The effective resonance energy\overline {E_r } as a parameter for the correction of resonance integrals in 1/E1+α epithermal neutron spectra; tabulation of\overline {E_r } -values for 96 isotopesfor 96 isotopes

The present paper shows that the effective resonance energy \(\overline {E_r } \) introduced by RYVES, is a useful parameter for the correction of resonance integrals in non-ideal epithermal neutron spectra, which can be approximated by a 1/E^1+α-flux distribution. The definition, the characteristics and the calculation of \(\overline {E_r } \) are discussed thoroughly. Tabulations are included, giving \(\overline {E_r } \) for 96 isotopes.     

Fragmentation of doubly charged ammonia cations NH 3 ++ studied by the photoion-photoion coincidence (PIPICO) method

Doubly charged NH ₃ ⁺⁺ cations were produced by double photoionization of neutral ammonia molecules by using the synchrotron radiation from ACO as a photon source of variable energy in the 35–49 eV energy range. The fragmentation of NH ₃ ⁺⁺ was studied by the photoion-photoion coincidence (PIPICO) method. NH ₃ ⁺⁺ cations were produced in the \(\tilde X^1 \) A ₁ and \(\tilde B^1 \) electronic states of which the onset energies were measured at, respectively, 35.4±0.5 eV and 44.5±0.5 eV. It was shown that the NH ₃ ⁺⁺ ions, initially produced in their \(\tilde X^1 \) A ₁ state, rapidly dissociate (in less than 50 ns), into NH ₂ ⁺ + H⁺. Furthermore, the comparison with results obtained by other methods indicates that NH ₃ ⁺⁺ ions can either be long-lived (τ>10 µs) or slowly dissociating (1 µs<τ<10 µs) or rapidly dissociating (τ<50 ns), depending on their geometry and/or internal energy in their \(\tilde X^1 \) E A ₁ electronic state.     

The effect of pressure on the formation of alkali metal borate ion pairs at 25°C

Pressure dependent UV-visible spectrophotometric measurements were used to determine \(\Delta \bar V^ * \) and \(\Delta \bar \kappa ^ * \) for the formation of alkali metal borate ion pairs. The association constant for each ion pair was measured at 25°C and at ionic strengths of 0.1 and 1.0m over a pressure range of 1 to 2000 atm. The pressure dependence of the apparent association constants, K _A (P)/K _A (1), have been fitted to $$[RT/(P - 1)]ln[K_A (P)]/[K_A (1)] = - \Delta \bar V^0 + \Delta \bar \kappa ^0 [(P - 1)/2]$$ to determine \(\Delta \bar V^0 and \Delta \bar \kappa ^0 \) . The \(\Delta \bar V^0 \) for the alkali metal borate ion pairs range from 5–9 cm³-mol^?1. The association constants were also measured as a function of ionic strength at 1 atm. Extrapolation to I=0 yielded K _A of 2.12, 0.66, 0.76 and 1.12 for [LiB(OH)₄], [KB(OH)₄], [RbB(OH)₄] and [CsB(OH)₄], respectively. The trend generally indicates less ion pairing and a smaller volume change for the ion pair formation as the size of the cation increases. The concept of localized hydrolysis is used to explain the trend observed in the equilibrium constant of the ion pair as the cation size is changed.     

Doppelnebenklassen als Klassenbegriff und Nomenklaturprinzip für Isomere und ihre AbzÄhlung

The general principle of classifying molecules of a common gross formula according to “configurations” is founded on the combination of two abstractions among rigid molecular models with a common molecular frame, numbered places for ligands, and numbered ligands. It is shown that the various points of view, which can be taken for the classification are determined by two accordingly chosen subgroups \(\mathfrak{A}\) and \(\mathfrak{B}\) of a permutation group \(\mathfrak{S}\) , the configurations being defined by the double cosets of the product \(\mathfrak{A}\mathfrak{B}\) . Just as the irreducible representations of the symmetry group of an observable furnish the nomenclature for different types of eingenfunctions the double cosets here provide a nomenclature for the configurations. The special principle of classification is given by the choice of \(\mathfrak{A}\) , \(\mathfrak{B}\) and \(\mathfrak{S}\) . Thus, the enumeration of configuration leads to the generalised problem of enumerating double cosets. For this, three formulas are derived. In case of the special group \(\mathfrak{S} = \mathfrak{S}_n \) G. Pólya found a formula of enumeration which is shown to reduce to our formulas in the appendix.     

Apparent molal volumes of butylammonium chlorides and sodium butanecarboxylates in dilute aqueous solutions

The densities of dilute aqueous solutions of the isomers of butylammonium chlorides (n-, iso-, sec-, andtert-BuNH₃Cl) and sodium butanecarboxylates (n-, iso-, sec-, andtert-BuCOONa) have been determined at 5, 25, and 45°C using a buoyancy technique. The limiting partial molal volumes \(\bar V^\circ\) and expansibilities of the solutes have been evaluated. The branching of alkyl chain causes larger \(\bar V^\circ\) values for BuNH₃Cl series but smaller values for BuCOONa series. The \(\bar V^\circ\) values of branched isomers have been calculated using the data for volume increment accompanying methyl substitution. Good agreement with the experimental values was obtained. It is suggested that the volumetric behavior of the organic electrolytes studied is governed by the influences of the ionic groups on the hydrophobic hydration. The results have been compared with the data for butanol isomers.     

Rendements de fission cumulatifs du252Cf

The cumulative yields of 28 isotopes have been measured in the spontaneous fission of²⁵²Cf. Measurements were made by Ge(Li) gamma-spectrometry. An average number of neutrons per fission \(\bar V:3.71\) was derived from the mass distribution. Using Terrell's method, and with the mass distribution before neutron emission, measured in an other laboratory and with our results, the mass-dependent variation of \(\bar V\) was also deduced.     

Quadrupole moment of theNS 1/2-state of the hydrogen atom

The result of the quadrupole \(Q_{ns_{1/2} } \) calculation of the excitedns _1/2-state of the hydrogen atom is presented. It is shown that \(Q_{ns_{1/2} } \) turns out to be a factor (n ²+2)/3 larger than the ground-state quadrupole moment \(Q_{1s_{1/2} } \) .     

Determination of perturbed angular correlation parameter\overline {G_{22} } for111In in hydrochloric acid solutions by the sum peak methodfor111In in hydrochloric acid solutions by the sum peak method

Application of the sum peak method to indium solutions in hydrochloric acid has been studied. A calibration line to determine a PAC parameter \(\overline {G_{22} } \) has been adopted using two samples with known values of \(\overline {G_{22} } \) . The results show feasibility of the method because of its simplicity and of smaller amounts of radioactivity required in the measurement compared to the ordinary PAC method.     

The first lonization constant of carbonic acid from 25 to 250°C and to 2000 bar

The apparent first ionization constant of carbonic acid has been determined by conductivity measurements and found to vary from 4.32×10^?7 at 25°C to 1.6×10^?8 at 250°C. The pressure effect to 2000 bar has been measured, and the ratio K_p/K₁ is 7.3 at 25°C and 19 at 250°C. The standard partial molar volume change for the ionization at 1 bar, \(\Delta \bar V_1^0\) , increases from ?27.6 cm³-mole^?1 at 25°C to ?88 cm³-mole^?1 at 250°C. The volume changes are smaller at higher pressures. A linear correlation between \(\Delta \bar V_1^0\) and the partial molar compressibility for the ionization reaction has been noted. A similar correlation exists between the partial molar entropy and volume changes for the reaction.     

Röntgenkleinwinkeluntersuchungen der strahleninduzierten Aggregation von Ribonuclease,Lactat-Dehydrogenase,Glycerinaldehyd-3-phosphat-Dehydrogenase und Serumalbumin. Ein Vergleich mit Malatsynthase

The X-ray induced aggregation of ribonuclease, lactate dehydrogenase (LDH), glyceraldehyde-3-phosphate dehydrogenase (GAPDH) and serum albumin in aqueous solution was monitored in situ by means of small-angle X-ray scattering. The time dependence of several molecular parameters viz. the apparent radius of gyration \(\tilde R\) , the maximum visible diameterD, the mean degree of aggregation \(\bar x\) , and the mean radius of gyration \(\bar R\) was used to compare the various proteins with each other and with malate synthase which has been studied previously (P. Zipper andH. Durchschlag, Radiat. and Environm. Biophys., 1980). Measurements carried out with ribonuclease,LDH and serum albumin in the absence of dithiothreitol (DTT) and withGAPDH in the presence of 0.2mM DTT established the following series for the rates of aggregation of the proteins under these conditions: ribonuclease>LDH>GAPDH>serum albumin. The rate of aggregation ofGAPDH was found to be of similar magnitude as that obtained for malate synthase under comparable experimental conditions (presence of 0.2mM DTT, similar X-ray intensity) in our previous study. Within six hours from the beginning of irradiation (i.e. about the time required for the exposure of one complete scattering curve under the conditions of our experiments) the following increases of \(\tilde R\) resulted: ribonuclease 9%,LDH 7%,GAPDH 4%, serum albumin<1%. Changes of \(\tilde R\) exceeding 1% are, of course, too high to be tolerated in conventional scattering experiments.     

A topological index for the totalπ-electron energy

A modified topological index \(\tilde Z_G \) is proposed to be defined as $$\tilde Z_G = \sum\limits_{k = 0}^{[N/2]} {( - 1)^k } a_{2k} $$ for characterising theπ-electronic system of a conjugated hydrocarbonG withN carbon atoms, wherea _2k is the coefficient of the characteristic polynomial ofG defined as $$P_G (X) = ( - 1)^N \det |A - XE| = \sum\limits_{k = 0}^N { a_k X^{N - k} } $$ with an adjacency matrixA and the unit matrixE. \(\tilde Z_G \) is identical toZ _G for a tree graph, or a chain hydrocarbon.Z _G increases with a (4n+2)-membered ring formation and decreases with a 4n-membered ring formation. The totalπ-electron energyE _π of the Hückel molecular orbital is shown to be related with \(\tilde Z_G \) asE _π =Cln \(\tilde Z_G \) . With this relation generalised and extended Hückel rules for predicting the stability of an arbitrary network are proved.     

Auswertung von EMK-Messungen zur Bestimmung thermodynamischer Exzeßgrößen im System Silberchlorid—Lithiumchlorid

The partial molar excessGibbs energies \(\Delta \overline G _{AgCl}^E \) of AgCl in the binary system AgCl?LiCl have been measured over the entire composition range at temperatures between 923.15K and 1175.15K in steps of 50K, using the reversible formation cell $${{Ag\left( s \right)} \mathord{\left/ {\vphantom {{Ag\left( s \right)} {AgCl\left( l \right)}}} \right. \kern-\nulldelimiterspace} {AgCl\left( l \right)}}---LiCl\left( l \right)/C,Cl_2 $$ The measured \(\Delta \overline G _{AgCl}^E \) values were fitted by the use of theRedlich-Kister-Ansatz for thermodynamic excess functions. The evaluatedRedlich-Kister parameters have been used to calculate the molar excessGibbs energies ΔG ^E and the partial molar excessGibbs energies \(\Delta \overline G _{LiCl}^E \) of LiCl. From the temperature dependence of theRedlich-Kister parameters for ΔG ^E the partial and integral molar heats of mixing and excess entropies were calculated. For 1073 K and the mole fractionx=0.5 the following values were obtained: $$\Delta G^E = 2130\left[ {J mol^{ - 1} } \right], \Delta H^E = 1994\left[ {J mol^{ - 1} } \right], \Delta S^E = 0.127 \left[ {J mol^{ - 1} K^{ - 1} } \right]$$      

Thermodynamics of bolaform electrolytes. III. Partial and apparent molal volumes in H2O and D2O

The apparent,φ _v, and partial, \(\bar V\) ₂, molal volumes of a series of homologousbis-tetraalkylammonium bromides have been determined in H₂O and D₂O at 25°C from precision density measurements carried out with a buoyancy densimeter and a dilatometer. The Debye-Hückel theoretical limiting slope forφ _v and \(\bar V\) ₂ as a function of the square root of molar concentration is approached for all of the salts studied. the concentration dependence ofφ _v and \(\bar V\) ₂ is anomalously large and negative in both solvents, with the deviations being less negative in D₂O than in H₂O. The bolaform salts have larger \(\bar V\) ₂ ^o values in H₂O than in D₂O, contrary to the observed behavior of R₄NX salts. Possible origins of the solvent isotope effects observed are discussed in terms of structural and cavity contributions to the measured volumes. A comparison of thermodynamic transfer functions (H₂O→D₂O) for Et₄N Br and the corresponding bolaform analog appropriate in the consideration of cation-cation pairing of Et₄N⁺ ions shows inconclusive evidence for the support of the cation pair theory.     

Volumetric properties of a stoichiometric mixture of K+ and Br− ions in H/D isotope-substituted aqueous methanol at 278.15–318.15 K: I. The H2O-CH3OH-KBr system

The densities of potassium bromide solutions in aqueous methanol mixtures have been measured with an error of at most ±(1 × 10^?5) g/cm³ for methanol mole fractions x ₂ of 0.06, 0.1, 0.3, or 0.6 and for the potassium bromide mole fractions up to about 2.65 × 10^?2 at 278.15, 288.15, 298.15, 308.15, and 318.15 K. Limiting partial molar volumes $\overline V _3^\infty $ , excess molar volumes $\overline V _3^{E, \infty } $ , and expansibilities $\overline E _{p, 3}^\infty $ have been calculated for a stoichiometric mixture of solvated K⁺ and Br^? ions in the mixed solvents. In the region of x ₂ ≈ 0.25, $\overline E _{p, 3}^\infty $ changes its sign from positive to negative. The $\overline V _3^{E, \infty } $ (x ₂) trend, on the whole, reflects the topologic features of the molecular structure of aqueous methanol associated through H-bonding.     

Half-width and asymmetry of glow peaks and their consistent analytical representation

The kinetic equation which describes many electronic as well as atomic or chemical reactions under the condition of a steadily linear raise of the temperature, is considered in a mathematically exact and straightforward way. Therefore, the equation has been transformed into a dimensionsless form, using with profit the maximum condition for the intensity peak. The two temperatures T₁ and T₂, corresponding to the half-height of the intensity peak, are found as unique polynomials of the small argument \(\bar y \equiv {{k\bar T} \mathord{\left/ {\vphantom {{k\bar T} E}} \right. \kern-0em} E}\) only ( \(\bar T\) =temperature of peak maximum). Thereupon, further combinations give half-widthδ, peak asymmetryA=δ₂/δ₁ or \(\tilde A = {{\bar C} \mathord{\left/ {\vphantom {{\bar C} {(1 - \bar C)}}} \right. \kern-0em} {(1 - \bar C)}}\) and the maximum of the intensity peakJ; they again all depend only on¯y. In some cases this dependence is weak, so that e.g. it is deduced that the half-width energy product divided by \(\bar T^2 \) is an invariant, different for every kinetic orderπ: $$\frac{{\delta \cdot E[eV]}}{{\bar T^2 }} = \left\{ {\begin{array}{*{20}c} {{1 \mathord{\left/ {\vphantom {1 {4998 K for monomolecular process}}} \right. \kern-\nulldelimiterspace} {4998 K for monomolecular process}}} \\ {{1 \mathord{\left/ {\vphantom {1 {3542 K for bimolecular process}}} \right. \kern-\nulldelimiterspace} {3542 K for bimolecular process}}} \\ {{1 \mathord{\left/ {\vphantom {1 {2872 K for trimolecular process}}} \right. \kern-\nulldelimiterspace} {2872 K for trimolecular process}}} \\ \end{array} } \right.$$ By means of these correlations, activation energy valuesE [eV] can be determined accurately to within 0.5 %, so that for most experiments the inaccuracy of theδ values becomes dominant and limiting. A special nomogram for the express estimation ofE from experimentally observedδ and \(\bar T\) is demonstrated.     

Spectral variational principle for Green's functions

For a suitable approximation \(\tilde K\) (q, q′, τ) to the Dirac-Feynman Green's function of a quantummechanical system, the parameter \({\mathcal{L}\tilde K}\) is defined, where ?≡i?/?τ??. It is shown thatΔ≧0 andΔ→0 asK→K, the exact Green's function, thus providing a criterion on approximate Green's functions analogous in its role to the variational principle for wavefunctions. A second somewhat weaker criterion is also proposed, based on \(\Sigma \equiv \left[ {tr\tilde K*tr\mathcal{L}^2 \tilde K - |tr\mathcal{L}\tilde K|^2 } \right]_{\tau avg} \geqq 0\) . Recipes are given for projecting out continuum contributions toΔ or∑ and for analyzing for the discrete eigen-value spectrum.     

C(methyl)–H ⋅ ⋅ ⋅ π(aryl) Interaction Stabilizing Molecular Conformation. X-Ray Crystal Structure of an Inclusion Compound of a Nonprotic Host with Nitromethane Guest

In the cocrystal formation of a nonprotic polar (host) molecule (1) with nitromethane (guest) several weak, but directional, intermolecular interactions have vital importance. The endo conformation of the (N)-xylene group of the polycyclic succinimide-based host 1 is stabilized by a C_methyl $---$ H ??? π interaction [C ??? π /H ??? π distances are 3.554(7)/2.57 Å, the C $---$ H ??? π angle is 159^○], and the crystal packing is governed by dipole–dipole type interhost (C $ =$ )O ??? C( $ =$ O) connection [C ??? O $ =$ 3.000(5) Å and <C $ =$ O ??? C $ =$ 159.8(3)^○] in conjunction with possible C $---$ H ??? O interactions [with C ??? O distances ranging between 3.20 and 3.50 Å] involving the polar groups of both host and guest. Crystal data: 1 ??? nitromethane (1:1), C₂₆H₂₁O₂ N ? CH₃NO₂, M _w = 440.50, P2 ₁/n, a = 14.143(1), b = 7.973(1), c = 20.291(2) Å, β = 95.183(9)^○, Z = 4, D _c = 1.2840(2) g cm^?3, R = 0.055 for 1709 reflections.     

Electromagnetic structure of lighter antiprotonic atoms

The electric and magnetic fine structures of \(\bar p\) -atoms are tabulated up toZ=20. They are calculated perturbatively to second order in the Uehling potential, to first order in relativity and to all orders in recoil.     

The thermodynamic properties and solvation of lithium halides in N-methylpyrrolidone at 298.15 K

The heat capacity and density of solutions of lithium chloride, bromide, and iodide in N-methylpyrrolidone (I) were determined by calorimetry and densimetry techniques. The standard partial molar heat capacities and volumes ( $\overline {C^\circ _{p2} } $ and $\overline {V^\circ _2 } $ ) of lithium halides in I were calculated. The $\overline {C^\circ _{pi} } $ and $\overline {V^\circ _i } $ values for halogen and lithium ions in I were determined. The coordination numbers of the Li⁺, Cl^?, Br^?, and I^? ions in solutions in I at 298.15 K were calculated.