A covariant gauge-invariant three-dimensional description of relativistic bound-states

A formalism is presented which allows covariant three-dimensional bound-state equations to be derived systematically from four-dimensional ones without the use of delta-functions. The amplitude for the interaction of a bound state described by these equations with an electromagnetic probe is constructed. This amplitude is shown to be gauge invariant if the formalism is truncated at the same coupling-constant order in both the interaction kernel of the integral equation and the electromagnetic current operator.Comment: 17 pages, RevTeX, uses BoxedEPS.te

Herschel observations in the ultracompact HII region Mon R2: Water in dense photon-dominated regions (PDRs)

Context. Monoceros R2, at a distance of 830 pc, is the only ultracompact Hii region (UC H_(II)) where the photon-dominated region (PDR) between the ionized gas and the molecular cloud can be resolved with Herschel. Therefore, it is an excellent laboratory to study the chemistry in extreme PDRs (G_0 > 10^5 in units of Habing field, n > 10^6 cm^9−3)). Aims. Our ultimate goal is to probe the physical and chemical conditions in the PDR around the UC H_(II) Mon R2. Methods. HIFI observations of the abundant compounds ^(13)CO, C^(18)O, o-H_2^(18)O, HCO^+, CS, CH, and NH have been used to derive the physical and chemical conditions in the PDR, in particular the water abundance. The modeling of the lines has been done with the Meudon PDR code and the non-local radiative transfer model described by Cernicharo et al. Results. The ^(13)CO, C^(18)O, o-H^(18)_2O, HCO^+ and CS observations are well described assuming that the emission is coming from a dense (n = 5 × 10^6 cm^(−3), N(H_2) > 10^(22) cm^(−2)) layer of molecular gas around the H_(II) region. Based on our o-H^(18)_2O observations, we estimate an o-H_2O abundance of ≈2 × 10^(−8). This is the average ortho-water abundance in the PDR. Additional H^(18)_2O and/or water lines are required to derive the water abundance profile. A lower density envelope (n ~ 10^5 cm^(−3), N(H_2) = 2−5 × 10^(22) cm^(−2)) is responsible for the absorption in the NH 1_1 → 0_2 line. The emission of the CH ground state triplet is coming from both regions with a complex and self-absorbed profile in the main component. The radiative transfer modeling shows that the ^(13)CO and HCO^+ line profiles are consistent with an expansion of the molecular gas with a velocity law, v_e = 0.5 × (r/R_(out))^(−1) km s^(−1), although the expansion velocity is poorly constrained by the observations presented here. Conclusions. We determine an ortho-water abundance of ≈2 × 10^(−8) in Mon R2. Because shocks are unimportant in this region and our estimate is based on H^(18)_2O observations that avoids opacity problems, this is probably the most accurate estimate of the water abundance in PDRs thus far

The magnetic form factor of the deuteron in chiral effective field theory

We calculate the magnetic form factor of the deuteron up to O(eP^4) in the chiral EFT expansion of the electromagnetic current operator. The two LECs which enter the two-body part of the isoscalar NN three-current operator are fit to experimental data, and the resulting values are of natural size. The O(eP^4) description of G_M agrees with data for momentum transfers Q^2 < 0.35 GeV^2.Comment: 4 pages, 2 figure

Gas morphology and energetics at the surface of PDRs: New insights with Herschel observations of NGC 7023

Context. We investigate the physics and chemistry of the gas and dust in dense photon-dominated regions (PDRs), along with their dependence on the illuminating UV field. Aims. Using Herschel/HIFI observations, we study the gas energetics in NGC 7023 in relation to the morphology of this nebula. NGC 7023 is the prototype of a PDR illuminated by a B2V star and is one of the key targets of Herschel. Methods. Our approach consists in determining the energetics of the region by combining the information carried by the mid-IR spectrum (extinction by classical grains, emission from very small dust particles) with that of the main gas coolant lines. In this letter, we discuss more specifically the intensity and line profile of the 158 μm (1901 GHz) [C ii] line measured by HIFI and provide information on the emitting gas. Results. We show that both the [C ii] emission and the mid-IR emission from polycyclic aromatic hydrocarbons (PAHs) arise from the regions located in the transition zone between atomic and molecular gas. Using the Meudon PDR code and a simple transfer model, we find good agreement between the calculated and observed [C ii] intensities. Conclusions. HIFI observations of NGC 7023 provide the opportunity to constrain the energetics at the surface of PDRs. Future work will include analysis of the main coolant line [O i] and use of a new PDR model that includes PAH-related species