the X$^+\ (v^+=17,N^+=7)$ and X$^+\ (v^+=18,N^+=4)$ quasibound levels. Calculations of the level structure of H$_2^+$ have been carried out and the influence of adiabatic, nonadiabatic, relativistic and radiative corrections on the positions of these levels, and in the case of the shape resonances also on their widths, has been investigated. Different methods of calculating the widths and profiles of the shape resonances have been tested for comparison with the experimental observations. Slow oscillations of the dissociative-ionization yield have been observed and reflect, in first approximation, the Franck-Condon factors of the $\bar{\text H}$ $\rightarrow$ X$^+$, A$^+$ bound - free transitions.