QED confronts the radius of the proton

Recent results on muonic hydrogen [1] and the ones compiled by CODATA on ordinary hydrogen and $ep$-scattering [2] are $5\sigma$ away from each other. Two reasons justify a further look at this subject: 1) One of the approximations used in [1] is not valid for muonic hydrogen. This amounts to a shift of the proton's radius by $\sim 3$ of the standard deviations of [1], in the "right" direction of data-reconciliation. In field-theory terms, the error is a mismatch of renormalization scales. Once corrected, the proton radius "runs", much as the QCD coupling "constant" does. 2) The result of [1] requires a choice of the "third Zemach moment". Its published independent determination is based on an analysis with a $p$-value --the probability of obtaining data with equal or lesser agreement with the adopted (fit form-factor) hypothesis-- of $3.92\times 10^{-12}$. In this sense, this quantity is not empirically known. Its value would regulate the level of "tension" between muonic- and ordinary-hydrogen results, currently {\it at most} $\sim 4\sigma$. There is no tension between the results of [1] and the proton radius determined with help of the analyticity of its form factors.Comment: Extended for publication in Physics Letter

Radiative Correction to the Nuclear-Size Effect and Hydrogen-Deuterium Isotopic Shift

The radiative correction to the nuclear charge radius contribution to the Lamb shift of order $\alpha(Z\alpha)^5m_r^3$ is calculated. In view of the recent high precision experimental data, this theoretical correction produces a significant contribution to the hydrogen-deuterium isotopic shift.Comment: 5 pages, REVTEX, replaced with the final version, to be published in Phys.Rev. A, two references adde

Higher-Order Nuclear-Polarizability Corrections in Atomic Hydrogen

Nuclear-polarizability corrections that go beyond unretarded-dipole approximation are calculated analytically for hydrogenic (atomic) S-states. These retardation corrections are evaluated numerically for deuterium and contribute -0.68 kHz, for a total polarization correction of 18.58(7) kHz. Our results are in agreement with one previous numerical calculation, and the retardation corrections completely account for the difference between two previous calculations. The uncertainty in the deuterium polarizability correction is substantially reduced. At the level of 0.01 kHz for deuterium, only three primary nuclear observables contribute: the electric polarizability, $\alpha_E$, the paramagnetic susceptibility, $\beta_M$, and the third Zemach moment, $_{(2)}$. Cartesian multipole decomposition of the virtual Compton amplitude and its concomitant gauge sum rules are used in the analysis.Comment: 26 pages, latex, 1 figure -- Submitted to Phys. Rev. C -- epsfig.sty require

Nuclear Sizes and the Isotope Shift

Darwin-Foldy nuclear-size corrections in electronic atoms and nuclear radii are discussed from the nuclear-physics perspective. Interpretation of precise isotope-shift measurements is formalism dependent, and care must be exercised in interpreting these results and those obtained from relativistic electron scattering from nuclei. We strongly advocate that the entire nuclear-charge operator be used in calculating nuclear-size corrections in atoms, rather than relegating portions of it to the non-radiative recoil corrections. A preliminary examination of the intrinsic deuteron radius obtained from isotope-shift measurements suggests the presence of small meson-exchange currents (exotic binding contributions of relativistic order) in the nuclear charge operator, which contribute approximately 1/2%.Comment: 17 pages, latex, 1 figure -- Submitted to Phys. Rev. A -- epsfig.sty require

The twilight of the Liberal Social Contract? On the Reception of Rawlsian Political Liberalism

This chapter discusses the Rawlsian project of public reason, or public justification-based 'political' liberalism, and its reception. After a brief philosophical rather than philological reconstruction of the project, the chapter revolves around a distinction between idealist and realist responses to it. Focusing on political liberalism’s critical reception illuminates an overarching question: was Rawls’s revival of a contractualist approach to liberal legitimacy a fruitful move for liberalism and/or the social contract tradition? The last section contains a largely negative answer to that question. Nonetheless the chapter's conclusion shows that the research programme of political liberalism provided and continues to provide illuminating insights into the limitations of liberal contractualism, especially under conditions of persistent and radical diversity. The programme is, however, less receptive to challenges to do with the relative decline of the power of modern states

Constitutivism

A brief explanation and overview of constitutivism

Precision physics of simple atoms: QED tests, nuclear structure and fundamental constants

Quantum electrodynamics is the first successful and still the most successful quantum field theory. Simple atoms, being essentially QED systems, allow highly accurate theoretical predictions. Because of their simple spectra, such atoms have been also efficiently studied experimentally frequently offering the most precisely measured quantities. Our review is devoted to comparison of theory and experiment in the field of precision physics of light simple atoms. In particular, we consider the Lamb shift in the hydrogen atom, the hyperfine structure in hydrogen, deuterium, helium-3 ion, muonium and positronium, as well as a number of other transitions in positronium. Additionally to a spectrum of unperturbed atoms, we consider annihilation decay of positronium and the g factor of bound particles in various two-body atoms. Special attention is paid to the uncertainty of the QED calculations due to the uncalculated higher-order corrections and effects of the nuclear structure. We also discuss applications of simple atoms to determination of several fundamental constants

Philosophy of action

The philosophical study of human action begins with Plato and Aristotle. Their influence in late antiquity and the Middle Ages yielded sophisticated theories of action and motivation, notably in the works of Augustine and Aquinas.1 But the ideas that were dominant in 1945 have their roots in the early modern period, when advances in physics and mathematics reshaped philosophy

Second sex = Kehidupan perempuan

s.l.xxix, 662 p.: indeks; 23 c