Semiclassical theory of spin-orbit interaction in the extended phase space

We consider the semiclassical theory in a joint phase space of spin and orbital degrees of freedom. The method is developed from the path integrals using the spin-coherent-state representation, and yields the trace formula for the density of states. We discuss special cases, such as weak and strong spin-orbit coupling, and relate the present theory to the earlier approaches.Comment: 36 pages, 8 figures. Version 2: revised Sec. 4.4 and Appendix B; minor corrections elsewher

A spectral line survey of Orion KL in the bands 486-492 and 541-577 GHz with the Odin satellite I. The observational data

Spectral line surveys are useful since they allow identification of new molecules and new lines in uniformly calibrated data sets. Nonetheless, large portions of the sub-millimetre spectral regime remain unexplored due to severe absorptions by H2O and O2 in the terrestrial atmosphere. The purpose of the measurements presented here is to cover wavelength regions at and around 0.55 mm -- regions largely unobservable from the ground. Using the Odin astronomy/aeronomy satellite, we performed the first spectral survey of the Orion KL molecular cloud core in the bands 486--492 and 541--576 GHz with rather uniform sensitivity (22--25 mK baseline noise). Odin's 1.1 m size telescope, equipped with four cryo-cooled tuneable mixers connected to broad band spectrometers, was used in a satellite position-switching mode. Two mixers simultaneously observed different 1.1 GHz bands using frequency steps of 0.5 GHz (25 hours each). An on-source integration time of 20 hours was achieved for most bands. The entire campaign consumed ~1100 orbits, each containing one hour of serviceable astro-observation. We identified 280 spectral lines from 38 known interstellar molecules (including isotopologues) having intensities in the range 80 to 0.05 K. An additional 64 weak lines remain unidentified. Apart from the ground state rotational 1(1,0)--1(0,1) transitions of ortho-H2O, H218O and H217O, the high energy 6(2,4)--7(1,7) line of para-H2O and the HDO(2,0,2--1,1,1) line have been observed, as well as the 1,0--0,1 lines from NH3 and its rare isotopologue 15NH3. We suggest assignments for some unidentified features, notably the new interstellar molecules ND and SH-. Severe blends have been detected in the line wings of the H218O, H217O and 13CO lines changing the true linewidths of the outflow emission.Comment: 21 pages, 10 figures, 7 tables, accepeted for publication in Astronomy and Astrophysics 30 August 200

Submillimeter Emission from Water in the W3 Region

We have mapped the submillimeter emission from the 1(10)-1(01) transition of ortho-water in the W3 star-forming region. A 5'x5' map of the W3 IRS4 and W3 IRS5 region reveals strong water lines at half the positions in the map. The relative strength of the Odin lines compared to previous observations by SWAS suggests that we are seeing water emission from an extended region. Across much of the map the lines are double-peaked, with an absorption feature at -39 km/s; however, some positions in the map show a single strong line at -43 km/s. We interpret the double-peaked lines as arising from optically thick, self-absorbed water emission near the W3 IRS5, while the narrower blue-shifted lines originate in emission near W3 IRS4. In this model, the unusual appearance of the spectral lines across the map results from a coincidental agreement in velocity between the emission near W3 IRS4 and the blue peak of the more complex lines near W3 IRS5. The strength of the water lines near W3 IRS4 suggests we may be seeing water emission enhanced in a photon-dominated region.Comment: Accepted to A&A Letters as part of the special Odin issue; 4 page

Separating the regular and irregular energy levels and their statistics in Hamiltonian system with mixed classical dynamics

We look at the high-lying eigenstates (from the 10,001st to the 13,000th) in the Robnik billiard (defined as a quadratic conformal map of the unit disk) with the shape parameter $\lambda=0.15$. All the 3,000 eigenstates have been numerically calculated and examined in the configuration space and in the phase space which - in comparison with the classical phase space - enabled a clear cut classification of energy levels into regular and irregular. This is the first successful separation of energy levels based on purely dynamical rather than special geometrical symmetry properties. We calculate the fractional measure of regular levels as $\rho_1=0.365\pm 0.01$ which is in remarkable agreement with the classical estimate $\rho_1=0.360\pm 0.001$. This finding confirms the Percival's (1973) classification scheme, the assumption in Berry-Robnik (1984) theory and the rigorous result by Lazutkin (1981,1991). The regular levels obey the Poissonian statistics quite well whereas the irregular sequence exhibits the fractional power law level repulsion and globally Brody-like statistics with $\beta = 0.286\pm0.001$. This is due to the strong localization of irregular eigenstates in the classically chaotic regions. Therefore in the entire spectrum we see that the Berry-Robnik regime is not yet fully established so that the level spacing distribution is correctly captured by the Berry-Robnik-Brody distribution (Prosen and Robnik 1994).Comment: 20 pages, file in plain LaTeX, 7 figures upon request submitted to J. Phys. A. Math. Gen. in December 199

Semiclassical limits for the QCD Dirac operator

We identify three semiclassical parameters in the QCD Dirac operator. Mutual coupling of the different types of degrees of freedom (translational, colour and spin) depends on how the semiclassical limit is taken. We discuss various semiclassical limits and their potential to describe spectrum and spectral statistics of the QCD Dirac operator close to zero virtuality.Comment: 34 pages, 1 figur

Neutron-proton interaction in rare-earth nuclei: Role of tensor force

We investigate the role of the tensor force in the description of doubly odd deformed nuclei within the framework of the particle-rotor model. We study the rare-earth nuclei 174Lu, 180Ta, 182Ta, and 188Re using a finite-range interaction, with and without tensor terms. Attention is focused on the lowest K=0 and K=1 bands, where the effects of the residual neutron-proton interaction are particularly evident. Comparison of the calculated results with experimental data evidences the importance of the tensor-force effects.Comment: 8 pages, 5 figures, to be published on Physical Review

Chaos in Axially Symmetric Potentials with Octupole Deformation

Classical and quantum mechanical results are reported for the single particle motion in a harmonic oscillator potential which is characterized by a quadrupole deformation and an additional octupole deformation. The chaotic character of the motion is srongly dependent on the quadrupole deformation in that for a prolate deformation virtually no chaos is discernible while for the oblate case the motion shows strong chaos when the octupole term is turned on.Comment: 6 pages LaTex plus 4 figures available by contacting the authors directly, published in PHYS.REV.LETT. 72(1994) 235

Isotopic ratios of H, C, N, O, and S in comets C/2012 F6 (Lemmon) and C/2014 Q2 (Lovejoy)

The apparition of bright comets C/2012 F6 (Lemmon) and C/2014 Q2 (Lovejoy) in March-April 2013 and January 2015, combined with the improved observational capabilities of submillimeter facilities, offered an opportunity to carry out sensitive compositional and isotopic studies of the volatiles in their coma. We observed comet Lovejoy with the IRAM 30m telescope between 13 and 26 January 2015, and with the Odin submillimeter space observatory on 29 January - 3 February 2015. We detected 22 molecules and several isotopologues. The H$_2^{16}$O and H$_2^{18}$O production rates measured with Odin follow a periodic pattern with a period of 0.94 days and an amplitude of ~25%. The inferred isotope ratios in comet Lovejoy are $^{16}$O/$^{18}$O = 499 $\pm$ 24 and D/H = 1.4 $\pm$ 0.4 $\times 10^{-4}$ in water, $^{32}$S/$^{34}$S = 24.7 $\pm$ 3.5 in CS, all compatible with terrestrial values. The ratio $^{12}$C/$^{13}$C = 109 $\pm$ 14 in HCN is marginally higher than terrestrial and $^{14}$N/$^{15}$N = 145 $\pm$ 12 in HCN is half the Earth ratio. Several upper limits for D/H or 12C/13C in other molecules are reported. From our observation of HDO in comet C/2014 Q2 (Lovejoy), we report the first D/H ratio in an Oort Cloud comet that is not larger than the terrestrial value. On the other hand, the observation of the same HDO line in the other Oort-cloud comet, C/2012 F6 (Lemmon), suggests a D/H value four times higher. Given the previous measurements of D/H in cometary water, this illustrates that a diversity in the D/H ratio and in the chemical composition, is present even within the same dynamical group of comets, suggesting that current dynamical groups contain comets formed at very different places or times in the early solar system.Comment: Accepted for publication in Astronomy and Astrophysic

Semiclassical theory of spin-orbit interactions using spin coherent states

We formulate a semiclassical theory for systems with spin-orbit interactions. Using spin coherent states, we start from the path integral in an extended phase space, formulate the classical dynamics of the coupled orbital and spin degrees of freedom, and calculate the ingredients of Gutzwiller's trace formula for the density of states. For a two-dimensional quantum dot with a spin-orbit interaction of Rashba type, we obtain satisfactory agreement with fully quantum-mechanical calculations. The mode-conversion problem, which arose in an earlier semiclassical approach, has hereby been overcome.Comment: LaTeX (RevTeX), 4 pages, 2 figures, accepted for Physical Review Letters; final version (v2) for publication with minor editorial change

Water and ammonia abundances in S140 with the Odin satellite

We have used the Odin satellite to obtain strip maps of the ground-state rotational transitions of ortho-water and ortho-ammonia, as well as CO(5-4) and 13CO(5-4) across the PDR, and H218O in the central position. A physi-chemical inhomogeneous PDR model was used to compute the temperature and abundance distributions for water, ammonia and CO. A multi-zone escape probability method then calculated the level populations and intensity distributions. These results are compared to a homogeneous model computed with an enhanced version of the RADEX code. H2O, NH3 and 13CO show emission from an extended PDR with a narrow line width of ~3 kms. Like CO, the water line profile is dominated by outflow emission, however, mainly in the red wing. The PDR model suggests that the water emission mainly arises from the surfaces of optically thick, high density clumps with n(H2)>10^6 cm^-3 and a clump water abundance, with respect to H2, of 5x10^-8. The mean water abundance in the PDR is 5x10^-9, and between ~2x10^-8 -- 2x10^-7 in the outflow derived from a simple two-level approximation. Ammonia is also observed in the extended clumpy PDR, likely from the same high density and warm clumps as water. The average ammonia abundance is about the same as for water: 4x10^-9 and 8x10^-9 given by the PDR model and RADEX, respectively. The similarity of water and ammonia PDR emission is also seen in the almost identical line profiles observed close to the bright rim. Around the central position, ammonia also shows some outflow emission although weaker than water in the red wing. Predictions of the H2O(110-101) and (111-000) antenna temperatures across the PDR are estimated with our PDR model for the forthcoming observations with the Herschel Space Observatory.Comment: 13 pages, 14 figures, 10 tables. Accepted for publication in Astronomy & Astrophysics 14 November 200