Rotational spectroscopy of the HCCO and DCCO radicals in the millimeter and submillimeter range

The ketenyl radical, HCCO, has recently been detected in the ISM for the first time. Further astronomical detections of HCCO will help us understand its gas-grain chemistry, and subsequently revise the oxygen-bearing chemistry towards dark clouds. Moreover, its deuterated counterpart, DCCO, has never been observed in the ISM. HCCO and DCCO still lack a broad spectroscopic investigation, although they exhibit a significant astrophysical relevance. In this work we aim to measure the pure rotational spectra of the ground state of HCCO and DCCO in the millimeter and submillimeter region, considerably extending the frequency range covered by previous studies. The spectral acquisition was performed using a frequency-modulation absorption spectrometer between 170 and 650 GHz. The radicals were produced in a low-density plasma generated from a select mixture of gaseous precursors. For each isotopologue we were able to detect and assign more than 100 rotational lines. The new lines have significantly enhanced the previous data set allowing the determination of highly precise rotational and centrifugal distortion parameters. In our analysis we have taken into account the interaction between the ground electronic state and a low-lying excited state (Renner-Teller pair) which enables the prediction and assignment of rotational transitions with $K_a$ up to 4. The present set of spectroscopic parameters provides highly accurate, millimeter and submillimeter rest-frequencies of HCCO and DCCO for future astronomical observations. We also show that towards the pre-stellar core L1544, ketenyl peaks in the region where $c$-$\mathrm{C_3H_2}$ peaks, suggesting that HCCO follows a predominant hydrocarbon chemistry, as already proposed by recent gas-grain chemical models

Spectral determinants and zeta functions of Schr\"odinger operators on metric graphs

A derivation of the spectral determinant of the Schr\"odinger operator on a metric graph is presented where the local matching conditions at the vertices are of the general form classified according to the scheme of Kostrykin and Schrader. To formulate the spectral determinant we first derive the spectral zeta function of the Schr\"odinger operator using an appropriate secular equation. The result obtained for the spectral determinant is along the lines of the recent conjecture.Comment: 16 pages, 2 figure

A new proof of the Vorono\"i summation formula

We present a short alternative proof of the Vorono\"i summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics as a trace formula for a Schr\"odinger operator on a non-compact quantum graph \mathfrak{G} [S. Egger n\'e Endres and F. Steiner, J. Phys. A: Math. Theor. 44 (2011) 185202 (44pp)]. As a byproduct we give a new proof of a non-trivial identity for a particular Lambert series which involves the divisor function d(n) and is identical with the trace of the Euclidean wave group of the Laplacian on the infinite graph \mathfrak{G}.Comment: Enlarged version of the published article J. Phys. A: Math. Theor. 44 (2011) 225302 (11pp

Optical conductivity of wet DNA

Motivated by recent experiments we have studied the optical conductivity of DNA in its natural environment containing water molecules and counter ions. Our density functional theory calculations (using SIESTA) for four base pair B-DNA with order 250 surrounding water molecules suggest a thermally activated doping of the DNA by water states which generically leads to an electronic contribution to low-frequency absorption. The main contributions to the doping result from water near DNA ends, breaks, or nicks and are thus potentially associated with temporal or structural defects in the DNA.Comment: 4 pages, 4 figures included, final version, accepted for publication in Phys. Rev. Let

The CDMS view on molecular data needs of Herschel, SOFIA, and ALMA

The catalog section of the Cologne Database for Molecular Spectroscopy, CDMS, contains mostly rotational transition frequencies, with auxiliary information, of molecules observable in space. The frequency lists are generated mostly from critically evaluated laboratory data employing established Hamiltonian models. The CDMS has been online publicly for more than 12 years, e.g., via the short-cut http://www.cdms.de. Initially constructed as ascii tables, its inclusion into a database environment within the Virtual Atomic and Molecular Data Centre (VAMDC, http://www.vamdc.eu) has begun in June 2008. A test version of the new CDMS is about to be released. The CDMS activities have been part of the extensive laboratory spectroscopic investigations in Cologne. Moreover, these activities have also benefit from collaborations with other laboratory spectroscopy groups as well as with astronomers. We will provide some basic information on the CDMS and its participation in the VAMDC project. In addition, some recent detections of molecules as well as spectroscopic studies will be discussed to evaluate the spectroscopic data needs of Herschel, SOFIA, and ALMA in particular in terms of light hydrides, complex molecules, and metal containing speciesComment: 14 pages, 1 figure; AIP Conf. Proc., accepted; Proceedings of the Eighths International Conference on Atomic and Molecular Data and Their Applicatio

Zeta functions of quantum graphs

In this article we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle. We start by considering the special case of the star graph with Neumann matching conditions at the center of the star. We then extend the technique to allow any matching conditions at the center for which the Laplace operator is self-adjoint and finally obtain an expression for the zeta function of any graph with general vertex matching conditions. In the process it is convenient to work with new forms for the secular equation of a quantum graph that extend the well known secular equation of the Neumann star graph. In the second half of the article we apply the zeta function to obtain new results for the spectral determinant, vacuum energy and heat kernel coefficients of quantum graphs. These have all been topics of current research in their own right and in each case this unified approach significantly expands results in the literature.Comment: 32 pages, typos corrected, references adde

Topological phases for bound states moving in a finite volume

We show that bound states moving in a finite periodic volume have an energy correction which is topological in origin and universal in character. The topological volume corrections contain information about the number and mass of the constituents of the bound states. These results have broad applications to lattice calculations involving nucleons, nuclei, hadronic molecules, and cold atoms. We illustrate and verify the analytical results with several numerical lattice calculations.Comment: 4 pages, 1 figure, version to appear in Phys. Rev. D Rapid Communication

The Berry-Keating operator on L^2(\rz_>, x) and on compact quantum graphs with general self-adjoint realizations

The Berry-Keating operator H_{\mathrm{BK}}:= -\ui\hbar(x\frac{ \phantom{x}}{ x}+{1/2}) [M. V. Berry and J. P. Keating, SIAM Rev. 41 (1999) 236] governing the Schr\"odinger dynamics is discussed in the Hilbert space L^2(\rz_>, x) and on compact quantum graphs. It is proved that the spectrum of $H_{\mathrm{BK}}$ defined on L^2(\rz_>, x) is purely continuous and thus this quantization of $H_{\mathrm{BK}}$ cannot yield the hypothetical Hilbert-Polya operator possessing as eigenvalues the nontrivial zeros of the Riemann zeta function. A complete classification of all self-adjoint extensions of $H_{\mathrm{BK}}$ acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of $H_{\mathrm{BK}}$. In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue counting function are derived. Furthermore, we introduce the "squared" Berry-Keating operator $H_{\mathrm{BK}}^2:= -x^2\frac{ ^2\phantom{x}}{ x^2}-2x\frac{ \phantom{x}}{ x}-{1/4}$ which is a special case of the Black-Scholes operator used in financial theory of option pricing. Again, all self-adjoint extensions, the corresponding secular equation, the trace formula and the Weyl asymptotics are derived for $H_{\mathrm{BK}}^2$ on compact quantum graphs. While the spectra of both $H_{\mathrm{BK}}$ and $H_{\mathrm{BK}}^2$ on any compact quantum graph are discrete, their Weyl asymptotics demonstrate that neither $H_{\mathrm{BK}}$ nor $H_{\mathrm{BK}}^2$ can yield as eigenvalues the nontrivial Riemann zeros. Some simple examples are worked out in detail.Comment: 33p

Investigation of octupole vibrational states in 150Nd via inelastic proton scattering (p,p'g)

Octupole vibrational states were studied in the nucleus $^{150}\mathrm{Nd}$ via inelastic proton scattering with \unit[10.9]{MeV} protons which are an excellent probe to excite natural parity states. For the first time in $^{150}\mathrm{Nd}$, both the scattered protons and the $\gamma$ rays were detected in coincidence giving the possibility to measure branching ratios in detail. Using the coincidence technique, the $B(E1)$ ratios of the decaying transitions for 10 octupole vibrational states and other negative-parity states to the yrast band were determined and compared to the Alaga rule. The positive and negative-parity states revealed by this experiment are compared with Interacting Boson Approximation (IBA) calculations performed in the (spdf) boson space. The calculations are found to be in good agreement with the experimental data, both for positive and negative-parity states