An investigation of the three-body reaction He^3(He^3, 2p)He^4

Reactions produced by the He³ bombardment of the He³ have been investigated for bombarding energies from 1 to 20 MeV using a tandem Van de Graaff accelerator. Proton spectra from the three-body reaction He³(He³, 2p)He⁴ have been measured with a counter telescope at 13 angles for 9 bombarding energies between 3 and 18 MeV. The results are compared with a model for the reaction which includes a strong p-He⁴ final-state interaction. Alpha-particle spectra have been obtained at 12 and 18 MeV for forward angles with a magnetic spectrometer. These spectra indicate a strongly forward-peaked mechanism involving the ¹S₀ p-p interaction in addition to the p-He⁴ interaction. Measurements of p-He⁴ and p-p coincidence spectra at 10 MeV confirm these features of the reaction mechanism. Deuteron spectra from the reaction of He³(He³, d)pHe³ have been measured at 18 MeV. A triton spectrum from the reaction He³(He³, t)3p at 20 MeV and 4⁰ is interpreted in terms of a sequential decay through an excited state of the alpha particle at 20.0 MeV. No effects are observed which would indicate an interaction in the residual (3p) system. Below 3 MeV the He³(He³, 2p)He⁴ reaction mechanism is observed to be changing and further measurements are suggested in view of the importance of this reaction in stellar interiors.

A study of T=1, T=3/2, and T=2 states in some light nuclei using (He^3,n) reactions

The (He³, n) reactions on B¹¹, N¹⁵, O¹⁶, and O¹⁸ targets have been studied using a pulsed-beam time-of-flight spectrometer. Special emphasis was placed upon the determination of the excitation energies and properties of states with T = 1 (in Ne¹⁸), T = 3/2 (in N¹³ and F¹⁷) and T = 2 (in Ne²⁰). The identification of the T = 3/2 and T = 2 levels is based on the structure of these states as revealed by intensities and shapes of angular distributions. The reactions are interpreted in terms of double stripping theory. Angular distributions have been compared with plane and distorted wave stripping theories. Results for the four reactions are summarized below:

1) O¹⁶ (He³, n). The reaction has been studied at incident energies up to 13.5 MeV and two previously unreported levels in Ne¹⁸ were observed at E_x = 4.55 ± .015 MeV (Γ = 70 ± 30 keV) and E_x = 5.14 ± .018 MeV (Γ = 100 ± 40 keV).

2) B¹¹ (He³, n). The reaction has been studied at incident energies up to 13.5 MeV. Three T = 3/2 levels in N¹³ have been identified at E_x = 15.068 ± .008 MeV (Γ ˂ 15 keV), E_x = 18.44 ± .04, and E_x 18.98 ± .02 MeV (Γ = 40 ± 20 keV).

3) N¹⁵ (He³, n). The reaction has been studied at incident energies up to 11.88 MeV. T = 3/2 levels in F¹⁷ have been identified at E_x = 11.195 ± .007 MeV (Γ ˂ 20 keV), E_x = 12.540 ± .010 MeV (Γ ˂ 25 keV), and E_x = 13.095 ± .009 MeV (Γ ˂ 25 keV).

4) O¹⁸ (He³, n). The reaction has been studied at incident energies up to 9.0 MeV. The excitation energy of the lowest T = 2 level in Ne²⁰ has been found to be 16.730 ± .006 MeV (Γ ˂ 20 keV).

Angular distributions of the transitions leading to the above higher isospin states are well described by double stripping theory. Analog correspondences are established by comparing the present results with recent studies (t, p) and (He³, p) reactions on the same targets.

Dynamics of non-Abelian Aharonov-Bohm systems

This thesis examines several examples of systems in which non-Abelian magnetic flux and non-Abelian forms of the Aharonov-Bohm effect play a role. We consider the dynamical consequences in these systems of some of the exotic phenomena associated with non-Abelian flux, such as Cheshire charge holonomy interactions and non-Abelian braid statistics. First, we use a mean-field approximation to study a model of U(2) non-Abelian anyons near its free-fermion limit. Some self-consistent states are constructed which show a small SU(2)-breaking charge density that vanishes in the fermionic limit. This is contrasted with the bosonic limit where the SU(2) asymmetry of the ground state can be maximal. Second, a global analogue of Chesire charge is described, raising the possibility of observing Cheshire charge in condensedmatter systems. A potential realization in superfluid He-3 is discussed. Finally, we describe in some detail a method for numerically simulating the evolution of a network of non-Abelian (S₃) cosmic strings, keeping careful track of all magnetic fluxes and taking full account of their non-commutative nature. I present some preliminary results from this simulation, which is still in progress. The early results are suggestive of a qualitatively new, non-scaling behavior.

Photodisintegration of helium-3 at energies between 200 and 600 MEV

We have measured differential cross-sections for the two-body photodisintegration of Helium-3, ɣ + He³ → p + d, between incident photon energies of 200 and 600 MeV, and for center of mass frame angles between 30° and 150°. Both final state particles were detected in arrays of wire spark chambers and scintillation counters; the high momentum particle was analyzed in a magnet spectrometer. The results are interpreted in terms of amplitudes to produce the ∆(1236) resonance in an intermediate state, as well as non-resonant amplitudes. This experiment, together with an (unfinished) experiment on the inverse reaction, p + d → He³ + ɣ, will provide a reciprocity test of time reversal invariance.

Observations of hydrogen and helium isotopes in solar cosmic rays

The isotopic composition of hydrogen and helium in solar cosmic rays provides a means of studying solar flare particle acceleration mechanisms since the enhanced relative abundance of rare isotopes, such as ²H, ³H and ³He, is due to their production by inelastic nuclear collisions in the solar atmosphere during the flare. In this work the Caltech Electron/Isotope Spectrometer on the IMP-7 spacecraft has been used to measure this isotopic composition. The response of the dE/dx-E particle telescope is discussed and alpha particle channeling in thin detectors is identified as an important background source affecting measurement of low values of (³He/⁴He).

The following flare-averaged results are obtained for the period, October, 1972 - November, 1973: (²H/¹H) = 7⁺¹⁰_-6 X 10^-6 (1.6 - 8.6 MeV/nuc), (³H/¹H) less than 3.4 x 10^-6 (1.2 - 6.8 MeV/nuc), (³He/⁴He) = (9 ± 4) x 10^-3, (³He/¹H) = (1.7 ± 0.7) x 10^-4 (3.1 - 15.0 MeV/nuc). The deuterium and tritium ratios are significantly lower than the same ratios at higher energies, suggesting that the deuterium and tritium spectra are harder than that of the protons. They are, however, consistent with the same thin target model relativistic path length of ~ 1 g/cm² (or equivalently ~ 0.3 g/cm² at 30 MeV/nuc) which is implied by the higher energy results. The ³He results, consistent with previous observations, would imply a path length at least 3 times as long, but the observations may be contaminated by small ³He rich solar events.

During 1973 three "³He rich events," containing much more ³He than ²H or ³H were observed on 14 February, 29 June and 5 September. Although the total production cross sections for ²H,³H and ³He are comparable, an upper limit to (²H/³He) and (³H/³He) was 0.053 (2.9-6.8 MeV/nuc), summing over the three events. This upper limit is marginally consistent with Ramaty and Kozlovsky's thick target model which accounts for such events by the nuclear reaction kinematics and directional properties of the flare acceleration process. The 5 September event was particularly significant in that much more ³He was observed than ⁴He and the fluxes of ³He and ¹H were about equal. The range of (³He/⁴He) for such events reported to date is 0.2 to ~ 6 while (³He/¹H) extends from 10^-3 to ~ 1. The role of backscattered and mirroring protons and alphas in accounting for such variations is discussed.

A quantitative investigation of the solar modulation of cosmic-ray protons and helium nuclei

The differential energy spectra of cosmic-ray protons and He nuclei have been measured at energies up to 315 MeV/nucleon using balloon- and satellite-borne instruments. These spectra are presented for solar quiet times for the years 1966 through 1970. The data analysis is verified by extensive accelerator calibrations of the detector systems and by calculations and measurements of the production of secondary protons in the atmosphere.

The spectra of protons and He nuclei in this energy range are dominated by the solar modulation of the local interstellar spectra. The transport equation governing this process includes as parameters the solar-wind velocity, V, and a diffusion coefficient, K(r,R), which is assumed to be a scalar function of heliocentric radius, r, and magnetic rigidity, R. The interstellar spectra, j_D, enter as boundary conditions on the solutions to the transport equation. Solutions to the transport equation have been calculated for a broad range of assumed values for K(r,R) and j_D and have been compared with the measured spectra.

It is found that the solutions may be characterized in terms of a dimensionless parameter, ψ(r,R) = ^∞∫_r V dr'/(K(r',R). The amount of modulation is roughly proportional to ψ. At high energies or far from the Sun, where the modulation is weak, the solution is determined primarily by the value of ψ (and the interstellar spectrum) and is not sensitive to the radial dependence of the diffusion coefficient. At low energies and for small r, where the effects of adiabatic deceleration are found to be large, the spectra are largely determined by the radial dependence of the diffusion coefficient and are not very sensitive to the magnitude of ψ or to the interstellar spectra. This lack of sensitivity to j_D implies that the shape of the spectra at Earth cannot be used to determine the interstellar intensities at low energies.

Values of ψ determined from electron data were used to calculate the spectra of protons and He nuclei near Earth. Interstellar spectra of the form j_D α (W - 0.25m)^-2.65 for both protons and He nuclei were found to yield the best fits to the measured spectra for these values of ψ, where W is the total energy and m is the rest energy. A simple model for the diffusion coefficient was used in which the radial and rigidity dependence are separable and K is independent of radius inside a modulation region which has a boundary at a distance D. Good agreement was found between the measured and calculated spectra for the years 1965 through 1968, using typical boundary distances of 2.7 and 6.1 A.U. The proton spectra observed in 1969 and 1970 were flatter than in previous years. This flattening could be explained in part by an increase in D, but also seemed to require that a noticeable fraction of the observed protons at energies as high at 50 to 100 MeV be attributed to quiet-time solar emission. The turnup in the spectra at low energies observed in all years was also attributed to solar emission. The diffusion coefficient used to fit the 1965 spectra is in reasonable agreement with that determined from the power spectra of the interplanetary magnetic field (Jokipii and Coleman, 1968). We find a factor of roughly 3 increase in ψ from 1965 to 1970, corresponding to the roughly order of magnitude decrease in the proton intensity at 250 MeV. The change in ψ might be attributed to a decrease in the diffusion coefficient, or, if the diffusion coefficient is essentially unchanged over that period (Mathews et al., 1971), might be attributed to an increase in the boundary distance, D.

Excitation energies and decay properties of T = 3/2 states in ^(17)O, ^(17)F and ^(21)Na

The two lowest T = 3/2 levels in ²¹Na have been studied in the ¹⁹F(³He, n), ²⁰Ne (p,p) and ²⁰Ne (p,p’) reactions, and their excitation energies, spins, parities and widths have been determined. In a separate investigation, branching ratios were measured for the isospin-nonconserving particle decays of the lowest T = 3/2 levels in ¹⁷O and ¹⁷F to the ground state and first two excited states of ¹⁶O, by studying the ¹⁵N(³He,n) ¹⁷F*(p) ¹⁶O and ¹⁸O(³He, α)¹⁷O*(n) ¹⁶O reactions.

The ¹⁹F(³He,n) ²¹Na reaction was studied at incident energies between 4.2 and 5.9 MeV using a pulsed-beam neutron-time-of-flight spectrometer. Two T = 3/2 levels were identified at excitation energies of 8.99 ± 0.05 MeV (J > ½) and 9.22 ± 0.015 MeV (J ^π = ½⁺, Γ ˂ 40 keV). The spins and parities were determined by a comparison of the measured angular distributions with the results of DWBA calculations.

These two levels were also obsesrved as isospin-forbidden resonances in the ²⁰Ne(p,p) and ²⁰Ne(p,p’) reactions. Excitation energies were measured and spins, parities, and widths were determined from a single level dispersion theory analysis. The following results were obtained:

E_x = 8.973 ± 0.007 MeV, J ^π = 5/2 ⁺ or 3/2⁺, Γ ≤ 1.2 keV,

^Γp_o = 0.1 ± 0.05 keV; E_x = 9.217 ± 0.007 MeV, J^π = ½ ⁺,

Γ = 2.3 ± 0.5 keV, ^Γp_o = 1.1 ± 0.3 keV.

Isospin assignments were made on the basis of excitation energies, spins, parities, and widths.

Branching ratios for the isospin-nonconserving proton decays of the 11.20 MeV, T = 3/2 level in ¹⁷F were measured by the ¹⁵N(³He,n) ¹⁷ F*(p) ¹⁶O reaction to be 0.088 ± 0.016 to the ground state of ¹⁶O and 0.22 ± 0.04 to the unresolved 6.05 and 6.13 MeV levels of ¹⁶O. Branching ratios for the neutron decays of the analogous T = 3/2 level, at 11.08 MeV in ¹⁷O, were measured by the ¹⁶O(³He, α)¹⁷O*(n)¹⁶O reaction to be 0.91 ± 0.15 to the ground state of ¹⁶O and 0.05 ± 0.02 to the unresolved 6.05 and 6.13 MeV states. By comparing the ratios of reduced widths for the mirror decays, the form of the isospin impurity in the T = 3/2 levels is shown to depend on T_z.

The separation of atomic and molecular gases from helium by cataphoresis

The cataphoretic purification of helium was investigated for binary mixtures of He with Ar, Ne, N₂, O₂, CO, and CO₂ in DC glow discharge. An experimental technique was developed to continuously measure the composition in the anode end-bulb without sample withdrawal. Discharge currents ranged from 10 ma to 100 ma. Total gas pressure ranged from 2 torr to 9 torr. Initial compositions of the minority component in He ranged from 1.2 mole percent to 7.5 mole percent.

The cataphoretic separation of Ar and Ne from He was found to be in agreement with previous investigators. The cataphoretic separation of N₂, O₂, and CO from He was found to be similar to noble gas systems in that the steady-state separation improved with (1) increasing discharge current, (2) increasing gas pressure, and (3) decreasing initial composition of the minority component. In the He-CO₂ mixture, the CO₂ dissociated to CO plus O₂. The fraction of CO₂ dissociated was directly proportional to the current and pressure and independent of initial composition.

The experimental results for the separation of Ar, Ne, N₂, O₂, and CO from He were interpreted in the framework of a recently proposed theoretical model involving an electrostatic Peclet number. In the model the electric field was assumed to be constant. This assumption was checked experimentally and the maximum variation in electric field was 35% in time and 30% in position. Consequently, the assumption of constant electric field introduced no more than 55% variation in the electrostatic Peclet number during a separation.

To aid in the design of new cataphoretic systems, the following design criteria were developed and tested in detail: (1) electric field independent of discharge current, (2) electric field directly proportional to total pressure, (3) ion fraction of impurity directly proportional to discharge current, and (4) ion fraction of impurity independent of total pressure. Although these assumptions are approximate, they enabled the steady-state concentration profile to be predicted to within 25% for 75% of the data. The theoretical model was also tested with respect to the characteristic time associated with transient cataphoresis. Over 80% of the data was within a factor of two of the calculated characteristic times.

The electrostatic Peclet number ranged in value from 0.13 to 4.33. Back-calculated ion fractions of the impurity component ranged in value from 4.8x10^-6 to 178x10^-6.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.