the exact wave function zfz from the truncated representation for g, i.e. , what is V,qq if (1 -PgV, tt) P= 0 yields the exact wave function given in Kq. (51). Since we can write Kq. (52) as S=PgVL1/(1 gQV-) j4 and using the calculable expression for (1 -gQV) from Kq. (51), we obtain P= PgV(1+Gpl) [1/(1+GpPl GprtpGoQl)]fWe then see that the effective operator which permits the use of a truncated representation for g, and yet yields the exact wave function, is V,tt= t[1/(1+GoPt GortsG-oQt) g.Neglecting the compact operator in the denominator of V ff we see that the wave function should again be approximately calculated from the lowest-order term:Q~Pgtf.We see that the t operator of the residual interaction rather than the residual interaction potential is the one that appears in a convergent formulation of three-body shell-model calculations if only a finite set of basis states, Pf, is used in the diagonalization of the residual interaction. Calculations that use an approximation for the t matrix have recently been performed by Hodgson. "He finds that there is no definite improvement over a calculation that just employs the potential. Kuo and Brown" make use of the second Born term in the series for t, i.e. , t V+VGpV. They use core polarization states in the intermediate states of the term VGOV. This implies that Kuo and Brown have included a structure in the core and have departed from a strict three-body shell-model interpretation of the problem.At any rate, they find the second Born term to be important."R.A detailed study of the wave properties of the nuclear optical model is presented to elucidate the problem of barrier penetration by charged particles and to remove some of the mystique of optical-model calculations. The wave properties and the concomitant penetration are most straightforward for square wells, for which the resonance, reflection, and penetration are easily ascribed to separate factors. We show that the wave properties of more general diffuse-edge optical potentials achieve a similar simplicity by the construction of an equivalent square well (ESW) which has the same resonance, penetration, and absorption factors as the optical potential, but which differs in its reflection factor. A general construction of the ESW is given, and we apply it to the following problems: (1) the very narrow single-particle resonances of real optical potentials that occur at energies far below the Coulomb barrier, (2) the nuclear absorption cross sections in the presence of barriers, (3) the calculation of absorption cross sections at astrophysical energies (extreme barrier penetration) employing optical models fitted to data at higher energies, and (4) the value of the nuclear radius and sum-rule limits appropriate to the analysis of nuclear reactions. In some cases of extreme barrier penetration, the ESW fails to yield all the properties. For example, cases are described where the bulk of the absorption may attain in the distant "tail" of the imaginary term in the optical potential: The corresponding reaction ra...

In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and Study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives.It is understood that copying or publication of this thes.is for. financial gain shall not be allowed without my written permission. ABSTRACTThe optical interaction of low energy f^30 MeV) pions with nuclei is discussed. In particular, it is shown that, since the nuclear density enters the low energy pion-nucleus interaction in a very direct manner, this interaction provides a sensitive means of investigating such properties of the nuclear density.as the diffuseness of the nuclear surface. A.geometric discussion of the structure of the low energy pion-nucleus interaction is given which emphasizes the analogy hetween adding the scattered pion waves in the nuclear medium and adding electric potentials in a classical dielectric. The parameters of the optical potential which represents the interaction are taken to he those calculated by earlier authors who have used a multiple-scattering formalism to deduce the details of the-optical interaction from a microscopic point of view. The interaction is strongly momentumdependent and the local part of the interaction is repulsive. It is shown that in optical scattering and absorption, the resonance aspects of the problem depend mainly only upon the height of the local potential barrier (^15 MeV) because of the long wavelength of the pion inside the nucleus. The optical absorption of low energy pions is shown to be sensitive to the diffuseness of the nuclear surface through the strong suppression of momentum-dependent absorption near the top of the potential barrier. It is argued that low energy pions can therefore be used to resolve the conflicts which presently exist in the information available from i i i several experiments concerning the distribution of neutrons in the nuclear surface. The ideas developed in discussing the optical absorption of pions are extended to the excitation by pions of rotational states in strongly deformed nuclei. It is shown that, unlike the excitation cross sections obtained with more conventional interactions (such as the Coulomb interact!on) , the excitation cross sections obtained from the pion-nucleus optical interaction depend strongly upon such characteristics of the nuclear density as its surface thickness. The rotational model of strongly deformed nuclei is assumed and an analysis of the excitation cross sections is made in the Distorted Wave Born Approximation. It is shown that the sensitivity to the nuclear surface thickness in the excitation cross sections arises from the suppression of the excitation processes due to the momentum-dependent interaction near the top of the potential barrier. It is' suggested that the excitation of rotational levels in strongly deform...

An expression is derived for the lifetime of a negative ion in a weak and static electric field. Using this expression, existing experimental data are analyzed to improve the empirical value of the electron affinity of the negative hydrogen ion by an order of magnitude.

The alpha-decay rates in heavy nuclei are analyzed by a method in which the decay rates are factored into one-body widths and spectroscopic factors. It is shown that the discrepancy between the absolute values of the experimental alpha-decay rates and those calculated with the nuclear shell model has mainly resided in the incorrect assessment of the one-body widths and that it can be largely removed by a more direct treatment of the average interaction between the alpha particle and the residual nucleus.

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