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The hydrogen molecule is the simplest neutral molecule. This simplicity makes it one of the best calculable systems and thus a principal testbed for comparisons between measurements and ab initio calculations. These calculations are based on quantum electrodynamics (QED), and by extension the Standard Model. One of the best calculable properties of H2 is the dissociation energy (D0) of the ground state, the lowest amount of energy that is needed to dissociate the molecule into two separate atoms. The same holds for the deuterated isotopologues, HD and D2. Over the last century, the uncertainties in the experimental and theoretical values of D0 have been reduced by eight orders of magnitude. The first part of Chapter 1 describes previous measurements and calculations of D0, and how these are used to test fundamental physics. In this thesis a more accurate value of D0 is determined from the ionization energies of the neutral molecule, the molecular ion and the atoms. The ionization energy of the neutral molecule is determined by combining measurements on the GK1Σ+g-X1Σ+g transition with measurements of the ionization energy of the GK1Σ+g state. The ionization energy of the GK1Σ+g state is determined by measurements on high lying Rydberg states and extrapolating the Rydberg series to the ionization continuum using Multi-channel Quantum Defect Theory. To generate laser light at a wavelength of 179 nm, required to drive the GK1Σ+g-X1Σ+g two-photon transition, a special KBBF crystal is exploited, using second-harmonic generation of 358 nm pulses. The 358 nm pulses are generated by the upconversion of 716 nm pulses using a BBO crystal. The 716 nm pulses are the output of a narrowband Ti:Sa oscillator-amplifier system. The oscillator-amplifier system is seeded by a continuous wave (cw) Ti:Sa seed laser. To stabilise the frequency of the 716 nm laser light the cw Ti:Sa seed laser is locked to an optical frequency comb, which is referenced by a Cs-clock. The second part of Chapter 1 describes the used methods and introduces the experimental setup. The first part of Chapter 5 describes the molecular beam, and the detection process. There are four main sources of systematic offsets on the determined frequency of the GK1Σ+g-X1Σ+g two-photon resonance: frequency-chirp, AC-Stark effects, Doppler effects and hyperfine structure. Frequency-chirp is reduced using an intra-cavity EOM, and any residual chirp is measured shot-by-shot and compensated for. Chapter 4 describes the effect of frequency-chirp in pulse generation and the scheme to measure and counteract it. Systematic offsets due to AC-Stark effects are assessed by measuring the transition at different laser intensities. The first order Doppler effect is reduced by performing the two-photon transition in a counter-propagating configuration. Any systematic offset due to a residual Doppler effect is assessed by measuring the transition at different molecular beam velocities. Possible uncertainties due to hyperfine splittings, are extrapolated from the known hyperfine structure of high-lying Rydberg states. The GK1Σ+g-X1Σ+g transition was measured at sub-MHz accuracy in both spin isomers of H2 (ortho- and para-H2) and in D2 and HD. These four measurements, and all systematic effects involved, are described in Chapter 2, 3, 5 and 6 respectively. The results of these measurements lead to the improved determination of the dissociation energies of para-H2, ortho-H2 and D2, reducing the relative uncertainty to below 10^(−9), and will lead to an improved determination of the dissociation energy of HD in the near future. Due to these results the strength of a hypothetical fifth-force with an interaction range of 1 ˚A must be 10 orders of magnitude weaker than the electromagnetic force. Chapter 7 describes the impact of these measurements, and an outlook on further measurements.

The hydrogen molecule is the simplest neutral molecule. This simplicity makes it one of the best calculable systems and thus a principal testbed for comparisons between measurements and ab initio calculations. These calculations are based on quantum electrodynamics (QED), and by extension the Standard Model. One of the best calculable properties of H2 is the dissociation energy (D0) of the ground state, the lowest amount of energy that is needed to dissociate the molecule into two separate atoms. The same holds for the deuterated isotopologues, HD and D2. Over the last century, the uncertainties in the experimental and theoretical values of D0 have been reduced by eight orders of magnitude. The first part of Chapter 1 describes previous measurements and calculations of D0, and how these are used to test fundamental physics. In this thesis a more accurate value of D0 is determined from the ionization energies of the neutral molecule, the molecular ion and the atoms. The ionization energy of the neutral molecule is determined by combining measurements on the GK1Σ+g-X1Σ+g transition with measurements of the ionization energy of the GK1Σ+g state. The ionization energy of the GK1Σ+g state is determined by measurements on high lying Rydberg states and extrapolating the Rydberg series to the ionization continuum using Multi-channel Quantum Defect Theory. To generate laser light at a wavelength of 179 nm, required to drive the GK1Σ+g-X1Σ+g two-photon transition, a special KBBF crystal is exploited, using second-harmonic generation of 358 nm pulses. The 358 nm pulses are generated by the upconversion of 716 nm pulses using a BBO crystal. The 716 nm pulses are the output of a narrowband Ti:Sa oscillator-amplifier system. The oscillator-amplifier system is seeded by a continuous wave (cw) Ti:Sa seed laser. To stabilise the frequency of the 716 nm laser light the cw Ti:Sa seed laser is locked to an optical frequency comb, which is referenced by a Cs-clock. The second part of Chapter 1 describes the used methods and introduces the experimental setup. The first part of Chapter 5 describes the molecular beam, and the detection process. There are four main sources of systematic offsets on the determined frequency of the GK1Σ+g-X1Σ+g two-photon resonance: frequency-chirp, AC-Stark effects, Doppler effects and hyperfine structure. Frequency-chirp is reduced using an intra-cavity EOM, and any residual chirp is measured shot-by-shot and compensated for. Chapter 4 describes the effect of frequency-chirp in pulse generation and the scheme to measure and counteract it. Systematic offsets due to AC-Stark effects are assessed by measuring the transition at different laser intensities. The first order Doppler effect is reduced by performing the two-photon transition in a counter-propagating configuration. Any systematic offset due to a residual Doppler effect is assessed by measuring the transition at different molecular beam velocities. Possible uncertainties due to hyperfine splittings, are extrapolated from the known hyperfine structure of high-lying Rydberg states. The GK1Σ+g-X1Σ+g transition was measured at sub-MHz accuracy in both spin isomers of H2 (ortho- and para-H2) and in D2 and HD. These four measurements, and all systematic effects involved, are described in Chapter 2, 3, 5 and 6 respectively. The results of these measurements lead to the improved determination of the dissociation energies of para-H2, ortho-H2 and D2, reducing the relative uncertainty to below 10^(−9), and will lead to an improved determination of the dissociation energy of HD in the near future. Due to these results the strength of a hypothetical fifth-force with an interaction range of 1 ˚A must be 10 orders of magnitude weaker than the electromagnetic force. Chapter 7 describes the impact of these measurements, and an outlook on further measurements.

Nowadays scientific study of Cultural Heritage accompanies most of the time historical artistic evaluation and an assessment of the conservation state by humanistic experts and restorers. Several laboratory methods with high sensitivity are well established (ICP-MS, FTIR,…), and many methods for in situ rough characterization of large surface are widely diffused (thermovision, UV photography,…), in addition to instrumentation for punctual analysis to be applied also in field (XRF, colorimetry,…). However, the request for systems that can provide rapid detailed characterization on large surface in any storage conditions is still a hot topic. This is combined with the ever-increasing demand for digital material for documentation, fruition and study. Laser-based systems, and in particular Laser Induced Fluorescence (LIF), Laser Induced Breakdown Spectroscopy and Raman spectroscopy, due to the characteristics of these sources and the detectors to which they can be coupled, respond well to these needs. The TECFIS-DIM (Diagnostic and Metrology) Laboratory of the ENEA center of Frascati (Rome, Italy) in the last decade has put an effort to develop more and more compact and efficient laser systems for in situ material characterization on cultural heritage surfaces. Here two prototypal LIF systems have been used to characterize marble surfaces treated with ancient and modern materials and a rapid recognition and mapping method has been developed and tested thanks to the individuation of discriminant spectral features. Results are reported on test samples created in lab with known substances and in situ on real artworks.