Trapped ion magnetic resonance: concepts and designs

A novel spectroscopy of trapped ions is proposed which will bring single-ion detection sensitivity to the observation of magnetic resonance spectra. The approaches developed here are aimed at resolving one of the fundamental problems of molecular spectroscopy, the apparent incompatibility in existing techniques between high information content (and therefore good species discrimination) and high sensitivity. Methods for studying both electron spin resonance (ESR) and nuclear magnetic resonance (NMR) are designed. They assume established methods for trapping ions in high magnetic field and observing the trapping frequencies with high resolution (<1 Hz) and sensitivity (single ion) by electrical means. The introduction of a magnetic bottle field gradient couples the spin and spatial motions together and leads to a small spin-dependent force on the ion, which has been exploited by Dehmelt to observe directly the perturbation of the ground-state electron's axial frequency by its spin magnetic moment.

A series of fundamental innovations is described m order to extend magnetic resonance to the higher masses of molecular ions (100 amu = 2x 10^5 electron masses) and smaller magnetic moments (nuclear moments = 10^(-3) of the electron moment). First, it is demonstrated how time-domain trapping frequency observations before and after magnetic resonance can be used to make cooling of the particle to its ground state unnecessary. Second, adiabatic cycling of the magnetic bottle off between detection periods is shown to be practical and to allow high-resolution magnetic resonance to be encoded pointwise as the presence or absence of trapping frequency shifts. Third, methods of inducing spindependent work on the ion orbits with magnetic field gradients and Larmor frequency irradiation are proposed which greatly amplify the attainable shifts in trapping frequency.

The dissertation explores the basic concepts behind ion trapping, adopting a variety of classical, semiclassical, numerical, and quantum mechanical approaches to derive spin-dependent effects, design experimental sequences, and corroborate results from one approach with those from another. The first proposal presented builds on Dehmelt's experiment by combining a "before and after" detection sequence with novel signal processing to reveal ESR spectra. A more powerful technique for ESR is then designed which uses axially synchronized spin transitions to perform spin-dependent work in the presence of a magnetic bottle, which also converts axial amplitude changes into cyclotron frequency shifts. A third use of the magnetic bottle is to selectively trap ions with small initial kinetic energy. A dechirping algorithm corrects for undesired frequency shifts associated with damping by the measurement process.

The most general approach presented is spin-locked internally resonant ion cyclotron excitation, a true continuous Stern-Gerlach effect. A magnetic field gradient modulated at both the Larmor and cyclotron frequencies is devised which leads to cyclotron acceleration proportional to the transverse magnetic moment of a coherent state of the particle and radiation field. A preferred method of using this to observe NMR as an axial frequency shift is described in detail. In the course of this derivation, a new quantum mechanical description of ion cyclotron resonance is presented which is easily combined with spin degrees of freedom to provide a full description of the proposals.

Practical, technical, and experimental issues surrounding the feasibility of the proposals are addressed throughout the dissertation. Numerical ion trajectory simulations and analytical models are used to predict the effectiveness of the new designs as well as their sensitivity and resolution. These checks on the methods proposed provide convincing evidence of their promise in extending the wealth of magnetic resonance information to the study of collisionless ions via single-ion spectroscopy.

Charged pion contribution to the anomalous magnetic moment of the muon

The model dependence inherent in hadronic calculations is one of the dominant sources of uncertainty in the theoretical prediction of the anomalous magnetic moment of the muon. In this thesis, we focus on the charged pion contribution and turn a critical eye on the models employed in the few previous calculations of $a_\mu^{\pi^+\pi^-}$. Chiral perturbation theory provides a check on these models at low energies, and we therefore calculate the charged pion contribution to light-by-light (LBL) scattering to $\mathcal{O}(p^6)$. We show that the dominant corrections to the leading order (LO) result come from two low energy constants which show up in the form factors for the $\gamma\pi\pi$ and $\gamma\gamma\pi\pi$ vertices. Comparison with the existing models reveal a potentially significant omission - none include the pion polarizability corrections associated with the $\gamma\gamma\pi\pi$ vertex. We next consider alternative models where the pion polarizability is produced through exchange of the $a_1$ axial vector meson. These have poor UV behavior, however, making them unsuited for the $a_\mu^{\pi^+\pi^-}$ calculation. We turn to a simpler form factor modeling approach, generating two distinct models which reproduce the pion polarizability corrections at low energies, have the correct QCD scaling at high energies, and generate finite contributions to $a_\mu^{\pi^+\pi^-}$. With these two models, we calculate the charged pion contribution to the anomalous magnetic moment of the muon, finding values larger than those previously reported: $a_\mu^\mathrm{I} = -1.779(4)\times10^{-10}\,,\,a_\mu^\mathrm{II} = -4.892(3)\times10^{-10}$.

Hyperfine interactions and nuclear structure

An automatic experimental apparatus for perturbed angular correlation measurements, capable of incorporating Ge(Li) detectors as well as scintillation counters, has been constructed.

The gamma-gamma perturbed angular correlation technique has been used to measure magnetic dipole moments of several nuclear excited states in the osmium transition region. In addition, the hyperfine magnetic fields, experienced by nuclei of 'impurity' atoms embedded in ferromagnetic host lattices, have been determined for several '4d' and '5d' impurity atoms.

The following magnetic dipole moments were obtained in the osmium transition region μ_2⁺(¹⁹⁰Os) = 0.54 ± 0.06 nm μ_4⁺(¹⁹⁰Os) = 0.88 ± 0.48 nm μ_2⁺(¹⁹²Os) = 0.56 ± 0.08 nm μ_2⁺(¹⁹²Pt) = 0.56 ± 0.06 nm μ_2^+’(¹⁹²Pt) = 0.62 ± 0.14 nm.

These results are discussed in terms of three collective nuclear models; the cranking model, the rotation-vibration model and the pairing-plus-quadrupole model. The measurements are found to be in satisfactory agreement with collective descriptions of low lying nuclear states in this region.

The following hyperfine magnetic fields of 'impurities' in ferromagnetic hosts were determined; H_int(Cd Ni) = - (64.0 ± 0.8)kG H_int(Hg Fe) = - (440 ± 105)kG H_int(Hg Co) = - (370 ± 78)kG H_int(Hg Ni) = - (86 ± 22)kG H_int(Tl Fe) = - (185 ± 70)kG H_int(Tl Co) = - (90 ± 35)kG H_int(Ra Fe) = - (105 ± 20)kG H_int(Ra Co) = - (80 ± 16)kG H_int(Ra Ni) = - (30 ± 10)kG, where in H_int(AB); A is the impurity atom embedded in the host lattice B. No quantitative theory is available for comparison. However, these results are found to obey the general systematics displayed by these fields. Several mechanisms which may be responsible for the appearance of these fields are mentioned.

Finally, a theoretical expression for time-differential perturbed angular correlation measurement, which duplicates experimental conditions is developed and its importance in data analysis is discussed.

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.

Influence of composition on the structure, electric and magnetic properties of Pd-Mn-P and Pd-Co-P amorphous alloys

The influence of composition on the structure and on the electric and magnetic properties of amorphous Pd-Mn-P and Pd-Co-P prepared by rapid quenching techniques were investigated in terms of (1) the 3d band filling of the first transition metal group, (2) the phosphorus concentration effect which acts as an electron donor and (3) the transition metal concentration.

The structure is essentially characterized by a set of polyhedra subunits essentially inverse to the packing of hard spheres in real space. Examination of computer generated distribution functions using Monte Carlo random statistical distribution of these polyhedra entities demonstrated tile reproducibility of the experimentally calculated atomic distribution function. As a result, several possible "structural parameters" are proposed such as: the number of nearest neighbors, the metal-to-metal distance, the degree of short-range order and the affinity between metal-metal and metal-metalloid. It is shown that the degree of disorder increases from Ni to Mn. Similar behavior is observed with increase in the phosphorus concentration.

The magnetic properties of Pd-Co-P alloys show that they are ferromagnetic with a Curie temperature between 272 and 399°K as the cobalt concentration increases from 15 to 50 at.%. Below 20 at.% Co the short-range exchange interactions which produce the ferromagnetism are unable to establish a long-range magnetic order and a peak in the magnetization shows up at the lowest temperature range . The electric resistivity measurements were performed from liquid helium temperatures up to the vicinity of the melting point (900°K). The thermomagnetic analysis was carried out under an applied field of 6.0 kOe. The electrical resistivity of Pd-Co-P shows the coexistence of a Kondo-like minimum with ferromagnetism. The minimum becomes less important as the transition metal concentration increases and the coefficients of ℓn T and T^2 become smaller and strongly temperature dependent. The negative magnetoresistivity is a strong indication of the existence of localized moment.

The temperature coefficient of resistivity which is positive for Pd- Fe-P, Pd-Ni-P, and Pd-Co-P becomes negative for Pd-Mn-P. It is possible to account for the negative temperature dependence by the localized spin fluctuation model and the high density of states at the Fermi energy which becomes maximum between Mn and Cr. The magnetization curves for Pd-Mn-P are typical of those resulting from the interplay of different exchange forces. The established relationship between susceptibility and resistivity confirms the localized spin fluctuation model. The magnetoresistivity of Pd-Mn-P could be interpreted in tenns of a short-range magnetic ordering that could arise from the Rudennan-Kittel type interactions.

New search for the Neutron Electric Dipole Moment using ultracold neutrons at the Spallation Neutron Source

This document introduces the planned new search for the neutron Electric Dipole Moment at the Spallation Neutron Source at the Oak Ridge National Laboratory. A spin precession measurement is to be carried out using Ultracold neutrons diluted in a superfluid Helium bath at T = 0.5 K, where spin polarized 3He atoms act as detector of the neutron spin polarization. This manuscript describes some of the key aspects of the planned experiment with the contributions from Caltech to the development of the project.

Techniques used in the design of magnet coils for Nuclear Magnetic Resonance were adapted to the geometry of the experiment. Described is an initial design approach using a pair of coils tuned to shield outer conductive elements from resistive heat loads, while inducing an oscillating field in the measurement volume. A small prototype was constructed to test the model of the field at room temperature.

A large scale test of the high voltage system was carried out in a collaborative effort at the Los Alamos National Laboratory. The application and amplification of high voltage to polished steel electrodes immersed in a superfluid Helium bath was studied, as well as the electrical breakdown properties of the electrodes at low temperatures. A suite of Monte Carlo simulation software tools to model the interaction of neutrons, 3He atoms, and their spins with the experimental magnetic and electric fields was developed and implemented to further the study of expected systematic effects of the measurement, with particular focus on the false Electric Dipole Moment induced by a Geometric Phase akin to Berry’s phase.

An analysis framework was developed and implemented using unbinned likelihood to fit the time modulated signal expected from the measurement data. A collaborative Monte Carlo data set was used to test the analysis methods.

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.

Influence of composition on the structure and properties of Fe-Pd-P and Ni-Pd-P amorphous alloys

Ternary alloys of nickel-palladium-phosphorus and iron-palladium- phosphorus containing 20 atomic % phosphorus were rapidly quenched from the liquid state. The structure of the quenched alloys was investigated by X-ray diffraction. Broad maxima in the diffraction patterns, indicative of a glass-like structure, were obtained for 13 to 73 atomic % nickel and 13 to 44 atomic % iron, with palladium adding up to 80%.

Radial distribution functions were computed from the diffraction data and yielded average interatomic distances and coordination numbers. The structure of the amorphous alloys could be explained in terms of structural units analogous to those existing in the crystalline Pd₃P, Ni₃P and Fe₃P phases, with iron or nickel substituting for palladium. A linear relationship between interatomic distances and composition, similar to Vegard's law, was shown for these metallic glasses.

Electrical resistivity measurements showed that the quenched alloys were metallic. Measurements were performed from liquid helium temperatures (4.2°K) up to the vicinity of the melting points (900°K- 1000°K). The temperature coefficient in the glassy state was very low, of the order of 10^-4/°K. A resistivity minimum was found at low temperature, varying between 9°K and 14°K for Ni_x-Pd_80-x -P₂₀ and between 17°K and 96°K for Fe_x-Pd_80-x -P₂₀, indicating the presence of a Kondo effect. Resistivity measurements, with a constant heating rate of about 1.5°C/min,showed progressive crystallization above approximately 600°K.

The magnetic moments of the amorphous Fe-Pd-P alloys were measured as a function of magnetic field and temperature. True ferromagnetism was found for the alloys Fe₃₂-Pd₄₈-P₂₀ and Fe₄₄-Pd₃₆-P₂₀ with Curie points at 165° K and 380° K respectively. Extrapolated values of the saturation magnetic moments to 0° K were 1.70 µ_B and 2.10 µ_B respectively. The amorphous alloy Fe₂₃-Pd₅₇-P₂₀ was assumed to be superparamagnetic. The experimental data indicate that phosphorus contributes to the decrease of moments by electron transfer, whereas palladium atoms probably have a small magnetic moment. A preliminary investigation of the Ni-Pd-P amorphous alloys showed that these alloys are weakly paramagnetic.

Spin wave resonance in ferromagnetic films

The objective of this investigation has been a theoretical and experimental understanding of ferromagnetic resonance phenomena in ferromagnetic thin films, and a consequent understanding of several important physical properties of these films. Significant results have been obtained by ferromagnetic resonance, hysteresis, torque magnetometer, He ion backscattering, and X-ray fluorescence measurements for nickel-iron alloy films.

Taking into account all relevant magnetic fields, including the applied, demagnetizing, effective anisotropy and exchange fields, the spin wave resonance condition applicable to the thin film geometry is presented. On the basis of the simple exchange interaction model it is concluded that the normal resonance modes of an ideal film are expected to be unpinned. The possibility of nonideality near the surface of a real film was considered by means of surface anisotropy field, inhomogeneity in demagnetizing field and inhomogeneity of magnetization models. Numerical results obtained for reasonable parameters in all cases show that they negligibly perturb the resonance fields and the higher order mode shapes from those of the unpinned modes of ideal films for thicknesses greater than 1000 Å. On the other hand for films thinner than 1000 Å the resonance field deviations can be significant even though the modes are very nearly unpinned. A previously unnoticed but important feature of all three models is that the interpretation of the first resonance mode as the uniform mode of an ideal film allows an accurate measurement of the average effective demagnetizing field over the film volume. Furthermore, it is demonstrated that it is possible to choose parameters which give indistinguishable predictions for all three models, making it difficult to uniquely ascertain the source of spin pinning in real films from resonance measurements alone.

Spin wave resonance measurements of 81% Ni-19% Fe coevaporated films 30 to 9000 Å thick, at frequencies from 1 to 8 GHz, at room temperature, and with the static magnetic field parallel and perpendicular to the film plane have been performed. A self-consistent analysis of the results for films thicker than 1000 Å, in which multiple excitations can be observed, shows for the first time that a unique value of exchange constant A can only be obtained by the use of unpinned mode assignments. This evidence and the resonance behavior of films thinner than 1000 Å strongly imply that the magnetization at the surfaces of permalloy films is very weakly pinned. However, resonance measurements alone cannot determine whether this pinning is due to a surface anisotropy, an inhomogeneous demagnetizing field or an inhomogeneous magnetization. The above analysis yields a value of 4πM=10,100 Oe and A = (1.03 ± .05) x 10^-6 erg/cm for this alloy. The ability to obtain a unique value of A suggests that spin wave resonance can be used to accurately characterize the exchange interaction in a ferromagnet.

In an effort to resolve the ambiguity of the source of pinning of the magnetization, a correlation of the ratio of magnetic moment and X-ray film thickness with the value of effective demagnetizing field 4πNM as determined from resonance, for films 45 to 300 Å has been performed. The remarkable agreement of both quantities and a comparison with the predictions of five distinct models, strongly imply that the thickness dependence of both quantities is related to a thickness dependent average saturation magnetization, which is far below 10,100 Oe for very thin films. However, a series of complementary experiments shows that this large decrease of average saturation magnetization cannot be simply explained by either oxidation or interdiffusion processes. It can only be satisfactorily explained by an intrinsic decrease of the average saturation magnetization for very thin films, an effect which cannot be justified by any simple physical considerations.

Recognizing that this decrease of average saturation magnetization could be due to an oxidation process, a correlation of resonance measurements, He ion backscattering, X-ray fluorescence and torque magnetometer measurements, for films 40 to 3500 Å thick has been performed. On basis of these measurements it is unambiguously established that the oxide layer on the surface of purposefully oxidized 81% Ni-19% Fe evaporated films is predominantly Fe-oxide, and that in the oxidation process Fe atoms are removed from the bulk of the film to depths of thousands of angstroms. Extrapolation of results for pure Fe films indicates that the oxide is most likely α-Fe₂O₃. These conclusions are in agreement with results from old metallurgical studies of high temperature oxidation of bulk Fe and Ni-Fe alloys. However, X-ray fluorescence results for films oxidized at room temperature, show that although the preferential oxidation of Fe also takes place in these films, the extent of this process is by far too small to explain the large variation of their average saturation magnetization with film thickness.

Nuclear Hartree-Fock calculations on parallel computers

Hartree-Fock (HF) calculations have had remarkable success in describing large nuclei at high spin, temperature and deformation. To allow full range of possible deformations, the Skyrme HF equations can be discretized on a three-dimensional mesh. However, such calculations are currently limited by the computational resources provided by traditional supercomputers. To take advantage of recent developments in massively parallel computing technology, we have implemented the LLNL Skyrme-force static and rotational HF codes on Intel's DELTA and GAMMA systems at Caltech.

We decomposed the HF code by assigning a portion of the mesh to each node, with nearest neighbor meshes assigned to nodes connected by communication· channels. This kind of decomposition is well-suited for the DELTA and the GAMMA architecture because the only non-local operations are wave function orthogonalization and the boundary conditions of the Poisson equation for the Coulomb field.

Our first application of the HF code on parallel computers has been the study of identical superdeformed (SD) rotational bands in the Hg region. In the last ten years, many SD rotational bands have been found experimentally. One very surprising feature found in these SD rotational bands is that many pairs of bands in nuclei that differ by one or two mass units have nearly identical deexcitation gamma-ray energies. Our calculations of the five rotational bands in ^(192)Hg and ^(194)Pb show that the filling of specific orbitals can lead to bands with deexcitation gamma-ray energies differing by at most 2 keV in nuclei differing by two mass units and over a range of angular momenta comparable to that observed experimentally. Our calculations of SD rotational bands in the Dy region also show that twinning can be achieved by filling or emptying some specific orbitals.

The interpretation of future precise experiments on atomic parity nonconservation (PNC) in terms of parameters of the Standard Model could be hampered by uncertainties in the atomic and nuclear structure. As a further application of the massively parallel HF calculations, we calculated the proton and neutron densities of the Cesium isotopes from A = 125 to A = 139. Based on our good agreement with experimental charge radii, binding energies, and ground state spins, we conclude that the uncertainties in the ratios of weak charges are less than 10^(-3), comfortably smaller than the anticipated experimental error.

Mössbauer effect investigations of the hyperfine interactions and relaxation phenomena in salts of thulium

Two new phenomena have been observed in Mössbauer spectra: a temperature-dependent shift of the center of gravity of the spectrum, and an asymmetric broadening of the spectrum peaks. Both phenomena were observed in thulium salts. In the temperature range 1˚K ≤ T ≤ 5˚K the observed shift has an approximate inverse temperature dependence. We explain this on the basis of a Van Vleck type of interaction between the magnetic moment of two nearly degenerate electronic levels and the magnetic moment of the nucleus. From the size of the shift we are able to deduce an “effective magnetic field” H = (6.0 ± 0.1) x 10⁶ Gauss, which is proportional to ‹r^-3›_M‹G|J|E› where ‹r^-3›_M is an effective magnetic radial integral for the 4f electrons and |G› and |E› are the lowest 4f electronic states in Tm Cl₃·6H₂O. From the temperature dependence of the shift we have derived a preliminary value of 1 cm^-1 for the splitting of these two states. The observed asymmetric line broadening is independent of temperature in the range 1˚K ≤ T ≤ 5˚K, but is dependent on the concentration of thulium ions in the crystal. We explain this broadening on the basis of spin-spin interactions between thulium ions. From size and concentration dependence of the broadening we are able to deduce a spin-spin relaxation time for Tm Cl₃·6H₂O of the order of 10^-11 sec.

Anomalous electric dipole internal conversion

Electric dipole internal conversion has been experimentally studied for several nuclei in the rare earth region. Anomalies in the conversion process have been interpreted in terms of nuclear structure effects. It was found that all the experimental results could be interpreted in terms of the j ∙ r type of penetration matrix element; the j ∙ ∇ type of penetration matrix element was not important. The ratio λ of the El j ∙ r penetration matrix element to the El gamma-ray matrix element was determined from the experiments to be:

Lu¹⁷⁵,396 keV, λ = - 1000 ± 100;

282 keV, λ = 500 ± 100;

144 keV, λ = 500 ± 250;

Hf¹⁷⁷, 321 keV λ = - 1400 ± 200;

208 keV λ = - 90 ± 40;

72 keV |λ| ≤ 650;

Gd¹⁵⁵, 86 keV λ = - 150 ± 100;

Tm¹⁶⁹, 63 keV λ = - 100 ± 100;

W¹⁸², 152 keV, λ = - 160 ±80;

67 keV, λ = - 100 ± 100.

Predictions for λ are made using the unified nuclear model.

Isotope shift measurements using k x-rays in Sn, Sm, and W

Electronic Kαl x-ray isotope shifts have been measured for Sn 116-124, Sm 148-154, W 182-184, W 184-186, and W 182-186 using a curved crystal Cauchois spectrometer. The analysis of the measurements has included the electrostatic volume effect, screening by the transition electron as well as the non-transition electrons, normal and specific mass shifts, dynamical nuclear qudrupole polarization, and a radiative correction effect of the electron magnetic moment in the nuclear charge radii are obtained. Where other experimental data are available, the agreement with the present measurements is satisfactory. Comparisons with several nuclear model predictions yield only partial agreement.

Beta and gamma vibrational bands in deformed nuclei

Energies and relative intensities of gamma transitions in ¹⁵²Sm, ¹⁵²Gd, ¹⁵⁴Gd, ¹⁶⁶Er, and ²³²U following radioactive decay have been measured with a Ge(Li) spectrometer. A peak fitting program has been developed to determine gamma ray energies and relative intensities with precision sufficient to give a meaningful test of nuclear models. Several previously unobserved gamma rays were placed in the nuclear level schemes. Particular attention has been paid to transitions from the beta and gamma vibrational bands, since the gamma ray branching ratios are sensitive tests of configuration mixing in the nuclear levels. As the reduced branching ratios depend on the multipolarity of the gamma transitions, experiments were performed to measure multipole mixing ratios for transitions from the gamma vibrational band. In ¹⁵⁴Gd, angular correlation experiments showed that transitions from the gamma band to the ground state band were predominantly electric quadrupole, in agreement with the rotational model. In ²³²U, the internal conversion spectrum has been studied with a Si(Li) spectrometer constructed for electron spectroscopy. The strength of electric monopole transitions and the multipolarity of some gamma transitions have been determined from the measured relative electron intensities.

The results of the experiments have been compared with the rotational model and several microscopic models. Relative B(E2) strengths for transitions from the gamma band in ²³²U and ¹⁶⁶Er are in good agreement with a single parameter band mixing model, with values of z₂= 0.025(10) and 0.046(2), respectively. Neither the beta nor the gamma band transition strengths in ¹⁵²Sm and ¹⁵⁴Gd can be accounted for by a single parameter theory, nor can agreement be found by considering the large mixing found between the beta and gamma bands. The relative B(E2) strength for transitions from the gamma band to the beta band in ²³²U is found to be five times greater than the strength to the ground state band, indicating collective transitions with strength approximately 15 single particle units.

Sputtering of insulators in the electronic stopping region

Using track detectors we have measured sputtering yields induced by MeV light ions incident on a uranium containing glass, UO₂ and UF₄. No deviation from the behavior predicted by the Sigmund theory was detected in the glass or the UO₂. The same was true for UF₄ bombarded with ⁴He at 1 MeV and with ¹⁶O and ²⁰Ne at 100 keV. In contrast to this, 4.75 MeV ¹⁹F(+2) sputters uranium from UF₄ with a yield of 5.6 ± 1.0, which is about 3 orders of magnitude larger than expected from the Sigmund theory. The energy dependence of the yield indicates that it is generated by electronic rather than nuclear stopping processes. The yield depends on the charge state of the incident fluorine but not on the target temperature. We have also measured the energy spectrum of the uranium sputtered from the UF₄. Ion explosions, thermal spikes, chemical rearrangement and induced desorption are considered as possible explanations for the anomalous yields.