THE TOTAL CAPTURE PROBABILITY OF MUONS BY C$sup 1$$sup 2$
Thesis/Dissertation
·
OSTI ID:4751855
The total capture probability of negative muons by the C/sup 12/ nucleus was calculated as a sum of partial transition rates to the individual levels of B/ sup 12/. The general formalism for calculating the transition rate between two definite nuclear states was used. The theory for muon capture was basically the same as that used in beta decay calculations. Upon comparison of the theoretical predictions with the results of experimental measurements for the beta decay of B/ sup 12/ it was found that the results of theory were too large by a factor of 4.8 when a shell model of the nucleus was used. The assumption made is that the nuclear matrix elements describing muon capture by C/sup 12/ are in error by the same factor. A shell model of the nucleus was used in order that the wave function of each boron level may be given the correct spin and parity. This has the advantage that the forbiddenness of each transition is accounted for. The eightparticle configuration rendered a consideration of the mixing of states implausible, so that an extreme single-particle model was used. It was assumed that jj-coupling is a reasonable approximation. Where the spin and parity assignments of a particular B/sup 12/ level remain doubtful, calculations were made to place upper and lower limits upon the transition rate to this level. By writing a general wave function which represents any one of the final states, the nuclear matrix elements may be reduced to simplified form and numerical values obtained simply by substitution of the quantum numbers of the level under consideration. According to the calculation, captures to the 0.95 Mev level of B/ sup 12/ should be between 0,5 and 0.8% of all bound state captures. Predictions regarding the 1.67 Mev level were in poor agreement with experiment, the lower limit to the calculated value being too large by a factor of 2.3. It is possible that the spin and parity assignments currently accepted for this level are in error, but a more accurate estimation of the error in the nuclear matrix elements should be made before a correction is suggested. If the captures to the 2.62 and 2.72 Mev levels are considered to be second forbidden, then the predictions are in good agreement with experimental data available. (Dissertation Abstr., 23: No. 4, 1962)
- Research Organization:
- Originating Research Org. not identified
- NSA Number:
- NSA-17-005409
- OSTI ID:
- 4751855
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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