Up to this time, the design of Pressurizers in Nuclear Power Plants has been quite empirical due to the deficiency of standard thermodynamic relationships when applied to the solution of two phase systems. Recently, a new thermodynamic approach was expounded to the 2nd Nuclear Engineering and Science Conference which attempts to deal with the problem of two phase systems by breaking the thermodynamic unit into various subsystems and solving each separately. However, no experimental proof of the new theory was given. The object of this investigation was to prove or disprove the validity of this new thermodynamic approach as applied to the prediction of the performance of a Pressurizer. A small, simplified model of a pressurizer was constructed, and surge tests were conducted. The surges were then calculated by means of the new thermodynamic equations and compared with the actual results. It was found that the prediction of pressurizer surges depends greatly upon the exactness to which the transient heat loss to the walls of the pressurizer can be calculated. Nevertheless, the use of standard heat transfer relationships when used in the theoretical surge equations, predicted the pressure surges to within 40%. An attempt to obtain closer theoretical results by determining the transient heat loss from pressure and temperature decay curves was unsuccessful due to improper pressure recording equipment. Some doubt has been cast on one of the assumptions of the theoretical equations, in that the pressurizer steam was not compressed isentropically as assumed. It is felt that this deviation from the theoretical was due to the small size of the model pressurizer, but proof of this is left to future experimenters. This investigation did prove that with this new thermodynamic approach of subsystems, and with the use of standard heat transfer expressions, the performance of nuclear power plant pressurizers can be predicted within reasonable limits. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Measurements of the angular distributions of the gamma-rays from the reaction N¹⁵ (p,αɤ)C¹² indicate that the 4.43 Mev excited state of C¹² has spin 2 and even (+) parity and that the 12.51 Mev and 12.95 Mev levels of O¹⁶ have spin 2 and odd (-) parity. The level in O¹⁶ at 13.24 Mev was not determined uniquely since the theoretical distributions for assignments 3- and 4+ differ only by small amounts. The angular distribution of the ground-state alpha-particles from the reaction N¹⁵(pα) C¹²has been studied for proton energies from 500 kev to 975 kev. The most striking feature of the angular distribution patterns is the strong forward-backward asymmetry which indicates interference between levels of the compound nucleus of opposite parity. The distributions can be explained most simply by assuming two levels in O¹⁶; one at 12.43 Mev excitation with spin O and even parity; the other at 13.09 Mev excitation with spin 1 and odd parity. The strong interference term can also be explained by assuming that there exist broad unresolved O+ and 2+ energy levels in this region, as suggested by recent work on the elastic scattering of alpha-particles by C¹². A fast neutron spectrometer, using the time-of-flight method, which may also be used to study reactions involving the simultaneous emission of neutrons and gamma-rays, is described. One stilbene scintillation counter is placed close to the source, the other a suitable distance away. The two counters are connected to a new type of coincidence time-sorter which converts delay-time between associated events into a pulse-amplitude distribution which may be analysed by a "kicksorter," enabling the whole range of delay times or energies to be displayed and recorded at one time. The delay time may result from the neutron flight-time following scattering in the first counter or from the time-of-flight of a neutron from the target when a coincident gamma-ray has been detected in the first counter. Typical results are presented for the reactions D(dn)He³ and Be⁹(dn i )B¹⁰. The reaction Li¹⁶ (dn ɤ)Be¹⁷ has been studied with the new type of neutron spectrometer. This spectrometer has made possible the- study of the angular correlations between the monoenergetic neutron group to the 0.43 Mev state of Be⁷ and the gamma-rays which follow neutron emission. The results of these angular correlations indicate that the first excited state of Be⁷ has spin ½ and odd parity in agreement with values found for the mirror nucleus Li⁷. The excitation function for the neutron group to the first excited state of Be⁷ has also been studied for deuteron-bombarding energies from 300 kev to 1500 kev and was found to be very similar in shape to that found by other workers for the total neutron yield from the reaction Li⁶+ d. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The pure quadrupole resonance frequencies due to B¹¹ nuclei at two different sites (denoted by E and F) in a single crystal of kernite (Na₂B₄O₇.4H₂O) have been determined both by observing the B¹¹ lines in zero external magnetic field, and also by investigating their Zeeman splitting in magnetic fields up to 30 gauss. The values obtained are 1281.1 ± 2 Kc/sec and 1287.0 ± 1 Kc/sec for the E and F sites respectively. These frequencies agree within experimental error with values predicted on the basis of studies in a high magnetic field. The agreement for the F site is much better than for the E site. Some other interaction, such as asymmetric nuclear shielding, may account for the discrepancy. Resonances also have been obtained in zero field with a polycrystalline sample. Indications of B¹⁰ resonances were observed at the frequencies expected assuming Dehmelt's value for the ratio of the quadrupole coupling constants for B¹¹ and B¹⁰. A Na²³ resonance line was observed at 1560 ± 1 Kc/sec in agreement with Proctor's result for this line. The other Na²³ resonance expected from high field work has not been observed to date. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The general case of the dependence on crystal orientation of the frequency splitting of the nuclear magnetic resonance absorption line in a single crystal sample into 21 components due to the coupling between the nuclear electric quadrupole moment and the electric field gradient in the crystal at the site of the nuclei in question is examined both theoretically and experimentally. The theoretical part of this thesis consists of a detailed exposition of the first order perturbation theory applicable to crystals with axially symmetric fields which was outlined in condensed form by Prof. R. V. Pound, and of the extension of this first order theory to non-axially symmetric cases suggested by Prof. G. M. Volkoff. The experimental part of this thesis consists of the description of an exploratory experiment proposed by the author, and performed by him, with some assistance from Mr. H. E. Petch, for the purpose of obtaining a preliminary check on the theory, and of demonstrating the feasibility of a later more carefully performed experiment. Such an experiment with an improved crystal mount has since then been performed by Mr. Petch. A single crystal of spodumene was used, and the angular dependence of the frequency splitting for Li⁷was measured as the crystal was rotated about the C-axis of its monoclinic structure. The apparatus used was an oscillating detector type of nuclear magnetic resonance spectrometer previously designed and built by Dr. T. L. Collins. The axis of rotation of the crystal was kept perpendicular to the uniform magnetic field of the spectrometer. The direction of the b-axis of the crystal inferred from this rotation was found to coincide within experimental error with, its orientation as obtained later by standard optical methods. An experiment was designed to indicate the relative magnitudes of the spin-lattice relaxation by magnetic dipole and electric quadrupole coupling is proposed. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Let J’, J, J" represent the total angular momenta of the initial, intermediate, and final states of a nucleus respectively and J₁, J₂ the total angular momenta of the first and second emitted particles. Then, in terms of this notation, the following results can be found in this thesis. α – γ and γ – γ correlation functions have been calculated explicitly in terms of cos²θ for those transition schemes satisfying the following conditions: (i) J' = J +J₁, J = J" + J₂ for arbitrary J₁, J₂ = 1, 2. (ii) J' = J - J₁, J = J" - J₂ for arbitrary J₁, J₂ = 1, 2. (iii) J' = J₁ - J, J = J" +J₂ for arbitrary J₁, J₂ = 1, 2. (iv) J' = J - J₁, J = J₂ - J" for J₁ = 1, 2, arbitrary J₂. These are called the "special transitions" in the text. α – mixed γ correlation functions have been tabulated explicitly in terms of cos²θ for an α particle with total angular momentum 1 or 2 and a photon corresponding to a mixture of electric quadrupole and magnetic dipole radiation. For an α particle with total angular momentum 3 the α –mixed γ correlation functions can be obtained from a table which lists the sums of products of angular momentum coefficients appearing in these correlation functions. These correlation functions are too clumsy to be expressed explicitly In terms of cos²θ in general, however they can be fairly easily evaluated once numerical values of the angular momenta of the nuclear states are prescribed. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The two theories of low energy nuclear reactions which are mainly used for the interpretation of experimental data are compared. The two theories of interest are the R-Matrix theory of Wigner and Eisenbud and the S-Matrix theory of Humblet and Rosenfeld. The two approaches to resonance reactions are quite different and the differences are discussed with reference to a variety of specific examples. A simple soluble model - the threshold resonances of scattering by a square potential well - is analysed in detail using the two approaches. The approximate formulae are then compared numerically with the exact solution. It proves necessary to modify the usual S-Matrix approach and to use expansions other than the Mittag-Leffler which was used in the development of the general theory. We discuss two alternate expansions. With the modification to the S-Matrix theory both approaches give very accurate approximate formulae. The theories give different interpretations of the position and width of the threshold level. If the level is unbound the R-Matrix interpretation is fully satisfactory. The S-Matrix interpretation is unsatisfactory because the level has the characteristics of a bound state but none exists. If the threshold level is bound the position is reversed. S-Matrix theory correctly locates the bound state but R-Matrix theory does not. For threshold resonances one R-Matrix level is involved but two S-Matrix poles (except for the 1-S state) give rise to the resonance cross section. The physical interpretations are consolidated by describing the cross section for n-p, n-l60 and n-208Pb scatterings. The slow neutron cross section of ¹³⁵Xe is discussed using both formalisms. This is an example of a narrow compound nucleus resonance very close to a channel threshold. The theories fit the data with different parameters and very near threshold they give quite different shapes to the cross section. The origin of this difference is traced to unitarity. S-Matrix theory, in this situation, fails to give the cross section the correct behaviour very near threshold, because its approximation to the collision matrix is not unitary. Two level interference is discussed. Artificial cross sections are constructed to illustrate the very different interpretations that the two approaches may give to an interference cross section. The (p, y) and (p, n) cross sectionsof ¹⁴C are analysed using both R-Matrix and S-Matrix formalisms. ¹⁵N* has two very wide ½+ levels near neutron threshold. Both approaches fit the data to very good accuracy. The level positions and widths are quite different but the partial widths are similar. An analytic method of relating the parameters of the two theories by a transformation is given with the necessary approximations noted. The accuracy of the method is confirmed by application to the ¹⁴C+p cross section parameters. The transformation is used to discuss some theoretical points. Unitarity is discussed and the unitarity of the R-Matrix collision matrix is demonstrated for all approximations. It is possible to satisfy the unitarity requirements explicitly in the S-Matrix theory in only the simplest situations and with poor approximations and the reasons for this are discussed. It is concluded that in most situations both theories are capable of fitting experimental data. The only situation in which there is a measurable (though small) difference is very near threshold. If one requires that unitarity be satisfied for all approximate formulae the S-Matrix theory is poor. Except for isolated resonances far from threshold the R-Matrix and S-Matrix theories give quite different values for the parameters of resonance levels. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This thesis seeks simplifications to the formulation of the radiative three-nucleon reactions (i.e. direct capture, and partial and total photodisintegration) by means of group theory and other methods, similar to the simplifications to the three-nucleon Schroedinger equation made by other workers (e.g. Derrick and Blatt (1958)). Some useful results are derived for the S₃ group, the group of permutations of three things. In addition to the usual projection operators (e.g. Eichmann (1963))> operators are formed analogous to the operators J², J₂, and J± of the SU₂ group, and new methods of defining and generating permutation eigenfunctions, which transform according to the irreducible representations of S₃ are developed. Also, properties of the Derrick-Blatt (1958) addition coefficients which simplify their use are demonstrated, expressions are derived for permutations of product functions, a simplification is given for integration of permuted functions, and a Wigner-Eckart theorem for S₃ is derived, A new body-fixed coordinate system is derived which greatly simplifies the formation and use of Euler-angle functions. Three internal coordinate systems, each advantageous for a different problem, are defined, and their interconversions given. For each of them, necessary trigonometric formulae and expressions for integration are given. The Derrick-Blatt (1958) expansion for three-nucleon wave functions in permutation eigenfunctions is modified to take advantage of the new body-fixed coordinates, and relations between functions in the new and old expansions are derived. Expansions of bound states are discussed, and the continuum states of deuteron plus free nucleon and of three free nucleons are expanded in the new basis functions. Previous, erroneous attempts at similar expansions are discussed. The electric dipole and quadrupole and the magnetic-dipole orbital and spin-flip components of the interaction Hamiltonian representing an emitted or absorbed gamma ray are expressed in permutation-eigenfunction operators, using the long-wavelength and first-order-perturbation approximations, whose validity is discussed. Exact, closed, general forms are derived for matrix elements of the Hamiltonian in Euler-angle and spin-isospin variables, and the internal integrations are considerably simplified. Exact expressions, involving integrals over the three internal variables, are thus derived for matrix elements of the overall Hamiltonian between completely general initial and final states. Expressions are given for the cross section in terms of the matrix elements, and further simplifications are given for some of the reactions involved. A few numerical results are given, which show that the cross section depends sensitively on the wave functions used. The application of this work to the study of nuclear structure and interactions is discussed. Three-quark states are also expressed in the new formalism. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

A study has been made which demonstrates the feasibility of developing a nuclear particle detector utilizing tunneling between superconductors. For optimum detector performance, temperatures lower than 1.2°K are mandatory. Accordingly, a He⁴ cryostat capable of being modified to a He³ cryostat has been constructed and tested. The detectors, which have been fabricated and tested at 1.4° K, consist of thin aluminum and lead films separated by an insulating layer of aluminum oxide. The d-c tunneling currents have been observed and are found to compare favourably with the results of previous workers. The d-c response of the device to gamma radiation was, as expected, unobservable. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Threshold electron impact spectra have been obtained for helium, neon, argon, krypton, xenon and carbon monoxide using a velocity-selected electron beam. Zero energy electrons ejected at excitation thresholds are scavenged by sulfur hexafluoride and the resulting SF(6)¯ ions are detected using a mass filter. Optically forbidden transitions are observed to make a large contribution to the total threshold excitation. Singlet-triplet transitions are especially prominent in helium and carbon monoxide. Excitation of outer s and p electrons is observed for neon, argon, krypton and xenon. / Science, Faculty of / Chemistry, Department of / Graduate

Triple correlation cross sections have been measured for the reaction T(He³,He⁴)np in a complete experiment at a He³ bombarding energy of 1.5 MeV. Three similar experimental geometries were used which allow the observation of low relative energies in the n-p system, and energies of 0.96 MeV in the He⁴-n system. Therefore the n-p singlet and He⁵ (g.s.) final state interactions were observed. Events from the two body reaction channel T(He³,d)He⁴ and overlapping kinematic contours were eliminated by particle identification. A least squares fit to the experimental triple correlation cross section for one geometry was made using two approximate theories for three body reactions. These were the Watson, and Phillips, Griffy and Biedenharn (P.G.B.) final state interaction theories. Both theories give the theoretical cross section to be proportional to a density of states (D.O.S.) function. The P.G.B. theory gives two forms for this function (P.G.B.1 and P.G.B.2). The D.O.S. functions for the state of He⁵ and Li⁵ were calculated using only the P.G.B. 1 and Watson forms. The P.G.B.1 form gives an inadequate description of both the n-p singlet and He⁵(g.s.) final state enhancements. The He⁵(g.s.) enhancement is well described by the Watson form of the D.O.S. function. The triple correlation cross section, for high proton energies, was dominated by a sequential breakup through the ground state of He⁵ and by direct three body breakup. No evidence for contributions from the states of Li⁵ or for any well defined contributions from the first excited state of He⁵ were observed. The Watson and P.G.B.2 forms of the singlet n-p D.O.S. function gave indistinguishable predictions of the n-p singlet enhancement. The P.G.B. 2 form was used, for seven values of the n-p singlet scattering length, to fit the experimental data. The value of the singlet n-p scattering length extracted in the fitting procedure was [formula omitted]. The large experimental errors assigned were caused by the sensitivity of the extracted value on the background terms included in each fit. / Science, Faculty of / Physics and Astronomy, Department of / Graduate