Summing correction

A rough idea of the electronic distribution is conveyed by the requirements that the partial charges must sum correctly and likewise for the partial bonds. 

The accepted wisdom is that the Hiickel Hamiltonian matrix should be identified with the matrix (h where G is the electron repulsion matrix of Chapter 6. The basis for this belief is that that the matrix (h has eigenvalues that do sum correctly to the electronic energy. 

Wang, Z., Kahn, B., and Valentine, J. D. 2002. Efficiency calculation and coincidence summing correction for germanium detectors by Monte Carlo simulation. IEEE T Nucl Sci 49, 1925-1931. 

One of the difficulties faced when collecting the information needed to perform reliable summing corrections is the rehabUity of the nuclear data in the literature. Of course, the quality of the data is worst for those nuchdes for which summing is a particular problem. I can only remind the reader once more of the data given in Appendix B. 

In Chapter 6,1 mentioned the moves being made in the direction of providing detector calibrations based upon the dimensions and physical parameters of the detector and its encapsulation. Once this happy state of affairs has been attained, then the extension of that to include true coincidence corrections becomes possible. Again, one can envisage a situation where a new detector is delivered with a CD-ROM holding the theoretical calibration curve and the latest nuclear data for the nuclides of most common interest that would be accessed by spectrum-analysis programs for automatic summing corrections. For that, we must wait, but help does now appear to be on the horizon. 

Debertin, K. and Schotzig, U (1979). Coincidence summing corrections in Ge(Li)-spectrometry at low source-to-detector distances, Nucl. Instr. Meth. Phys. Res., 158, 471-477. 

Sima, O. and Arnold, D. (2000). Accurate computation of coincidence summing corrections in low level gamma-ray spectrometry, Appl. Radiat. Isotopes, 53, 51—56. 

The programs within modem portable gamma spectrometers can, in some cases, rival that of the more sophisticated PC-based systems, especially where acquisition is controlled by a laptop PC. However, improvements have also been made to the PC-based software. In particular, and most laudable, is the introduction of trae coincidence summing corrections into GammaVision and Genie 2000, even though, as 1 explained in Chapter 7, there... 

The random summing correction may not be implemented as implied by Chapter 7, Equation (7.26). Under most conditions, this correction is small and an approximation is made which results in a correction of the type ... 

A pulse generator that can simulate detector pulses is perhaps not essential but is certainly desirable. It should provide pulses with variable rise time (perhaps 10 to 500 ns) and variable fall-time (perhaps 10 to 500 j,s). The output from the pulser is put into the TEST INPUT of the preamplifier. It allows a distinction to be made between detector problems and pulse processing problems. Some laboratories routinely use a pulser for dead time and random summing correction purposes. For systems with TRP preamplifiers, a simpler pulser providing square pulses would be adequate. 

This test is similar to the procedure outlined earlier in Chapter 7, Section 7.6.8 to derive a random summing correction factor for conventional systems. It was pointed out that, regardless of the use of pile-up rejection circuitry, there will always be a small proportion of random... 

In accord with equations (4a, b), the natural populations necessarily satisfy the Pauli principle (0 < q- < 2) and sum correctly to the total number of electrons (Sa a = )- Equations (7a-c) summarize natural population analysis. (Some numerical NPA atomic charges for formaldehyde at correlated and uncorrelated levels will be presented in Section 4.2.)... 

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