What makes the solution for the electronic motion in a molecule so much more difficult from that for an atom (which as we have seen is certainly not easy!) is that the problem, in general, is multicentered. In an atom, with a single nucleus, one may use spherical coordinates for the multielectron problem. The angular part of the problem is effectively solved by invoking spherical harmonics for the basis functions for each electron. In a molecule, spherical symmetry is broken, and one cannot even use the same quantum numbers that one could use for an atom. It is little wonder that most texts that do treat the quantum mechanics of molecules ignore the atomic underpinnings. One can hardly blame the authors; the methodology is fundamentally different.

Much of the material in Chap. 1 will be a review for many of the students using this text. However, indicial notation for vectors will be used throughout this chapter and much of the book, and while most students have been exposed to this notation previously, experience has shown that many have yet to master it. It is not at all difficult and allows for such straightforward proofs of angular momentum relations that it is highly effective to become proficient with it.

This chapter will include all of those static interactions that can in some way effect the total energy of any given level of an atom or ion of interest. That’s a tall order. Consider that the total energy of an atom is known, having solved the problem presented in the previous chapter; that is, all of the electrons are in stationary states about some nucleus, with the only interactions being electrostatic attraction to the nucleus and repulsion to other electrons. The solution to such a problem would have ignored additional interactions. The largest, and one alluded to in previous chapters, is the fine-structure interaction. This is the coupling of the angular momenta of the outer electrons, the ones in open subshells. All filled shells and subshells have zero total angular momentum, so those electrons cannot take part. Whichever way one chooses to couple the angular momenta, and there are many different possible ways (Russell–Saunders coupling being just one), the total angular momentum, J, is a good quantum number.

With the electronic part of the problem treated in the previous chapter, the nuclear motion shall occupy our attention in this one. In many ways the motion of two nuclei in a potential well formed by the electron cloud is among the simpler of all quantum mechanical problems. The reason is that it readily reduces to the motion of a single particle in a potential well. The derivation of how that comes about is given in detail in case some have not seen it before.

A method has been developed to improve the accuracy with which the polarization state of light can be characterized by the rotating quarter-wave plate technique. Through detailed analysis, verified by experiment, we determine the positions of the optic axes of the retarder and linear polarizer, and the wave plate retardance, to better than 1° for typical signal-to-noise ratios. Accurate determination of the Stokes parameters can be achieved using a single wave plate for a wide range of optical wavelengths using this technique to determine the precise retardance at each of the wavelengths of interest.

Optical transitions from two microwave discharge excited states of argon have been observed using cavity ring-down spectroscopy. These transitions originate on the high-lying levels, 3d[1/2]degrees(1) and 3d[3/2]degrees(2), and terminate on the nf'[5/2] Rydberg (n = 8 to 22) levels, which, except for n = 8, lie between the P-2(3/2) and P-2(1/2) ionization thresholds. In total, 24 such spectral lines have been observed. The quantum defect for the f' series has been measured and is compared to previously measured values. We observe a nearly threefold jump in line width in going from n = 8 to n = 9, below and above the P-2(3/2) threshold, respectively. The line widths are broad and increase monotonically with n (above 9), in contrast to the narrowing of line widths usually observed. We cannot attribute this to a single source but conclude that collisional, quasielastic l-mixing of the nf'[5/2] Rydberg states plays a significant role.

Optical transitions from two microwave discharge excited states of argon have been observed using cavity ring-down spectroscopy. These transitions originate on the high-lying levels, 3d[1/2] 1° and 3d[3/2] 2° , and terminate on the nf ′[5/2] Rydberg (n = 8 to 22) levels, which, except for n = 8, lie between the 2P3/2 and 2P1/2 ionization thresholds. In total, 24 such spectral lines have been observed. The quantum defect for the f ′ series has been measured and is compared to previously measured values. We observe a nearly threefold jump in line width in going from n = 8 to n = 9, below and above the 2P3/2 threshold, respectively. The line widths are broad and increase monotonically with n (above 9), in contrast to the narrowing of line widths usually observed. We cannot attribute this to a single source but conclude that collisional, quasielastic l-mixing of the nf ′[5/2] Rydberg states plays a significant role.

We present direct measurements of the lifetime of the F 5 / 2 4 and H ( 2 ) 9 / 2 2 manifold in Nd 3 + : Y 3 Al 5 O 12 and Nd 3 + : LaF 3 , using a fluorescence-based pump-probe technique. The measured lifetimes of 17.9 ± 0.7 ps for Nd 3 + : Y 3 Al 5 O 12 , and 550 ± 80 ps for Nd 3 + : LaF 3 , agree well with the energy gap law, based on other nonradiative lifetime measurements from the literature for Nd 3 + : Y 3 Al 5 O 12 and Nd 3 + : LaF 3 .

We present direct measurements of the lifetime of the F5/24 and H(2)9/22 manifold in Nd3+:Y3Al5O12 and Nd3+:LaF3, using a fluorescence-based pump-probe technique. The measured lifetimes of 17.9±0.7ps for Nd3+:Y3Al5O12, and 550±80ps for Nd3+:LaF3, agree well with the energy gap law, based on other nonradiative lifetime measurements from the literature for Nd3+:Y3Al5O12 and Nd3+:LaF3.

We present direct measurements of the lifetime of the 4F5/2 and 2H(2)9/2 manifold in Nd3+:YLiF4, using a fluorescence pump–probe technique. The technique populates the 4F5/2 and 2H(2)9/2 manifold directly with a pump pulse. Via excited state absorption from this excited manifold, the 2F(2)5/2 manifold of Nd3+ is populated with a delayed probe pulse. The population in the 4F5/2 and 2H(2)9/2 manifold is monitored as a function of time by observing the change in integrated UV fluorescence from the 2F(2)5/2 manifold for each time delay between pump and probe pulses. The pump (∼780nm) and probe (∼390nm) beams come from the fundamental and second harmonic wavelengths of a femtosecond Ti:sapphire regenerative amplifier. The measured lifetime (230±30ps) agrees well with the energy gap law, based on other nonradiative lifetime measurements from the literature for Nd3+:YLiF4.

After H-2 and water, CO and CO2 are the most common molecules in stellar and interstellar environments. They are often dominant components in icy mantles of comets and interstellar dust grains. These ice mantles are subject to a varying degree of cosmic radiation, leading to chemical alterations. This paper presents a study of the near-IR absorption spectrum (1900 - 4000 cm(-1)) of proton-irradiated CO thin films. The spectra of such films display several features arising in the vicinity of the CO fundamental that are attributed to carbon oxides such as CnO and CnO2 for n less than or equal to 7. The formation mechanisms of carbon chains in interstellar environments are of interest since carbon chains ( or molecules derived from them) have been considered to be carriers of some of the diffuse interstellar bands.

High-resolution measurements of the photoionization cross sections of the Na-isoelectronic ions Mg+ and Al2+ are presented, to be compared with earlier measurements in which structure in the most prominent peaks was unresolved. These measurements have been normalized to the earlier ones in order to provide values of the oscillator strengths of the newly resolved peaks, and comparison is made with multiconfiguration Hartree-Fock calculations.

Cavity ring-down spectroscopy (CRDS) has been used to obtain the visible overtone spectra (Δ v CH =6) of neo -pentane, C(CH 3 ) 4 , propane, C 3 H 8 , and n -butane, C 4 H 10 , yielding absolute f -values for the transitions to better than 3%. For the neo -pentane overtone intensity, comparison with a recent measurement using intra-cavity laser photoacoustic spectroscopy (ICL-PAS) provides favourable agreement, with improved precision. Being absolute this value may be used as a standard for relative intensity measurements obtained by ICL-PAS. The measured propane and n -butane overtone intensities, when compared to recent work using phase-shift CRDS, indicate a lack of agreement to quoted uncertainties.