# Characterization of ultracold neutron production in thin solid deuterium
films at the PSI UCN source

G. Bison  B. Blau  Paul Scherrer Institut, CH-5232 Villigen-PSI, Switzerland
W. Chen  P.-J. Chiu  Paul Scherrer Institut, CH-5232 Villigen-PSI, Switzerland
ETH Zürich, Zürich, Switzerland  M. Daum  Paul Scherrer Institut, CH-5232
Villigen-PSI, Switzerland  C. Doorenbos  N. Hild  K. Kirch  V. Kletzl  Paul
Scherrer Institut, CH-5232 Villigen-PSI, Switzerland  ETH Zürich, Zürich,
Switzerland  B. Lauss<EMAIL_ADDRESS>Paul Scherrer Institut, CH-5232
Villigen-PSI, Switzerland  D. Pais  I. Rienäcker<EMAIL_ADDRESS>Paul
Scherrer Institut, CH-5232 Villigen-PSI, Switzerland  ETH Zürich, Zürich,
Switzerland  D. Ries  Department of Chemistry - TRIGA site, Johannes Gutenberg
University, 55128, Mainz, Germany  P. Schmidt-Wellenburg  Paul Scherrer
Institut, CH-5232 Villigen-PSI, Switzerland  V. Talanov  Paul Scherrer
Institut, CH-5232 Villigen-PSI, Switzerland  G. Zsigmond  Paul Scherrer
Institut, CH-5232 Villigen-PSI, Switzerland

###### Abstract

We determined the ultracold neutron (UCN) production rate by superthermal
conversion in the solid deuterium (sD2) moderator of the UCN source at the
Paul Scherrer Institute (PSI). In particular, we considered low amounts of
less than 20 $\mathrm{mol}$ of D2, deposited on the cooled moderator vessel
surfaces in thin films of a few mm thickness. We measured the isotopic
($c\textsubscript{HD}<0.2$ %) and isomeric ($c\textsubscript{para}\leq 2.7$ %)
purity of the deuterium to conclude that absorption and up-scattering at 5
$\mathrm{K}$ have a negligible effect on the UCN yield from the thin films. We
compared the calculated UCN yield based on the previously measured thermal
neutron flux from the heavy water thermal moderator with measurements of the
UCN count rates at the beamports. We confirmed our results and thus
demonstrate an absolute characterization of the UCN production and transport
in the source by simulations.

##  I Introduction

Ultracold neutrons (UCN) are free neutrons with kinetic energies below about
300 neV that experience total reflection under all angles of incidence from
surfaces of suitable materials [1]. Thus, UCN can be contained in storage
bottles for hundreds of seconds by surface reflections, as well as by magnetic
and gravitational confinement [2, 3, 4, 5]. The storage of UCN is a technique
well suited for precision experiments that require long observation times. A
prominent example is the search for a permanent electric dipole moment of the
neutron (nEDM) [6, 7, 8], which tests physics beyond the Standard Model [9]. A
sizeable nEDM would provide a new source of CP violation, one necessary
ingredient of baryogenesis [10], that could help to explain the matter anti-
matter asymmetry in the Universe [11]. The to-date most stringent limit on the
nEDM [12] was obtained at the UCN source at the Paul Scherrer Institute (PSI)
[13], currently hosting the follow-up experiment n2EDM [14] aiming for a
tenfold improvement in sensitivity. Achieving these high sensitivities
requires high UCN statistics. Hence there is an ongoing effort to fully
understand the physics of the source, to characterize all its aspects, and to
identify components for possible improvements.

The PSI UCN source moderates free spallation neutrons from a lead target [15]
produced in up to 8 $\mathrm{s}$ long pulses of the 590 $\mathrm{MeV}$ proton
beam of the High Intensity Proton Accelerator (HIPA) at beam currents of up to
2.4 $\mathrm{mA}$ [16]. The target is surrounded by a heavy water moderator
thermalizing neutrons at room temperature. Thermal neutrons entering the solid
deuterium (sD2) moderator vessel, itself cooled by supercritical helium to 5
$\mathrm{K}$, are further moderated to cold neutrons with energies below 10
$\mathrm{meV}$ which can be converted to UCN by phonon excitations [17]. The
UCN accumulate in the evacuated storage volume above the moderator vessel and
can be guided to the experiments along three beamlines. Figure 1 shows an
illustration of the deuterium moderator vessel (yellow) and the UCN transport
system (green). A full characterization and the simulation model of the
neutron optics of the beamlines and storage volume was published recently [13,
18].

Neutron absorption and scattering [19, 20, 21] limit the extraction
efficiency, i.e. the fraction of UCN that escape from the bulk sD2 into
vacuum. However, UCN losses become negligible in the case of thin films of sD2
with thicknesses much smaller than the mean free path for UCNs in sD2. Indeed,
a thin film source for ultracold neutrons was already conceptualized in [17,
22]. We profit from vanishing UCN losses and vanishing moderation in thin
films of sD2 deposited on the cooled walls of the moderator vessel, to
determine the UCN production rate and test its calculation and our source
model. For this we rely on the previously simulated and measured thermal
neutron flux [23] from the heavy water moderator as input. The benchmarked UCN
transport simulation code MCUCN [24] and model of the source [13, 18] can be
used to relate the computed UCN downscattering rate to detected UCN count
rates at the beamports. A verification of the UCN yield from a thin film by
measurements at the beamports can be considered as a full and absolute
characterization of the neutron production by spallation, thermal moderation,
UCN conversion, storage, and transport in the PSI UCN source. Furthermore,
together with MCNP6 [25] simulations of cold moderation in solid deuterium, it
allows us to study the UCN extraction from standard sD2 filling levels of 13
$\mathrm{c}\mathrm{m}$ [13] in the moderator vessel, i.e. 1100
$\mathrm{m}\mathrm{o}\mathrm{l}$ of deuterium, and thus the quality of the sD2
polycrystal in a next step.

Figure 1: Drawing of the lead spallation target (purple) surrounded by the
heavy water moderator (blue). The sD2 moderator vessel (yellow) is suspended
from above into the vertical UCN guide. The cooled surfaces at the bottom and
side wall of the sD2 moderator vessel are indicated in cyan. Closing of the
valve at the top of the vertical guide confines the UCN in the storage vessel
and beamlines above. The surfaces of the UCN storage and transport system are
indicated in green, including the neutron guide shutters of the beamlines,
visible in the drawing at the opening towards the West-1 beamline.

In section II and III we discuss our simulation and computation models,
including the thermal neutron spectrum, the evaluation of the downscattering
cross section, and the UCN transport. In addition, we present the measured
high isotopic and isomeric purity of the deuterium to demonstrate their
negligible contribution to UCN losses in the thin film source. The procedure
to fill the moderator vessel with small, accurately known amounts of sD2 with
an uncertainty of approximately 0.1 $\mathrm{mol}$, and the measurements of
the corresponding UCN yield is described in section IV and V. We compare these
measurements with the predicted UCN yield by our simulation models in section
VI and find good agreement within model uncertainties.

##  II Thermal neutron flux and UCN downscattering

A detailed geometry model of the source was implemented in MCNP for the
determination of the thermal and epithermal neutron flux from the target and
heavy water moderator. The measured activation of gold foils with and without
cadmium shielding [23] was consistent with MCNP simulations of the
(epi)thermal neutron flux. We employed the identical geometrical model and
performed a MCNP6 [25] simulation to tally the neutron flux in the empty
moderator vessel. We confirmed that in the energy range of interest, between
$10^{-3}\,$\mathrm{eV}$$ and $10^{-1}\,$\mathrm{eV}$$, the flux decreases from
the bottom to the top of the empty moderator vessel by less than 15 %. The
energy dependence of the neutron flux $\frac{d\phi}{dE}|\textsubscript{therm}$
for this energy range is very well approximated by a Maxwell-Boltzman
distribution
$\frac{\Phi_{0}E}{(k\textsubscript{B}T_{n})^{2}}e^{-E/k\textsubscript{B}T_{n}}$
with $T_{n}=293.5$ $\mathrm{K}$, as shown in Fig. 2. As the variation was less
than 15 %, we averaged the neutron flux over the moderator vessel volume to
obtain $\Phi_{0}=\int_{0}^{\infty}\frac{d\phi}{dE}dE=1.6\times
10^{-3}\,${\mathrm{cm}}^{-2}$$ per proton on target.

Figure 2: Simulated energy spectrum of the average neutron flux per primary
proton in the empty moderator vessel (red points). The blue line indicates a
Maxwellian fit to the thermal spectrum with $E_{n}=25.30\,$\mathrm{meV}$$,
corresponding to $T_{n}=293.5$ $\mathrm{K}$, and $\Phi_{0}=1.6\times
10^{-3}\,${\mathrm{cm}}^{-2}$$ per proton on the spallation target.

Based on a simulated neutron flux $\frac{d\phi}{dE}(E)$, we compute the
specific UCN downscattering rate per unit volume and per primary proton

$\frac{dR}{dE}(E)=\int_{0}^{\infty}\frac{d\Sigma\hbox
to0.0pt{\textsuperscript{5\,K}\hss}\textsubscript{down}}{dE}(E_{0},E)\frac{d\phi}{dE_{0}}(E_{0})\
dE_{0}.$ (1)

The macroscopic downscattering cross section $\Sigma\hbox
to0.0pt{\textsuperscript{5\,K}\hss}\textsubscript{down}$ at 5 $\mathrm{K}$
from initial to final energy $E_{0}\rightarrow E$ was evaluated in references
[17, 22, 26] based on the incoherent approximation and the Debye model for the
phonon density of states in sD2, as well as for a more realistic phonon
spectrum with about the same result. We use an effective scattering length per
molecule of
$b\textsubscript{eff}^{2}(Q)=4\left(b\textsubscript{coh}^{2}+\frac{5}{8}b\textsubscript{inc}^{2}\right)j_{0}^{2}(Qa_{s}/2)$
[27], with the spherical Bessel function of order zero $j_{0}$, the momentum
transfer $Q=\sqrt{\frac{2\,mE_{0}}{\hbar^{2}}}$ (for $E\ll E_{0}$), and the
separation between the deuterons $a_{s}=0.742\,$\AA$$ [28] in the molecule.
Evaluation of Eq. (1) with the average thermal neutron flux
$\frac{d\phi}{dE}|\textsubscript{therm}$ per $\mathrm{\SIUnitSymbolMicro C}$
protons on the spallation target yields a downscattering rate of

$\frac{dR}{dE}\Big{|}_{\text{therm}}(E)=4.0\times
10^{-3}\,${\mathrm{cm}}^{-3}\text{\,}{\mathrm{\SIUnitSymbolMicro
C}}^{-1}\text{\,}{\mathrm{neV}}^{-3/2}$\times\sqrt{E}.$ (2)

##  III UCN losses and transport

The deuterium inventory of the PSI UCN source is about 1500 $\mathrm{mol}$
which can be stored in gaseous form at room temperature. For operation, the D2
is first solidified into a condenser vessel, melted, and then transferred as a
liquid to a para-to-ortho converter vessel [29, 30] filled with
OXYSORB${}^{\text{\textregistered}}$ [31]. The paramagnetic centers of the
chromium-oxide-based catalyzer material lead to a fast para-to-ortho
conversion [32] of liquid deuterium, kept at around 21.5 $\mathrm{K}$, to
achieve a high ortho-D2 concentration of 97.3 % [33]. The D2 is then
transferred to the moderator vessel, where it is frozen and cooled down to 5
$\mathrm{K}$. The ortho-D2 concentration was measured by Raman spectroscopy of
gas samples [33] collected from the vapor of liquefied deuterium in the
moderator vessel via a connection to a sample port. Below, we show that the
ortho-D2 concentration of 97.3 % is sufficient for the measurements presented
here. However, within weeks of operation the measured ortho-D2 concentration
increases to well above 99 % by an accelerated conversion process [34, 35, 36,
37, 33] induced by radiation from the spallation target. While the H2 content
is negligible and below the sensitivity of the measurement, the concentration
of HD compounds in the gas sample was measured to be $(0.18\pm 0.03)$ %,
including a correction for a distillation effect due to the different vapor
pressures of D2 and HD [33, 38].

Based on the measured isotopic and isomeric purity, as well as the sD2
temperature, we can determine the UCN lifetime in the sD2 of the PSI source,
similar to the computations in [20]. We consider zero-phonon rotational de-
excitation ($J\\!=\\!1\rightarrow J\\!=\\!0$) upscattering with
$(\Sigma\textsubscript{para}v)^{-1}=2.5$ $\mathrm{ms}$ on a maximum remaining
para-D2 concentration of 2.7 % and thermal one-phonon upscattering at 5
$\mathrm{K}$ of $\sigma\textsubscript{phonon}=0.25$ $\mathrm{b}$ (at
$v=7.92\,$\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$$), both derived in [19].
$\Sigma=\rho\sigma$ denotes the corresponding macroscopic neutron cross
section based on the density $\rho=3.02\times 10^{22}\,${\mathrm{cm}}^{-3}$$
of sD2 at $5\,$$\mathrm{K}$ [38]. Neutron absorption cross sections
$\sigma\textsubscript{abs}$ of deuterium and hydrogen were taken from [39]. We
employed the $1/v$ scaling of the UCN loss cross sections to obtain a velocity
independent total lifetime of

$\displaystyle\tau$ $\displaystyle=\frac{1}{v}\big{[}c_{\text{para}}\
\Sigma_{\text{para}}+\Sigma_{\text{phonon}}+\Sigma_{\text{abs,D${}_{2}$}}+c_{\text{HD}}\
\Sigma_{\text{abs,HD}}\big{]}^{-1}$ (3)
$\displaystyle=\Big{[}\frac{1}{56\,$\mathrm{ms}$}+\frac{1}{168\,$\mathrm{ms}$}+\frac{1}{146\,$\mathrm{ms}$}+\frac{1}{269\,$\mathrm{ms}$}\Big{]}^{-1}$
$\displaystyle=29\,$\mathrm{ms}$,$

corresponding to a mean free path of $\lambda=9\,$\mathrm{cm}$$ at
$v=3.2\,$\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$$, the minimum transmitted
neutron velocity111Taking into account that the energy boost when exiting the
sD2 is compensated by the gravitational deceleration in the vertical guide
above the moderator vessel. to the UCN source beamports due to the AlMg3
vacuum separation windows in the beamlines [13].

From the calculated mean free path and earlier measurements of the total UCN
scattering cross section [21] in sD2, we conclude that UCN losses are
negligible for a total path length of a few mm in sD2 thin films. Thus we can
directly multiply the downscattering spectrum $\frac{dR}{dE}(E)$, Eq. (1),
with the energy-dependent transmission probability $t(E)$ for a UCN starting
in the empty moderator vessel to reach the detector at beamport West-1 to
obtain the number of detectable UCN,

$N=\int_{0}^{\infty}\frac{dR}{dE}\ t(E)\ dE.$ (4)

The transmission probabilities shown in Fig. 3 as a function of the UCN
kinetic energy in the moderator vessel before the sD2 boost were obtained from
a simulation model of the source [13] with UCN optics parameters from
calibration measurements [18]. The distribution of starting positions and
initial velocity vectors of the UCN was adjusted to reflect a production of
UCN in a thin film of sD2 on the moderator vessel surfaces. For configurations
A, B and C shown in Fig. 3, the UCNs were generated with isotropic velocities
at a random position at a distance of 1 $\mathrm{mm}$ from the base and side
wall222The surface areas are 1665 ${\mathrm{cm}}^{2}$ for the base and 2405
${\mathrm{cm}}^{2}$ of the cooled part of the side wall of the moderator
vessel. up to a height of 16 $\mathrm{cm}$ inside the moderator vessel. This
distribution of UCN starting positions corresponds to a uniform D2 deposition
from the gas phase on all surfaces in direct contact with the helium cooling
channels in the wall and base of the moderator vessel [13], as discussed in
more detail in section IV. Upon leaving sD2, UCN experience a velocity boost
due to the Fermi potential of sD2 of 105 $\mathrm{neV}$, computed based on its
density at 5 $\mathrm{K}$ [38] and coherent scattering length [39], confirmed
within experimental uncertainty by measurements in [40, 41]. To model a high
surface roughness and a potentially uneven distribution of deuterium frozen on
cold surfaces in the moderator vessel [42], we consider a diffuse boost by
adding a corresponding isotropically distributed velocity component from the
sD2 into vacuum to the UCN starting velocity. Since the calibration
measurements [18] for the UCN source simulation model were not sensitive to
the probability of diffuse reflection in the vertical guide below the storage
vessel (see Fig. 1), we scanned this parameter in a large range from
$p\textsubscript{vert.guide,diff}=4\,$% (configuration A) to $50\,$%
(configuration C). We also scanned other UCN optics parameters obtained from
the calibration measurements within their uncertainties [18] and found no
significant variations of the corresponding UCN yield.

Figure 3: Simulated transmission probability $t(E)$ of UCN to be counted at
the detector on beamport West-1 integrated over 280 $\mathrm{s}$ after
generation in the moderator vessel. The red, black and blue markers show the
transmission of configurations A, B and C of UCN starting with a diffuse boost
from all cooled surfaces in the moderator vessel and different probabilities
of diffuse reflection $p\textsubscript{vert.guide,diff}$ in the vertical guide
below the storage volume (see Fig.1). The green and orange open markers,
configuration D and E, show the transmission when the UCN start exclusively
from the base of the moderator with a vertical boost or from the side wall
with a horizontal boost, respectively. Further simulation parameters are
described in the text.

During the measurements and in our simulations, the UCN valve at the bottom of
the storage volume stayed permanently open. The neutron guide shutters (see
Fig. 1) to the West-1 and West-2 beamlines were fully open, while the shutter
to the South beamline was closed. The simulated UCNs were counted behind a 100
$\mathrm{\SIUnitSymbolMicro m}$ AlMg3 surface, placed at the end of a 1
$\mathrm{m}$ neutron guide mounted at beamport West-1 and an additional
shutter, corresponding to the detection setup described in section V. The
number of UCNs arriving at the virtual detector were integrated during 280
$\mathrm{s}$ after generation and divided by the number of started UCNs to
obtain the transmission probability.

We found that for a diffuse boost, the transmission of UCN starting
exclusively from the base of the moderator vessel differs only by a small
amount from the transmission of UCN starting from the side walls. In contrast
to that, a strictly vertical boost of UCN starting from the base of the
moderator vessel (configuration D, Fig. 3) leads to a significantly higher
transmission and increases the UCN yield by $40\,$% (Tab. 2), while a
horizontal boost of UCN starting from the side walls of the moderator vessel
(configuration E) reduces the transmission slightly. A similar increase of
approximately $40\,$% of the measured UCN yield was observed in [43] after
melting small amounts of deposited sD2 and re-solidifying it from the melt at
the bottom of the moderator vessel. The sD2 was previously deposited by a
procedure identical to the one presented in section IV in the cold moderator
vessel from the gas phase, presumably as a thin film with very high surface
roughness, while it was subsequently frozen from the liquid phase with a
smoother surface. This observation is consistent with the hypothesis that a
diffuse boost describes more accurately the velocity distribution of UCN from
the deuterium deposited from the gas phase on the cold moderator vessel
surfaces, i.e. the condition during the measurements reported here.

In our simulations, we also tallied the number of wall reflections on the
cooled surfaces in the moderator vessel to estimate the total path length
$\mathit{l}$ from multiple passages of the UCN through sD2 with a maximum film
thickness of 0.9 $\mathrm{mm}$ (see section IV). Based on this, we confirm
that the expected average attenuation $e^{-l/\lambda}$ due to neutron losses
(with mean free path $\lambda=9\,$\mathrm{cm}$$) is below $2\,$%.

##  IV Preparation of solid deuterium

At the end of an annual operation cycle of the UCN source, the deuterium
content of the moderator vessel was evaporated into the storage tanks [30].
During this process, some of the high-ortho-D2 was collected in the condenser
vessel, which was cooled below the triple point of deuterium of 18.7
$\mathrm{K}$ [38]. After evaporation, the residual pressure in the 51.66
liters333The volumes were taken from a fully detailed CAD model of the source
and include small volumes of all transfer lines up to corresponding valves.
moderator vessel and auxiliary piping was 0.3 $\mathrm{mbar}$ at 24.5
$\mathrm{K}$, i.e. less than 0.01 $\mathrm{mol}$ of D2 gas. We proceeded by
heating the 44.87 liters33footnotemark: 3 condenser vessel to 24.9
$\mathrm{K}$. The quoted temperature is the average reading of two temperature
sensors at the top and bottom of the vessel, which were consistent within 0.2
$\mathrm{K}$. We obtained a stable pressure of $(858\pm 2)\,$\mathrm{mbar}$$,
corresponding to $(18.5\pm 0.1)\,$\mathrm{mol}$$ of deuterium gas.

sD2 amounts |  uncertainty | UCN
---|---|---
($\mathrm{mol}$) |  ($\mathrm{mol}$) | ($10^{3}\,$/ 280 $\mathrm{s}$)
0.0 |  0.0 |  3.05(6) |  2.93(5) |  2.91(5)
0.6 |  0.1 |  4.70(7) |  4.77(7) |  4.89(7)
1.4 |  0.1 |  7.15(9) |  7.29(9) |  7.33(9)
2.4 |  0.1 |  10.0(1) |  10.1(1) |  10.1(1)
4.9 |  0.1 |  17.4(1) |  17.7(1) |  17.6(1)
9.9 |  0.1 |  30.7(2) |  30.8(2) |  30.6(2)
14.8 |  0.1 |  46.3(2) |  45.6(2) |  45.5(2)
18.5 |  0.1 |  58.9(2) |  58.9(2) |  58.5(2)
Table 1: Measured UCN count rates during 280 $\mathrm{s}$ after 2 $\mathrm{s}$
norm pulses at beamport West-1 for different amounts of sD2. For each sD2
amount three proton beam pulses were performed. The beam current was monitored
during each pulse and the count rates normalized to a current of 2.2
$\mathrm{mA}$. The quoted uncertainties on the count rates are the Poisson
error.

To fill the moderator vessel with accurate amounts of deuterium, a valve
between condenser and moderator vessel was opened, while monitoring the
decrease of pressure in the condenser. The AlMg3 top lid of the moderator
vessel was heated to 24 $\mathrm{K}$ (measured with a thermocouple) by
thermoelectric heaters [42], while the side wall and base of the vessel were
cooled to approximately 5 $\mathrm{K}$, indicated by the measured helium in-
and outflow temperatures. We assume a deposition of deuterium on all surfaces
in direct contact with the helium cooling channels on the bottom and side wall
of the moderator vessel, while a deposition on the upper lid of the vessel is
excluded by its temperature. After reaching a certain pressure reduction in
the condenser, the valve was closed and the UCN count rate at the beamport was
measured with the known amount of sD2 (see Tab. 1). During the UCN
measurements the heating of the lid was turned off.

For subsequent measurements with larger amounts of sD2, the above described
sequence was repeated and deuterium gas added to the cold moderator vessel.
This way, the moderator vessel was filled with small amounts of sD2, ranging
from 0.6 to 18.5 $\mathrm{mol}$ with an uncertainty of 0.1 $\mathrm{mol}$. The
maximum amount corresponds to a solid thin film thickness of less than 0.9
$\mathrm{mm}$ if the sD2 is deposited uniformly on all helium-cooled surfaces,
or 2.2 $\mathrm{mm}$ if the sD2 would be distributed uniformly only on the
bottom.

##  V UCN detection setup and measurements

Figure 4: Measured UCN counts (red squares) at beamport West-1 during 280
$\mathrm{s}$ after a 2 $\mathrm{s}$ proton pulse of 4400
$\mathrm{\SIUnitSymbolMicro C}$. The Poisson error of the individual
measurements and the uncertainty of the amount of sD2 is smaller than the
marker size. The slope (dashed line) and intercept (dotted line) from a linear
fit are indicated in the plot. The intercept is consistent with the detected
background rate listed in Tab. 1.

A CASCADE 2D U-200 detector444www.n-cdt.com/cascade-2d-200 counted UCNs for
$280\,$s after receiving a trigger indicating the imminent proton beam pulse.
The CASCADE detection efficiency is determined mostly by UCN losses in the 100
$\mathrm{\SIUnitSymbolMicro m}$ AlMg3 entrance window. The entrance window is
made from the exact same raw material as the AlMg3 vacuum separation windows
in the beamlines and was included in our MCUCN simulation with parameters
consistent with calibration measurements (see Fig. 28 in Ref. [18]) and
measured transmission through material foils [44]. The detector was mounted on
a vacuum shutter at the end of a 1 $\mathrm{m}$ long Ni/Mo 85/15 [18] coated
glass guide, which in turn was connected to the West-1 beamport. The setup was
identical to the one presented in [18] used for the calibration measurements
of the MCUCN simulation model of the source. The HIPA beam current during the
measurements was 2.2 $\mathrm{mA}$ and the duration of the proton beam pulses
was set to $2$ $\mathrm{s}$. Thus, 4400 $\mathrm{\SIUnitSymbolMicro C}$
protons per beam pulse were deposited on average on the spallation target, the
individual values were monitored for each pulse. The UCN valve on the bottom
of the storage vessel of the UCN source was permanently open. This
configuration, called ‘norm pulse’, has been used many years as a standard
setting for comparison of UCN yield measurements.

Simulated UCN yield | diffuse boost | perpendicular
---|---|---
($10^{-3}\,${\mathrm{cm}}^{-3}$\,${\mathrm{\SIUnitSymbolMicro C}}^{-1}$$) |  A |  B |  C |  D |  E
|  |  |  |  |
from base |  36.3 |  34.6 |  29.8 |  48.3 |  -
from side walls |  32.5 |  32.4 |  33.3 |  - |  30.3
|  |  |  |  |
combined |  34.1 |  33.3 |  31.9 | 37.7
Table 2: Simulated UCN yield based on the thermal neutron flux and on
different UCN transmission spectra (A - E) from the configurations with
diffuse boost and boost perpendicular to the surface, as defined in section
III, Fig. 3. The combined yield from the moderator vessel base and side wall
is the sum weighted by the corresponding surface areas.

##  VI Analysis and discussion

The measured UCN rates at the beamport West-1 with different amounts of sD2
are listed in Tab. 1. For each pulse the proton beam current was monitored and
the corresponding UCN count rate normalized to a beam current of 2.2 mA. The
spread of the count rates per amount of sD2 exceeds the Poisson errors in a
few cases due to the influence of small fluctuations of proton beam alignment
[43] and other beam parameters on the UCN yield that have not been corrected
for in this analysis. To estimate the count rate per mol of sD2 and its
uncertainty, we performed a least square fit of the individual measurements
(see Fig. 4) and obtain an intercept of
$(2976\,\pm\,83)\,/\,280\,$\mathrm{s}$$, consistent with the average of the
measured count rates from the empty moderator vessel. We attribute this rate
to UCN and VCN (very cold neutron) production in the moderator vessel material
or surrounding structure, as well as to fast neutron radiation from the
spallation target during the proton beam pulse. The fitted slope of
$(2923\,\pm\,20)\,/\,280\,$\mathrm{s}\text{\,}{\mathrm{mol}}^{-1}$$
corresponds to a UCN yield per sD2 volume and proton charge on the spallation
target of

$(33.3\pm 0.2)\times
10^{-3}\,${\mathrm{cm}}^{-3}$\,${\mathrm{\SIUnitSymbolMicro
C}}^{-1}$\quad\text{(measured)},$

where we used the molar volume
$V_{\textsubscript{m}}=19.93\,${\mathrm{cm}}^{3}\text{\,}{\mathrm{mol}}^{-1}$$
of sD2 at approximately 5 $\mathrm{K}$ from Ref. [38].

The simulated UCN yield per sD2 volume and protons on the spallation target,
based on the evaluation of Eq. (4) with the downscattering rate, Eq. (2) and
the transmission probabilities shown in Fig. 3, are listed in Table 2. We used
the volume average of the thermal neutron flux (see Fig. 2) from the bottom to
the top of the moderator vessel, which is a valid approximation with a less
than 5 % effect on the total UCN yield when assuming a uniform deposition of
the sD2 on all cold moderator vessel surfaces (base and side walls). The
measured UCN yield is consistent with the simulated yield within model
uncertainties of approximately 10 % for configurations with diffuse boost and
within 15 % for the configuration with perpendicular boost from the moderator
vessel base and side wall.

##  VII Conclusion

The linearity of the measured UCN count rates at beamport West-1 as a function
of the amount of sD2 in the moderator vessel validates our model, Eq. (4). In
particular, it is consistent with the assumption that the D2 vapor was
deposited sufficiently uniform, such that the thin film thickness is well
below the mean free path of neutron losses computed from the lifetime Eq. (3)
in sD2. Otherwise, one would expect deviations from a linear behavior towards
lower measured UCN count rates for increasing sD2 filling levels.

We conclude that the process of spallation, thermal moderation, as well as the
UCN transport to the beamports has been modelled accurately within
approximately 10 % by our simulations (with the more likely scenario of a
diffuse boost from the sD2 surfaces) and previous calibration measurements
[23, 18]. The measured UCN yield (Fig. 4) obtained from thin films of sD2 of
less than 20 $\mathrm{mol}$ corroborates the calculated downscattering rate
Eq. (2) based on the thermal neutron flux (Fig. 2). It also provides an
absolute calibration of the UCN transport from the moderator vessel to UCN
detector in the experimental area. This result serves as a benchmark for
future characterizations of the UCN production and extraction from sD2 with
filling levels in the moderator vessel of around 13 $\mathrm{cm}$ [13] during
standard operation, corresponding to approximately 1100 $\mathrm{mol}$
deuterium.

## Acknowledgements

We thank Michael Wohlmuther for programming the first version of the UCN
source MCNP model. We acknowledge the PSI proton accelerator operations
section, all colleagues who have been contributing to the UCN source operation
at PSI, and especially the BSQ group which has been operating the PSI UCN
source during the measurements, namely P. Erismann and also A. Anghel.
Excellent technical support by F. Burri and M. Meier is acknowledged. This
work was supported by the Swiss National Science Foundation Projects 117696,
137664, 163413, 169596, 172626, 178951, 188700 and 200441.

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