Space Infrared Telescope for Cosmology and Astrophysics (SPICA), the cryogenic infrared space telescope recently pre-selected for a ‘Phase A’ concept study as one of the three remaining candidates for European Space Agency (ESA's) fifth medium class (M5) mission, is foreseen to include a far-infrared polarimetric imager [SPICA-POL, now called B-fields with BOlometers and Polarizers (B-BOP)], which would offer a unique opportunity to resolve major issues in our understanding of the nearby, cold magnetised Universe. This paper presents an overview of the main science drivers for B-BOP, including high dynamic range polarimetric imaging of the cold interstellar medium (ISM) in both our Milky Way and nearby galaxies. Thanks to a cooled telescope, B-BOP will deliver wide-field 100–350 $\mu$m images of linearly polarised dust emission in Stokes Q and U with a resolution, signal-to-noise ratio, and both intensity and spatial dynamic ranges comparable to those achieved by Herschel images of the cold ISM in total intensity (Stokes I). The B-BOP 200 $\mu$m images will also have a factor $\sim $30 higher resolution than Planck polarisation data. This will make B-BOP a unique tool for characterising the statistical properties of the magnetised ISM and probing the role of magnetic fields in the formation and evolution of the interstellar web of dusty molecular filaments giving birth to most stars in our Galaxy. B-BOP will also be a powerful instrument for studying the magnetism of nearby galaxies and testing Galactic dynamo models, constraining the physics of dust grain alignment, informing the problem of the interaction of cosmic rays with molecular clouds, tracing magnetic fields in the inner layers of protoplanetary disks, and monitoring accretion bursts in embedded protostars.

The Millimetre Astronomy Legacy Team 90 GHz (MALT90) survey aims to characterise the physical and chemical evolution of high-mass star-forming clumps. Exploiting the unique broad frequency range and on-the-fly mapping capabilities of the Australia Telescope National Facility Mopra 22 m single-dish telescope1, MALT90 has obtained 3′ × 3′ maps towards ~2 000 dense molecular clumps identified in the ATLASGAL 870 μm Galactic plane survey. The clumps were selected to host the early stages of high-mass star formation and to span the complete range in their evolutionary states (from prestellar, to protostellar, and on to $\mathrm{H\,{\scriptstyle {II}}}$ regions and photodissociation regions). Because MALT90 mapped 16 lines simultaneously with excellent spatial (38 arcsec) and spectral (0.11 km s−1) resolution, the data reveal a wealth of information about the clumps’ morphologies, chemistry, and kinematics. In this paper we outline the survey strategy, observing mode, data reduction procedure, and highlight some early science results. All MALT90 raw and processed data products are available to the community. With its unprecedented large sample of clumps, MALT90 is the largest survey of its type ever conducted and an excellent resource for identifying interesting candidates for high-resolution studies with ALMA.

Extended abstract of a paper presented at Microscopy and Microanalysis 2011 in Nashville, Tennessee, USA, August 7–August 11, 2011.

Submillimeter dust continuum emission traces high molecular column densities and, thus,dense cloud regions in which new stars are forming. Surveys of the Galactic plane in suchemission have the potential of delivering an unbiased view of high-mass star formationthroughout the Milky Way. The location of the APEX telescope on the Chajnantor plateau inChile is ideally suited for mapping the inner Galaxy. ATLASGAL, The APEX Telescope LargeArea Survey of the Galaxy at 870 μm, is a survey of the Galactic planeusing the Large APEX Bolometer Camera (LABOCA), in the Galactic longitude and latituderanges of  ±60 and  ±1.5°, respectively. This survey is providing an unbiased sample ofcold dusty clumps in the Galaxy at submillimeter wavelength and a variety of molecularline follow-up observations have been started to characterize the physical and chemicalconditions in the newly found clumps. Here, first results from this survey and itsfollow-up programs are described.

The Rosette molecular cloud has a characteristic morphology, where the central OB cluster NGC 2244 has blown a circular-shaped cavity into the cloud and the expanding HII-region now interacts with the cloud. We use continuum data obtained with the PACS (70 and 160 μm) and SPIRE instruments (250, 350, 500 μm) of the Herschel telescope to investigate the spatial distribution of cold and warm gas and to locate all star-forming sites in Rosette. We detected a clear negative temperature gradient and a positive density gradient (running from the HII-region/molecular cloud interface into the cloud), and an age-sequence (from more evolved to younger) with increasing distance to the cluster NGC 2244. The existence of such temperature and density gradients and the observed age-sequence imply that star formation in Rosette may indeed be influenced by the radiative impact of the central NGC 2244 cluster.

A systematic, high angular-resolution study of IR-quiet Massive Dense Cores (MDCs) of Cygnus-X in continuum and high-density molecular tracers is presented. The results are compared with the quasi-static and the dynamical evolutionary scenario. We find that the fragmentation properties are not compatible with the quasi-static, monolithic collapse scenario, nor are they entirely compatible with the formation of a cluster of mostly low-mass stars. The kinematics of MDCs shows individual velocity components appearing as coherent flows, which indicate important dynamical processes at the scale of the mass reservoir around high-mass protostars.

The Wigner 6j–symbol, written in the form

is shown to be invariant under separate permutations of A, B, C alone, separate permutations of α, β, γ alone and separate change in sign of any pair of α, β, γ; results equivalent to the new symmetry relations of Regge. Alternatively, written in the form

with J0 + J1 + J2 + J3 = K1 + K2 + K3, Jr(r = 0, 1, 2, 3) and K3 (s = 1, 2, 3) integral, it is invariant for separate permutations of the Jr and of the Ks. If Jm = max (J0, J1, J2, J3), then each 6j-symbol with distinct value may be associated with an ordered partition of Jm into 6 integral parts: Jm = n1 + n2 + n3 + p1 + p2 + p3, n1 ≥ n2 ≥ n3; p1 ≥ p2 ≥ n3. The 6j-symbol is proportional to the Saalschützian

of unit argument.

Classical dynamics is generally considered as the prototype of a deterministic theory; the equations of motion determine the coordinates q and the momenta p at any time provided they are given at an initial instant. It is pointed out that this is an unrealistic assumption, for it is inevitable that there should be small uncertainties Δq, Δp; a point of the mathematical continuum has no physical significance. The uncertainties can be taken into account without violating the deterministic equations by introducing a probability density P in phase space p, q. The function P satisfies the partial differential equation which expresses Liouville's theorem. Thus it can be shown that an initial uncertainty spreads out in phase space, so that finally all states of the system consistent with the mean initial values of the constants of the motion are equally probable. This property holds for one degree of freedom just as well as for many, and is not a consequence of our ignorance concerning large numbers of particles. The essential difference between classical mechanics and quantum mechanics consists not in the physical necessity of a statistical interpretation, but in the further introduction of a probability amplitude, the square of which is the probability density; thisimplies the restriction of the initial uncertainties as expressed by the uncertainty laws, and the phenomenon of interference of probabilities which makes necessary a revision of our concepts of physical reality. It is remarkable that the product of the uncertainties of a properly chosen pair of variables is constant also in classical mechanics, although of course its value is not a universal constant as in the quantum case.

The Tamm-Dancoff theory of meson-nucleon scattering (pseudoscalar coupling) leads to a series of singular integral equations. The asymptotic behaviour of the solutions of these equations is obtained here for all scattering states. For attractive states there is a critical coupling constant beyond which no normalizable solutions exist for these equations; for repulsive states another critical coupling constant appears, beyond which the solutions oscillate infinitely often but are still normalizable. It is concluded that the renormalization procedures proposed previously (3) are consistent and successfully define finite vertex-functions, and that the equations obtained for these vertex-functions have satisfactory properties for numerical work.

The conditions for equilibrium in an elastically stressed hexagonal aeolotropic medium (transversely isotropic) are formulated, and solutions are found in terms of two ‘harmonic’ functions ø1, ø2, which are solutions of

ν1, ν2 being the roots of a certain quadratic equation.

It is also shown that in the case of axially symmetrical stress systems the solution may be expressed in terms of the third-order differential coefficients of a single stress function Φ.

The solutions for an isotropic medium may be deduced as a special case.

The problems of nuclei of strain in such a hexagonal solid are solved, and the results for zinc and magnesium contrasted with those for an isotropic solid.

According to quantum mechanics there exists in any non-metallic crystal a band of allowed electronic energy levels which are unoccupied when the crystal is in its state of lowest energy. We call this band the conduction band; the crystal can conduct electricity if electrons are raised into the conduction level from lower levels. According to the theory of semi-conductors given by Wilson, there exist in these substances lattice imperfections at which an electron can exist in a bound stationary state below the conduction band, electrons being raised from these levels into the conduction band by the thermal agitation of the surrounding atoms.

1. As is well known, the electrical resistance of a metal is very greatly in-creased by the addition of a second metal with which it forms a solid solution. The increase Δρ in the resistivity due to the addition of a small percentage of the second metal is in general independent of the temperature (Matthiessen's rule), though there are oertain exceptions (e.g. Cr in Au). The quaritum-mechanical explanation of both these facts was first given by Nordheim, and may be expressed as follows: the electrical conductivity of any metal may be written in the form

where τ is the “time of relaxation”, equal to half the time between collisions, and N is the effective number of free electrons per unit volume: hence, for the resistivity, we have

The purpose of this note is to calculate the specific heat and paramagnetic susceptibility of an electron gas obeying the Fermi-Dirac statistics for all temperatures, including those temperatures for which the gas is partially degenerate. The results are applicable to the electrons in a metal, whether free or moving in a periodic field, provided only that the number of electronic states per gram atom with energy between E and E + dE can be expressed in the form

as for free electrons.

Three main stages may be marked in the development of the theory of the optical properties of metals. First, there is Drude's original theory, based on Maxwell's equations; in this theory the current density j at any point in a metal is supposed to be equal to the product of the electric vector of the light and of the conductivity of the metal. The theory yields the well-known Hagen-Rubens formula for the reflecting power, which appears to be in agreement with experiment for very long wave-lengths (λ > 10μ), but leads to completely incorrect results in the optical region. Various investigators ‡ have therefore modified the theory to take account of the finite mass of the electron; the formulae obtained pass over into the Drude formulae for sufficiently long wave-lengths. Finally a quantum theory of the phenomenon has been given by Kronig§, the electrons being treated as moving in a periodic field due to the crystal lattice in the manner originated by Bloch; this theory, in its turn, becomes identical with the modified classical theory if the periodic lattice is neglected.

1. It has been shown, in a well-known paper by Born and Oppenheimer, that in evaluating the energy levels of a molecule, the nuclei may be treated as fixed, or slowly vibrating, centres of force. If M be the average mass of the nuclei, and m the mass of an electron, the error involved in doing this is of order of magnitude (m/M)½. The possibility therefore of treating the nuclei as fixed depends on their great mass, compared with that of the electron.

1. The formulae usually given for the scattering of electrons by atoms are calculated without taking into account the radiative forces. It has been suggested by the author in a former paper that in the case of the large-angle scattering of electrons with velocity comparable with that of light (for which case the scattering is entirely nuclear), these forces might influence the scattering by an appreciable amount, which would explain the divergence between the theoretical formula and the results of Chadwick and Mercier, which are some 40 per cent. greater. In this paper we shall show that for electrons–of any velocity the influence of these forces cannot be greater than 2 or 3 per cent., and so cannot be invoked to explain discrepancies between theory and experiment.

The problem of the collision between an electron and an atom was first considered on the Quantum theory by Born, who has worked out in detail the case of atomic hydrogen, and has obtained formulae giving the variation of scattering with angle both for elastic and inelastic collisions. Born's solution is only approximate. The purpose of this note is to discuss the physical nature of the approximations used by him, and also to extend his results to Helium, for which experimental evidence is now available. It is found that the theoretical curve agrees with the experimental as well as the approximations used would lead one to expect. We shall confine ourselves to elastic collisions.

The Statistical Mechanics which has been developed in accordance with the requirements of the new Quantum Theory is concerned with distribution laws over energy values only—over, that is, the characteristics of Schrödinger's equation. To obtain a space distribution law, even for the Classical limit, some use must be made of the characteristic functions. A formula has been suggested by Fowler, but it has not been shown that this formula gives the Classical law for gases at ordinary temperatures and pressures. In this paper we shall show that this is so, but before doing so we shall sketch the analogous method of obtaining the law, on the Classical theory.