Volume 27, Issue 1

By use of the quasiparticle-quasihole space as model space, a model is established in order to determine excitation energies and transition probabilities of atomic nuclei. The equations derived show a remarkable correspondence to those in Migdal’s quasiparticle theory. The validity of the quasiparticle hypothesis, which is fundamental in Migdal’s theory, is not a necessary condition for a weak dependency of the effective interaction. This energy dependency is also independent of the choice of the one particle basis.

The representation of infinitesimal generators corresponding to the group representation dis-cussed in the preceding paper is analyzed in the Hilbert space of functionals over real test functions. Explicit expressions for these unbounded operators are constructed by means of the functio-nal derivative and by canonical operator pairs on dense domains. The behaviour under certain basis transformations is investigated, also for non-Hermitian generators. For the Hermitian ones a common, dense domain is set up where they are essentially selfadjoint. After having established a one-to-one correspondence between the real test function space and a complex Hilbert space the theory of quantum observables is applied to the functional version of a relativistic quantum field theory.

Mercier’s criterion is computed numerically for an exact class of axisymmetric MHD equilibria having possibly elliptical cross sections and a flat current profile. The main result is that the toroidal current density and the plasma beta can be increased by one order of magnitude if a) the eccentricity of the magnetic surfaces, b) the poloidal current, and c) the aspect ratio are adequately chosen, and if the ellipses are vertical.

The pulse rise times of an n-type silicon surface barrier detector were measured at 4.2 °K. At this temperature the detector was fully depleted even at very low bias and the measured pulse rise times gave direct information about the driftvelocity and the mobility. Instead of E -0.5 , an E -0.8 dependence of the mobility at moderate electric fields was found. At high electric fields agreement exists with theory.

A new method is described to obtain information on the true difference potential of interatomic interaction from the quasistatic wings of spectral lines broadened by neutral atoms. Based on the one-particle-approximation of the quasistatic theory of line broadening, it does not rely on any particular model function. Furthermore, from measurements of the temperature dependence of the line wings it may yield additional information on the potentials for the initial or final state of the line separately. The method is appplied to measurements of the red wing of the mercury absorption line 6 1 S 0 - 6 3 P 1 λ 2537 Å, perturbed by argon.

The properties of flashlamp-and laser-pumped cresyl violet lasers emitting between 620 and 710 nm were studied. In mixed cresyl violet-rhodamine 6G solutions, the excitation efficiency was found to be enhanced by more than a factor of two, the major part of the excitation energy being supplied by the rhodamine 6G fluorescence radiation. Self-modelocking in a 3-component solution, containing cresyl violet, rhodamine 6G and a saturable absorber dye, was observed.

The longitudinal proton relaxation time T 1 in methyl naphthalene crystals, differing in the arrangement and number of the substituted CH 3 groups, was measured as a function of the temperature above 77 °K and the magnetic field between 0.9 and 20 kOe. The results can be described by hindered rotation of the methyl groups with the jumping times and activation energies strongly dependent on the group arrangement. In the β-position the rotational barrier of 0.8 kcal/mol is predominantly determined by the infermolecular interaction, whereas in the case of the a-position and for adjacent CH 3 ’s the hindering potential of 2.4 kcal/mol arises largely from the intramolecular term.

The spin lattice relaxation time T 1 of protons in naphthalene and anthracene crystals is decreased by the presence of metastable triplet excitons in these crystals. The exciton induced relaxation time T 1, Exc is measured at 300 °K and 77 °K and at Larmor frequencies between 0.4 and 44 MHz. From the frequency dependence of T 1, Exc the exciton-proton correlation time τ c at the two temperatures is determined to 5.5 · 10 -12 sec and 4.1·10 -12 sec (±10%) in anthracene and 2.1·10 -11 sec and 1·10 -11 sec in naphthalene, assuming scalar proton-electron interaction and statistical incoherent hopping motion of the excitons. The predictions of a theoretical model for exciton-migration are in satisfying agreement with the experimental results as far as experimental data for the parameters of that model are available.

A high-resolution Raman spectrum of the oxygen molecule has been analysed taking into account the spin-splitting of its rotational levels, the contribution of 16 O 18 O-isotope and N 2 -impurity. The intensity contour has been simulated by a computer program.

A computer program for simulation of the rotational structure of Raman bands is described. The program is used for an analysis of the Raman spectra of gaseous chlorine.

The wave functions, calculated by the method described in a preceding article, are used for the evaluation of the r-centroids relative to the 1 - 0 transition of the X 1 Σ + state. By means of experimental line intensities, it is shown that in the expansion of the electric dipole moment, the quadratic and higher terms are not negligible.

The NMR signals of the nuclei 2 H, 35 Cl, 37 Cl, 79 Br and 81 Br have been investigated in aqueous solutions. The concentration dependence of the NMR signals of 35 Cl and 81 Br has been determined in solutions of alkali halides and alkali perchlorates in H 2 O and D 2 O and the large solvent isotope effect on the chemical shift has been established. The ratios of the Larmor frequencies of the halide nuclei relative to 2 H have been measured with high accuracy. Using the concentration dependence, the ratios of the Larmor frequencies of the halide nuclei for infinite dilution relative to 2 H in pure D 2 O are given. From these ratios, magnetic moments for the halide nuclei have been derived.

Hyperfine structure, Stark effect and Zeeman effect of the TlCl molecule have been measured with a molecular beam apparatus using electric four poles as deflecting fields and a homogeneous electric field parallel to a superimposed magnetic field in the transition region. Electric dipole transitions were induced between the hyperfine structure levels of the first rotational state J = 1 in both strong and weak external field. The following quantities could be evaluated from the spectra: the electric dipole moment µ el and the magnetic rotational dipole moment µJ of the molecule, the nuclear spin-rotational interactions c 1 and c 2 , the scalar and tensor part of the nuclear dipole-dipole interaction d S and d T , the quadrupole coupling constant e q Q of the Cl nucleus, the anisotropy of the magnetic susceptibility ξ ⊥ − ξ ∥ , the anisotropy of the magnetic shielding of the external magnetic field at the position of both nuclei (σ ⊥ - σ ∥ ) 1 and (σ ⊥ - σ ∥ ) 2 , the magnetic moment of the Cl nucleus multiplied by the scalar part of the magnetic shielding tensor µ 2 · (1 - σ S ) 2 . For the most abundant isotop 205 Tl 35 Cl the vibrational dependence of most of these quantities was measured in the vibrational states v =0, 1, 2, 3. Isotopic effects for 203 Tl 35 Cl, 205 Tl 37 Cl and 203 Tl 37 Cl were investigated in the ground vibrational state. In addition the vibrational dependence of the electric dipole moment was measured for all isotopic species. It is pointed out that the usual connections between (σ ⊥ - σ ∥ ) 1,2 and c 1,2 and between ξ ⊥ − ξ ∥ and µ J do not hold when the excited electronic states of the molecule obey Hund’s coupling case c, which occurs most probably in TlCl.

The electric and magnetic properties of the molecule 87 RbF in the rotational state J = 1 and the vibrational states v = 0, 1 were studied by a molecular beam resonance apparatus. The rotational state (J, m J ) was separated by an electric quadrupole lense as A-field and focused to the detector by a similar lense as B-field. The vibrational states could be resolved by their different Stark-effect-energies. In the transition region homogeneous electric and magnetic fields were superimposed. The observed (Δ mJ = ±1) transitions were induced electrically. The measured spectra permitted the calculation of the following molecular constants: the electric dipole moment µ el , the rotational magnetic dipole moment µ J /J, the scalar and tensor nuclear dipole-dipole-interaction d S and d T the nuclear spin-rotational interactions c Rb and c F , the nuclear quadrupole interaction e q Q Rb the nuclear magnetic moment µ(1 - σ s ) Rb , the anisotropy of the diamagnetic susceptibility (ξ ⊥ - ξ ∥ ) the anisotropy of the diamagnetic shielding of the external field by the electrons at the position of the nuclei (σ ⊥ -σ ∥ ]). The results were (J = 1, v = 0) :

The dominant contribution to the Stark-effect energy of polar 1 Σ diatomic molecules can be calculated from the model of the rigid rotator. Additional terms arise from the anharmonicity of vibration, the centrifugal distortion, the vibration-rotation interaction and the electronic polarizability. These contributions to the Stark-effect have been investigated for the molecules 205 TlF and 39 KF with a molecular beam electric resonance apparatus suitable to detect rotational transitions. Measure-ments have been performed at values of electrical field corresponding a) to a minimum in the frequency for the transition (J, m J ) = (1, 0) → (2,0) for vibrational states v = 0, 1, 2 and b) cor-responding to the electrical field where the transitions (J, m J ) = (1, 0) (0, 0) and (1, 0) → (2, 0) for v = 0 occur at the same frequency. Interpretation of our data requires more precise values of the Dunham coefficients than have been published to date. These coefficients therefore have been recalculated from rotational transitions measured at zero electrical field.

On the basis of a simple MO-approach a model to interprete the IR-absorption intensity of the aromatic CH-stretching vibration is developed. Accordingly the gradient of the CH-bond moment is a linear function of the ionicity of the CH-bond. Eight azulenes, which were deuterated at various specified positions, were synthetisized and out of their IR-spectra the gradients of the CH-bond moment at all positions of azulene could be determined. From these experimental data it is concluded, that in relation to benzene the electrons of the CH-bonds in azulene are displaced towards the C-atom at positions with high and towards the H-atom at positions with low π-electron density. Such a polarisation of the CH-bonds in azulene is confirmed, although only qualitatively, by the ionicities of the CH-bonds calculated by the CNDO/2-method and is also in accordance with other experimental observations such as bond lengths and angles, C 13 H-coupling constants, and the frequencies of the CH-stretching vibrations. It is demonstrated that experiment and calculation fail to correlate quantitatively due to in-adequacies inherent in the CNDO/2-method.

The variation of the ratio L 12 /L 21 (where L ij refers to the element of the L matrix) as a function of the mass coupling term T=G 12 /|G| 1/2 has been studied for molecules of the type XY 4 (Td), XY 3 (D 3h ) and XY 2 C 2v ) using the exact force field data. In the case of the XY 4 and XY 3 type molecules, the ratio L 12 /L 21 is nearly independent of the mass coupling and in the case of the XY 2 type, it shows a nearly linear dependence on T. The force constants have been evaluated using an empirically determined constraint for L 12 /L 21 . The values are generally in good agreement with the exact ones. In all cases except VCl 4 the exact interaction term of the F matrix is in agreement with the sign rule of Müller et al.

By means of Frost’s FSGO-method the systems Ne, Ne -Ne, Be -Be, and the molecules B 2 as a single and triple bond, CO as a double and triple bond, N 2 as a triple bond, and LiH have been calculated. The resulting energies are between 10% and 15% above the HF-limit, but the energy differences of the distinct bond representations are evidently sufficient to give an information about bond relations of a molecule. The type of bond is characterized, defining a “bond-strength”, by the position of the Gaussian orbitals.

Steady-state distributions of Au, Ag and Cu tracers in Pb wafers subjected to temperature gradients have been determined. The effective heats of transport were + 5.8 ± 1.1 for Ag, - 0.5 ± 0.3 for Au, and of the order of + 35 for Cu (all in kcal/mole, positive values denoting the impurity migrating to the cold side of the Pb wafer). No significant temperature dependence of the heats of transport could be detected. The results are difficult to reconcile with existing theories of the intrinsic and electronic contribution to the heat of transport.

EMF measurements were performed on a chemical cell containing a silver and a nitrate electrode. The systems NaNO 3 + AgNO 3 , LiNO 3 + AgNO 3 , and pure AgNO 3 were investigated in a temperature range of 240 °C to 310 °C and in the total concentration range permitted by the phase diagram. We found a linear dependence of the EMF on temperature. Six constants, characteristic for the investigated molten salts depending neither on composition nor on temperature, were determined by the analytical construction of the activity coefficients. Together with the analytically constructed excess molar Gibbs function, the excess molar entropy was calculated from calorimetric data in the literature.

Miscibility gaps for the solid systems AgCl + NaCl and AgBr+NaBr have been measured by a high temperature X-ray technique. For the two studied systems the solubility curves are very nearly symmetrical in respect to the compositions x NaCl = .513 and x NaBr = .506, while the upper critical temperature are 198 °C for AgCl + NaCl and 285 °C for AgBr+NaBr. The thermodynamic properties of the two solid systems have been calculated using only experimental solubility data. Values of activity and of enthalpy of mixing were estimated and compared with those reported in literature.

The ion-molecule reactions of thiothionylfluoride have been studied by ion cyclotron resonance spectrometry. The major secondary ions are S 2 F 3 + , S 3 F + , and S 3 F 2 + . In a consecutive reaction of S 3 F 2 + the tertiary ion S 4 F 2 + is formed. The rate constant of the IMR with the greatest yield S 2 F 2 + + SSF 2 → S 3 F 2 + + SF was estimated to k = 2 · 10 -9 cm 3 molecule -1 sec -1 . The results were compared with the mass spectrum of thiothionylfluoride. They permit conclusions on chemical reactions of lower sulphurfluorides.

Solid-liquid equilibria were studied by a visual method in order to draw the polythermal pro-jections of the (Tl, Na, Li)NO 3 , (Tl, Na, Rb)NO 3 , and (Tl, Na, Cs)NO 3 ternary systems. The seven pertinent binaries are also discussed and data concerning the invariant points and crystallization regions are given.

An electron attachment ion source was modified in order to be used for quantitative measurement of pure organic substances at pressures up to 1.5 ·10 -3 Torr in the space around the ion source. The ion intensity was determined by counting the electron pulses produced by single ions in the secondary electron multiplier. This resulted in higher sensitivities. The measurements of different organic compounds showed that molecular polymers are held together primarily by hydro-gen bonding and by dipole interaction. No molecular polymers could be identified in nonpolar substances. The pressure dependence of the ion intensities indicates that the molecular polymers originate from the gas phase of the reservoir. During the ionization process the hydroxide loses its hydrogen atom as was shown with deuterated samples.