Spectrum unfolding by the least-squares methods

Conference · Sat Jan 01 04:00:00 EST 1977

OSTI ID:5207996

Perey, F G

The method of least squares is briefly reviewed, and the conditions under which it may be used are stated. From this analysis, a least-squares approach to the solution of the dosimetry neutron spectrum unfolding problem is introduced. The mathematical solution to this least-squares problem is derived from the general solution. The existence of this solution is analyzed in some detail. A chi/sup 2/-test is derived for the consistency of the input data which does not require the solution to be obtained first. The fact that the problem is technically nonlinear, but should be treated in general as a linear one, is argued. Therefore, the solution should not be obtained by iteration. Two interpretations are made for the solution of the code STAY'SL, which solves this least-squares problem. The relationship of the solution to this least-squares problem to those obtained currently by other methods of solving the dosimetry neutron spectrum unfolding problem is extensively discussed. It is shown that the least-squares method does not require more input information than would be needed by current methods in order to estimate the uncertainties in their solutions. From this discussion it is concluded that the proposed least-squares method does provide the best complete solution, with uncertainties, to the problem as it is understood now. Finally, some implications of this method are mentioned regarding future work required in order to exploit its potential fully.

• Research Organization: Oak Ridge National Lab., Tenn. (USA)
• DOE Contract Number: W-7405-ENG-26
• OSTI ID: 5207996
• Report Number(s): CONF-771096-1
• Country of Publication: United States
• Language: English

Related Subjects

61 RADIATION PROTECTION AND DOSIMETRY
655003* -- Medical Physics-- Dosimetry
658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
COMPARATIVE EVALUATIONS
COMPUTER CALCULATIONS
DATA PROCESSING
DOSIMETRY
LEAST SQUARE FIT
MATHEMATICAL LOGIC
MAXIMUM-LIKELIHOOD FIT
NEUTRON DOSIMETRY
NUMERICAL SOLUTION
PROCESSING
SPECTRA UNFOLDING