writeup/progress14/Neutrons.tex

\subsubsection{Goals}

	We propose to obtain the neutron emission spectrum due to muon
	capture on Al, Ti, and H$_{2}$O.  The focus will be on
	Al. Ti remains a secondary target and capture on O would
	be interesting as existing neutron data is of
	reasonable quality, and shows a prominent peak near 5 MeV,
	purportedly due to a giant resonance excitation. The unfolded neutron
	energies would lie between 1 to somewhat over 10 MeV.  

\subsubsection{Geometry/Detectors}

	The main emphasis of R2013 was on the detection of charged
	particle emission after muon capture, however, some neutron
	emission data were collected and used to develop analysis
	codes, efficiencies, and rates.  In R2015, the basic
	experimental setup will be
	modified from that of R2013, by removing the vacuum chamber 
        and hanging the stopping target in
	air by thin wires from a large frame far from the
	beam line. Thus while the associated beamline components remain, the
	vacuum chamber, veto scintillators, and their readout electronics are
	removed. The target is rotated approximately $45^\circ$ with
	respect to the beam line to minimise the target material
	through which emitted particles travel to reach the
	detectors. 


        We will borrow two neutron BC501 detectors ($5'' \times
	2''$) from the Triangle Universities Nuclear Laboratory (TUNL)
	for the proposed experiment. They are placed horizontally at
	distances approximately 30 cm from the target.  If the
	LYSO array is used, it can be placed beneath the target and the
	target rotated around the horizontal as well as the vertical
	axis. A beam momentum of approximately \SI{40}{MeV\per\cc} and rate of
	40 kHz is anticipated.  The stopping thickness in an Al
	target is approximately 0.2 cm (2000 $\mu$m), and with a
	target rotation the Al target dimensions would be
	$10\times10\times(0.1\textrm{\,--\,}0.2) \textrm{cm}^3$.  

\subsubsection{Electronics}

Analysis of the R2013 data demonstrated that a waveform digitizer of
at least 250 MHz sampling rate is needed to optimise the pulse shape
discrimination (PSD) allowing separation of neutron from gamma events.
%Figure~\ref{psdplot_2013} shows the pulse shape discrimination
%Figure~\ref{fig:neutron-psd} shows the pulse shape discrimination
%achieved in a R2013 run. 
Data will be acquired using the MIDAS
framework and stored in MIDAS banks for offline analysis. Real time
spectra will be available for online analysis and will be monitored
from the counting house via the software tools developed during 2013
run. 

\subsubsection{Calibration}

The neutron counters will be calibrated periodically using radioactive
sources ($^{22}$Na, $^{137}$Cs, $^{22}$Na, AmBe). Data will be taken
with $^{137}$Cs daily to monitor the gain of detector system. Also,
data will be taken with beam-off to obtain a measure of
backgrounds. The AmBe source is particularly useful to set the gain
for higher energy neutrons as it has a Compton edge at 4.19 MeV, as
well as neutron emission up to 10 MeV. The neutron detectors will be
characterized at TUNL using $^7$Li(p,n)$^7$Be reaction and
time-of-flight~\cite{gonzales2009}.

In 2014 a similar detector was calibrated at TUNL, although the proton
beam energy was restricted keeping neutron energies below 5 MeV.   
The results of this characterization 
are being used to calibrate a MC simulation of the response
function, NRESP7~\cite{dietze1982}, in order to simulate the
detector response function for an arbitrary incident neutron
energy. The MC can then be used to obtain the folding matrix for the
detector for any detected energy. 
 The true neutron energy distribution must be obtained by
spectrum unfolding techniques~\cite{matzke1994}, and this
requires the knowledge of response of the detectors to
neutrons in the relevant energy range of the experiment. Thus the
detectors to be used in R2015 will be calibrated prior to their use at
PSI.  As the neutron spectrum of AmBe is known, the measured spectrum will be unfolded after the unfolding function is determined and will be  compared to the known
AmBe spectrum.

\subsubsection{Rates}
	
%Analysis of error propagation in unfolding neutron spectra
%indicate that a general error of 5\%  in the folded 
%data can be amplified at least an order of magnitude in the
%unfolding process~\cite{suman2014}. Thus in 2015, the intent  
%is to hold statistical
%error to better than 5\% per energy bin.

In order to determine a neutron rate in the
detector, a data run using a 50 \textmu m target was analyzed
using timing cuts.  The beam rate corresponding to the 
collected data was 4.5 kHz and after PSD cuts a neutron detector 
observed 1.1 neutrons/s. If the beam intensity is increased to 40 kHz
using an incident momentum of \SI{40}{MeV\per\cc} and a sufficiently thick target
is used to stop the total beam, the rate in a similar neutron detector
would be expected to increase by a factor of 100 to approximately 100
per second. 
However, the scintillator in the neutron detectors proposed for R2015 
are thinner by approximately a factor of 2. This provides better
resolution but decreases the detection efficiency.  
The folded neutron spectrum in an energy bin between 5.5 to 6.0
MeVee is approximately 0.2\% of the total spectrum. Thus not including the
loss in detection efficiency due to the thinner scintillator, 
approximately 19\,000 neutrons are expected to be obtained in 24 hours
within the energy bin.  
%However, this does not include  inefficiencies in data collection. 

 \subsubsection{Anticipated results}
	A two day run provides a 1\% statistical error in a 0.5 MeV
	energy bin. Obviously there are
	other errors which we  hope to control to a level
	of 5\%. A data run for Al and perhaps a smaller
	statistical run on Ti and H$_{2}$O is foreseen.