Exact solution of the Zeeman effect in single-electron systems

Contrary to popular belief, the Zeeman effect can be treated exactly in single-electron systems, for arbitrary magnetic field strengths, as long as the term quadratic in the magnetic field can be ignored. These formulas were actually derived already around 1927 by Darwin, using the classical picture of angular momentum, and presented in their proper quantum-mechanical form in 1933 by Bethe, although without any proof. The expressions have since been more or less lost from the literature; instead, the conventional treatment nowadays is to present only the approximations for weak and strong fields, respectively. However, in fusion research and other plasma physics applications, the magnetic fields applied to control the shape and position of the plasma span the entire region from weak to strong fields, and there is a need for a unified treatment. In this paper we present the detailed quantum-mechanical derivation of the exact eigenenergies and eigenstates of hydrogen-like atoms and ions in a static magnetic field. Notably, these formulas are not much more complicated than the better-known approximations. Moreover, the derivation allows the value of the electron spin gyromagnetic ratio $g_s$ to be different from 2. For completeness, we then review the details of dipole transitions between two hydrogenic levels, and calculate the corresponding Zeeman spectrum. The various approximations made in the derivation are also discussed in details.Comment: 18 pages, 4 figures. Submitted to Physica Script

Should human chondrocytes fly? The impact of electromagnetic irradiation on chondrocyte viability and implications for their use in tissue engineering

A significant logistic factor as to the successful clinical application of the autologous tissue engineering concept is efficient transportation: the donor cells need to be delivered to tissue processing facilities which in most cases requires air transportation. This study was designed to evaluate how human chondrocytes react to X-ray exposure. Primary cell cultures were established, cultured, incubated and exposed to different doses and time periods of radiation. Subsequently, quantitative cell proliferation assays were done and qualitative evaluation of cellular protein production were performed. Our results show that after irradiation of chondrocytes with different doses, no significant differences in terms of cellular viability occurred compared with the control group. These results were obtained when chondrocytes were exposed to luggage transillumination doses as well as exposure to clinically used radiation doses. Any damage affecting cell growth or quality was not observed in our study. However, information about damage of cellular DNA remains incomplet

“No research on a dead planet”: preserving the socio-ecological conditions for academia

Despite thousands of higher education institutions (HEIs) having issued Climate Emergency declarations, most academics continue to operate according to ‘business-as-usual’. However, such passivity increases the risk of climate impacts so severe as to threaten the persistence of organized society, and thus HEIs themselves. This paper explores why a maladaptive cognitive-practice gap persists and asks what steps could be taken by members of HEIs to activate the academy. Drawing on insights from climate psychology and sociology, we argue that a process of ‘socially organized denial’ currently exists within universities, leading academics to experience a state of ‘double reality’ that inhibits feelings of accountability and agency, and this is self-reenforcing through the production of ‘pluralistic ignorance.’ We further argue that these processes serve to uphold the cultural hegemony of ‘business-as-usual’ and that this is worsened by the increasing neo-liberalization of modern universities. Escaping these dynamics will require deliberate efforts to break taboos, through frank conversations about what responding to a climate emergency means for universities’ – and individual academics’ – core values and goals

Compactification near and on the light front

We address problems associated with compactification near and on the light front. In perturbative scalar field theory we illustrate and clarify the relationships among three approaches: (1) quantization on a space-like surface close to a light front; (2) infinite momentum frame calculations; and (3) quantization on the light front. Our examples emphasize the difference between zero modes in space-like quantization and those in light front quantization. In particular, in perturbative calculations of scalar field theory using discretized light cone quantization there are well-known ``zero-mode induced'' interaction terms. However, we show that they decouple in the continuum limit and covariant answers are reproduced. Thus compactification of a light-like surface is feasible and defines a consistent field theory.Comment: 24 pages, 4 figure

Tritium concentration measurements in the JET divertor by optical spectroscopy of a Penning discharge

Obtaining precision measurements of the relative concentrations of hydrogen, deuterium, tritium, and helium in the divertor of a tokamak are an important task for nuclear fusion research. Control of the deuterium-tritium isotopic ratio while limiting the helium ash content in a fusion plasma are key factors for optimizing the fuel burn in a fusion reactor, like the International Tokamak Experimental Reactor (ITER). A diagnostic technique has been developed to measure the deuterium-tritium isotopic ratio in the divertor of the Joint European Torus (JET) with a species-selective Penning vacuum gauge. The Penning discharge provides a source of electrons to excite the neutral hydrogen isotopes in the pumping duct. Subsequently, the visible light from the hydrogen isotopes is collected in an optical fiber bundle, transferred away from the tokamak into a low radiation background area, and analyzed in a high resolution Czerny-Turner spectrometer, which is equipped with a fast charge coupled device (CCD) camera for optical detection. The intensity of the observed line emission (D{sub {alpha}} -- 6561.03 {angstrom}; and T{sub {alpha}} -- 6560.44 {angstrom}) is directly proportional to the partial pressure of each gas found in the divertor. The line intensity of each isotope is calibrated as a function of pressure. The ratio of the line intensities thus provides a direct measurement of the deuterium-tritium isotopic ratio. The lower limit for the determination of the deuterium-tritium isotopic ratio is about 0.5%. The applicable pressure range for this system is from 10{sup {minus}5} mbar to a few times 10{sup {minus}3} mbar

A study of the breakdown of the quasi-static approximation at high densities and its effect on the helium-like K ALPHA complex of nickel, iron, and calcium

The General Spectral Modeling (GSM) code employs the quasi-static approximation, a standard, low-density methodology that assumes the ionization balance is separable from a determination of the excited-state populations that give rise to the spectra. GSM also allows for some states to be treated only as contributions to effective rates. While these two approximations are known to be valid at low densities, this work investigates using such methods to model high-density, non-LTE emission spectra and determines at what point the approximations break down by comparing to spectra produced by the LANL code ATOMIC which makes no such approximations. As both approximations are used by other astrophysical and low-density modeling codes, the results should be of broad interest. He-like K$\alpha$ emission spectra are presented for Ni, Fe, and Ca, in order to gauge the effect of both approximations employed in GSM. This work confirms that at and above the temperature of maximum abundance of the He-like ionization stage, the range of validity for both approximations is sufficient for modeling the low- and moderate-density regimes one typically finds in astrophysical and magnetically confined fusion plasmas. However, a breakdown does occur for high densities; we obtain quantitative limits that are significantly higher than previous works. This work demonstrates that, while the range of validity for both approximations is sufficient to predict the density-dependent quenching of the z line, the approximations break down at higher densities. Thus these approximations should be used with greater care when modeling high-density plasmas such as those found in inertial confinement fusion and electromagnetic pinch devices.Comment: Accepted by Physical Review A (http://pra.aps.org/). 11 pages + LANL cover, 5 figures. Will update citation information as it becomes available. Abbreviated abstract is listed her