Describing the exponential tail as a function of energy and including the attenuation of the rad source package (11 Mar 2004, updated on 17 Mar 2004)

Spectral Model

variables :
1.  sigma         : energy resolution [channel]
2.  gain_coeff    : gain_coeff * E^gain_index [channel/keV]
3.  gain_index    : 
4.  exp_lambda    : 1.0/(peak*exp_lambda) * exp( (E-main_peak)/(peak*exp_lambda) )
5.  exp_coeff     : exp_ratio = exp_coeff * (E/31.0keV)^(-exp_index)
6.  exp_index     : 
7.  norm          : overall incident phtoton flux before absorbed [photons/sec/cm^2]

constants :
8.  voltage       : bias voltage, fixed to 200 V
9.  src_x         : source position in bat_x
10. src_y         : source position in bat_y
11. src_z         : source position in bat_z

Exponential tail The definition of the parameter "exp_lambda" was the length of the tail in channel. But here, in order to generalize the "exp_lambda" to all energy line, it seems better to change the definition to the ratio of the length to the main peak position.
```
1.0/(peak*exp_lambda) * exp( (E-main_peak)/(peak*exp_lambda) )
```
The parameter "exp_ratio" has also been changed to be dependent on the energy. The ratio is now given as:
```
exp_coeff*(E/31.0keV)^(-exp_index).
```

Transmission through the rad source package

  // t0 : the transmission through the rad source package
  Double_t ri_rho = 1.0; // [g/cm^3]
  A=2133.5; B=3.044; C=0.5490; D=0.2552; n=1.226; // assuming the composition as CH2, valid for 10-200 keV
  Double_t ri_mu = pow(pow(A*pow(energy,-B),n) + pow(C*pow(energy,-D),n),1.0/n); 
  Double_t thickness = 0.277; // [cm] for type D tablet
  t0 = exp(-ri_mu*ri_rho*thickness/cos(theta));

Fitting Results


.cg06_x_ba133_030304_8_c_ff.pha	cg08_x_ba133_030304_10_c_ff.pha	cg09_x_ba133_030304_11_c_ff..pha

cg10_x_ba133_030304_12_c_ff.pha	cg11_x_ba133_030304_13_c_ff.pha	cg12_x_ba133_030304_14_c_ff.pha

cg13_x_ba133_030304_15_c_ff.pha	cg15_x_ba133_030304_17_c_ff.pha	cg16_x_ba133_030304_18_c_ff.pha

cg17_x_ba133_030304_19_c_ff.pha	cg18_x_ba133_030304_20_c_ff.pha	cg19_x_ba133_030304_21_c_ff.pha

cg20_x_ba133_030304_22_c_ff.pha	cg21_x_ba133_030304_23_c_ff.pha	cg23_x_ba133_030304_25_c_ff.pha

cg24_x_ba133_030304_26_c_ff.pha	cg25_x_ba133_030304_27_c_ff.pha	cg31_x_ba133_030304_33_c_ff.pha

cg33_x_ba133_030304_35_c_ff.pha	cg34_x_ba133_030304_36_c_ff.pha	cg35_x_ba133_030304_37_c_ff.pha

cg36_x_ba133_030304_38_c_ff.pha	cg37_x_ba133_030304_39_c_ff.pha	cg38_x_ba133_030304_40_c_ff.pha

cg39_x_ba133_030304_41_c_ff.pha	cg_x_ba133_030304_3_c_ff.pha	cg_x_ba133_030304_4_c_ff.pha

cg_x_ba133_030304_5_c_ff.pha	cg_x_ba133_200_21_030306_1_c_ff.pha	cg_x_ba133_200_21_030306_2_c_ff.pha

cg_x_ba133_200_21_030306_3_c_ff.pha	cg_x_ba133_200_21_030306_4_c_ff.pha

Correlation between fitted parameters and source angle

reduced chi-squared, sigma, and gain parameters

norm

Predicted Flux

According to Nadine's calibration report (calibhigh.xls), the source activity on 6/26/03 is 30.448 MBq.
The rate on 3/4/03 is calculated as 30.448 x 2^115/3839 = 31.8682 MBq,
making the flux at the distance of 304 cm:
 31.8682 x 10⁶ x (sum of the branching ratios) / (4 pi x distance²)
 = 31.8682 x 10⁶ x 1.6324 / (4 pi x 304²)
 = 44.8 photons/s/cm²

Error of relative peak efficiency   : +-  5%
Error of an absolute efficiency     : +- 10%

Distributions of fitted parameters

The mean or peak values for each parameters are listed below:

variables :
1.  sigma         : 5.6 [channel] = 1.4 [keV]
2.  gain_coeff    : 3.925 [channel/keV]
3.  gain_index    : 1.0064
4.  exp_lambda    : 0.26
5.  exp_coeff     : 0.23
6.  exp_index     : 6.5

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