Relative efficiency

Some papers

File:Nn correlation extraction.pdf

File:Ynn vs Dnn.pdf

Rletive efficiency obtained from the 2n opening angle w/ uncorrelated neutrons

The result of simulation of 2n openeing angle obtained by different neutron detectors (each neutron hit different detector) having y-resolution is presented below. The source of neutrons was isotropic.

Empty target, [math]10^8[/math] events sampled	DU target, [math]10^8[/math] events sampled
Point isotropic n-source w/o material	Volume isotropic n-source + DU material

The result of simulation of 2n openeing angle obtained by the same neutron detectors (2 neutrons hit same detector) having y-resolution is presented below:

In the experiment our expereimental setup did not have y-resolution across the surface of the neutron detectors. So it was necessary to simulate the 2n opening angle for the neutron detectors w/o y-resolution. The result of the simulation of 2n opening angle (the 2n angles detected by all detectors are superimposed) for the case where thre was no y-resolution is going to be noted as [math]D_{nn}[/math]. The experimental data obtained from run 4172 (DU target) on 2n opening angle for uncorrelated neutrons (i.e. in the case of isotropic source of neutrons) from different pulses is going to be noted as [math]Y_{nn}[/math]. The relative efficiency is defined as [math]\epsilon=Y_{nn}/D_{nn}[/math] and it is plotted below as a result of bib-by-bin division of [math]Y_{nn}[/math] over [math]D_{nn}[/math].

Relative efficiency of the detecting system obtained using experimental data only (all runs)

In this part the experimantal data are presented for the cases when (1) the 2n opening angle was measured for neutrons correlated and (2) the 2n opening angle was measured for neutrons uncorrelated (neutrons from separate pulses). In the figure below the experimental data on the 2n opening angle measured for the case of correlated neutrons is presented where the statistical error bar width is equal to [math]\pm \sqrt{N_{bin}}[/math] along y-axis and 4.5 deg along x-axis (the bin width). The total number of triggering pulses during the experiment was Nexp_pulses=2.469256E+7.

The experimental data on the 2n opening angle measured for the case of uncorrelated neutrons is presented in the next figure. 80 neutrons from different pulses were taken uniformly to reproduce 2n opening angle for the case of uncorrelated neutrons. The total number of uncorrelated neutron pairs was Npair_uncorr = 3.608397E+7. The width of the error bars is smaller then the size of the markers.

The result of the division of the two histograms ([math]Y_{nn}^{correlated}/Y_{nn}^{uncorrelated}[/math]) obtained for the described two cases is shown below. In order to obtain the resulting histogram as a division of the previous two histograms we need to do the division on the bin-by-bin basis as [math]\frac{a \pm \delta a}{b \pm \delta b}[/math], where [math]a[/math] and [math]b[/math] are the contents of the corresponding bins and [math]\delta a[/math] and [math]\delta b[/math] are the coresponding statistical errors for the bin contents [math]a[/math] and [math]b[/math]. The error bars were obtained by the propagation in the following way: [math]\delta Err = \frac{a}{b}\sqrt{(\frac{\delta a}{a})^2+(\frac{\delta b}{b})^2}[/math]. The resulting histogram wa normalized to the ratio of the total number of pulses to the total number of uncorrelated neutron pairs considered Norm = Nexp_pulses/Npair_uncorr = 2.469256E+7/3.608397E+7 . It should be noted that the total number of uncorrelated neutron pairs can be varied by changing the number of corresponding combinations and the number of pulses involved into the 2n opening angle reproduction, so the normalization may change.

Normalization

Thick DU target run#	# of multi-hit events per run	Total # of events per run
4118	0	1,668,482
4119	0	2,135,901
4133	0	1,704,331
4134	0	1,732,490
4135	0	1,603,604
4137	0	800,699
4144	0	1,645,667
4145	0	1,544,605
4146	0	510,826
4153	0	1,750,657
4154	0	1,631,436
4155	0	1,062,048
4166	0	214,600
4169	0	191,592
4170	0	429,974
4171	0	1,141,113
4172	0	650,734
4173	0	354,992
4174	0	953,831
4175	0	299,086
4176	0	144,774
4177	0	225,877
4203	0	659,050
4204	0	1,636,192

run#	80 puls pairs	all nonZ pairs	total # of pairs
run4118	1949796	35168980	58460510939894
run4119	2470399	57115623	95803579611944
run4133	1741760	30145143	60999663129029
run4134	1832885	33384324	63031990015343
run4135	1727993	28580648	54002495269034
run4137	833189	7099684	13463513489481
run4144	1770693	26603021	56872651957830
run4145	1592222	20562899	50101929186175
run4146	491705	2157292	5479817982802
run4153	8753312	177560268	64360835399566
run4154	1695297	26345381	55893286150871
run4155	1182325	12257834	23686887361551
run4166	174390	226636	967120869210
run4169	175558	235498	770861409690
run4170	319678	1008712	3882439488990
run4171	1415700	19159461	27344940440490
run4172	623978	3412116	8892563188751
run4173	395573	1327163	2646413182232
run4174	894440	5765727	19105685150123
run4175	255450	619705	1878507428108
run4176	110058	119818	440152774689
run4177	976415	1721476	1071433552715
run4203	3003073	23564022	9121298818219
run4204	1682843	28829022	56219643867161
totals	36068732	542970453	734498220663898