Applying the model formulated for the transmission to the 32 coarse grid run data (04 Mar 2004)

We have formulated the transmission through the passive materials such as air, the mask, and the honeycomb under the mask etc, which is a function of energy, angle, and the distance between the source and the detector array. Thus, the model can be constructed with a single normalization parameter instead of diffetent normalizations for each lines. Here, we will apply the model to more data from 32 coarse grid runs, and try to figure out how well the model fits the data obtained with different source positions.

Spectral Model

The current model is composed of the multi-mutau-model (based on 36 sets of measured mutau products) and the exponential tail (only for 31 and 35 keV lines). Though the calibraion data are processed with a gain of 4.0 bins/keV, the mutau-model gives slightly non-linear peak positions due to the different interaction depth for differet energy lines. We therefore adjust it as a power-law function ( gain_coeff * E^gain_index ). We have formulated the transmission through the passive materials such as air, the mask, and the honeycomb under the mask etc, which is a function of energy, angle, and the distance between the source and the detector array. Thus, the model have only one normalization parameter, which corresponds to a total photon flux in units of photons/sec/cm^2.

variables :
1.  sigma         : energy resolution [channel]
2.  gain_coeff    : gain_coeff * E^gain_index [channel/keV]
3.  gain_index    : 
4.  exp_lambda    : exp( (E-main_peak) / exp_lambda ) [channel]
5.  exp_ratio     : the ratio of counts which comes into exponential tail from photo-absorption events
6.  norm          : overall incident phtoton flux before absorbed [photons/sec/cm^2]

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

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 emission rate out of the souce package (on 6/27/03) is
 2.96 x 10⁷ + 6.53 x 10⁶ + 5.53 x 10⁵ + 9.85 x 10⁶  = 4.65 x 10⁷ photons/s in 4pi.
The rate on 3/4/03 is calculated as 4.65 x 10⁷ x 2^115/3839 = 4.75 x 10⁷ photons/s in 4pi,
making the flux at the distance of 304 cm:
 4.75 x 10⁷ / (4 pi x 304²) = 40.9 photons/s/cm²
(The manufacturer activity is ~10% higher than the measured activity, making it ~45 photons/s/cm².)

Possible improvements of the model

To include the attenuation of the source package (Ba 133-037).
Looking at the fitting result, 35 keV line should have smaller exponential tail. Making the ratio of exponential tail dependent on the line energy might improve the fit around 31 and 35 keV lines. This is preferable from another point of view that if we have a constant ratio of exponential tail to main peak, we have no criterion of putting exponential tail to different energy lines.

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