1. Neutronics Studies for the Nab Experiment
By Elizabeth Mae Scott for the Nab Collaboration
Nab: A search for “a” and “b”
Dose Plot
The Nab experiment aims to measure the beta decay products of unpolarized neutrons to determine the electron-neutrino correlation coefficient “a” and the Fierz interference term “b”.
The electron-neutrino correlation will be measured using the proton time of flight (TOF) and the electron energy of each beta decay. Knowing electron energy Ee and proton momentum pp, we can extract all three momenta.
Alternating SS and borated poly shielding
SS and borated Poly Roof shielding
Lead shielding pe pp
FnPB:
Fundamental neutron Physics Beamline
θev
Beam Stop
Fiducial Decay Volume pv
Lead shielding
Rad/hour
Lower Detector
Coincidence Signaling
Compared to the electrons and neutrinos, protons are much more massive, and therefore have a relatively low recoil kinetic energy at approximately .3 keV. To be more easily detected, they are accelerated via a 30 V potential difference between the decay volume and the upper Si detector.
The detected electrons will have a kinetic energy range of keV. Setting a trigger limit of 30 keV, we first look for an electron signal in the keV range.
Because the protons are low energy, they are difficult to distinguish. We take advantage of coincidence timing to signal a decay. If an electron in the expected energy range is detected, we then look for the corresponding proton. We expect to see the proton within microseconds after the electron signal.
Background Results
Current collimation and geometry gives a decay rate of 1833 Hz for a cylindrical decay volume with height 8 cm and radius 2.7 cm. Background rates were found for the 1) the inner 8 cm diameter disk and 2) the outer 15 cm diameter ring of the Si detectors.
Lower Detector
Background Rate (Hz)
Upper Detector
Deposited Neutrons
Deposited Gammas
No Shielding
830
2423
15404
45993
115
2678
6806
Optimized Shielding
145
233
Background Reduction
Due to the 30 V potential difference, proton detection is only in the upper detector. This detectors sees about 1/8th of the total protons produced- giving only 200 protons per second for the upper detector. About 98% of the electrons corresponding to these protons reach a detector, therefore the coincidence signal is approximately 200 Hz.
Slow neutron capture in materials in the beam line isotropically emits gammas and neutrons. If these products deposit similar energies in the Si detector as the protons within the time window after a detected electron, they give a false coincidence. The probability of a false coincidence is scaled by the time window- a background rate on the order of 103 Hz and a time window of 3 x 10-5 s will give a false background rate of about 3 x 10-2 Hz.
The uncertainty σa is proportional to 1/√N, where N is the number of decays observed. Reducing the background rate and thereby the statistical error will help to give a larger uncertainty budget for systematic errors. The shielding must reduce the number of background singles events so that the rate of false coincidences is low compared to our true signal. A one to one ratio of background single events to decays gives a statistical error on the order of 10-4.
Conclusion
The greatest source of background was neutron capture in aluminum windows. Lead shielding and alternating layers of SS and borated polyurethane effectively shielded this. Additional background was reduced by lining the beam line with Li6 to avoid neutron capture on surrounding materials.
Current shielding design gives an acceptably low background rate of ~ 400 Hz in the lower detector only. This significantly reduced background in both the upper and lower detectors. However, the dose plot shows that roof shielding allows for a leak in dose near the magnet. This roof shielding design is still in progress and the dose will be taken into account in its design.
Methods and Materials
Geometry and neutronics behavior were modeled using Monte Carlo N-Particle 6 (MCNP6)
Background rates were approximated by the reaction rate of the incident particle in a slab of silicon 15 cm in diameter and 2 mm thick.
Gamma shielding included lead and stainless steel
Neutron shielding included borated polyurethane and Li6