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Register a new userAn Alternative Parameterization of R-matrix Theory
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Carl R. Brune
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An alternative parameterization of R-matrix theory is presented which is mathematically equivalent to the standard approach, but possesses features which simplify the fitting of experimental data. In particular there are no level shifts and no boundary-condition constants which allows the positions and partial widths of an arbitrary number levels to be easily fixed in an analysis. These alternative parameters can be converted to standard R-matrix parameters by a straightforward matrix diagonalization procedure. In addition it is possible to express the collision matrix directly in terms of the alternative parameters.
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We investigate an alternative quantization of R-NS string theory. In the alternative quantization, we define the distinct vacuum for the left-moving mode and the right-moving mode by exchanging the role of creation operators and annihilation operators in the left-moving sector. The resulting string theory has only a finite number of propagating degrees of freedom. We show that an appropriate choice of the GSO projection makes the theory tachyon free. The spectrum coincides with the massless sector of type IIA or type IIB superstring theory without any massive excitations.
Supersymmetrizable theories, such as M(em)branes and associated matrix-models related to Yang-Mills theory, possess r-matrices
We review some aspects of R-matrix theory and its application to the semi-empirical analysis of nuclear reactions. Important applications for nuclear astrophysics and recent results for the ${}^{12}{rm C}(alpha,gamma){}^{16}{rm O}$ reaction are emphasized.
Background: Spectroscopic factors, overlaps, and isospin symmetry are often used in conjunction with single-particle wave functions for the phenomenological analysis of nuclear structure and reactions. Many differing prescriptions for connecting these quantities to physically relevant asymptotic normalization constants or widths are available in the literature, but their relationship and degree of validity are not always clear. Purpose: This paper derives relationships among the above quantities of interest using well-defined methodology and starting assumptions. Method: $R$-matrix theory is used as the primary tool to interoperate between the quantities of interest to this work. Particular attention is paid to effects arising from beyond the nuclear surface, where isospin symmetry is strongly violated. Results: Relationships among the quantities of interest are derived. Example applications of these methods to mirror levels in nucleon+${}^{12}{rm C}$, nucleon+${}^{16}{rm O}$, and nucleon+${}^{26}{rm Al}$ are presented. A new approach to multi-level mirror symmetry is derived and applied to the first three $2^+$ states of ${}^{18}{rm O}$ and ${}^{18}{rm Ne}$. Conclusions: The relationship between the quantities of interest is clarified and certain procedures are recommended. It is found that the asymptotic normalization constant of the second $2^+$ state in ${}^{18}{rm Ne}$ deduced from the mirror state in ${}^{18}{rm O}$ is significantly larger than found in previous work. This finding has the effect of increasing the ${}^{17}{rm F}(p,gamma){}^{18}{rm Ne}$ reaction rate in novae.
Notes from 11 October 2004 lecture presented at the Joint Institute for Nuclear Astrophysics R-Matrix School at Notre Dame University.
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