Citation
Ludewig, Hans (1966) Geometrical effects on the resonance absorption of neutrons. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:09242015135757893
Abstract
An investigation was conducted to estimate the error when the flatflux approximation is used to compute the resonance integral for a single absorber element embedded in a neutron source.
The investigation was initiated by assuming a parabolic flux distribution in computing the fluxaveraged escape probability which occurs in the collision density equation. Furthermore, also assumed were both wide resonance and narrow resonance expressions for the resonance integral. The fact that this simple model demonstrated a decrease in the resonance integral motivated the more detailed investigation of the thesis.
An integral equation describing the collision density as a function of energy, position and angle is constructed and is subsequently specialized to the case of energy and spatial dependence. This equation is further simplified by expanding the spatial dependence in a series of Legendre polynomials (since a onedimensional case is considered). In this form, the effects of slowingdown and flux depression may be accounted for to any degree of accuracy desired. The resulting integral equation for the energy dependence is thus solved numerically, considering the slowing down model and the infinite mass model as separate cases.
From the solution obtained by the above method, the error ascribable to the flatflux approximation is obtained. In addition to this, the error introduced in the resonance integral in assuming no slowing down in the absorber is deduced. Results by Chernick for bismuth rods, and by Corngold for uranium slabs, are compared to the latter case, and these agree to within the approximations made.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  Applied Mathematics  
Degree Grantor:  California Institute of Technology  
Division:  Engineering and Applied Science  
Major Option:  Applied Mathematics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  11 November 1965  
Funders: 
 
Record Number:  CaltechTHESIS:09242015135757893  
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:09242015135757893  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  9174  
Collection:  CaltechTHESIS  
Deposited By:  Leslie Granillo  
Deposited On:  24 Sep 2015 21:29  
Last Modified:  24 Sep 2015 21:29 
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