# A modular apparatus for use in high-precision measurements of parity
violation in polarized eV neutron transmission

D. C. Schaper1,2, C. Auton3, L. Barrón-Palos4, M. Borrego2, A. Chavez2, L.
Cole1, C. B. Crawford1, J. Curole3, H. Dhahri1, K. A. Dickerson3, J. Doskow3,
W. Fox3, M.H. Gervais1, B. M. Goodson5, K. Knickerbocker2, C. Jiang6, P. M.
King7, H. Lu3, M. Mocko2, D. Olivera-Velarde8, J. G. Otero Munoz3, S.I.
Penttilä6, A. Pérez-Martín4, B. Short9, W. M. Snow3, K. Steffen3, J.
Vanderwerp3, G. Visser3 1University of Kentucky, Lexington, KY, 40506, USA
2Los Alamos National Laboratory, Los Alamos, NM, 87545, USA  3Indiana
University, Bloomington, IN, 47405, USA  4Instituto de Física, Universidad
Nacional Autónoma de México, Apartado Postal 20-364, 01000, México  5Southern
Illinois University, Carbondale, IL 62901, USA  6Oak Ridge National
Laboratory, Oak Ridge, TN, 37830, USA  7Ohio University, Athens, OH, 45701,
USA  8Berea College, Berea, KY, 40404, USA  9University of Minnesota Twin
Cities, Minneapolis, MN, 55455

###### Abstract

We describe a modular apparatus for use in parity-violation measurements in
epithermal neutron-nucleus resonances with high instantaneous neutron fluxes
at the Manuel Lujan Jr. Neutron Scattering Center at Los Alamos National
Laboratory. This apparatus is designed to conduct high-precision measurements
of the parity-odd transmission asymmetry of longitudinally polarized neutrons
through targets containing nuclei with p-wave neutron-nucleus resonances in
the 0.1-10 eV energy regime and to accommodate a future search for time
reversal violation in polarized neutron transmission through polarized nuclear
targets. The apparatus consists of an adjustable neutron and gamma collimation
system, a 3He-4He ion chamber neutron flux monitor, two identical cryostats
for target cooling, an adiabatic eV-neutron spin flipper, a near-unit
efficiency 6Li-7Li scintillation detector operated in current mode, a flexible
CAEN data acquisition system, and a neutron spin filter based on spin-exchange
optical pumping of 3He gas. We describe the features of the apparatus design
devoted to the suppression of systematic errors in parity-odd asymmetry
measurements. We describe the configuration of the apparatus used to conduct a
precision measurement of parity violation at the 0.7 eV p-wave resonance in
139La which employs two identical 139La targets, one to polarize the beam on
the p-wave resonance using the weak interaction and one to analyze the
polarization.

###### keywords:

Parity violation , Scintillator detector , Neutron resonance , Fundamental
symmetry , Time reversal violation

††journal: arXiv

##  1 Introduction

Compound neutron-nucleus resonance reactions have proven to be an excellent
laboratory in which to study parity violation [2, 3]. The complex, many-body
nature of this nuclear system with its very high level density was predicted
theoretically [4, 5] and confirmed by experiment [6, 7] to provide a natural
amplification mechanism for Parity Violating (PV) neutron-nucleus
interactions. Statistical spectroscopy has been used to successfully analyze
the widths of the distributions of observed parity-odd asymmetries in several
heavy nuclei in the isolated resonance regime corresponding to eV-keV neutron
energies [9]. The present theory involving the mixing of nearby s-wave and
p-wave resonances that accounts for this amplification of parity-odd
amplitudes also predicts a similar amplification of Time Reversal Invariance
Violating (TRIV) amplitudes [10]. Parity- (P) and Time- (T) odd effects in
forward transmission provide null tests for time reversal invariance [11].
Compound nuclear systems are therefore attractive candidates for T-violation
searches. With the advent of high-flux MW-class short-pulsed spallation
neutron sources, sensitive tests of TRIV in neutron-nucleon interactions can
be realized.

Due to the proportionality between potential TRIV amplitudes and PV
amplitudes, these future TRIV tests will need more complete and precise
information on the properties of the resonances which exhibit large parity
violation effects. In addition to new measurements of (n, $\gamma$) angular
distributions [12] which can be used to determine the details of the quantum
numbers of these $\ell=1$ (p-wave) resonances, it is also important to repeat
previous measurements of P-odd neutron transmission asymmetries [6, 13, 14,
15, 16] with higher precision. By measuring the transmission asymmetry of
longitudinally polarized neutrons through an unpolarized target, one can
determine the parity-odd helicity dependence of the total cross section. The
transmission asymmetry is defined as

$A=\frac{Y^{+}-Y^{-}}{Y^{+}+Y^{-}}=\tanh(f_{n}nt\sigma_{p}P)$ (1)

where $Y^{\pm}$ is the neutron transmission yield for the two neutron
helicities, $f_{n}$ is the polarization of the neutron beam, $\sigma_{p}$ is
the p-wave cross section for unpolarized neutrons, $n$ is the number density
of the target nuclei, $t$ is the target thickness, and $P$ is the parity-odd
longitudinal analyzing power, defined by its relationship to the helicity-
dependent cross section, $\sigma^{\pm}$:

$\sigma^{\pm}=\sigma_{p}(1\pm f_{n}P)$ (2)

The two most effective and well-known methods to polarize neutron beams [19]
in the eV energy range are spin-dependent scattering from a polarized proton
target [20] and spin-dependent absorption in a polarized 3He target [21].
There also exists a third, lesser-known polarization method which is at
present practical only for the 139La nucleus. The 139La nucleus possesses a
p-wave resonance near 0.7 eV, whose interference with nearby s-wave resonances
results in a 10% parity-odd asymmetry. This is larger than expected on
dimensional grounds alone by about a factor of $10^{6}$. As demonstrated by
C.D. Bowman et al. [22] and later Yuan et al. [23] this parity violating
asymmetry is large enough that one can use it to polarize the beam using the
(intrinsically parity-odd) weak interaction. By transmitting such a weakly-
polarized beam through a second 139La target, one can realize a measurement of
the P-odd asymmetry in which the 139La targets act as both a polarizer and as
a polarization analyzer, resulting in the aptly-named ‘Double Lanthanum’
measurement method. Although the beam polarization produced on the parity-odd
0.7 eV resonance in 139La is small [22][23], its use in this configuration
eliminates certain systematic errors associated with measuring $P$, especially
the absolute knowledge of the neutron beam polarization $f_{n}$. In this paper
we describe how our apparatus may be modified to accommodate setups for both
the ‘Double Lanthanum’ $P$ measurement method as well as a traditional $P$
measurement using a 3He neutron spin filter.

In addition to its relevance for future time reversal violation experiments, a
precise determination of $P$ for 139La is of potential use as a standard
analyzer in eV neutron scattering and transmission experiments by allowing one
to measure the absolute polarization of epithermal neutron beams containing
$\ell=1$, 0.7 eV neutrons. 139La was already used for this purpose in the
measurements of P-odd asymmetries in heavy nuclei conducted by the TRIPLE
collaboration [3]. It was also used in some pioneering measurements of the
depolarization of polarized eV neutrons in transmission through magnetic
fields in polarized and aligned nuclear targets to extract information on the
internal magnetic domain structure [24][25][26]. The large P-odd asymmetry on
the $0.88$ eV $\ell=1$ resonance in 81Br could also be used for this purpose.
The possibility of constructing a compact eV neutron polarization analyzer at
these two energies based on neutron absorption in LaBr3 scintillating crystals
is under analysis.

In this paper we describe the apparatus and experimental setup we have
realized to perform precision measurements of the parity violation, $P$,
present in the eV neutron energy range as configured for the Double Lanthanum
experiment. The Los Alamos Neutron Science Center (LANSCE) beam facility is
described in Section 2. The mechanical apparatus used for the parity violation
measurement, including the collimation, cryostats, mechanical rotation stage,
and detector shieldhouse, are all described in Section 3. The custom spin
flipper constructed for this experiment and optimized for 0.7 eV neutrons is
described in Section 4. Details of the electronics design for the spin flipper
are described in Section 5. The fast-response current mode 6Li-7Li glass
scintillator detector designed for this experiment is discussed in Section 6.
Section 7 describes the data acquisition system, including all measured
parameters and their experimental relevance. Section 8 describes the design of
the polarized 3He neutron spin filter for eV neutrons to be installed for
future parity violation measurements. A brief summary and description of
possible future measurements which can be conducted with this instrument is
given in Section 9.

##  2 The FP12 neutron beam facility at LANSCE

The apparatus described in this paper was located in an experimental hutch on
Flight Path 12 (FP12) at LANSCE. Neutrons which are delivered to FP12 are
produced by the 1L Lujan Target-Moderator-Reflector-Shield (TMRS) Mark-III
assembly and are moderated by a partially-coupled cold hydrogen moderator. The
flight path is equipped with an $m=3$, 10 cm$\times$10 cm supermirror neutron
guide designed to transport a large fraction of cold neutrons to the
experimental hutch [27]. The neutron flux and spectrum in the slow neutron
regime between 1-80 meV was already measured in the past and described in the
literature [29]. MCNPX simulations of FP12 were performed to extract the
energy spectrum and emission time distributions of 0.7 eV neutrons. The
detailed 3D geometry as implemented in the MCNPX model is shown in Figure 1.
The model included a detailed implementation of the TMRS Mark-III surrounded
by the Bulk Shielding. The neutron guide is surrounded with
concrete/steel/polyethylene shielding and the experimental hutch is shielded
with borated polyethylene clad in 3/8” thick steel. The neutron beam
terminates in a beam stop made of steel and borated polyethylene.

The calculations of the time-emission spectra followed the methodology
outlined in [30]. The TMRS model used in these simulations was based on the
as-built engineering design. The thermal neutron scattering kernels that were
used are for hydrogen and deuterium in water, ortho- and para-hydrogen in
liquid hydrogen, aluminum in alloys, and iron in steel. All calculations
utilized the next-event-estimator (point detector) variance reduction
technique [33] to ensure efficient convergence of all extracted observables.
The relatively sharp proton pulse (270 ns pulse width) incident on the
spallation target at a short-pulsed spallation neutron source like LANSCE is a
very valuable feature for precision measurements of parity violation and time
reversal violation on neutron-nucleus resonances as it greatly improves the
time resolution of the neutron time-of-flight measurements necessary to
accurately determine the neutron energy.

Figure 1: Elevation view of the FP12 geometry as implemented in the MCNPX
model. Figure 2: An MCNPX calculation of the neutron energy spectrum for FP12,
normalized to the peak flux intensity. This was generated using MCNPX
simulations with the most recent FP12 geometry. Figure 3: A calculation of the
time emission spectra for neutrons of energy 0.7 eV, normalized to the peak
intensity.

The FP12 hutch is a steel enclosure shaped like a trapezoid, as seen in Figure
4. It is approximately 4.73 m long in the beam direction, 2.74 m tall, and
4.61 to 6.22 meters in the transverse direction. The beam pipe is centered
1.37 meters above the floor. The most upstream components are collimators that
scrape the neutron beam to a 10 cm diameter and a 3He-4He ion chamber to
measure the neutron flux. Next downstream is the first cryogenically cooled
139La target, an adiabatic spin flipper, and a second 139La target. The
furthest downstream component is a shielded 6Li-rich scintillator neutron
detector buried in shielding designed to attenuate both neutrons and gamma
rays to reduce background noise. Figure 5 shows a detailed view of these
components and their placement.

Figure 4: Top-down view of the FP12 hutch at LANSCE showing the hutch
dimensions and general position of the experimental setup. Figure 5:  A cross-
section view of the experimental setup in FP12 at LANSCE as viewed from the
side. The three components are the collimator stand, the main apparatus
containing the cryostats and the spin flipper coil assembly, and the
detector/shieldhouse assembly.

##  3 Mechanical Apparatus Components

Previous experiments have measured $P$ on the 0.7 eV resonance in 139La to
$\sim 4\%$ accuracy [23]. In order to achieve a measurement with 1% accuracy
as needed for the future time reversal and neutron polarimetry physics, we
decided to use cryogenic targets to minimize the Doppler broadening of the
transmitted resonance profile. To prepare for the future NOPTREX time reversal
search experiment described in [11], we mounted these cryostats on a rotating
turntable and chose a 3He neutron spin filter polarized by spin-exchange
optical pumping (SEOP) methods which can later be placed in the position of
the upstream cryostat. These decisions strongly influenced the apparatus
design, which otherwise possesses several components very similar to an
earlier instrument built by the TRIPLE Collaboration [17]. The apparatus also
possesses some common features with the POLYANA instrument at the IBR-30
pulsed reactor neutron source at Dubna [18].

The apparatus can be divided into three major beamline components; the
collimator stand; the main apparatus stand (mounted on the rotation stage);
and the detector stand/shieldhouse. One key feature of almost all components
is the use of non-magnetic materials. Due to the oscillating magnetic fields
produced by the neutron spin-flip coils, any magnetic material could be
magnetized, leading to stray fields that could affect the neutron spin-flip
efficiency as well as cause magnetic-field dependent gain shifts in our
detector electronics. Therefore much of the apparatus is constructed from
aluminum, brass, and plastic.

###  3.1 Collimators and Stand

The collimator stand, located furthest upstream at the exit of the beam pipe,
supports interchangeable collimators and the 3He-4He beam monitor. The stand
is made from aluminum held together with brass screws and bolts. A 96 cm long
rectangular aluminum channel provides a reliable way to interchange up to 16
collimators and ensures that all collimators are coaxial with the beam.
Adjustable feet allow for precision alignment of the collimators to the beam
axis using a theodolite. The beam monitor rests at the downstream end of the
stand and is electrically isolated from the rest of the stand via a
polycarbonate plastic base. The collimators define the neutron beam and
minimize the contribution of fast neutrons and gamma rays to the radiation
backgrounds in the hutch. 5.01 cm thick borated polyethylene collimators
attenuate fast neutrons outside of the desired beam profile. The borated
polyethylene collimator located the furthest upstream has an additional 1 mm
layer of 6Li-loaded fluorinated plastic which collimates slow neutrons and
produces a very small number of gamma rays per absorbed neutron. After the
borated polyethylene collimators, 3.65 cm thick brass collimators attenuate
gamma rays produced both by the ‘gamma flash’ characteristic of spallation
targets as well as any gamma rays produced by neutrons absorbing in the
borated polyethylene collimators. The collimator collection is also draped
with 6Li fluorinated plastic to absorb high energy neutrons scattered by the
hydrogen but not absorbed by the boron in the fast neutron collimators before
they can create additional neutron and gamma ray backgrounds signals in the
detector. Collimators made of 10B-loaded plastic are also placed outside the
upstream ends of the cryostat vacuum flanges to sharply define the beam that
passes through the targets. The stand is stable enough to also support a
calibration resonance target wheel and a local neutron chopper if needed.

We measure the neutron time-of-flight spectrum on a pulse-by-pulse basis using
a beam monitor, which is a low efficiency ion chamber with 3He and 4He gas
chambers located back-to-back along the neutron beam and operated in current
mode. Since the neutron absorption cross section in 3He is very large (of
order kilobarns) and well known [35], the neutron absorption cross section in
4He is extremely small, and the gamma interactions of these two isotopes are
essentially identical, the difference signal from these two chambers is
directly proportional to the instantaneous neutron flux. We do not elaborate
any more on the details of the design for this device as it is identical to
the one used by the TRIPLE collaboration as it is already described in great
detail in the scientific literature [36].

###  3.2 Main Apparatus and Rotation Stage

The main apparatus frame is constructed from extruded aluminum profiles
(manufactured by 80/20 Inc, hereafter referred to as “8020”) mounted to a
large rotation stage with adjustable feet. The base of the main apparatus is a
large aluminum table with large 8020 support legs. On top of this table sits a
Franke TSD-830M rotation stage, labeled in Figure 6. The rotation stage has a
57,000 N load rating and allows for 360 degree rotation of the main apparatus.
The rotation stage is mounted to adjustable feet which allow for fine-tuned
adjustments to center the targets on the beam axis. A large (1.22 m diameter
and 2.54 cm thick) circular aluminum plate rests on the rotation stage and
supports the main rectangular frame constructed from 8020. The frame supports
the cryostat/cryogenic target assemblies, adiabatic spin-flipper coils, and
can be modified to include additional equipment such as a 3He polarizer
(described in further detail in Section 8). The spin-flipper coils are affixed
directly to the 8020 aluminum frame using specially-designed plastic clamps.

The aluminum housing for the cryostats are supported from the top of the 8020
frame on sliding rails, allowing for easy adjustment of the target location
along the neutron beam. The maximum distance between the two targets is 152
cm. The cryogenic housing is mounted to the sliding rails by three V-groove-
and-ball kinematic mounts. This allows for reproducible, precision placement
of the targets when moving or replacing the cryogenic housing during a target
change. In this modular design other components such as a large 3He polarizer
can also couple to the sliding rails or the 8020 frame. One nice feature of
using 8020 for the frame is the ease with which components can be precisely
and repeatably aligned using mechanically-defined reference points. The
aluminum table was aligned to the beam using a theodolite. All other
components used mechanically-defined reference points to define alignment.

Figure 6: The main apparatus in the Double Lanthanum experimental setup as
configured with two cryogenic 139La targets installed. The lefthand diagram
shows a downstream view of the apparatus (i.e. looking down the axis of the
neutron trajectory) whereas the righthand shows a sidelong, cross-section
view.

###  3.3 Target Environment

Cryo-Torr 8 cryopumps were stripped of their internal cryopumping surfaces and
used as mechanical refrigerators to cool the targets to $\sim$15 K. The
cryopumps couple to the aluminum housing and then to an aluminum vacuum
chamber below. The neutron beam passes through 1.27 mm thick aluminum vacuum
windows centered on the beam. Inside the cryostat vacuum chamber, the target
cell is thermally coupled to the 15 K stage of the cold head, while a
surrounding radiation shield is coupled to the 80 K stage of the cold head.
The target cells are contained in 12.03 cm diameter aluminum cans, filled in
an inert argon atmosphere in a glovebox and sealed with indium o-rings. This
prevents potential oxidation of sensitive or reactive target materials such as
lanthanum to preserve the integrity of the target and to promote the safe
handling of activated targets. To monitor the temperatures inside of the
cryostats, four silicon diode temperature sensors were placed at different
stages of the cryostat; one on the radiation shield, one on the coldhead, one
at the top of the cell clamp, and one at the bottom of the cell clamp. The
temperatures measured by diode thermometers were read using a Lakeshore 218
temperature monitor. The temperature distribution in the cryogenic system
under steady state operation was stable at the level of 0.2 K.

###  3.4 Detector and Shieldhouse

Located furthest downstream from the beam pipe entrance to the hutch is the
detector stand and shielding assembly, known as the shieldhouse. The purpose
of this shieldhouse is to protect the 6Li neutron detector from any neutrons
and gamma rays originating from outside the defined neutron beam (e.g.
multiply-scattered neutrons from the hutch or gamma rays produced in neutron
capture reactions on materials in the hutch). The support structure frame is
made of 8020 and sheets of borated polyethylene. The outermost layer of
shielding consists of 15 cm of borated polyethylene, followed by 10 cm of lead
bricks and 5 cm of lithium carbonate powder as seen in Figure 5. The detector
sits in an aluminum tube and was aligned to the neutron beam axis using a
theodolite and crosshairs of fishing line anchored to the aluminum tube using
offset set screws.

###  3.5 Field Mapper

In order to successfully make a precision measurement of the parity violation
in the target nuclei, it is critical to understand the dynamics of the neutron
spin motion in the fields and determine the spin-flip efficiency. To do so,
detailed maps of the magnetic fields produced by the spin flipper array
(discussed in more detail in Section 4) were needed.

One of the challenges presented with the design of the spin flipper coils was
a difficulty in mapping the magnetic field. Mounting a magnetic probe to a
motorized mapper system was very difficult due to spatial constraints enforced
by the coils, their supports, and lead wires. A simple mapping system was
constructed by mounting a Lakeshore 460 triple axis probe to a three-
dimensional, manually translatable apparatus. Continuous translational range
of motion was possible in the $xy$ plane perpendicular to the direction of the
neutron beam. In the longitudinal $z$ direction, pairs of threaded holes were
machined into a long, metal plank; pairs of screws were then placed in each
set of holes and by laying the y-directional translation stage such that an
edge was laid flush to both screws, unique points along the $z$ axis were
defined. Cross-sectional $x,y$ slices of the magnetic field were then mapped
for each of the points defined along the $z$-axis. 12 planar maps were taken
for each configuration of the spin flip field. This data, shown in Figure 10,
was then reconstructed and interpolated using COMSOL and used in calculating
the neutron spin flip efficiency as discussed further in Section 4.

Figure 7:  CAD drawing of the mapper used to map the B-field. Note the pairs
of holes machined into the longitudinal plank; these were used to uniquely
define points along the $z$-axis for maps to be taken.

##  4 Adiabatic Spin Flipper for eV Neutrons

Following the design of Roberson et al. [17], we simulated and built a neutron
Adiabatic Spin Flipper (ASF) based on adiabatic spin motion in static magnetic
fields. This spin flipper is mounted and aligned to the 8020 frame, ensuring
that the ASF longitudinal coils shown in Figure 6 are coaxial with both the
lanthanum targets and the neutron beam. The coil geometry and currents were
optimized for neutron energies near 1 eV as needed for the Double Lanthanum
experiment, though the adiabatic condition can be met for a broad range of
neutron energies. As in the TRIPLE apparatus, the neutron spin flipper
consists of longitudinal and transverse coils that produce static gradient
magnetic fields. The combination of these fields produces a total field with
approximately constant amplitude $B_{0}$ that turns the neutron spin over the
distance $L$ on the $z$-axis over which the spin rotation occurs. The spin
flipper operates in two field configurations, which we shall call the no-flip
and flip configurations. For the no-flip configuration, only the longitudinal
$B_{z}$ coils are turned on. If the direction of the neutron beam is along the
$z$-axis and $x=y=z=0$ is taken to be the center of the spin flipper as shown
in Figure 8, then the magnetic field produced by the longitudinal coils in the
no-flip state can be approximated as

$B_{z}=\begin{cases}B_{0}&\text{if $z<-L/2$}\\\ -B_{0}\sin{(\pi z/L)}&\text{if
$-L/2\leq z\leq L/2$}\\\ -B_{0}&\text{if $z>L/2$}\end{cases}$ (3)

Recall that the magnetic torque $\vec{\tau}$ experienced by a particle with a
magnetic moment $\vec{\mu}$ in an external magnetic field $\vec{B}$ is

$\vec{\tau}=\vec{\mu}\times\vec{B}$ (4)

For the flip configuration, the transverse $B_{y}$ coils are turned on (in
addition to the $B_{z}$ coils). The component produced by the transverse coils
is given by

$B_{y}=\left\\{\begin{array}[]{ll}\pm B_{0}\cos(\pi z/L)&\mbox{if }-L/2\leq
z\leq L/2\\\ \;\;\;0&\mbox{otherwise}\end{array}\right.$ (5)

The $\pm$ sign indicates that the $B_{y}$ component can be either parallel or
anti-parallel to the $y$-axis, depending on the direction of the current in
the transverse coils. The superposition of the $B_{z}$ and $B_{y}$ fields
produces a field $\vec{B}_{\textnormal{total}}$ that is constant in magnitude
but rotates by $180^{\circ}$ in the $zy$ plane over the length $L$. A positive
$B_{y}$ component will produce a counter-clockwise rotation of the total field
in the $zy$ plane, while a negative $B_{y}$ component produces a clockwise
rotation.

As the neutron magnetic moment $\vec{\mu}_{n}$ is related to the neutron spin
$\vec{\sigma}$ by the gyromagnetic ratio $\gamma_{n}$, one can construct the
Hamiltonian of the magnetic interaction with an external magnetic field
$\vec{B}$. Substituting this Hamiltonian into the Schrödinger equation for a
time dependent $\vec{B}$ field, the Larmor equation for the spin can be
obtained [8]:

$\displaystyle\frac{d}{dt}\vec{\sigma}(t)=\gamma_{n}\vec{\sigma}(t)\times{}\vec{B}(t)$
(6)

The change in the neutron spin direction is normal to both $\vec{B}$ and
$\vec{\sigma}$ at any given time. For the no-flip state there should not be a
change in the neutron spin as the spin and the magnetic field are parallel. If
the field as seen in the rest frame of the neutron varies slowly enough (i.e.
adiabatically), the neutron spin will precess about the field direction with
the Larmor frequency $\omega_{L}=\gamma_{n}B$ and will “follow” the direction
of the external field from its initial direction $+z$ to the opposite
direction $-z$ at the end of the flipper. The rotation frequency $\omega_{B}$
of the magnetic field as seen in the rest frame of the neutron is given by

$\displaystyle\omega_{B}=\frac{\pi}{t}=\frac{\pi}{L/v}$ (7)

where $t$ is the time the neutron spends in the spin flipper and is given by
$L/v$, where $v$ is the neutron speed and $L$ is the length of the spin flip
region. The ratio of the field rotation frequency $\omega_{B}$ and the Larmor
frequency $\omega_{L}$, is defined as the adiabaticity parameter for this
system:

$\displaystyle\gamma=\frac{\omega_{B}}{\omega_{L}}=\frac{\pi v}{\gamma_{n}LB}$
(8)

If $\gamma<<1$ the spin direction will undergo several rotations around the
$\vec{B}$ direction for every small variation of the field, keeping its
precession axis approximately aligned with $\vec{B}$ at any given time. In
other words, as long as the neutron speed $v$ is below a certain limit, the
transport of the spin will be adiabatic.

Figure 8 shows the magnetic field configuration for the flip and no-flip
states of the spin flipper, as well as the total magnetic field and neutron
spin projection along the field direction as neutrons propagate across the
spin flipper length.

Figure 8: Components of the magnetic field in the a) spin-flip and b) no-spin-
flip configurations. The elements of the apparatus producing each component of
the magnetic field (longitudinal -red- coils and transverse -blue- coils) are
highlighted. Also the total magnetic field $\vec{B}_{\textnormal{total}}$ and
the projection of the neutron spin $\langle\vec{\sigma}\rangle$ along its axis
of precession are shown in the $zy$ plane for each case.

This simplified description assumes that all of the neutrons travel directly
down the longitudinal axis of the coils. Realistic spin flipper efficiency
calculations must account for the finite radius of the beam as well as
deviations away from the on-axis magnetic field. Bowman, Penttilä, and Tippens
[28] investigated these effects for neutrons whose trajectories deviate
slightly from the axis of symmetry. One must consider not only the efficiency
of the spin flipper in the flip configuration but the efficiency in the no-
flip configuration. The total efficiency of the spin flipper is the average of
the efficiencies for the flip state and the no-flip state:

$\epsilon_{\textnormal{flip}}=1-\frac{1}{\sqrt{1+\gamma^{-2}}}\left[1-\cos\left(\pi\sqrt{\gamma^{-2}+1}\right)\right],$
(9)

and the spin-preserving efficiency in the no-flip state is

$\epsilon_{\textnormal{no-flip}}=1-\frac{\pi^{3}r^{2}}{8\gamma L^{2}},$ (10)

with $r$ the distance of the neutron trajectory from the spin flipper axis. It
can be seen that $\epsilon_{\textnormal{flip}}\rightarrow 1$ when
$\gamma\rightarrow 0$; the smaller the adiabaticity parameter, the higher the
spin-flip efficiency. Also, $\epsilon_{\textnormal{no-flip}}=1$ when $r=0$; if
all neutrons travel over the beam axis every spin remains unchanged in the no-
flip state.

It now makes sense to define a ‘total’ efficiency, $\epsilon_{tot}$, as a
figure of merit for the design which describes both how well the flip
configuration flips the spin and how well the no-flip configuration preserves
the spin. We therefore define

$\epsilon_{\textnormal{total}}=\frac{\epsilon_{\textnormal{flip}}+\epsilon_{\textnormal{no-
flip}}}{2}$ (11)

For an ideal spin flipper that flips all neutron spins in the flip
configuration and leaves all neutron spins unchanged in the no-flip
configuration, we see $\epsilon_{tot}=1$.

To define the optimum parameters for our spin flipper, we calculated the flip,
no-flip and total efficiency for different values of magnetic field amplitude
$B_{0}$ and spin flipper length $L$ using equations 9-11. We assumed a 10 cm
diameter neutron beam and used the square root of the average value of
$r^{2}$, $\sqrt{\langle r^{2}\rangle}$=3.54 cm to calculate the spin-
preserving efficiency. Figure 9 shows these calculations. Considering the
constraints in length for the Double Lanthanum experiment at FP12, we chose
$L=120$ cm for the flipping length, the maximum allowed in the apparatus. From
$z=-60$ cm to $z=60$ cm the field $\vec{B}$ has the described form for the
flip and no-flip states (equations 3 and 5). For 60 cm $<\lvert z\rvert<$ 75
cm we aimed to produce a longitudinal constant field of amplitude $\pm B_{0}$,
providing a uniform field in the region of the La targets (see Figure 10). The
choice of $B_{0}$ values were constrained by practical experimental and safety
reasons: it has to be generated by reasonably attainable electric currents and
voltages, yet also has to be large enough to assure a good efficiency. We
found that for $L=120$ cm, a magnetic field amplitude of $B_{0}$=16-17 G can
produce a total efficiency between 92%-98%, as seen in Figure 9.

Figure 9: Calculations of the a) spin flipper efficiency and b) spin
preserving efficiency as functions of the parameters $B_{0}$ and $L$ for 1 eV
neutrons at $r=3.54$ cm, the value of $\sqrt{\langle r^{2}\rangle}$ over a 10
cm diameter beam. The total efficiency is shown in c) and d).

To establish the position along $z$ and the parameter $NI$ (number of turns of
a particular coil multiplied by the current) for each of the coils comprising
the longitudinal field array (see Figure 10), we considered the current $I$ to
be fixed, and in an iterative process of varying the position and obtaining
the number of turns by the Single Value Decomposition (SVD) method, we
obtained the optimum coil configuration. With $I=15$ A and a maximum number of
turns that vary from 1-2 turns for the small coils to $\sim$80 for the large
coils, the voltage requirement using 10 AWG copper wire is close to 40 V,
which is achievable with the system described in Section 3.

Figure 10: a) Field maps for the longitudinal and transverse components of the
spin flipper; 14 $xy$ planes were scanned at positions between -50 to 50 cm
along the $z$-axis. b) Measured magnetic field components along the $z$-axis
and their comparison with the design model fields.

The field maps of the actual spin flipper that was constructed on FP12 were
obtained using the mapper described in Section 3.5. A total of 14 $xy$ planes
of 11 cm $\times$ 11 cm of cross section around the SF axis were scanned in
steps of $5$ mm. The field maps span the region between -50 to 50 cm in the
$z$-axis, as shown in Figure 10a. A comparison of the measured magnetic fields
and the initially calculated magnetic fields along the spin flipper axis is
shown in figure 10b; a good agreement is observed in general, however it is
important to point out that the longitudinal magnetic field (pictured in red),
has a higher amplitude than the transverse magnetic field, producing a total
magnetic field that, although performing the desired rotation by 180∘ in the
$yz$ plane, does not maintain a constant amplitude. The field map was obtained
in the middle of the experimental run; therefore the spin flipper was operated
with the magnetic fields configuration shown in figure 10.

These field maps, in combination with the images of the neutron beam profile
and data from a Monte Carlo neutron spin transport simulation, can be used to
estimate the actual spin flipper efficiency 0.7 eV neutrons.

###  4.1 Neutron Beam Intensity Maps

(a)

(b)

Figure 11: The image on the left shows the neutron beam spot as imaged on a
Gd-doped image plate. The neutron beam intensity distribution was extracted
using ImageJ software.

The radial dependence of the neutron beam intensity must be mapped to
sufficient accuracy that it can be included with the magnetic field map to
calculate the neutron spin flipper efficiency. We determined that an intensity
map with a few mm spatial resolution over the 10 cm diameter beam would
suffice to determine the spin flip efficiency with an accuracy more than one
order of magnitude better than our statistical accuracy goal. This measurement
was performed with a commercial imaging plate using a neutron-sensitive Gd-
doped film. Its spatial resolution is one order of magnitude better than
required for our purposes. Figure 11(a) shows an example of such a map. The
neutron imaging plate technology used to produce these intensity maps has been
demonstrated to possess a linear response over a dynamic range of about 4
orders of magnitude as determined in the course of careful studies conducted
at NIST for a Penning-trap-based neutron lifetime experiment [38].

##  5 Mechanical Design of the Adiabatic Spin Flipper and Controls

The spin flipper consists of twelve axially concentric longitudinal coils of
different radii and winding numbers connected in series to produce the
sinusoidally varying longitudinal field along the $z$-axis (Eq. 3) and one
pair of axially concentric Helmholtz coils that produce the cosinusoidally
varying transverse field along the $y$-axis (Eq. 5). The coils were designed
using COMSOL to determine the coil parameters (coil dimensions, number of
turns, positions, and necessary currents) needed to produce the desired
fields. In addition, one pair of ‘shunt’ coils was constructed, consisting of
two coils identical in construction to the transverse field coils. Because of
the relatively large ($\sim 15$ A) currents needed to produce these fields and
the relatively short timescales ($\sim$100 ms) needed for the transverse field
on/off transitions, the shunt coils were introduced to the circuit so that
instead of turning the current in the transverse coils on and off and
potentially producing electronic crosstalk, the current was instead diverted
to the shunt coils via a switch box module. The longitudinal and transverse
coils were mounted to the frame of the apparatus and the shunt coils were
placed in a corner of the experimental hutch as far away as possible from the
spin-flip region of interest, approximately 3 meters from the center of the
spin flipper. The field produced by the shunt coils at the center of the spin
flipper was measured and determined to be negligible.

###  5.1 Switch Box Design

To control the neutron spin flip coils, we designed a switch box containing an
array of FET switches with opto-isolated gate drivers controlled by TTL
signals sent from an Arduino Mega 2560 board. The switch box was designed to
be able to handle a maximum current of 20 A and to react quickly enough during
a change of state that viable neutron pulses were not lost due to a slow slew
time for the switch box. The limiting factor for the switching rate was found
to be the intrinsic 120 ms settling time that it took for the currents to
achieve a steady state in the coils. This characteristic time was due to the
large inductance of the coils and the settling time of the eddy currents in
the aluminum coil frames.

The switch box allowed complete control over the state of the spin flipper. By
sending the appropriate logic signal from the Arduino board to the switch box,
current to the coils could be turned on/off, reversed in polarity, or diverted
to/from the shunt coils. The Arduino board was connected to the external Lujan
Center $t_{0}$ signal as a trigger source, and its output 5 V logic signals
were sent through a simple conditioning circuit before entering the switch
box. Three LEDs were included in the conditioning circuit to visually confirm
that the state of the Arduino and that the states were changing as expected.

Figure 12: A simplified schematic of the spin flipper circuit including the
primary transverse coils and the shunt transverse coils. The circuit was
controlled by an Arduino Mega 2560 board.

###  5.2 Neutron Spin Flip Sequencing

The choice of neutron spin flip sequencing is a critical factor in avoiding
systematic errors that would create a false asymmetry and compromise the
validity of this experiment. For example, the gain of the detector may drift
linearly in time due to effects such as temperature-dependence of the detector
electronics. Even more dangerous are gain effects that correlate directly to
the absolute spin state of the neutron; stray magnetic fields produced by the
spin flipper may influence the gain of the PMT dynode chain and cause the
detector to have a different gain for each neutron spin state. An important
feature of the spin flipper is that it works equally well for both
configurations ($\pm$) of the field produced by the transverse coils.
Therefore, a careful choice of the pattern with which the neutron spins are
flipped can cancel systematic effects. Following the prescription by Roberson
et al [17], the base spin sequence pattern F N N F N F F N was chosen, where N
and F denote the no-flip and flip states, respectively. A discussion of how
the spin state was determined during the data analysis process is discussed in
section 7.2.

Because the neutron spin flip behavior is identical for the cases where the
transverse field is aligned ($+$) or anti-aligned ($-$) with the $y$-axis and
recalling that the transverse field off (0) is the no-flip state, we can
additionally alternate the polarity of the field used to produce the flip
states, making our spin flip sequence + 0 0 - 0 - + 0. One can write the
change in the neutron yield as a function of the stray field produced by the
spin flipper, $B_{s}$, as

$Y(B_{s})=Y(B_{0})+\frac{\partial Y}{\partial
B}B_{s}+\frac{1}{2}\frac{\partial^{2}Y}{\partial B^{2}}B^{2}_{s}+...$ (12)

then the difference in the neutron yields for the flip and no-flip states,
$\Delta Y$, is found to be [28]:

$\Delta
Y=\overline{Y(F)}-\overline{Y(N)}=\frac{1}{2}\frac{\partial^{2}Y}{\partial
B^{2}}B^{2}_{s}+...$ (13)

We can see here that the dependence on a term linear in $\vec{B_{s}}$
vanishes, leaving us to only have to measure the change in the gain of the
magnetic field at the detector location to estimate the quadratic term.

##  6 Fast-Response Current Mode 6Li Glass Scintillator Detector

The current mode detector used in our apparatus was designed to be identical
to one used by the TRIPLE Collaboration [37]. The reasons for this design
choice were the similarities in neutron flux and the sensitivities achieved in
the TRIPLE Collaboration’s previous experiments [22, 23]. The main goal of the
design is to convert the neutron flux in a neutron-absorbing scintillator
detector into an output current as a function of neutron time-of-flight. When
the neutron rate is low, the detector can also resolve individual pulses in
pulse counting mode.

###  6.1 Scintillator Characteristics

The neutron detector shown in Fig. 1 contains a 13.3 cm diameter $\times$ 1 cm
thick cylinder of Scintacor GS20 6Li loaded glass optically coupled to a
photomultiplier tube (PMT). The GS20 6Li loaded glass has a density of $2.5$
g/cm${}^{3}.$ The reaction n + 6Li $\rightarrow$ 7Li* $\rightarrow$ 4He + 3H +
4.8 MeV is used to detect neutrons. The GS20 glass is 6.6% lithium by weight,
enriched to 95% 6Li. The 1 cm thickness of lithium glass gives a neutron
absorption efficiency of 90% for 1 eV neutrons. Due to the 1/$v_{n}$
dependence of the n + 6Li $\rightarrow$ 4He + 3H reaction cross section, the
efficiency is lower at higher energies. The cross section of this reaction at
1 eV neutron energy is approximately 147 b [39]. The scintillation light from
neutron capture in GS20 glass has a fast 18 ns component, a slower 57 ns
component, and a 98 ns rise time for the signal to rise from 10% to 90% of its
full value. The scintillation light produced by the energy deposited by the
4He and 3H ions is detected in the PMT.

An otherwise identical detector/PMT combination was constructed which uses
glass depleted in 6Li so that it is very insensitive to neutrons but has an
almost identical response to gammas. The attenuation of gammas in the
materials used in the scintillator/PMT is low enough that one can place the
7Li-rich detector directly behind the 6Li-rich detector to measure and
subtract out the signal from the gammas in the beam if needed. Based on the
high signal/background ratio of our signal at neutron time of flights
corresponding to the 1 eV region, we decided not to install the 7Li-rich
backing detector for the double lanthanum measurements.

Figure 13:  Side view of the detector design. From left to right: an aluminum
window 18 cm in diameter, the 6Li glass scintillator, the Hamamatsu R1513 PMT
with its $\mu$-metal magnetic shield, the PCB, and the exit window with
electrical feedthroughs. Not shown in this cutaway is the LED installed to
produce pulsed light used for calibration purposes.

###  6.2 PMT and Analog Electronics

We chose a Hamamatsu R1513 PMT with a S-20 photocathode for its low
photocathode resistivity and corresponding superior performance in current
mode [37]. The maximum gain for this PMT is around 3.3 $\times 10^{5}$. A
single photoelectron pulse at the anode of the PMT has a rise-time of around 7
ns. The PMT base circuitry is shown in Figure 14. The photocathode current was
specified to output 2 $\mu$A with a full scale of 2 mA. The full scale current
requires a gain of 1000 within the dynode chain. This gain was achieved with a
1050 V input. The 2 $\mu$A current enables the detector to handle an
instantaneous rate of 1011 neutrons/s striking the detector given that there
are typically 100 photoelectrons produced in the PMT when a single neutron is
captured. The cathode within the PMT was grounded to ensure stable, low-noise
operation of the PMT. The baseline level was designed to be 0.0 V which
corresponded to 0 $\mu$A. A 2 $\mu$A current in the PMT produced an output
voltage of -2.0 V. The PMT uses an active voltage divider so that the divider
ratio is unaffected by load currents from the PMT. A light emitting diode was
also included in the design of the PMT assembly so that testing could be
performed with a internal LED. In addition to the high voltage supply needed
to run the PMT, a +8V/-8V supply powers a buffering stage operational
amplifier. All output signal cables are LEMO connections.

Figure 14:  A simplified schematic of the PMT assembly.

##  7 Data Acquisition

This setup was designed to measure the total neutron transmission through
matched disks of 139La. Because of the high instantaneous flux rates needed
for such a transmission measurement, it is not feasible to count individual
neutron pulses; instead, the total integrated current output of the detector
is measured. Our data acquisition system, like our detector, must be designed
to handle the output signal in real time.

We used a CAEN V1724 8-channel, 14-bit digitizer with a maximum sampling rate
of 100 MS/s to record the signals from the 3He ion chamber, current-mode
neutron detector, and 3 Faraday pickup loops (5 signals in total). The
facility $t_{0}$ signal from the 20 Hz Lujan Center accelerator proton current
pickup coil was used to simultaneously trigger the spin-flipper controller and
the data acquisition. Upon receiving a $t_{0}$ trigger, 75000 2-byte samples
were recorded for each of the 5 input voltage signals and stored in the
onboard memory buffers where it was read out via an optical link to the data
acquisition computer. In order to reduce the data file size, the respective
waveforms were then decimated in software before being written to long-term
storage. All further data manipulation and analysis was handled offline.

###  7.1 Signal processing

Higher-resolution spectroscopy of the 0.7 eV resonance was desired in order to
increase the precision with which we could measure the Doppler-narrowed 0.7 eV
resonance peak. To do so, each of the 5 signals were sampled every 10 ns by
the V1724 digitizer and then decimated on-board by a factor of $2^{6}=64$.
After being read out by the CAEN board to the data acquisition desktop
computer, the data underwent further decimation where it was structured into
‘windows,’ i.e. different regions of the waveform were decimated by different
factors in order to keep the data files at a reasonable size. The total data
set for the Double Lanthanum experiment was $\sim 4$ TB. If such a decimation
scheme had not been implemented, the data set was expected to be well over 400
TB, which is unwieldy in terms of data storage and manipulation during the
analysis process.

###  7.2 Determination of Spin State

Extreme caution must be exercised when deciding how to record the spin state
of the flipper in the datastream. If one chooses to measure a signal that
correlates directly with the absolute spin state of the flipper (e.g. using a
magnetic field probe to monitor the actual value of the $\vec{B}$ field in
real time), then it is possible that nonzero false asymmetries may creep into
the data via insidious means such as electronic cross-talk between channels on
the data acquisition modules. Although data acquisition modules are designed
to minimize cross-talk, we did not want to risk such an occurrence in a high-
statistics, precision experiment. Systematic ucertainties that effectively
mimic a physics asymmetry completely compromise the validity of such an
experiment.

To monitor the spin flipping process, each of the three coil sets
(longitudinal, transverse, and shunt) had a respective lead wire threaded
through its own pickup coil. Each pickup coil consisted of a toroidal solenoid
wrapped around an iron core. The ferromagnetic core ensured that maximal
magnetic flux was captured. Because the state of the flipper is determined by
the direction of the current through the coils, any change in current will
induce a voltage in the pickup coil. We measured these induced voltages to
determine spin state transitions, from which the preceding and succeeding spin
states could be determined.

Because the longitudinal spin transport field is always on, our spin flipper
state can be defined by the state of the transverse field coil, of which there
are three: off, no transverse field (0); on, positive transverse field (+);
on, negative transverse field (-). For some early test runs, a Lakeshore 460
triple axis magnetic field probe was placed at the center of the spin flipper
to record the absolute state of the transverse field to be used to test our
sorting algorithm (this probe was later removed so that there was no chance of
interference with our dataset). Figure 15 shows the overlaid field probe
readings of a few thousand pulses. We can see that there are three stable
magnetic field states, indicated by the three distinct levels in Figure 15, as
well as the transitions happening between them. We have developed a method to
sort the spins by identifying the pickup coil voltage signature for each
transition and used this information to tag each pulse as either flip or no-
flip, described below.

Given our spin flip pattern of ($+00-0-+0$), we can see that we should have
six unique transitions between states: $(+\rightarrow 0),(0\rightarrow
0),(0\rightarrow-),(-\rightarrow 0)$, $(-\rightarrow+)$, and
$(0\rightarrow+)$. Figure 16 shows a few examples of these voltage signatures
that were produced when the spin flipper transitioned states, and Figure 17
shows these same traces superimposed on one another to show relative
lineshapes and amplitudes. However, we have found that all eight transitions
(the six unique transitions and the two degenerate $(0\rightarrow-)$ and
$(+\rightarrow)$ transitions)

between states can be uniquely identified by the pickup loop signature–this is
due to the small differences in the placement of the pickup coils in relation
to the spin flipper, allowing each to capture dissimilar enough magnetic flux
changes to produce distinct voltage signatures.

Figure 15:  This figure shows the pulses that were identified using the cuts
made on the histograms of integrated voltage signals. Note all eight
transitions are present, including the ‘no change in state’ transition, shown
in yellow. Figure 16: Voltage signals were produced in the pickup coils by
changing the currents flowing through the spin flipper coils. Here we see
examples of 6 different spin state transitions. Figure 17: Induced voltage
signals for all 6 spin state transitions, superimposed to allow for
comparison.

To sort the data pulses by spin state, each voltage signal for a given pickup
coil was integrated over the 50 ms pulse to return a single value for each
pulse. These values were then histogrammed and clear peaks emerged for each
spin state transition. By defining the upper and lower bounds for each peak on
the histogram, we were able to determine and sort each spin state by
understanding which transition was happening for each pulse and tagging the
preceding spin states appropriately. Figure 18 shows a sample of some of the
peaks, though it is worth noting that there were more than 8 peaks due to the
summation of the pulses immediately preceding the initial transitional pulses
causing small peaks very near the ‘no spin state change’ peak.

Figure 18: A histogram showing the summation of each voltage signal produced
by a spin state transition shows unique values for each of the states. These
values were then used to sort pulses into their appropriate spin states.

##  8 3He Spin Filter Apparatus and Design

A polarized 3He gas neutron spin-filter works by utilizing the spin dependent
neutron absorption cross section of polarized 3He. Neutrons with their spins
parallel to that of the 3He gas will be transmitted while neutrons with anti-
parallel spins will be absorbed. A polarized 3He neutron spin filter of
sufficient thickness and 3He polarization can polarize the neutron energies of
interest between 0.1-10 eV with neutron polarization and transmission high
enough to conduct several interesting experiments. The efficient removal of
the antiparallel spins by absorption rather than scattering as in a neutron
spin filter based on polarized proton scattering, combined with the spatial
uniformity of the 3He gas polarization in the cell, makes the polarized
neutron beam phase space highly uniform, This is an advantageous property for
an eventual time reversal violation experiment as it suppresses possible
sources of systematic error associated with neutron small angle scattering in
the polarized target. The energy-dependent neutron transmission measurements
possible at a pulsed spallation neutron source like LANSCE allow the neutron
beam polarization produced by such a neutron spin filter to be determined to
high accuracy by comparing the relative neutron transmission intensity for the
3He in the spin filter polarized versus unpolarized [42]. Polarized 3He gas is
produced using spin-exchange optical pumping (SEOP) [45]. SEOP refers to the
process of using optical pumping to polarize rubidium vapor and allowing the
spin polarization of the Rb electrons to be transferred to 3He nuclei via spin
exchange during gas-phase collisions. This spin-exchange is mediated by the
hyperfine interaction between the Rb valence electron and the 3He nucleus.
Below we include a brief description of the physics behind this process and
our design of the system. Extensive references to previous work on polarized
3He neutron spin filters can be found in a recent review [46].

###  8.1 Spin Exchange Optical Pumping (SEOP) Theory

####  8.1.1 Rubidium Optical Pumping

Optical pumping describes the process by which photons are used to
redistribute the occupied states of some collection of atoms. Resonant
absorption of light stimulates these states out of thermodynamic equilibrium
toward a single desired state. Rubidium, as an alkali metal, is hydrogen-like
because its outermost electron is shielded by complete inner shells. The
Hamiltonian for the ground state of Rb in a static magnetic field
$B_{0}\hat{z}$ is:

${\cal H}=A_{g}\vec{I}\cdot\vec{S}+g_{s}\mu_{B}S_{z}B_{0}\
-\frac{\mu_{I}}{I}I_{z}B_{0}$ (14)

where $\vec{I}$ is the Rb nuclear spin, $\vec{S}$ is the electron spin,
$A_{g}$ is the isotropic magnetic dipole coupling coefficient, $g_{s}$ is the
electron g-factor, $\mu_{B}$ is the Bohr magneton, and $\mu_{I}$ is the
nuclear magnetic moment. The first term in the Hamiltonian is the hyperfine
interaction between the nucleus and electron, while the second and third terms
are the Zeeman interactions of the electron and nucleus with the external
magnetic field. In the weak-field limit, the hyperfine interaction is larger
than the Zeeman interaction, producing hyperfine splitting on the order of GHz
and Zeeman splitting on the order of MHz. The total angular momentum of the
atom is then $\vec{F}=\vec{I}+\vec{J}$ with its projection $m_{F}$ onto the
the $z$-axis.

For rubidium, the ground state ${}^{2}S_{1/2}$ and excited state
${}^{2}P_{1/2}$ have an energy separation corresponding to a light wavelength
of $\lambda=794.8$ nm. These states are separated further into two $F$ states
due to hyperfine splitting. Increasing the $B$-field further separates the
$F$-states into $2F+1$ subdivisions. In the 3He gas cell there are two
isotopes of Rubidium: 85Rb with nuclear spin $I=5/2$ and hyperfine levels
$F=3,2$ and 87Rb with nuclear spin $I=3/2$ and hyperfine levels $F=2,1$. An
unpolarized $794.8$ nm photon will cause a
${}^{2}S_{1/2}\rightarrow{}^{2}P_{1/2}$ transition according to the selection
rules: $\Delta F=0,\pm 1$ and $\Delta m_{F}=0,\pm 1$. However, if said photon
is circularly polarized with angular momentum pointing in the direction of the
static magnetic field, this further restricts the allowed transition. The new
selection rules are then: $\Delta F=0,\pm 1$ and $\Delta m_{F}=\pm 1$. The
excited state will then spontaneously decay back into the ground state by
emission of a photon with arbitrary polarization and $\Delta m_{F}=0,\pm 1$
selection rules. Given sufficient time, nearly all the Rb atoms will migrate
to the highest $m_{F}$ value possible because there is no transition out of
this state. This $m_{F}$ value corresponds to a situation where the electron
and nuclear magnetic moments point in the same direction as the static
magnetic field. The Rb atoms are therefore polarized and in the ground state.

To improve the efficiency of this process a small amount of $\rm{N_{2}}$ gas
is added to the cell. When an excited Rb atom spontaneously decays the emitted
photon has a random polarization and can re-excite another Rb atom. Because
the photon is not circularly polarized, this allows for $\Delta m_{F}=0,\pm 1$
transitions. This in turn will slow down the polarization of the Rb atoms. The
$N_{2}$ in the cell circumvents this bottleneck by allowing the Rb atoms to
de-excite before they spontaneously decay. This relaxation is achieved by
transferring the energy to the rotational and vibrational states of the
$N_{2}$ molecules. This is made possible by the large quenching cross section
of $5.8\times 10^{-15}$ cm-2 for $N_{2}$ gas [47]. The relaxation takes place
$\sim$10 times faster than the spontaneous decay.

####  8.1.2 Spin-Exchange

The next stage in polarization of 3He is the spin-exchange between the Rb
valence electron and the 3He nucleus. From the perspective of the spins, the
collision is dominated by two interactions:

$V=\gamma\vec{N}\cdot\vec{S}+\alpha\vec{K}\cdot\vec{S}$ (15)

The first interaction is between the Rb valence electron spin $\vec{S}$ and
the rotational angular momentum $\vec{N}$ of the Rb and 3He pair. The second
interaction is the hyperfine coupling between the Rb valence electron spin
$\vec{S}$ and the nuclear spin $\vec{K}$ of the 3He atom. The constants
$\gamma$ and $\alpha$ are functions of the separation distance $R$ and
determine the interaction strength. Spin relaxation of the Rb electron is from
the spin-rotation interaction while the spin-exchange is caused by the
hyperfine interaction. During a collision, the spin angular momentum of the Rb
electron is transferred to the 3He nucleus. Because this spin exchange is a
slow processes, acquiring maximally polarized 3He gas takes on the order of 10
hours.

####  8.1.3 Cell and Oven

The 3He gas cell, shown in Figure 19, is 12.1 cm in diameter and 10.8 cm thick
in the longitudinal direction. The cell contains 3He gas at 2 bar pressure,
0.09 bar of N2 gas, and solid Rb inside. To turn the solid Rb into a vapor,
the cell needs to be heated to an ambient temperature of about 200 ∘C. The
cell is held in place with a Teflon holder and high temperature polyimide
tape. Teflon is used because of its high heat-resistant properties and
flexibility. Additionally, the Teflon holder supports two coils used for free
induction decay (FID) NMR. The purpose of FID NMR is to measure the 3He
polarization in a non-destructive way.

Figure 19:  3He gas cell in its Teflon holder.

The oven used to heat the cell is a $26.7\times 26.7\times 63.5$ cm3
rectangular box with 3 layers. The first layer is made of 1.27 cm Garolite
“G7” and supports the gas cell and adiabatic fast passage (AFP) NMR coil. The
AFP NMR coil is used to flip the 3He polarization direction. The second layer
is made of aluminum and holds six 7.6 cm electrical heating cartridges (Omega:
CSH 103220). The third layer is also made of 1.9 cm G7, supports the first two
layers and provides insulation. The end caps, also made of 1.27 cm G7, hold
sapphire glass windows. G7 is a glass-silicon laminate, has a density of 4.57
g/cm3, tensile strength of 20,000 PSI, and a maximum continuous operating
temperature of 221∘C. These properties make it especially appropriate as a
support and as an insulator for an oven with a target temperature of 200∘C.
The purpose of the aluminum layer is to better distribute the heat created by
the cartridge heaters. The outermost layer is supported by an adjustable
support to better align the 3He gas cell to the neutron beam. Almost all oven
components are made with non-magnetic material such as aluminum and brass.
Figure 20 shows the 3He cell situated inside of the oven.

Figure 20:  Picture of oven with 3He gas cell and cartridges heaters
installed.

####  8.1.4 Laser Optics

To excite the Rb atoms, a 50 W fiber-coupled 795 nm laser is used. Circularly
polarized light is created by passing linearly polarized light through a
quarter wave plate at a 45∘ angle. First, the laser fiber is coupled to a beam
collimator (ThorLabs: F220SMA-780) that focuses and reduces the spread of the
beam. The laser is then incident on a polarizing cube beam-splitter (Edmund
Optics: 49-872) that linearly polarizes and splits the beam 90∘ into two
paths. Both paths are then incident on a 2.54 cm diameter, 795 nm quarter wave
plate (QWP). Each QWP is mounted on a precision motorized rotation device
(ThorLabs: K10CR1). These devices allow for remote flipping of the direction
of circular polarization by rotating the QWPs by 90∘. One path is then
reflected by 90∘ using a 50 mm diameter dielectric mirror (Edmund Optics:
33-189). Finally, both paths are reflected in the oven with large 8 inch
diameter dielectric coated silicon mirrors. The mirrors reflect the laser
light, but are nearly transparent to neutrons. The laser light then passes
through the sapphire glass windows and into the the 3He gas cell. Figure 21
shows a schematic of the optical layout. All optical components and oven are
mounted on to a $48.2\times 119.3\times 1.27$ cm ($19\times 47\times 0.5$
inch) optical breadboard. Additionally, the breadboard and optics are enclosed
in a black-anodized light tight box, shown in Figure 22. All optical
components are made as non-magnetic as possible by using brass and aluminum
parts.

Figure 21:  Diagram showing the optics layout for creating circularly
polarized light. Figure 22:  Picture of optics setup in black-anodized light
tight box.

####  8.1.5 $\mu$-Metal Solenoid and Support

A $\mu$-metal shielded solenoid provides the uniform magnetic field required
for the SEOP process. The $\mu$-metal shielded solenoid is approximately 61 cm
$\times$ 61 cm $\times$ 122 cm in size. The internal structure of of the
$\mu$-metal shield is made of an 8020 frame of 2.5 cm $\times$2.5 cm profiles.
The light tight box (with the optical components and oven mounted to the
optical bread board) slides into the $\mu$-metal shield on a Teflon sheet.
Figure 23 shows the shieldhouse that surrounds the solenoid, light tight box,
and oven assembly. The $\mu$-metal shield is critical due to the 3He spin-
filter’s close proximity to the adiabatic spin-flipper. Because a very small
magnetic field gradient is needed over the length of the 3He gas cell, it is
crucial to shield it from external magnetic fields; $\mu$-metal works well as
a magnetic shield due to its high magnetic permeability. Stray, slowly-varying
magnetic fields are distributed around the shielding and away from the center
where the 3He cell is located. The solenoid enclosed in the $\mu$-metal shield
produces a magnetic field along the neutron beam direction that holds the
polarization of 3He atoms. In the central 7 cm $\times$ 16 cm region where the
3He cell is located, the magnetic field has an average gradient
$\langle\frac{\nabla B_{x}}{B_{i}}\rangle=5.55\times 10^{-4}\pm 2.66\times
10^{-4}$ cm-1 along the longitudinal polarization direction, and an average
gradient $\langle\frac{\nabla B_{y}}{B_{i}}\rangle=6.03\times 10^{-4}\pm
1.68\times 10^{-4}$ cm-1 in the transverse direction. Based on these
measurements, the expected relaxation time of the 3He is $~{}100-200$ hours.
The solenoid has a resistance of $R=25.8$ $\Omega$, and is driven at 1.00 A
with a current stability of 0.1$\%$. At this current, the solenoid produces a
holding field of 9.26 gauss at its center which, along with an 30 kHz NMR
pickup coil, is tuned to the 3.24 kHz/gauss gyromagnetic ratio of 3 He[66].
The NMR signal is then used to determine the polarization of the 3He gas.

Due to the modular nature of the apparatus, this polarized 3He neutron spin
filter can be installed at the location of the first cryostat (upon removal of
the cryostat from the apparatus). It can then be operated continuously on-line
during measurements, as was successfully done several years ago using a
similar apparatus [40] for the first phase of the NPDGamma neutron-proton weak
interaction experiment [41].

Figure 23:  Picture of $\mu$-metal shielded solenoid.

##  9 Summary and Outlook

We have described a flexible, rotatable cryogenic apparatus for the
measurement of parity violation in the transmission of longitudinally
polarized neutrons in neutron-nucleus resonances in the 0.1-10 eV energy range
at a short-pulsed spallation neutron source. The apparatus employs beam
monitors and transmission detectors combining both (n, $\gamma$)
discrimination and current mode operation, a broadband neutron spin flipper
with a flipping mode and sequence designed to suppress systematic errors, and
a neutron polarizer based on spin-exchange optical pumping of 3He. The
apparatus design employs several features used in previous neutron parity
violation experiments at LANSCE, especially from work performed by the TRIPLE
and NPDGamma collaborations and referred to in the text.

The apparatus that we have described also possesses sufficient flexibility to
accommodate several modifications that can greatly extend the range of
possible experiments beyond the Double Lanthanum experiment that we
concentrated on as an example in this paper. The first major addition to the
apparatus we envision for the measurement of P-odd transmission asymmetries in
other nuclei beyond 139La is the addition of the polarized 3He neutron spin
filter based on spin-exchange optical pumping (described in Section 8) and
which was first demonstrated at LANSCE [21]. The experimental hutch on the
FP12 beamline possesses an access path through the ceiling near the present
location of the downstream refrigerator that we plan to use for the operation
of cryostats, which require safe venting of cryogenic liquids into a storage
volume on top of the hutch, as done in the past for liquid parahydrogen
targets operated on FP12 [43, 44]. In particular, this implementation would
allow us to conduct a new measurement of the parity-odd asymmetry in the 3.2
eV p-wave resonance in 131Xe, which is one of the leading candidates for a
sensitive time reversal test, using a solid xenon target. Liquid helium supply
and venting for the dilution refrigerator required for the polarized nuclear
targets to be used in the time reversal test can also be provided through this
path.

Much care was taken in designing this apparatus to minimize any systematic
effects that would affect the uncertainty associated with the P-violation
measurements. Because this apparatus was designed to be modified to
accommodate several nuclear species, each measurement will have its own
associated systematic effects. The most dominant systematic effect associated
with the design of the apparatus itself lies in how well one can determine the
neutron spin flip efficiency. In this paper, we present a method to calculate
this efficiency using flux monitor measurements of the beam intensity
convoluted with the image plate beam profiles and measurements of the
$B$-field combined with a Monte Carlo calculation of the neutron intensity-
weighted spin flip efficiency integrated over the beam cross sectional area.
In this case, the dominant uncertainty will lie in how well one can
reconstruct the $B$-field produced by the spin flipper coils, i.e. the spatial
resolution of the $B$-field maps, which is on the order of a few parts in 103.
If this accuracy does not suffice one can install a 3He polarizer/ analyzer
pair and measure the neutron spin flip efficiency directly using the method
described by Musgrave et al. in [42].

The beamline components can be translated upstream far enough to accept gamma
detector arrays downstream of the target to conduct parity violation
measurements using (n, $\gamma$) reactions [48] as well as in neutron
transmission measurements. The addition of a gamma detector array to this
apparatus would enable one to efficiently search for large P-odd asymmetries
between 0.1-10 eV in the several isotopes of heavy nuclei which have never
been measured. The TRIPLE collaboration concentrated its choice of nuclei for
measurement near the peaks of the 3p and 4p p-wave strength functions in an
attempt to maximize the number of p-wave resonance per unit energy interval in
the isolated resonance eV-keV regime for their statistical analysis of parity
violation in heavy nuclei. Since that work was conducted, improved data on the
p-wave strength function [49] has resolved an additional small peak near
A=160, which is split off from the 4p giant resonance due to nuclear
deformation effects as predicted long ago [50], whereas the spherical optical
model by contrast predicts a minimum at A=160. It therefore may be worthwhile
to search in this A range to see if one can discover more p-wave resonances
that amplify parity violation. One could also search for large parity-odd
effects in the (n, $\gamma$) channel for nuclei that undergo neutron-induced
fission and try to confirm and extend the many large P-odd asymmetries already
measured in the fission channel [51, 52, 53, 54, 55, 5, 56, 57, 58, 59, 60,
61]. In particular one could measure the P-odd asymmetries in the (n,
$\gamma$) channel in very low energy resonances in 235U [62, 63], which is a
nucleus that can be safely handled and supplied at the LANSCE facility. There
is an already-proven method for nuclear polarization of 235U using the very
large hyperfine fields produced at the nucleus in the low-temperature
ferromagnetic phase of uranium sulfide. This phenomenon was exploited in the
past to determine the spin assignments in 235U using spin-dependent polarized
neutron transmission through polarized 235U [64]. The nonmagnetic composition
of the apparatus also lends itself to the use of polarized xenon targets
produced by a spin-exchange optical pumping process very similar to that
described above for 3He. The 10 cm x 10 cm cross section, m=3 supermirror
neutron guide presently installed upstream of the LANSCE FP12 hutch [29] could
be replaced in the future with other types of neutron guides that can increase
the fraction of neutrons transmitted to the apparatus near 1 eV. The
dimensions of the FP12 hutch transverse to the neutron beam direction are wide
enough to allow for the complete rotation of the relevant components of the
apparatus by 180 degrees as envisioned in one of the modes of realization for
a precision test of time reversal invariance [11]. According to the results of
MCNP simulations of the new configuration of the LANSCE
target/moderator/reflector system scheduled to be installed in early 2020 [65]
we do not expect the projected changes, including the removal of the liquid
hydrogen slow neutron moderator, to significantly influence the beam
characteristics in our energy range of interest between 1-10 eV and therefore
the performance of the components of the apparatus presented above should
remain essentially unchanged after this upgrade.

##  10 Acknowledgements

This material is based upon work supported by the U.S. Department of Energy,
Office of Science, Office of Nuclear Physics, under Award Number DE-
SC-0014622. D. Schaper would also like to acknowledge support by the NSF
Graduate Research Fellowship Program under Grant Number 1247392. The work of
C. Auton, J. Curole, J. Doskow, W. Fox, H. Lu, W. M. Snow. K. Steffen, J
Vanderwerp, B. Short, and G. Visser was supported by NSF PHY-1614545, NSF
PHY-1913789, and the Indiana University Center for Spacetime Symmetries. J.
Curole also acknowledges support from the GAANN fellowship program of the US
Department of Education and the Department of Energy SCGSR program. L. Cole
and D. Olivera would like to acknowledge funding from the KY-NSF EPSCoR
Research Scholar Program. B.M. Goodson acknowledges funding from NSF
(CHE-1905341), DoD (W81XWH-15-1-0272), and a Cottrell SEED Award from the
Research Corporation for Science Advancement. We gratefully acknowledge the
local support of the LANSCE neutron facility at Los Alamos National Lab where
this measurement was performed. Test measurements for the current mode
detector electronics used for this work were conducted in part on the NOBORU
instrument at the JPARC MLF through proposal 2016B0021, Characterization of
High counting rate Epithermal Neutron Detectors

## References

  * [1]
  * [2] G. E. Mitchell, J. D. Bowman, and H. A. Weidenmuller, Rev. Mod. Phys. 71, 445 (1999).
  * [3] G. E. Mitchell, J. D. Bowman, S. I. Penttilä, and E. I. Sharapov, Phys. Rep. 354, 157 (2001).
  * [4] O. P. Sushkov and V. V. Flambaum, JETP Lett. 32, 352 (1980).
  * [5] O. P. Sushkov and V. V. Flambaum, Sov. Phys. Usp. 25, 1 (1982).
  * [6] V. P. Alfimenkov, S. B. Borzakov, V. Van Tkhuan, Yu. D. Mareev, L. B. Pikelner, A. S. Khrykin, and E. I. Sharapov, Nucl. Phys. A 398, 93 (1983).
  * [7] V. P. Alfimenkov, S. B. Borzakov, V. Van Tkhuan, Yu. D. Mareev, L. B. Pikel’ner, I. M. Frank, A. S. Khrykin, and E. I. Sharapov, JETP Lett. 39, 416 (1984).
  * [8] W. H. Kraan “Instrumentation to handle thermal polarized neutron beams” Ph.D thesis, Delft University, Deutschland (2004).
  * [9] S. Tomsovic, M. B. Johnson, A. Hayes, and J. D. Bowman, Phys. Rev. C 62, 054607 (2000).
  * [10] P. Fadeev and V. V. Flambaum, Phys. Rev. C 100, 015504 (2019).
  * [11] J. D. Bowman and V. Gudkov, Phys. Rev. C 90, 065503 (2014).
  * [12] T. Okudaira, S. Takada, K. Hirota, A. Kimura, M. Kitaguchi, J. Koga, K. Nagamoto, T. Nakao, A. Okada, K. Sakai, H. M. Shimizu, T. Yamamoto, and T. Yoshioka, Phys. Rev. C 97, 034622 (2018).
  * [13] H.M. Shimizu, T. Adachi, L. Ishimoto, A. Masaike, Y. Masuda, and K. Morimoto, Nucl. Phys. A 552, 293 (1993).
  * [14] C.M. Frankle et al., Phys. Rev. C 46, 1542 (1992).
  * [15] J.J. Szymanski, W. M. Snow, J. D. Bowman, B. Cain, B. E. Crawford, P. P. J. Delheij, R. D. Hartman, T. Haseyama, C. D. Keith, J. N. Knudson, A. Komives, M. Leuschner, L. Y. Lowie, A. Masaike, Y. Matsuda, G. E. Mitchell, S. I. Penttilä, H. Postma, D. Rich, N. R. Roberson, S. J. Seestrom, E. I. Sharapov, S. L. Stephenson, Y. F. Yen, and V. W. Yuan, Phys. Rev. C 53, R2576 (1996).
  * [16] V. R. Skoy et al., Phys. Rev. C 53, R2573 (1996).
  * [17] N.R. Roberson et al., Nucl. Inst. Meth. A 326, 549 (1993).
  * [18] V. P. Álfimenkov, Yu. D. Mareev, L. B. Pikelner, V. R. Skoy and V. N. Shvetsov, Sov. J. Nucl. Phys. 54, 9071 (1991).
  * [19] W. G. Williams, Polarized Neutrons, Clarendon Press, Oxford (1988).
  * [20] V. I. Lushchikov, Yu. V. Taran, and F. L. Shapiro, Sov. J. Nucl. Phys. 10, 669 (1970).
  * [21] K. P. Coulter et al., Nucl. Instrum. Meth. A 288, 463 (1990).
  * [22] C. D. Bowman, J. D. Bowman, and V. W. Yuan, Phys. Rev. C 39, 1721 (1989).
  * [23] V. W. Yuan et al., Phys. Rev. C 44, 5 (1991).
  * [24] V. P. Alfimenkov, A. N. Chernikov, L. Lason, Yu. D. Mareev, V. V. Novitsky, L. B. Pikelner, V. R. Skoy, M. I. Tsulaya, C. R. Gould, D. G. Haase and N. R. Roberson, Application of Accelerators in Research and Industry, edited by J. L. Duggan and I. L. Morgan (AIP Proceedings), 345 (1997).
  * [25] V. P. Alfimenkov, A. N. Chernikov, L. Lason, Yu.D. Mareev, V. V. Novitsky, L. B. Pikelner, V. R. Skoy, M. I. Tsulaya ,C. R. Gould, D. G. Haase, and N. R. Roberson, J. Appl. Phys. 81, 1358 (1997).
  * [26] V. P. Alfimenkov, Yu. D. Mareev, V. V. Novitsky, L. B. Pikelner, V. R. Skoy, C. R. Gould, D. G. Haase, N. R. Roberson, Nucl. Instrum. Meth. A352, 592 (1995).
  * [27] P. E. Koehler, 1L Mark-IV Target Design Review, Los Alamos National Laboratory Technical Report, 2017. doi:10.2172/1409747
  * [28] J. D. Bowman, S. I. Penttilä, and W. B. Tippens, Nucl. Inst. Meth. A 369, 195 (1995).
  * [29] P.-N. Seo, J.D. Bowman, M. Gericke, G. Greene, J. Long, G.S. Mitchell, S.I. Penttilä, and W.S. Wilburn, Nucl. Inst. Meth. A 517, 285 (2004).
  * [30] M. Mocko, G. Muhrer, T. Ino, M. Ooi, L. L. Daemen, and Y. Kiyanagi, Nucl. Inst. Meth. A 594, 373 (2008).
  * [31] M. Mocko, G. Muhrer, Ch. T. Kelsey, M. A. Duran, and F. Tovesson, Nucl. Inst. Meth. A 632, 101 (2011).
  * [32] M. Mocko, G. Muhrer, Nucl. Inst. Meth. A 704, 27 (2013).
  * [33] D. B. Pelowitz editor, MCNPX User’s Manual, LA-CP-07-1473.
  * [34] W. M. Snow et al, Rev. Sci. Instrum. 86, 055101 (2015).
  * [35] C. D. Keith, Z. Chowdhuri, D. R. Rich, W. M. Snow, J. D. Bowman, S. I. Penttilä, E. I. Sharapov, D. A. Smith, M. B. Leuschner, V. R. Pomeroy, and G. L. Jones, Phys. Rev. C69, 034005 (2004).
  * [36] J. J. Szymanski et al., Nucl. Instr. and Meth. A 340 564 (1994).
  * [37] J.D. Bowman, J.J. Szymanski, V.W. Yuan, C.D. Bowman, A. Silverman, and C. Zhu et al., Nucl. Inst. Meth. A 297, 183 (1990).
  * [38] J. S. Nico, M. S. Dewey, D. M. Gilliam, F. E. Wietfeldt, X. Fei, W. M. Snow, G. L. Greene, J. Pauwels, R. Eykens, A. Lamberty, J. Van Gestel, and R. D. Scott Phys. Rev. C 71, 055502 (2005).
  * [39] J.A. Harvey and N.W. Hill, Nucl. Instr. and Meth. 162,507 (1979).
  * [40] T. E. Chupp, K. P. Coulter, M. Kandes, M. Sarma, T. B. Smith, G. L. Jones, W. C. Chen, T. R. Gentile, D. R. Rich, B. Lauss, M. T. Gericke, R. C. Gillis, S. A. Page, J. D. Bowman, S. I. Penttilä, W. S. Wilburn, M. Dabaghyan, R. W. Hersman, and M. Mason, Nuc. Inst. Meth. A 574, 500 (2007).
  * [41] M. T. Gericke, R. Alarcon, S. Balascuta, L. Barron-Palos, C. Blessinger, J. D. Bowman, R. D. Carlini, W. Chen, T. E. Chupp, C. Crawford, S. Covrig, M. Dabaghyan, N. Fomin, S. J. Freedman, T. R. Gentile, R. C. Gillis, G. L. Greene, F. W. Hersman, T. Ino, G. L. Jones, B. Lauss, M. Leuschner, W. R. Lozowski, R. Mahurin, Y. Masuda, J. Mei, G. S. Mitchell, S. Muto, H. Nann, S. A. Page, S. I. Penttilä, W. D. Ramsay, A. Salas-Bacci, S. Santra, M. Sharma, P.-N. Seo, E. I. Sharapov, T. B. Smith, W. M. Snow, W. S. Wilburn, and V. Yuan, Phys. Rev. C 83, 015505 (2011).
  * [42] M. M. Musgrave et al., Nucl. Inst. Meth A895, 19 (2018).
  * [43] S. Santra, L. Barron-Palos, J. D. Bowman, R. D. Carlini, T. E. Chupp, K. P. Coulter, C. Crawford, M. Dabaghyan, M. Dawkins, S. J. Freedman, T. Gentile, M. T. Gericke, R. C. Gillis, G. L. Greene, F. W. Hersman, G. L. Jones, M. Kandes, B. Lauss, M. B. Leuschner, R. Mahurin, M. Mason, J. Mei, G. S. Mitchell, H. Nann, S. A. Page, S. I. Penttilä, W. D. Ramsay, A. Salas Bacci, P.-N. Seo, E. Sharapov, M. Sharma, T. B. Smith, W. M. Snow, W. S. Wilburn, and H. Zhu, Nucl. Inst. Meth. A620, 421 (2010).
  * [44] L. Barron-Palos, R. Alarcon, S. Balascuta, C. Blessinger, J. D. Bowman, T. E. Chupp, S. Covrig, C. Crawford, M. Dabaghyan, M. Dawkins, W. Fox, M. T. Gericke, R. C. Gillis, B. Lauss, M. B. Leuschner, B. Lozowski, R. Mahurin, M. Mason, J. Mei, H. Nann, S. I. Penttilä, W. D. Ramsay, A. Salas Bacci, P.-N. Seo, M. Sharma, W. M. Snow, W. S. Wilburn, and V. Yuan, Nucl. Inst. Meth. A659, 579 (2011).
  * [45] T. G. Walker and W. Happer, Rev. Mod. Phys. 69, 629 (1997).
  * [46] T. R. Gentile, P. J. Nacher, B. Saam, and T. G. Walker, Rev. Mod. Phys. 89, 045004 (2017).
  * [47] E. S. Hrycyshyn and L. Krause, Can. J. Phys. 48, 2761 (1970).
  * [48] S. J. Seestrom, C. M. Frankle, J. D. Bowman, B. C. Crawford, T. Haseyama, A. Masaike, A. Matsuda, S. I. Penttilä, R. N. Roberson, E. I. Sharapov, and S. L. Stephenson, Nucl. Inst. Meth. A 433, 603 (1999).
  * [49] S. F. Mughabghab, Atlas of Neutron Resonances: Resonance Properties and Thermal Cross Sections Z=1-60, 6th edition, Volume 1, Elsevier, Amsterdam (2018).
  * [50] B. Buck and F. Perey, Phys. Rev. Lett. 8, 444 (1962).
  * [51] A. K. Petukhov et al., JETP Lett. 30, 4951 (1979).
  * [52] N. V. Borovikova et al., JETP Lett. 30, 495 (1979).
  * [53] N. V. Borovikova et al., JETP Lett. 31, 6631 (1980).
  * [54] A. K. Petukhov et al., JETP Lett. 32, 41 (1980).
  * [55] G. V. Danilian, Sov. Phys. Usp. 23, 3231 (1980).
  * [56] V. E. Bunakov and V. P. Gudkov, Nucl. Phys. A401, 93 (1983).
  * [57] A. Ya. Alexandrovich et al., Sov. J. Nuct. Phys. 39, 5091 (1984).
  * [58] A. Ya. Alexandrovich et al., J. de Phys. Colloq. C3 45, 83 (1984).
  * [59] A. Ya. Alexandrovich et al., Sov. J. Nucl. Phys. 45, 772 (1987).
  * [60] G. A. Petrov, G. V. Valskii, A. K.Petukhov, A. Y. Alexandrovich, Y. S. Pleva, V. E. Sokolov, A. B. Laptev, O. A. Scherbakov, Nucl. Phys. A 502, 297 (1989).
  * [61] A. Y. Alexandrovich, A. M. Gagarski, I. A. Krasnoschekova, G. A. Petrov, V. I. Petrova, A. K. Petukhov, Yu. S. Pleva, P. Geltenbort, J. Last, and K. Schreckenbach, Nucl. Phys. A567, 541 (1994).
  * [62] V. P. Alfimenkov et. al, Nucl. Phys. A 645, 31 (1999).
  * [63] V. P. Alfimenkov et al., Phys. At. Nucl. 63, 539 (2000).
  * [64] M. S. Moore, J. D. Moses, G. A. Keyworth, J. W. T. Dabbs, and N. W. Hill, Phys. Rev. C 18, 1328 (1978).
  * [65] L. Zavorka, M. Mocko, and P. E. Koehler, Nucl. Inst. Meth. A 901, 189 (2018).
  * [66] J. L. Flowers et al., Metrologia 30 75 (1993).