Nuclear structure effects in internal conversion

Experimental studies of nuclear effects in internal conversion in Ta¹⁸¹ and Lu¹⁷⁵ have been performed. Nuclear structure effects (“penetration” effects), in internal conversion are described in general. Calculation of theoretical conversion coefficients are outlined. Comparisons with the theoretical conversion coefficient tables of Rose and Sliv and Band are made. Discrepancies between our results and those of Rose and Sliv are noted. The theoretical conversion coefficients of Sliv and Band are in substantially better agreement with our results than are those of Rose. The ratio of the M1 penetration matrix element to the M1 gamma-ray matrix element, called λ, is equal to + 175 ± 25 for the 482 keV transition in Ta¹⁸¹ . The results for the 343 keV transition in Lu¹⁷⁵ indicate that λ may be as large as – 8 ± 5. These transitions are discussed in terms of the unified collective model. Precision L subshell measurements in Tm¹⁶⁹ (130keV), W¹⁸² (100 keV), and Ta¹⁸¹ (133 keV) show definite systematic deviations from the theoretical conversion coefficients. The possibility of explaining these deviations by penetration effects is investigated and is shown to be excluded. Other explanations of these anomalies are discussed.

Depth-sensitive analysis of fluorine on lunar sample surfaces and in carbonaceous chondrites by a nuclear resonant reaction technique

The nuclear resonant reaction ¹⁹F(ρ,αγ)¹⁶O has been used to perform depth-sensitive analyses of fluorine in lunar samples and carbonaceous chondrites. The resonance at 0.83 MeV (center-of-mass) in this reaction is utilized to study fluorine surface films, with particular interest paid to the outer micron of Apollo 15 green glass, Apollo 17 orange glass, and lunar vesicular basalts. These results are distinguished from terrestrial contamination, and are discussed in terms of a volcanic origin for the samples of interest. Measurements of fluorine in carbonaceous chondrites are used to better define the solar system fluorine abundance. A technique for measurement of carbon on solid surfaces with applications to direct quantitative analysis of implanted solar wind carbon in lunar samples is described.

Nuclear hyperfine interactions in W^(182), W^(183), and Pt^(195) as studies by the Mossbauer effect

The Mössbauer technique has been used to study the nuclear hyperfine interactions and lifetimes in W¹⁸² (2⁺ state) and W¹⁸³ (3/2^- and 5/2^- states) with the following results: g(5/2^-)/g(2⁺) = 1.40 ± 0.04; g(3/2^- = -0.07 ± 0.07; Q(5/2^-)/Q(2⁺) = 0.94 ± 0.04; T_1/2(3/2^-) = 0.184 ± 0.005 nsec; T_1/2(5/2^-) >̰ 0.7 nsec. These quantities are discussed in terms of a rotation-particle interaction in W¹⁸³ due to Coriolis coupling. From the measured quantities and additional information on γ-ray transition intensities magnetic single-particle matrix elements are derived. It is inferred from these that the two effective g-factors, resulting from the Nilsson-model calculation of the single-particle matrix elements for the spin operators ŝ_z and ŝ₊, are not equal, consistent with a proposal of Bochnacki and Ogaza.

The internal magnetic fields at the tungsten nucleus were determined for substitutional solid solutions of tungsten in iron, cobalt, and nickel. With g(2⁺) = 0.24 the results are: |H_eff(W-Fe)| = 715 ± 10 kG; |H_eff(W-Co)| = 360 ± 10 kG; |H_eff(W-Ni)| = 90 ± 25 kG. The electric field gradients at the tungsten nucleus were determined for WS₂ and WO₃. With Q(2⁺) = -1.81b the results are: for WS₂, eq = -(1.86 ± 0.05) 10¹⁸ V/cm²; for WO₃, eq = (1.54 ± 0.04) 10¹⁸ V/cm² and ƞ = 0.63 ± 0.02.

The 5/2^- state of Pt¹⁹⁵ has also been studied with the Mössbauer technique, and the g-factor of this state has been determined to be -0.41 ± 0.03. The following magnetic fields at the Pt nucleus were found: in an Fe lattice, 1.19 ± 0.04 MG; in a Co lattice, 0.86 ± 0.03 MG; and in a Ni lattice, 0.36 ± 0.04 MG. Isomeric shifts have been detected in a number of compounds and alloys and have been interpreted to imply that the mean square radius of the Pt¹⁹⁵ nucleus in the first-excited state is smaller than in the ground state.

Applications of a nuclear technique for depth-sensitive hydrogen analysis : trapped H in lunar samples and the hydration of terrestrial obsidian

The resonant nuclear reaction ¹⁹F(p,αy)¹⁶O has been used to perform depth-sensitive analyses for both fluorine and hydrogen in solid samples. The resonance at 0.83 MeV (center-of-mass) in this reaction has been applied to the measurement of the distribution of trapped solar protons in lunar samples to depths of ~1/2µm. These results are interpreted in terms of a redistribution of the implanted H which has been influenced by heavy radiation damage in the surface region. Fluorine determinations have been performed in a 1-µm surface layer on lunar and meteoritic samples using the same ¹⁹F(p,αy)¹⁶O resonance. The measurement of H depth distributions has also been used to study the hydration of terrestrial obsidian, a phenomenon of considerable archaeological interest as a means of dating obsidian artifacts. Additional applications of this type of technique are also discussed.

I. Nuclear spin-internal-rotation-coupling. II. Fluorine spin-rotation interaction and magnetic shielding in fluorobenzene

Part I.

The interaction of a nuclear magnetic moment situated on an internal top with the magnetic fields produced by the internal as well as overall molecular rotation has been derived following the method of Van Vleck for the spin-rotation interaction in rigid molecules. It is shown that the Hamiltonian for this problem may be written

H_SR = Ῑ · M · Ĵ + Ῑ · M” · Ĵ”

Where the first term is the ordinary spin-rotation interaction and the second term arises from the spin-internal-rotation coupling.

The F¹⁹ nuclear spin-lattice relaxation time (T₁) of benzotrifluoride and several chemically substituted benzotrifluorides, have been measured both neat and in solution, at room temperature by pulsed nuclear magnetic resonance. From these experimental results it is concluded that in benzotrifluoride the internal rotation is crucial to the spin relaxation of the fluorines and that the dominant relaxation mechanism is the fluctuating spin-internal-rotation interaction.

Part II.

The radiofrequency spectrum corresponding to the reorientation of the F¹⁹ nuclear moment in flurobenzene has been studied by the molecular beam magnetic resonance method. A molecular beam apparatus with an electron bombardment detector was used in the experiments. The F¹⁹ resonance is a composite spectrum with contributions from many rotational states and is not resolved. A detailed analysis of the resonance line shape and width by the method of moments led to the following diagonal components of the fluorine spin-rotational tensor in the principal inertial axis system of the molecule:

F/Caa = -1.0 ± 0.5 kHz

F/Cbb = -2.7 ± 0.2 kHz

F/Ccc = -1.9 ± 0.1 kHz

From these interaction constants, the paramagnetic contribution to the F¹⁹ nuclear shielding in C₆H₅F was determined to be -284 ± ppm. It was further concluded that the F¹⁹ nucleus in this molecule is more shielded when the applied magnetic field is directed along the C-F bond axis. The anisotropy of the magnetic shielding tensor, σ_” - σ_⊥, is +160 ± 30 ppm.

I. The crystal structure of potassium bis(tricyanovinyl)amine. II. Nuclear magnetic resonance studies of alkali halide solutions. III. Elucidation of the intramolecular hydrogen bond in acetylacetone by the deuterium isotope effect on the chemical shift of the bridge hydrogen

Part I

Potassium bis-(tricyanovinyl) amine, K⁺N[C(CN)=C(CN)₂]₂^-, crystallizes in the monoclinic system with the space group Cc and lattice constants, a = 13.346 ± 0.003 Å, c = 8.992 ± 0.003 Å, B = 114.42 ± 0.02°, and Z = 4. Three dimensional intensity data were collected by layers perpendicular to b* and c* axes. The crystal structure was refined by the least squares method with anisotropic temperature factor to an R value of 0.064.

The average carbon-carbon and carbon-nitrogen bond distances in –C-CΞN are 1.441 ± 0.016 Å and 1.146 ± 0.014 Å respectively. The bis-(tricyanovinyl) amine anion is approximately planar. The coordination number of the potassium ion is eight with bond distances from 2.890 Å to 3.408 Å. The bond angle C-N-C of the amine nitrogen is 132.4 ± 1.9°. Among six cyano groups in the molecule, two of them are bent by what appear to be significant amounts (5.0° and 7.2°). The remaining four are linear within the experimental error. The bending can probably be explained by molecular packing forces in the crystals.

Part II

The nuclear magnetic resonance of ⁸¹Br and ¹²⁷I in aqueous solutions were studied. The cation-halide ion interactions were studied by studying the effect of the Li⁺, Na⁺, K⁺, Mg⁺⁺, Cs⁺ upon the line width of the halide ions. The solvent-halide ion interactions were studied by studying the effects of methanol, acetonitrile, and acetone upon the line width of ⁸¹Br and ¹²⁷I in the aqueous solutions. It was found that the viscosity plays a very important role upon the halide ions line width. There is no specific cation-halide ion interaction for those ions such as Mg⁺⁺, Di⁺, Na⁺, and K⁺, whereas the Cs⁺ - halide ion interaction is strong. The effect of organic solvents upon the halide ion line width in aqueous solutions is in the order acetone ˃ acetonitrile ˃ methanol. It is suggested that halide ions do form some stable complex with the solvent molecules and the reason Cs⁺ can replace one of the ligands in the solvent-halide ion complex.

Part III

An unusually large isotope effect on the bridge hydrogen chemical shift of the enol form of pentanedione-2, 4(acetylacetone) and 3-methylpentanedione-2, 4 has been observed. An attempt has been made to interpret this effect. It is suggested from the deuterium isotope effect studies, temperature dependence of the bridge hydrogen chemical shift studies, IR studies in the OH, OD, and C=O stretch regions, and the HMO calculations, that there may probably be two structures for the enol form of acetylacetone. The difference between these two structures arises mainly from the electronic structure of the π-system. The relative population of these two structures at various temperatures for normal acetylacetone and at room temperature for the deuterated acetylacetone were calculated.

Part I. Approximate Hartree-Fock wavefunctions one-electron properties and electronic structure of the water molecule. Part II. Perturbation-variational calculation of the nuclear spin-spin isotope coupling constant in HD

Part I

Several approximate Hartree-Fock SCF wavefunctions for the ground electronic state of the water molecule have been obtained using an increasing number of multicenter s, p, and d Slater-type atomic orbitals as basis sets. The predicted charge distribution has been extensively tested at each stage by calculating the electric dipole moment, molecular quadrupole moment, diamagnetic shielding, Hellmann-Feynman forces, and electric field gradients at both the hydrogen and the oxygen nuclei. It was found that a carefully optimized minimal basis set suffices to describe the electronic charge distribution adequately except in the vicinity of the oxygen nucleus. Our calculations indicate, for example, that the correct prediction of the field gradient at this nucleus requires a more flexible linear combination of p-orbitals centered on this nucleus than that in the minimal basis set. Theoretical values for the molecular octopole moment components are also reported.

Part II

The perturbation-variational theory of R. M. Pitzer for nuclear spin-spin coupling constants is applied to the HD molecule. The zero-order molecular orbital is described in terms of a single 1s Slater-type basis function centered on each nucleus. The first-order molecular orbital is expressed in terms of these two functions plus one singular basis function each of the types e^-r/r and e^-r ln r centered on one of the nuclei. The new kinds of molecular integrals were evaluated to high accuracy using numerical and analytical means. The value of the HD spin-spin coupling constant calculated with this near-minimal set of basis functions is J_HD = +96.6 cps. This represents an improvement over the previous calculated value of +120 cps obtained without using the logarithmic basis function but is still considerably off in magnitude compared with the experimental measurement of J_HD = +43 0 ± 0.5 cps.

Carbon-13 magnetic resonance spectroscopy

High-resolution, natural-abundance ¹³C spectra have been obtained from a wide variety of organic compounds; ¹³C chemical shifts and coupling constants have been correlated with other molecular properties.

Geminal and vicinal, carbon-proton couplings in benzene and the five- and six-membered aromatic heterocycles have been related to the corresponding proton-proton couplings in substituted ethylenes. The carbon-proton coupling constants in benzene are J_CCH = + 1.0, J_CCCH = +7.4 and J_CCCH = -1.1 Hz. Extended Hückel wavefunctions are uniformly poor in explaining the long-range, carbon-proton couplings in aromatic systems.

Couplings between carbon and elements other than hydrogen have been observed in proton decoupled ¹³C spectra. All of the carbons in fluorobenzene and 1-fluoronaphthalene, but only six of the carbons in 2-fluoronaphthalene are coupled to the fluorine. One-bond, carbon-phosphorus coupling in trialkylphosphines is negative, while one-bond, carbon-phosphorus coupling in tetra-alkylphosphonium ions is positive. Atoms which do not use hybrid orbitals to form bonds to carbon (F, P(III), Se, Te) may have negative, one-bond coupling constants because of the failure of the average energy approximation. One-bond couplings between carbon and carbon, silicon, tin, lead and mercury appear to be explainable in terms of an effective nuclear charge and the s-bond order of the metal. Couplings between carbon and nitrogen and phosphorus (IV) have significant negative contributions to the Fermi contact coupling expression, though, within one series, correlations with s-bond order may be valid. Carbon-carbon coupling in cyclopropane derivatives (10-15 Hz) is consistent with a high degree of p character in the interior orbitals. Some two- and three-bond carbon-carbon coupling constants have also been observed.

Substituent effects of hydroxyl groups on the ¹³C chemical shifts of continuous-chain alkanes depend both on steric and electronic factors. The hydroxyl substituent effects in the long-chain, primary alcohols are α = -48.3, β = -10.2, and γ = +6.0 ppm. The upfield γ effect is attributed to steric crowding in the gauche conformations. Additivity of the hydroxyl and carbonyl and alkyl substituent effects in alkyl-substituted cyclohexanols and cyclohexanones has been demonstrated.

I. Efforts toward the synthesis of aliphatic iodonium salts. II. Flourine-19 nuclear magnetic resonance spectroscopy of cyclic and bicyclic systems

The synthesis of iodonium salts of the general formula [C₆H₅IR]⁺X^-, where R is an alkyl group and x- is a stabilizing anion, was attempted. For the choice of R three groups were selected, whose derivatives are known to be sluggish in S_N1 and S_N2 substitutions: cyclopropyl, 7, 7 -dimethyl-1-norbornyl, and 9 -triptycyl. The synthetic routes followed along classical lines which have been exploited in recent years by Beringer and students. Ultimately, the object of the present study was to study the reactions of the above salts with nucleophiles. In none of the three cases, however, was it possible to isolate a stable salt. A thermodynamic argument suggests that this must be due to kinetic instability rather than thermodynamic instability. Only iodocyclopropane and 1-iodoapocamphane formed isolable iododichlorides.

Several methylated 2, 2-difluoronorbornanes were prepared with the intent of correlating fluorine -19 chemical shifts with geometric features in a rigid system. The effect of a methyl group on the shielding of a β -fluorine is dependent upon the dihedral angle; the maximum effect (an upfield shift of the resonance) occurs at 0° and 180°, whereas almost no effect is felt at a dihedral angle of 120°. The effect of a methyl group on a γ -fluorine is to strongly shift the resonance downfield when fluorine and methyl group are in a 1, 3 - diaxial-like relationship. Molecular orbital calculations of fluorine shielding in a variety of molecules were carried out using the formalism developed by Pople; the results are, at best, in modest agreement with experiment.

The oculomotor system: (1) Vertical-horizontal interaction and signal recognition, (2) Time delays and power spectra

In the first section of this thesis, two-dimensional properties of the human eye movement control system were studied. The vertical - horizontal interaction was investigated by using a two-dimensional target motion consisting of a sinusoid in one of the directions vertical or horizontal, and low-pass filtered Gaussian random motion of variable bandwidth (and hence information content) in the orthogonal direction. It was found that the random motion reduced the efficiency of the sinusoidal tracking. However, the sinusoidal tracking was only slightly dependent on the bandwidth of the random motion. Thus the system should be thought of as consisting of two independent channels with a small amount of mutual cross-talk.

These target motions were then rotated to discover whether or not the system is capable of recognizing the two-component nature of the target motion. That is, the sinusoid was presented along an oblique line (neither vertical nor horizontal) with the random motion orthogonal to it. The system did not simply track the vertical and horizontal components of motion, but rotated its frame of reference so that its two tracking channels coincided with the directions of the two target motion components. This recognition occurred even when the two orthogonal motions were both random, but with different bandwidths.

In the second section, time delays, prediction and power spectra were examined. Time delays were calculated in response to various periodic signals, various bandwidths of narrow-band Gaussian random motions and sinusoids. It was demonstrated that prediction occurred only when the target motion was periodic, and only if the harmonic content was such that the signal was sufficiently narrow-band. It appears as if general periodic motions are split into predictive and non-predictive components.

For unpredictable motions, the relationship between the time delay and the average speed of the retinal image was linear. Based on this I proposed a model explaining the time delays for both random and periodic motions. My experiments did not prove that the system is sampled data, or that it is continuous. However, the model can be interpreted as representative of a sample data system whose sample interval is a function of the target motion.

It was shown that increasing the bandwidth of the low-pass filtered Gaussian random motion resulted in an increase of the eye movement bandwidth. Some properties of the eyeball-muscle dynamics and the extraocular muscle "active state tension" were derived.