Field-free resonances

The CIS trapping experiment monitors the population in level 2 by an incoherent ionization step. In the weak-fleld limit of the pump laser this can be compared to an experiment detecting the fluorescence from level 2 to a spectator state (here level 1) at the field-free resonance frequency between levels 1 and 2. In such an experiment no fluorescence is expected at this frequency due to the strong shift of level 2 for resonant dump laser frequency. 

Pure MCD with no rotation occurs if the sample is optically thick and completely absorbing in one circular polarisation, but not in the other. Pure MOR will occur when both circular polarisations are equally absorbed, i.e. the absorption coefficients ot+ v) and ot-(v) are equal, but the refractive indices n+(v) and n-(v) are not equal. The latter condition is satisfied at the centre of symmetry of the rotation pattern, viz. the field-free resonance frequency vq.6 In principle, the situation seems simpler when either pure MOR or pure MCD occurs, which is why most of the effort has traditionally been expended in separating one from the other, leading to MOR and MCD spectroscopies. 

The conceptual framework of the treatment of the field-induced resonances of work discussed in this article follows from the one that has proven useful for the solution of the MEP for field-free resonances. Therefore, the... 

Regardless of the degree of rigor of the principles on which they are based, the methods used in the 1960s for the computation of field-free resonance states had serious intrinsic and/or practical limitations, which is natural given that the field was nascent, while the requirements are very demanding. 

The theory and computational methods for the analysis and calculation of field-free resonances in polyelecfronic afoms and molecules that are adumbrated here were initiated in 1972 [11a] as an alternative to the theoretical approaches mentioned above and in the review articles [12-16, 21], for the purpose of dealing efficiently with the MEP in arbitrary electronic structures. A complementary discussion based on the ideas in Ref. [11a] and on later publications dealing with various topics within energy-dependent and time-dependent frameworks was given a few years later [37b]. 

Table 4.2 Energies and widths of H resonances below the n = 4 threshold, as identified from the implementation of different theories for field-free resonances. The number in brackets, x, implies multiplication of the preceding number by 10 ... 

In analogy to the field-free problem, the "Stark CCR" and the "Floquet CCR" methods have serious limitations with respect to the MEP. The way out was proposed in the late 1980s, when ideas and the general methodology of the SSA for the field-free resonances that solves state-specific CESEs were adapted so as to achieve the nonperturbative solution of problems of interaction of strong dc-and ac- electric fields and static magnetic fields with atomic (molecular) ground or excited states in terms of non-Hermifian formulafions, e.g.. Refs. [103,179-190]. 

When discussing magnetic resonance phenomena, it is conventional to proceed along the lines of standard perturbation theory. If the field-free Hamiltonian is Hq then we write... 

A typical application is the use of the (2 + 1) REMPI scheme for measuring the (v,./) distribution of H2 produced in associative desorption from a surface. When the laser is tuned to a spectroscopic transition between individual quantum states in the X -> E electronic band, resonant two-photon absorption populates the E state and this is subsequently ionized by absorption of another photon. The ion current is proportional to the number in the specific (v,./) quantum state in the ground electronic state that is involved in the spectroscopic transition. Tuning the laser to another spectroscopic feature probes another (v, J) state. Therefore, recording the ion current as the laser is scanned over the electronic band maps out the population distribution of H2(v, J) produced in the associative desorption. Ef of the (v, J) state can also often be simultaneously measured using field - free ion TOF or laser pump - probe TOF detection techniques. The (2 +1) REMPI scheme for detecting H2 is almost independent of the rotational alignment and orientation f(M) of molecules so that only relative populations of the internal states... 

C.A. Nicolaides, Theory and State-Specific Methods for the Analysis and Computation of Field-Free and Field-Induced Unstable States in Atoms And Molecules, Adv. Quant. Chem. 60 (2010) 163 C.A. Nicolaides, Time-Dependence, Complex Scaling and the Calculation of Resonances in Many-Electron Systems, Int. J. Quant. Chem. 14 (1978) 457. 

The first volume contained nine state-of-the-art chapters on fundamental aspects, on formalism, and on a variety of applications. The various discussions employ both stationary and time-dependent frameworks, with Hermitian and non-Hermitian Hamiltonian constructions. A variety of formal and computational results address themes from quantum and statistical mechanics to the detailed analysis of time evolution of material or photon wave packets, from the difficult problem of combining advanced many-electron methods with properties of field-free and field-induced resonances to the dynamics of molecular processes and coherence effects in strong electromagnetic fields and strong laser pulses, from portrayals of novel phase space approaches of quantum reactive scattering to aspects of recent developments related to quantum information processing. 

The interference pattern of the (2p)x - (2p)2 components can be recorded by measuring the intensity of the short lived 2p part of the beam once it has passed through the interferometer. Thus, the detector placed behind zone II (i.e. in the field-free region) must count quanta corresponding to the single-photon transition 2p - Is, i.e. the resonant line of the Lyman series (A = 1216 A). One can also observe the interference of the (2s)x - (2s)2 components occurring in counterphase, for which purpose the beam should be passed through the additional field, either rf or constant. 

There can be no question that the most important species with a 3 E ground state is molecular oxygen and, not surprisingly, it was one of the first molecules to be studied in detail when microwave and millimetre-wave techniques were first developed. It was also one of the first molecules to be studied by microwave magnetic resonance, notably by Beringer and Castle [118]. In this section we concentrate on the field-free rotational spectrum, but note at the outset that this is an atypical system O2 is a homonuclear diatomic molecule in its predominant isotopomer, 160160, and as such does not possess an electric dipole moment. Spectroscopic transitions must necessarily be magnetic dipole only. 

We have already discussed the high-resolution spectroscopy of the OH radical at some length. It occupies a special place in the history of the subject, being the first short-lived free radical to be detected and studied in the laboratory by microwave spectroscopy. The details of the experiment by Dousmanis, Sanders and Townes [4] were described in section 10.1. It was also the first interstellar molecule to be detected by radio-astronomy. In chapter 8 we described the molecular beam electric resonance studies of yl-doubling transitions in the lowest rotational levels, and in chapter 9 we gave a comprehensive discussion of the microwave and far-infrared magnetic resonance spectra of OH. Our quantitative analysis of the magnetic resonance spectra made use of the results of pure field-free microwave studies of the rotational transitions, which we now describe. 

J = 3/2, 5/2 and 7/2 levels of both fine-structure states. Also shown are the /l-doublet transitions observed, first by Dousmanis, Sanders and Townes [4], and subsequently by ter Meulen and Dymanus [165] andMeertsandDymanus [166]. The later studies [166] used molecular beam electric resonance methods which were described in chapter 8, and the most accurate laboratory measurements of transitions within the lowest rotational level were those of ter Meulen and Dymanus [165] using a beam maser spectrometer, also described in chapter 8. In the years following these field-free experiments, attention... 

The CH radical is the simplest hydrocarbon and its rotational or /I-doublet spectrum has been sought by many. The first detection of rotational transitions was a triumph for far-infrared laser magnetic resonance the experiments carried out by Evenson, Radford and Moran [173] were described in detail in chapter 9. The A-doublet transition in the lowest rotational level was first observed through radioastronomy by Rydbeck, Ellder, Irvine, Sume and Hjalmarson [174]. It was almost a further ten years before laboratory observations of the field-free spectrum were reported. 

Figure 10.68. The low-energy rotational levels of CH, with the size of the Tl-doubling exaggerated for clarity. Transitions marked with an asterisk have been observed by far-infrared laser magnetic resonance. In addition many A J = 0, Tl-doublet transitions have been observed field-free, as listed in table 10.17.

Table 10.18. Molecular parameters (in MHz) for CH in thev = 0 level of the X2Il ground state, determined from a combination of the far-infrared laser magnetic resonance, field-free microwave measurements [181], andfield-free far-infrared measurements [185]...

Fig. 7.8 also shows the results of a classical calculation and a quantum calculation that both confirm the prediction of the giant resonance based on the simple overlap criterion discussed above. The crosses in Fig. 7.8 are the results of classical Monte Carlo calculations. They were performed by choosing 200 different initial conditions in the classical phase space at Iq = 57. The ionization probabihty in this case was defined as the excitation probability of actions beyond the cut-off action Ic = 86. This definition is motivated by experiments that, due to stray fields and the particular experimental procedures, cannot distinguish between excitation above Ic > 86 and true ionization, i.e. excitation to the field-free hydrogen continuum. The crosses in Fig. 7.8 are close to the full line and thus confirm the model prediction. The open squares are the results of quantum calculations within the one-dimensional SSE model. The computations were performed in the simplest way, i.e. no continuum was... 

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