Detector Efficiencies

The detector efficiency depends on the relationship between the energy deposited in

the scintillator and the light produced. Neutrons produce light via n −p scattering in the scintillator material. Although scattering is isotropic for neutron energies less

Table 4.1: Selected n−p scattering cross sections used for data normalization. Cross sections were obtained from the Nijmegen partial-wave analysis of N −N scattering data [Sto93, nn-12].

Lab angle n−p cross section (mb/sr)

(degrees) 4.0 MeV 5.0 MeV 6.0 MeV 7.0 MeV 8.0 MeV

30.0 523 448 391 347 311 32.0 513 439 384 340 305 34.0 501 430 375 333 299 36.0 490 420 367 325 292 38.0 478 409 358 317 285 40.0 465 398 348 309 277

deposited energy, but rather [Kno00]

L.O.=kE_n3/2, (4.3)

where the proportionality constant k depends on the dimensions and properties of

the liquid scintillator, specifically the density and hydrogen-to-carbon ratio. The

L.O. response for various liquid scintillators has been studied by many authors (ex.

[Pyw06, Nak01, Sas02, Ang79, Mas70, Cec79]). Combining the scintillator L.O. non-

linearity with the recoil energy distribution for neutrons on protons, and using the fact

that a neutron can impart up to all of its kinetic energy to a proton during a collision,

one can construct a reasonable scintillator response function for neutron energy deposits

in the liquid scintillator. In order to create a more realistic response function, carbon

scattering in the liquid scintillator must be also be accounted for. Because the scintil-

lation efficiency is low for high dE/dx particles, the carbon recoils do not contribute

much to the scintillator response. Neutrons can however lose some energy following a

scatter from 12C and then scatter from a proton. Because of the mass difference the

neutron cannot impart all of its energy to the 12C, but will lose between 0 and 28%

of its initial energy. This results in a decrease from 0.72En to En in the recoil energy

distort the response function in the vicinity of En.

If the scintillator response function is known for each En, it is straightforward to

construct a detector efficiency curve. For a given neutron energy, the total area under

the differential proton energy spectrum, which represents the scintillator response, is

proportional to the number ofn−pscatters at that energy. This can either be simulated in detail, calculated approximately, or measured experimentally. For neutron scattering

experiments, it is also common to use an energy threshold, which removes low-energy

recoil protons from the differential energy spectrum at a set discrimination level. As

a standard, the energy threshold is usually stated in terms of a fraction of the 137Cs

Compton edge, as described in Section 4.2.1.

Detector efficiencies at various thresholds were measured for both the four-meter

and six-meter detectors by Ref.[Ped86]. Because there was no measurement of the

efficiency at 1/2×Cs for the six-meter detector, the neutron response and detector efficiency was also simulated using the code neff7 [Die82]. The simulation code was

written for NE-213 liquid scintillators and was modified for the NE-218 detector by

changing the scintillator density and hydrogen-to-carbon ratio (Table 3.4).

For comparison to the experimental data and simulations, the efficiency was also

calculated using the expression given by [Dro72]:

(En) = 1− B En 1−e−ρH·t·σn(En)_{1 +} B E0 1−e−0.5·ρH·t·σn(E0n) . (4.4)

The first term is related to the light output. The neutron energy is En and B is the

bias (threshold energy). The quantityB was determined for NE-213 by fitting the data

from Ref.[Pyw06] to Equation 4.3. The best fit was for k = 0.15, where the L.O. was

in MeV electron equivalent (MeVee) and En was in MeV. Using this, a threshold of

MeVee) corresponds to B = 1.36 MeV. The second term accounts for a single n −p

scatter. The quantity ρH is the hydrogen density in the scintillator. The quantity

t is the thickness of the scintillator, which was 5.04 cm for both the four-meter and

six-meter detectors. The quantityσn(En) is the totaln−pscattering cross section. To

a very good approximation, this is given as [Kno00]

σn(En) =

4.83

√ En

−0.578, (4.5)

where the cross section is in barns and En is in MeV. The third term in Equation 4.4

accounts for multiplen−p scattering, which contributes when the light output of the first scatter plus the light output from the second scatter is greater than the bias energy.

E_n0 is the initial energy minus half the bias energy, giving the effective neutron energy after a single scatter. The term 0.5·ρH·tis an approximation for the areal density for

a second scatter. All first scatters resulting in a pulse hight much less thanB must be

small-angle scatters.

The efficiency curves for the four-meter and six-meter detectors are shown in Fig. 4.8

for energy thresholds of 1×Cs and 1/2×Cs from 0 to 20 MeV. There is good agreement between the data of Ref.[Ped86] and theneff7 simulation, which was used to determine

the efficiencies for the cross-section analysis. The calculation from the method outlined

in Ref.[Dro72] appears to be valid to about 10 MeV, which is also noted in the reference.

The disagreement above 10 MeV is due to the fact that 12_{C reactions are ignored in}

the calculation.