Measurement of the neutron lifetime by counting trapped protons in a cold neutron beam

A measurement of the neutron lifetime ${\tau }_n$ performed by the absolute counting of in-beam neutrons and their decay protons has been completed. Protons confined in a quasi-Penning trap were accelerated onto a silicon detector held at a high potential and counted with nearly unit efficiency. The neutrons were counted by a device with an efficiency inversely proportional to neutron velocity, which cancels the dwell time of the neutron beam in the trap. The result is ${\tau }_n=(886.3\pm 1.2[\mathrm{stat}]\pm 3.2[\mathrm{sys}])s$, which is the most precise measurement of the lifetime using an in-beam method. The systematic uncertainty is dominated by neutron counting, in particular, the mass of the deposit and the ${}^6\mathrm{Li}$$(n,t)$ cross section. The measurement technique and apparatus, data analysis, and investigation of systematic uncertainties are discussed in detail.

Figure 1

A comparison of recent neutron lifetime measurements. Shaded band is $\pm 1$ standard deviation of the weighted average including this result.

Figure 2

Experimental method for measuring lifetime by counting neutrons and trapped protons.

Figure 3

(Color online) Proton trap.

Figure 4

(Color online) Proton rate normalized to the neutron detector counting rate as a function of the horizontal position of the detector. The solid line is a fit to the data points.

Figure 5

Typical pulse-height spectrum from ${}^6\mathrm{Li}$ reaction products incident on a silicon detector in the neutron monitor.

Figure 6

Measured timing spectrum showing trap changes of state (arrows), and three regions of interest (dashed vertical lines) used to extract proton and background rates. As a first step in the analysis, this spectrum must be corrected for intrinsic dead time of the TDC.

Figure 7

(Color online) Linear fit of typical raw proton count rate ${\stackrel{·}{N}}_p$ versus trap length data. These data have not yet been corrected for nonlinearities discussed in Sec. 4c.

Figure 8

Measured neutron beam intensity as a function of radius on the deposit (dashed line) as well as data and fit for the Li deposit areal density versus radius (solid circles and line).

Figure 9

Relative solid angle efficiency of the neutron detector as a function of position on the Li deposit. The value is normalized to unity at the center of the deposit. The deviation from circular contour lines reflects the existence of the four symmetrically placed detectors.

Figure 10

(Color online) Measured count rate and scattering-induced enhancement factor f versus the number of Si blanks placed behind the detection deposit.

Figure 11

Measured fraction of neutrons outside a given radius from the centroid of the beam. The image was taken at the downstream end of the trap.

Figure 12

Calculated electrostatic potential of the trap corresponding to 10 grounded electrodes in the center region in (a) and (b), and 3 grounded electrodes in the center region in (c) and (d).

Figure 13

Axial magnetic field inside the trap, measured along the axis using an axial Hall probe. Also shown are the positions of the 16 trap electrodes.

Figure 14

Data from Monte Carlo case E. (a) Proton/neutron ratio ${\stackrel{·}{N}}_p/{\stackrel{·}{N}}_0$ versus trap length; (b) data/fit residuals.

Figure 15

Difference in ${\stackrel{·}{N}}_p/{\stackrel{·}{N}}_0$ between Monte Carlo cases A and E (solid circles), B and E (squares), C and E (triangles), and D and E (open circles). The statistical uncertainties are smaller than the plot symbols.

Figure 16

The fractional standard deviation ${\sigma }_B/B$ of the axial magnetic field $B_z$ versus axial position $z$. The open circles used only three measurements of $B_z$ to find ${\sigma }_B/B$ and the solid line includes the measurements from adjacent points for a total of nine.

Figure 17

Backscattering probability versus dead layer thickness and proton energy [Eq. (34)]. Each contour represents a line of constant Rutherford backscattering probability. The contour labels give the Rutherford backscattering probability for protons impinging on a layer of gold. The black circles indicate where lifetime measurements have been carried out. Those entries with zero thickness correspond to the runs where so-called windowless detectors were employed. In fact, these detectors have a nonnegligible dead layer consisting of silicon and silicon dioxide.

Figure 18

(Color online) A proton pulse-height spectrum for a typical run. The acceleration energy of the protons was 32.5 keV, and the detector was a surface barrier detector with $40\mathrm{\hspace{1em}\hspace{1em}}\mu$g/cm${}^2$ of gold. The energy loss $E_{\mathrm{loss}}$ is the difference between the acceleration energy and the energy of the peak, or 1.64 keV.

Figure 19

(Color online) srim calculation of the energy spectrum of protons with incident energy of 27.5 keV transmitted through a $20\mathrm{\hspace{1em}\hspace{1em}}\mu$g/cm${}^2$ gold dead layer. Of the initial $3\times {10}^5$ events for this example, 298 019 were transmitted with an average energy of 26.0 keV, 1980 backscattered and exited the detector, 18 entered the active silicon with an energy below the registration threshold, and 1 stopped in the dead layer.

Figure 20

(Color online) A linear fit of the measured neutron lifetime versus the detector backscattering fraction $f_{\mathrm{Bsc}}$. The extrapolation to zero backscattering gives the free neutron lifetime. The measured lifetime values plotted here have already been adjusted for the known neutron and proton counting loss mechanisms.