 161  Author
 D. H. Sutter  Requires cookie*   Title
 A Note on the OffDiagonal Elements of the Density Matrix in Thermal Equilibrium and Thermal Radiation    Abstract
 A closer look at the offdiagonal elements of the density matrix of a thermal gas phase molecular ensemble reveals, that they lead to a contribution to thermal radiation which increases in power proportional to the number of particles. A quantitative comparison of this contribution to the one originating from spontaneous emission is given. In treatments of relaxation processes in gas phase spectroscopy the offdiagonal elements of the density matrix are usually set to zero in thermal equilibrium [1]. To justify this approximation the following argument is used: "Due to collisions the phases, cpv, of the contributions of the individual molecules will be statistically spread and if the ensemble comprises a sufficiently large number of particles, N, the sum 1 £ • > e l<p ' n A e may be approximated by the integral which is zero". However, since one is usually interested to calculate most probable values for macroscopic observables, for instance the polarization of a sample, the factor 1 jN, present in the expression for the density matrix elements, is compensated by another factor of N (see below) and the basic problem is essentially that of calculating the N most probable absolute value of the sum 2 el<F 'With increasing N this value is known to go to infinity proportional to j/IV rather than to zero. Thus it is not immediately obvious that   
Reference
 Z. Naturforsch. 35a, 992—994 (1980)   
Published
 1980   
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 ZNA198035a0992_n    Volume
 35  
164  Author
 R. M. Agarwal, R.P S Rathore  Requires cookie*   Title
 Phonon Dispersion in Noble Metals    Abstract
 A new lattice dynamical model comprising various interactions among the constituents of noble metals is developed. The model assumes central corecore coupling extending to the first neighbours only. Overlap interactions among neighbouring dshells are expressed in terms of an angular parameter. Volume interactions for coreconduction electrons and dshellconduction electrons are described through a simple expression. Interactions between core and dshell are also accounted for adequately. The lattice is considered in equilibrium under the volume dependent energy of cores, conduction electrons and the dshell electrons. The obtained dispersion relations for copper and silver are compared with (a) experimental data, (b) results of a recent firstprinciple calculation and (c) results of a recent phenomenological study.   
Reference
 Z. Naturforsch. 35a, 1001—1005 (1980); received March 18 1980   
Published
 1980   
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 default:Reihe_A/35/ZNA198035a1001.pdf    Identifier
 ZNA198035a1001    Volume
 35  
165  Author
 MyriamS. De Giambiagi, Mario Giambiagi, HenriqueG P Lins De Barros  Requires cookie*   Title
 Convergence Problems and Energetic Regions in n Excited States of Certain Conjugated Molecules    Abstract
 When calculating n bond orders of excited and superexcited states of conjugated molecules, difficulties arise in applying the variation method; besides, the convergence problems involved are well known. For pyridazine, chosen for discussion, 27 states are considered; the convergence problem is envisaged through two criteria in the choice of a parameter introduced in the compromise Hamiltonian. This convergence parameter is related to the variation method. There exist three particular solutions for bond orders, which divide the 27 states into energetical regions.   
Reference
 Z. Naturforsch. 35a, 1006—1012 (1980); received June 10 1980   
Published
 1980   
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 default:Reihe_A/35/ZNA198035a1006.pdf    Identifier
 ZNA198035a1006    Volume
 35  
166  Author
 Friedrich Seitz, TerenceE. Wood, Peter Day  Requires cookie*   Title
 Optical Spectroscopy of Mixed Metamagnetic Fe,Co,_xCl2 Crystals    Abstract
 Electronic absorption spectra are reported for single crystals of composition Fe^Coi^C^ as a function of temperature from 300 K to 4 K. A broad band at 436 nm is assigned to Fe (II) > Co (II) charge transfer and the temperature dependence of its intensity is related to the magnetic exchange between the ions. The 2 Txg(2 H) excitation of Co (II) in the mixed crystals has an unusual temperature dependence which correlates with the Neel temperature.   
Reference
 Z. Naturforsch. 35a, 1013—1019 (1980); received July 26 1980   
Published
 1980   
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 default:Reihe_A/35/ZNA198035a1013.pdf    Identifier
 ZNA198035a1013    Volume
 35  
167  Author
 E. Ibisch, U. Andresen  Requires cookie*   Title
 High Resolution Spectroscopy of the v5 Band of Fluoroformd (CDF3) by the Laser Stark Method    Abstract
 The j'5 perpendicular band of CDF3 has been studied by means of laser Stark spectroscopy using the 10.4 [xm band of the 12 C 16 02 and the 12 C 18 02 laser as infrared radiation sources. The assignment was established for more than 500 resonances. The majority of them was measured in saturation dip technique. A leastsquares analysis of the Stark spectrum, together with recent microwave and infrared results, gave the rotationvibration parameters and the dipole moment of the j'5 state. A brief description of the apparatus is also given.   
Reference
 Z. Naturforsch. 35a, 1020—1029 (1980); received July 19 1980   
Published
 1980   
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 ZNA198035a1020    Volume
 35  
168  Author
 C. Bojarski, E. Grabowska  Requires cookie*   Title
 Effect of Acceptor Concentration upon Donor Fluorescence Decay and Quantum Yield    Abstract
 The fluorescence decay times (r/to) and quantum yields (rj/rjo) of rhodamine 6G (donor) in their dependence on the concentration of malachite green (acceptor) in ethanol were measured for the donor to acceptor concentration ratios yn/yA 3.48 and 0.35. At fixed the values of T/TO and r]/r]o are markedly lower for the systems with higher yr>/yAThe experimental results are compared with the theory of a multistep excitation energy transfer from donor to acceptor. Good agreement between theory and experiment was found for the critical distances Hod = 60.7 A and i?oA = 53.8Ä calculated from spectroscopic data. In the case of ynlyx = 0.35, the experimental results can also be properly described using the FörsterGalanin theory, whereas for the system with yn/yA — 3.48 the multistep energy transfer plays a significant role.   
Reference
 Z. Naturforsch. 35a, 1030—1035 (1980); received June 27 1980   
Published
 1980   
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 ZNA198035a1030    Volume
 35  
169  Author
 PaulR. Gerber, Martin Schadt, F. Hoffmann, La Roche, Co, Ltd  Requires cookie*   Title
 On the Measurement of Elastic Constants in Nematic Liquid Crystals: Comparison of Different Methods    Abstract
 Different methods of measuring elastic constants of nematic liquid crystals by deformation of homogeneously and homeotropically oriented layers through external magnetic and electric fields, respectively, are critically examined. Possible sources of uncertainties are quantitatively explored. An approximative numerical fitting procedure is proposed allowing to take conductivity effects in electrically deformed layers up to large conductivities and/or temperatures into account. A novel, accurate and simple monitoring method to determine twist elastic constants is described. The measurements of the temperature dependence of the splay bend and twist elastic constants of the positive dielectric mixture R0TN403 are presented.   
Reference
 Z. Naturforsch. 35a, 1036—1044 (1980); received June 19 1980   
Published
 1980   
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 default:Reihe_A/35/ZNA198035a1036.pdf    Identifier
 ZNA198035a1036    Volume
 35  
170  Author
 Masao Hashimoto, Norbert Weiden, Alarich Weiss  Requires cookie*   Title
 Chlorine NQR on Derivatives of Chloral    Abstract
 The 35 C1NQR spectrum of several derivatives of chloral, Cl3CCHO, was studied in the ranee 77 K ^ T Tm. By use of the spin echo double resonance technique a relative assignment of the resonances to different ClaCgroups within one crystallized compound was possible. The solid compounds studied are: High temperature phase of chloral hydrate, Cl3CCH(OH)2; parachloral, (Cl3CCHO)3, (aand ßisomer); the two phases of chloral hemihydrate CI3CCHO • 1/2 H20; chloralide (II); chloralhemithiohydrate, CI3CCHO • 1/2 H2S. The structure of the molecules in the solid state and the fade out of the NQR resonances are discussed.   
Reference
 Z. Naturforsch. 35a, 1045—1053 (1980); received July 28 1980   
Published
 1980   
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 ZNA198035a1045    Volume
 35  
171  Author
 FriedrichFranz Seelig  Requires cookie*   Title
 Unrestricted Harmonic Balance A General Method to Evaluate Periodic Structures in Time and/or Space of Arbi trary Stability for Nonlinear Chemical Reaction and ReactionDiffusion Systems. I. Theory and Computer Program for Timedependent Systems    Abstract
 Periodic structures in chemical kinetic systems can be evaluated by an extension of the wellknown method of harmonic balance, which yields very simple expressions in the case of linear systems containing only zero and first order reactions. The far more interesting nonlinear systems containing e.g. second order reactions which in case of open systems far from thermodynamic equilibrium give rise to nonclassical phenomena like oscillations, chemical waves, excitability, hysteresis, multistability, dissipative structures etc. can be treated in a similar way by introducing new pseudolinear quantities utilizing certain group properties of harmonic expansions. The resulting complicated implicit nonlinear algebraic equations are solved by a method developed by Powell and show good convergence. Since this method — in contrast to the conventional method of simulation — is independent from the stability of the periodic structure to be evaluated it can even be applied to unstable cases where the simulation method necessarily fails. An evaluation of the stability is included in the developed computer program.   
Reference
 Z. Naturforsch. 35a, 1054—1061 (1980); received July 26 1980   
Published
 1980   
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 ZNA198035a1054    Volume
 35  
172  Author
 S. J. Cvvin, J. Brunvoll, B. N. Cyvin, M. Somer, W. Brockner  Requires cookie*   Title
 Schwingungsberechnungen des käfigstrukturierten P4S3    Abstract
 Molecular Vibration Analysis of cagelike P4S3 The P4S3 molecule is supposed to have a cagestructure of C3V symmetry. A normal coordinate analysis for this molecule was performed, based on a very simple initial force field with three numerical parameters and valence coordinates including redundancies. A complete set of independent symmetry coordinates is given. The force field was refined by adjusting the symmetry force constants to fit exactly a set of observed frequencies. This final force field was used to calculate the firstorder Coriolis coupling coefficients and the mean amplitudes of vibrations. The standard thermodynamics functions from spectroscopic data are also given.   
Reference
 Z. Naturforsch. 35a, 1062—1065 (1980); eingegangen am 28. Juli 1980   
Published
 1980   
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 ZNA198035a1062    Volume
 35  
173  Author
 P. Rosmus, E.A Reinsch  Requires cookie*   Title
 Calculation of Molecular Constants for the Ground States of the NeH + and KrH + Ions    Abstract
 Potential energy and dipole moment functions have been calculated for the ground states of the NeH+ (1.0 ^ R ^ 15 a. u.) and the KrH+ (1.6 ^ R ^ 20 a. u.) ion from highly correlated SCEP/VAR and SCEP/CEPA electronic wave functions. The following spectroscopic constants have been derived: Ne2<>H+ re = 0.996±0.003 A, we = 2896±20cm" 1 , D0(Ne + H+) = 2.10 ± 0.05 eV; Kr 84 H + re = 1 419 ± 0.003 Ä, we = 2561 ±20 cm" 1 , Z>0(Kr + H+) = 4.65 ±0.05 eV. The Einstein transition probability coefficients of spontaneous emission have been calculated for all transitions of Ne 20 H+, Ne 20 D + , Kr 84 H+ and Kr 84 D+, respectively.   
Reference
 Z. Naturforsch. 35a, 1066—1070 (1980); received July 23 1980   
Published
 1980   
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 ZNA198035a1066    Volume
 35  
174  Author
 A. H. Jubert  Requires cookie*   Title
 Recombination Constants Calculation of Reactions between Fluorine Atoms and and CIF    Abstract
 Recombination constants for reactions between fluorine atoms and CO, NO2, SO3, FSO3, CIO2, NF2 and CIF were calculated by means of a method developed by J. Troe. N2 was used as bath gas and a temperature of 300 K was considered. The following values were obtained: 1.7 x 10 16 , 9.2 x 10 16 , 2.2 X 10 17 , 7.0 X 10 18 , 1.7 X 10 19 , 2.6 x 10 17 , 1.0 X 10 17 , 2.3 X 10 16 cm« mol" 2 s~i respectively.   
Reference
 Z. Naturforsch. 35a, 1071—1075 (1980); received July 22 1980   
Published
 1980   
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 ZNA198035a1071    Volume
 35  
175  Author
 M. Siegmund, J. Bendig  Requires cookie*   Title
 Die Lösungsmittelabhängigkeit der Elektronenspektren und die Änderung der Dipoleigenschaften Nsubstituierter Acridone bei elektronischer Anregung    Abstract
 The absorption and fluorescence spectra of acridone, Nmethylacridone and Nphenylacridone are measured at 298 K for 35 solvents of different polarity. For the long wave 1 Latransition, which shows a distinct positive solvatochromism, the oscillator strenght and the natural fluorescence lifetime are calculated. The change of the dipole moment (pa.), determined from the Stokes' shift as a function of solvent polarity, is nearly parallel to that of the ground state (pg). The absolute values and directions of pg and pe confirm the increasing polar character of the Sistate within the sequence Nphenylacridone, acridone and Nmethylacridone. These values are used for an interpretation of the charge distribution and solvatation of the Soand Sistates. By consideration of the solvent relaxation and the activation energy of the temperature dependent S1T2 intersystem crossing process it is shown that in addition to the decrease of the Sienergy with increasing solvent polarity the T2energy increases relative to So, especially in the case of protic solvents.   
Reference
 Z. Naturforsch. 35a, 1076—1086 (1980); eingegangen am 5. April 1980   
Published
 1980   
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 ZNA198035a1076    Volume
 35  
176  Author
 P. S. Grover, M.S A Muhammed, S. A. Sarai  Requires cookie*   Title
 Equilibrium Positron Decay Rates in Helium    Abstract
 Equilibrium positron decay rates in helium gas have been computed over a wide range of temperatures and electric fields based on the model due to McEachran et al. [7]. Agreement between the theoretical and experimental values of the decay rate at room temperature and zero electric field is quite good.   
Reference
 Z. Naturforsch. 35a, 1087—1089 (1980); received June 6 1980   
Published
 1980   
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 ZNA198035a1087    Volume
 35  
177  Author
 GregoryM. Neumann, PeterG. Cullis, PeterJ. Derrick  Requires cookie*   Title
 Mass Spectrometry of Polymers: Polypropylene Glycol    Abstract
 Mass spectra have been measured, using the field desorption technique, for polypropylene glycols with nominal massaverage relative molecular masses of 1000, 2000, 3000 and 4000. Ions of up to mjz 7400 have been observed. Major peaks in the spectra correspond to (Mf H) + ions. (M + Na) + ions are observed if sodium iodide is added to the sample. There are strong peaks corresponding to fragmentation of the polymer chains close to their termini. It is suggested that these fragmentations are induced by the strong electric fields at the emitter.   
Reference
 Z. Naturforsch. 35a, 1090—1097 (1980); received July 30 1980   
Published
 1980   
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 ZNA198035a1090    Volume
 35  
178  Author
 N. C. Haider  Requires cookie*   Title
 Structure Analysis of VacuumDeposited Mg Thin Films    Abstract
 Thin films of Mg, in the thickness range of 23,000 ~ 93,000 A, were prepared at 10~ 6 Torr pressure and 45° C temperature. The xray diffraction spectra (XDS) have been measured for several reflections with crystal monochromated and Nifiltered CuKai radiation. A detailed Fourier analysis of the broadening of xray lines indicated very strong effects of the oxidation of the surface, thermal stress along 100 and 002 planes, and preferred orientation along 002 planes parallel to the surface of the substrate.   
Reference
 Z. Naturforsch. 35a, 1098—1103 (1980); received July 30 1980   
Published
 1980   
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 ZNA198035a1098    Volume
 35  
179  Author
 H. Stumpf  Requires cookie*   Title
 Functional Quantum Theory of the Nonlinear Spinor Field as a LeptonHadron Model with Quark Confinement    Abstract
 The noncanonical Heisenberg dipole regularization of a nonlinear spinor field is interpreted as a system of lepton quark pairs in the oneparticle sector. In the framework of functional quantum theory a method is given to derive an independent leptonquark dynamics with quark confinement from the fundamental spinor field. Functional quantum theory is a new formulation of quantum theory and a new field theoretic calculational procedure which allows the treatment of quantized fields with positive metric as well as with indefinite metric beyond perturbation theory. It was developed by Stumpf and coworkers, cf. Stumpf [1]. In particular, it was devoted to the evaluation of Heisenberg's quantized nonlinear spinor equation with dipole ghost regularization, cf. Heisenberg [2]. The basic idea of this approach is to regularize the nonrenormalizable nonlinear spinor field by a combination of a real physical particle, a monopole ghost particle and a dipole ghost particle in the oneparticle sector of the corresponding state space. This leads to an indefinite metric in this space. In order to achieve a correct physical and probabilistic interpretation of this regularization procedure, the ghost particles must have the following properties: i) To any physical particle state with positive norm in the oneparticle sector belongs one monopole ghost state and one dipole ghost state which have to be combined in such a way that the propagator of the spinor field contains no singular distributions. ii) The monopole ghost states must have vanishing norm and have to be included in the physical state space, while the dipole ghosts have to form the unphysical part of the state space. The latter condition leads immediately to unitarization. The weakest assumption with respect to unitarization is that the dipole ghosts are not 03404811 / 80 / 10001104 $ 01.00/0. Please < allowed to form ingoing or outgoing states in scattering processes. Heisenberg [2] demonstrated for the Lee model that under this assumption unitarization is possible. To perform this kind of unitarization for the relativistic nonlinear spinor field, functional quantum theory is needed. It should be noted that under this assumption no local physical and probabilistic interpretation of the quantized spinor field is possible. Rather this interpretation is confined to the asymptotics, i.e. to the ^matrix. Furthermore, it is tacitly assumed that the manyparticle sectors of the state space which contain besides scattering states also bound states, do not show any irregular behavior, i.e. that from these sectors only the free manyparticle dipole ghost states have to be excluded while all other states must be physical ones. This, of course, has to be proven by direct construction as for bound states no general statements can be made. For this construction functional quantum theory is needed. With respect to the identification of the physical particles resulting from the quantized spinor field, the physical particles of the oneparticle state sector should be identified with the pointlike particles occurring in nature, while all other particles are considered to be bound states of the spinor field. In the original version of Heisenberg [2] the physical oneparticle states were assumed to represent nucleons, i.e . the theorj^ was based on the idea that the hadrons are the fundamental pointlike particles, w T hile, without detailed discussion, the leptons were sometimes identified with the dipole ghosts, cf. Heisenberg [2], Dürr [3]. The recent developments of elementary particle physics, however, indicate that just the opposite role of leptons and hadrons might be successful for an explanation of the elementary particle spectrum, i.e. that the leptons should be identified with the fundamental particle states of the oneparticle sector with positive norm, while quasihadrons should be considered as ghost particle states with indefinite metric. The present experimental identification rests on the following scheme of leptons and quarks, Harari [4], Zichichi [5] and corresponding righthanded singlets, er a reprint rather than making your own copy. Notizen 1105   
Reference
 Z. Naturforsch. 35a, 1104—1107 (1980); received July 31 1980   
Published
 1980   
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 default:Reihe_A/35/ZNA198035a1104_n.pdf    Identifier
 ZNA198035a1104_n    Volume
 35  
180  Author
 H. P. Trivedi  Requires cookie*   Title
 Equivalence of the Variational Criteria in the Calculation of the Nuclear SpinSpin Coupling Constant of HD    Abstract
 Using symmetry arguments it is shown that the variation of the self coupling, the cross coupling and the total second order energy are equivalent criteria for the calculation of the nuclear spinspin coupling constant of HD and larger symmetric molecules. A previously given condition guaranteeing this equivalence is shown to be unnecessarily restrictive. A wide variety of perturbationvariation methods have been applied to the study of the nuclear spinspin coupling constant of the simplest system, the molecule HD. Distinction has been routinely made [1—5] between the results obtained using three variational criterianamely, the variation of (i) the self coupling energy, (ii) the cross coupling energy, and (iii) the total second order energy. It has been stated [6] that the three criteria become equivalent if, and only if, the perturbed wavefunctions and are expanded over the same bases [7]. As it stands, this condition appears somewhat arbitrary and physically unsatisfactory because of its bases dependence. In this letter we seek a physical basis for it and find that it implies a certain unnecessarjr restriction on the form of the perturbed wavefunction ip^. We also point out that the charge symmetry of the nuclear framework directly guarantees a unique result and hence the equivalence of the three variational criteria for HD. This result is subsequently generalised to larger symmetric molecules. The proof is trivial and goes as follows. We rewrite the contact perturbation   
Reference
 Z. Naturforsch. 35a, 1108—1109 (1980); received May 27 1980   
Published
 1980   
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