&_&L&
Nuclear
Instruments
and Methods
in Physics
Research
A 366 (1995)
100-l 14
--
*! 1:l!i!J
NUCLEAR
INSTRUMENTS
A METHODS
IN PHVSICS
RESEARCH
SectlcoA
EISEVIER
Igloo: a neutral pion spectrometer for low energy
photoproduction
studies
J.M. Vogt*, J.C. Bergstrom,
Saskatchewan Accelerator
Laboratory,
R. Igarashi, K.J. Keeter
University of Saskatchewan,
107 North Road, Saskatoon, Saskatchewan S7N 5C6,
Canada
Received
27 April
199s
Abstract
A n” spectrometer
constructed from 68 lead glass Cherenkov counters has been installed on the tagged photon
beam line at the Saskatchewan Accelerator Laboratory. It is being used for the investigation of neutral pion
photoproduction
from light nuclei within about 25 MeV of threshold. It can be configured for total cross section
measurements with a large acceptance, or for angular distribution studies with a reduced acceptance.
1. Introduction
A 7~” spectrometer (“Igloo”) constructed from 68
lead glass Cherenkov counters has recently been
installed on the tagged photon beam line at the
Saskatchewan Accelerator Laboratory (SAL), for the
purpose of studying 7~~’photoproduction
from light
nuclei at low energies, specifically within about
25 MeV of threshold. The combination
of a pulse
stretcher ring [I] and photon tagging spectrometer [2]
at the 300MeV facility is well matched to this experimental program, providing a tagged photon beam
with the necessary energy resolution and photon flux.
For example, near threshold the user has optional
photon energy resolutions of either 0.5 MeV over an
extended range, or 0.2 MeV over a limited range.
Several constraints guided the design of Igloo. First,
it must cover a large fraction of the 47~ solid angle to
accommodate total cross section measurements. Second, it must be sensitive to the pion angular distributions to accommodate differential cross section
measurements.
In addition, the spectrometer
must
readily accommodate cryogenic target assemblies, and
finally for reasons described later, no charged-particle
veto counters are to be employed.
Since the spectrometer was to be constructed from
existing glass blocks and photomultipliers,
neither of
which were ideally suited for the present purpose, our
options for designing Igloo were somewhat limited.
The resulting compromises lead to a rather simple
* Corresponding
966 6058.
author.
Tel. + 1 306 966 6054, fax + 1 306
0168.9002/95/$09.50
@ 1995 Elsevier
SSDZ 0168-9002(95)00557-9
Science
B.V. All rights
instrument with modest resolution, but sufficient for
our purposes.
To date, the spectrometer has been utilized in two
photoproduction
experiments,
and
‘WY, n’))
“C(y, r”), both in a preliminary stage of analysis at
the time of writing. Our purpose here is to report on
the design of the device, to describe our solutions to
some common problems, and finally to present briefly
some preliminary experimental results to prove the
performance of the hardware.
2. Igloo
The photon calorimeter consists of four lead glass
walls forming a symmetric box oriented with the
corners in the vertical and horizontal planes (Fig. la).
The two vertical “ends” of the box are unobstructed
to accommodate the cryogenic target assembly and the
incident tagged photon beam. Each wall is comprised
of a 5 X 2 assembly of glass blocks, each block being
191 mm square and 305 mm long and viewed on the
square end by a photomultiplier. Additional blocks are
suitably situated to prevent shower leakage in the
vicinity of the box corners. These are referred to as
the “corner guard-blocks”.
On each end of the detector there is a single layer of
glass blocks which are referred to as the “end guardblocks”; they are used to define the active length of
the spectrometer and to provide additional calorimetry
for the exterior detector blocks. If a photon hits an
exterior regular block, the energy deposited in that
block and in the end guard-block are added together
(Fig. 2, photon A). If the photon hits the guard-block
reserved
J.M. Vogt et al. I Nuct. Instr. and Meth. in Phys. Rex A 366 (1995) 100-114
101
tion of the geometric efficiency of Igloo (see Section
Tagged Photon
Beam
J
,-..
-.;
__
-.-“-
.‘_
(b)
Fig. 1. Igloo
closed (a) and open (b).
only and deposits no energy in the previous block, it is
discarded in the data analysis (Fig. 2, photon B). That
still leaves the active length of the spectrometer with a
“soft edge”, because a photon can clip the corner of
the regular block without converting, and deposit all
its energy in the guard-block. That photon would also
be discarded in the analysis (Fig. 2, photon C). This
effect, however, is taken into account in the calcula-
Fig. 2. The purpose
of the guard-blocks
(see text).
7).
The above geometry describes the spectrometer
when operating in the “closed” configuration, used for
measuring total cross sections. To accommodate angular distribution
measurements,
the spectrometer
is
designed to separate at the horizontal corners and
become, in effect, two L-shaped arms viewing the
target symmetrically from above and below. Two rows
of corner guard-blocks now become active components of the spectrometer, increasing the acceptance
solid angle. In this operating mode, referred to as the
“open mode”, each arm is retracted 424 mm along a
line defined by the vertical diagonal of the original box
(Fig. lb). In the closed and open modes, the distance
between opposing walls is 420mm and 1020mm.
respectively.
Igloo was designed for the current (T,~F”) program.
However, to accommodate future (y, P”X) experiments, the detector support has been designed so that
the downstream, beam right quadrant permits an
unobstructed view of the target by additional detectors.
Initially, we considered using veto counters to reject
charged particles (beam related background, electromagnetic showers from the target, cosmic rays) and
those veto counters were to line the inside of the lead
glass cave. The disadvantage of this scheme is that
some photons would convert in the veto counters, and,
because of the geometry, their probability of being
rejected would be hard to determine and would be
threshold dependent. In a test run with a few counters
stacked in the same geometry as in the detector frame.
we found that we could omit the veto counters,
provided Igloo was adequately shielded. This is due to
the fact that lead glass counters have a natural threshold of several MeV (low energy particles do not emit
much Cherenkov light). According to the geometry of
Igloo and the angular dependence of the atomic cross
sections, only the downstream guard-blocks register a
significant number of shower hits from the target.
Those end guard-blocks are therefore shielded with
50mm of lead (Fig. 3) - enough to absorb the showers. This is feasible since the guard-blocks are not
meant to detect direct hits from the 7~’ decay photons.
In order to shield Igloo from photon beam related
background that is produced upstream in the collimator or in the photon tagger outrun window. a
1OOmm thick lead wall is mounted on the detector
frame at the upstream end (Fig. 3). The photon beam
passes through a 35 mm clean-up collimator in that
wall. With this shielding installed, in addition to the
other lead walls that are normally situated in the
experimental
hall, neither the single rates in the
counters nor the trigger rate from the whole detector
are a problem.
102
J.M.
Vogt et al.
I Nucl.
Instr.
and Meth.
in Phys. Res. A 366 (199-T) IOO-114
f
Fig. 3. Lead shielding permanently
Fig. 4 shows Igloo in Experimental Area 2 of the
SAL facility. After careful alignment with respect to
the photon beam line, the detector frame is anchored
to the wall. The spot size of the photon beam is
defined by a 10mm collimator near the tagger outrun
window and is about 30mm in diameter at the target.
The photon beam related background is greatly reduced by an arrangement of sweep magnets, clean up
collimators and shielding walls. The tagger lead glass
counter, which is shown just upstream of the photon
beam dump, is used to measure the tagger efficiency
(the percentage of tagged photons that pass through
the collimator). It can be moved in and out of the
photon beam on a remote controlled, movable table
that is mounted downstream of Igloo. This is done
routinely between production runs and no access to
the experimental area is necessary.
3. The counters
The majority of the glass blocks are 191 mm X
191 mm X 305 mm (6.2 X 10.0 radiation lengths) in size
and are made of F-2 glass. The exceptions are the
eight end guard-blocks which are made of SF-2 glass
and are 191 mm x 191 mm x 352 mm in size.
The individual counters were assembled as shown in
Fig. 5. Five-inch EM1 9870B photomultipliers
were
coupled to the glass blocks via acrylic adapters. Optical silicone was used to couple the photomultipliers to
the adapters and to couple the adapters to the glass
blocks. While providing sufficient strength, the silicone
allows removal of the photomultipliers from the adapters or of the adapters from the blocks without causing
Lead Shielding
for
End Guard-Bkxks
installed on Igloo.
damage. For simplicity and to keep electrical noise to
a minimum, the photomultiplier
bases were soldered
directly onto the pins of the sockets. An LED was
mounted on each light guide adapter. The lead glass
blocks and the adapters were then wrapped in
aluminum foil. After mounting magnetic shielding
shrouds, which are screwed to the acrylic adapters, the
counters were wrapped in 0.125 mm brass foil. Brass
was chosen because plastic foil was too weak and had
a tendency to tear. All standard size counters and 6 of
the 8 larger counters were assembled this way. Two of
the end guard-blocks are viewed from the side by two
photomultipliers
each. Other than that they were
assembled the same way.
The sole function of the LEDs is to pulse individual
counters for testing purposes. We did not install a
pulser system to drive all LEDs in order to monitor
the counter gains on-line. Our simpler approach to
gain monitoring will be discussed later (Section 5).
The EM1 9870B photomultipliers
are hardly ideal
for our application. Their performance
has been
studied in great detail in Ref. [3], where prepulsing,
non-linearity and a time jitter of several nanoseconds
are reported. However, those photomultipliers
were
available to us at no cost and monetary constraints
precluded the possibility of using state-of-the-art 5 in.
photomultipliers.
After the first prototype counter was assembled, the
detector response was studied by running the tagged
photon beam into the front face of the lead glass
block. Fig. 6 shows the pulse height as a function of
the photon energy. To reduce the non-linearity evident in the figure, we amplified the analog signal by a
factor of 10 and reduced the photomultiplier gain, so
J.M. Vogt et al. I Nucl. Instr. and Meth. in Phys. Res. A 366 (1995)
Primary
Beam
/-Primary
Electron
Beam
Experimental
that the anode signal pulse height was well below
1OOmV The dashed line in Fig. 7 shows the resulting
pulse height as a function of the photon energy. The
remaining non-linearity is a result of shower leakage
out of the sides and the back of the lead glass block.
The solid line in Fig. 7 shows the detector response
after correcting for shower losses. It is linear for
deposited energies of up to 150 MeV
103
Dump
Electron
Fig. 4. Igloo and the tagger in Experimental
lCfSII4
Area
2
Area 2.
Fig. 8 shows the time resolution between the photon
tagger and the lead glass counter. using a constant
fraction discriminator on the lead glass counter. The
width of the coincidence peak is 2.4 ns FWHM. Fig. 9
is a scatter plot of the pulse height of the lead glass
counter vs. the timing shown in Fig. 8. The lead glass
counter has a significant timing jitter at low pulse
heights. but other than that there is no pulse height
J.M. Vogt et al. I Nucl. Insir. and Meth. in PhJas. Res. A 366 (199-f) lOt-114
FWHM = 2.4 ns
hk;yk
ShieldingJ
Fig. 5. Lead
~PhotamuItipJier
glass counter
assembly.
Tagger TDC (ns)
Fig. 8. Timing spectrum
between
lead glass counters in a test run
2
600
3
500
5
400
2
300
the tagger
..
.. . .
........
800 -
:‘.:
~..,I,.,I...I.,.I...I...I...I...I
‘0
20
40
60
100
80
120
140
and one of the
.
. .
160
EY WV)
Fig. 6. Pulse height
the photon energy.
of the prototype
counter
as a function
of
.
dependence
of the timing. Fig. 10 shows the time
resolution between the tagger and one of the lead
glass counters in an actual experiment. The random
background here is due to the fact that the tagged
photon beam is not impinging directly into the lead
glass counter, and also the count rate in the tagger is
typically 3 to 4 orders of magnitude higher than in Fig.
signal-to-noise ratio is impacted by the width of
20
’
*.
30
40
50
Tagger TDC (ns)
Fig. 9. Pulse height as a function of the timing between the
tagger and one of the lead glass blocks using a constant
fraction discriminator.
800 700 600 500 400 300 200 100 III.II..ll,.I.I.I...JII.I..
‘0
20
40
60
80
100
120
140
E, (MeV)
Fig. 7. Pulse height
(dashed
line) using
phototubes.
Detector
leakage (solid line).
as a function
of the photon
amplifiers
and a lower gain
response
corrected
for the
energy
in the
shower
Tagger
TDC (ns)
Fig. 10. Timing spectrum between the tagger
lead glass counters in a real experiment.
and one of the
J.M. Vogt et al. I Nucl. Ins&. and Meth. in Phys. Res. A 346 (199s)
100-114
10s
the coincidence peak and poses one of the practical
limits to the count rate that Igloo can achieve (see
Section 8).
4. The Electronics
Fig. 11 shows the circuit diagram of the electronics
for each channel and for the trigger definition. The
analog signals of each counter are amplified by a fixed
factor of 10 in LeCroy 612A amplifiers. Two of the
downstream end guard-blocks have two photomultipliers each. However, due to the slow rise time of the
phototubes it was possible to tie their anodes together
without causing any ringing. These counters are subsequently wired up like all the other counters.
One amplifier output is delayed, attenuated by a
factor of 3 and connected to a LeCroy 2249A charge
integrating ADC. The other output is connected to a
EG&G CFSOOO constant fraction discriminator. The
discriminator thresholds are set to 40 mV which corresponds to a deposited energy of 10MeV in the lead
glass blocks. The ECL outputs of the discriminators
are connected to LeCroy 4434 scalers and LeCroy
2277 pipeline TDCs which are daisy chained (the input
terminators of the scalers are removed). The TDCs
are run in common stop mode to avoid delaying the
input signals. All 68 channels are wired up in this
fashion.
The discriminator OR-outputs are used to generate
the trigger signals. There are 12 discriminator modules
corresponding to the 12 rows of counters in Igloo as
shown in Fig. 12. The upstream end guard-blocks are
Fig. 11. Simplified
circuit
\-!YkZE
Wall 4
Fig. 12. The rows and the walls of Igloo
included in rows 2, 5, 8, 11, the downstream guardblocks are included in rows 3, 6, 9. 12. Each discriminator OR-signal is the OR of all counters in that
row. The 12 row signals are ORed into four “wall”
signals (l-3, 4-6, 7-9, 10-12). The trigger definition
during a (-r, 7~“) experiment requires any two of the
four walls to fire. This signal is sent to the tagger
electronics as the X-trigger [2].
The tagger generates the interrupts to the data
acquisition system. The tagger inhibit signal is used to
inhibit the scalers. The tagger X-reference signal is
used as the common stop for the TDCs and to gate the
ADCs. However, a stand-alone interrupt system is
diagram
of the Igloo electronics.
106
J.M.
Vogt et al.
I Nucl. Instr.
and Meih.
included in the Igloo electronics for testing, which
then provides scaler inhibits, ADC gates and TDC
stops as well as generating the CAMAC LAMS.
5. Energy calibration
and gain tracking
All lead glass counters were calibrated individually
with a tagged photon beam. During these calibration
runs the counters were connected to the same channels of the electronics as in the final Igloo configuration. The high voltage was adjusted so that the peak of
the pulse height distribution would be in the middle of
the ADC spectrum for 100 MeV photons. Spectra such
as displayed in Figs. 7-9 were obtained for all counters. In addition, the energy resolution of each counter
was determined as a function of the photon energy
(Fig. 13).
The counters were installed in the Igloo detector
frame immediately after their calibration. This was
followed by a cosmic ray calibration run of about 12 h.
An equivalent cosmic energy deposit was calculated
for each counter from its average cosmic ray peak
position and its in-beam calibration. This “reference
energy” provided the benchmark
for future gain
monitoring.
The procedure for determining
the cosmic peak
position, also used for tracking the gains of the
counters during experimental runs, is as follows. In
order to define the path of the cosmic rays through
Igloo, counters 1, 4, 7, and 10 (see Fig. 12) in each belt
of lead glass counters are used as cosmic trigger
counters in the software. So called “good cosmics”
spectra are accumulated for each counter if more than
40MeV is deposited in the corresponding
trigger
counters. If counters 1 and 4 fire, the “good cosmics”
spectra are incremented for counters 1, 2, 3, and 4. If
counters 4 and 7 fire, the “good cosmics” spectra are
incremented for counters 5 and 6. The same principle
is followed for counters 7 through 12. Thus, only
20
40
60
80
100 120 140 160 180
E, (MeV)
Fig. 13. Energy resolution
a function of the photon
of one of the lead glass counters
energy.
as
in Phw
Rcs. A .766 (199.c)
100
114
cosmic rays that hit all blocks sideways are used for
defining the reference energy and for gain monitoring.
Conversely. a hit along the length of a block deposits
too much energy and causes the ADC to overflow.
Igloo has to be in closed mode to do a complete
cosmic ray calibration, otherwise there is a gap between counters 6 and 7 as well as between counters 1
and 12. Valid “good cosmics” spectra can still be
acquired for counters 1-4 and 7-10 in each belt when
Igloo is open. To calibrate the guard-blocks at the
ends of Igloo, opposing blocks are used in coincidence.
At the beginning and at the end of each experimental run period, a 12 h cosmic run is taken to update the
gain coefficients of the counters. This can be done with
Igloo interfaced to the tagger or in stand-alone mode.
However, note that the cosmic ray hits that satisfy the
“good cosmics” cuts will always satisfy the trigger
definition: “any two walls out of the four”. It is
therefore possible to use cosmics for gain tracking
during an experiment as long as Igloo is closed. This
can be done by examining the cosmic events that occur
in random coincidence with the tagger during the
hardware coincidence resolving time of 50 ns (typically
50% of them), or by accepting each X-trigger from
Igloo as an interrupt. To establish the gains for each
counter, the reference energy of this counter is divided
by its cosmic ray peak position.
6. Photon recognition and calorimetry
One of the first steps in the data analysis is to
process the information read from Igloo in a photon
recognition algorithm which determines how many
photons were detected in Igloo during a particular
event, calculates their energies and assigns each
photon to the lead glass counter in Igloo which it most
likely hit.
In order to calculate the calorimetry information for
an event, the ADC values of the 68 counters are
converted into deposited energies in MeV. The algorithm then finds the counter with the highest deposited
energy. Using a map of the counter arrangement in
Igloo, the deposited energies of all adjacent counters
are added, provided each is clearly above the pedestal
(i.e. greater than 1 MeV). All those counters are then
removed from the list and the process is repeated until
the calorimetry has been calculated for all photons
that were detected.
Most photons deposit energy in more than one
counter. To obtain correct angular information, it is
necessary to determine which block was originally hit.
As illustrated by photon A in Fig. 2, the counter that
was originally hit does not have to be the one with the
highest deposited energy. A better approach than
choosing the counter with the highest deposited
J.M. Vogt et al.
I Nucl. Instr. und Meth. in Phys. Res. A 366 (1995) IO&114
energy is to assign the photon to the counter closest to
the target among those that detected some of its
shower energy. On the other hand. in the case of
photon B in Fig. 2, a small amount of shower energy
can leak back into the counter closer to the target. We
found that the best compromise is to assign the photon
to the counter closest to the target in which more than
7 MeV of shower energy were deposited. This is true
for all photons that are detected anywhere in Igloo.
But if. according to that algorithm, the photon is
assigned to one of the end guard-blocks, it is discarded
in the subsequent analysis.
7. Computer
simulations
7.1. Description
of the detector
of the Monte
Carlo code
The general response of Igloo, including the pion
detection efficiency and angular resolution. has been
evaluated by Monte Carlo simulation. Since caiculational speed and flexibility are essential in our application, the simulation code employs simple ray tracing of
the photon trajectories together with geometric constraints imposed by the detector lattice. The complete
detector has also been modelled in the shower code
GEANT in order to provide certain calibration benchmarks. However, the requisite computing time limits
the usefulness of the GEANT model in the analysis of
experimental data.
The simulation begins by creating a pion in the
y-nuclear center of mass frame for a given incident
photon energy. using a Monte Carlo method to choose
the 7~”direction in accordance with a specified angular
distribution. One then Lorentz transforms to the 7~”
rest frame where the back-to-back decay photons are
emitted with a random orientation. Finally, a Lorentz
boost carries the photons to the lab frame. A valid
event requires both photons to intercept any two walls
(except the same wall) of the detector. The energy
resolution of the lead glass is embodied by randomizing each photon energy about its true value using a
gaussian distribution whose width is determined by the
actual in-beam calibration of the glass blocks, as
typified in Fig. 13. A threshold of 10 MeV is placed on
each resulting energy to imitate the actual discriminator thresholds used to define a trigger.
The model described so far assumes a 100% photon
detection efficiency in the entire active volume of
Igloo. In reality, however, it is necessary to take into
account the photon shower-conversion
probability.
This has three important
consequences.
First, it
modifies the effective length of Igloo along the zdirection since event C in Fig. 2 will be rejected in the
data analysis. Second, it can shift photon “hits” to the
wrong detector block, depending on how the shower
107
propagates among adjacent blocks. Finally, there is a
small but finite probability that the photon can “punch
through” the active volume of Igloo and escape
detection.
The conversion efficiencies are incorporated
by
means of a look-up table which was calculated as a
function of glass thickness for three photon energies,
40, 70 and 100 MeV, using the shower code GEANT.
In application, the appropriate path length of a photon
in the glass is estimated using elementary geometry,
and the appropriate conversion efficiency is obtained
from the table by linear interpolation in energy and
path length. A conventional random number procedure subsequently accepts or rejects the photon. as
determined by the conversion probability above 710 MeV.
In order to obtain IT” detection efficiencies which
are reliable to l-2%,
it is necessary to properly
incorporate the physical dimensions of the lattice at
the level of a few millimeters. especially in the spacing
of opposing walls. The gaps between adjacent blocks
(about 9 mm) affect the efficiency at the 1% level and
are included. The position and physical extent of the
target are also taken into account in the Monte Carlo
simulations.
As noted, the paramount feature of our simulation
code, as compared to the more realistic GEANT
calculations, lies in its ability to process events rapidly
(10” pions require only a few minutes) permitting one
to quickly explore the effects of differing initial conditions. as well as assemble a multitude of histograms
such as missing-mass distributions, opening-angle distributions. and pion-detection efficiency as a function
of pion angle, to mention only a few applications.
The practical utility of the code of course depends
on how it fares in comparison to the GEANT simulations, especially with respect to the photon detection
efficiency. Consider, by way of example. Igloo in the
closed mode (for total cross section measurements),
with a point source of isotropic photons situated at the
center of the detector. For photon energies between
30 and 110 MeV. the photon detection efficiencies from
the Monte Carlo simulation agreed with the GEANT
predictions to better than 1% in relative magnitude.
The comparison
is equally favourable
when the
photon source is shifted 10 cm along the detector axis.
In the open mode, the Monte Carlo values are about
l-3% low of the GEANT predictions. depending on
the photon energy and source position. In view of the
complexity of the Igloo geometry. especially in the
open mode, these comparisons are acceptable.
7.2. Igloo pion detection efficiency
The results described in this section have been
calculated for the reaction 12C(y, a”)“C. The carbon
J.M. Vogt et al. I Nucl. ltzstr. atd Melh. in Phw. Res. A .766 (lY9.T) lOO-11-I
108
target is 12.7mm thick and 30mm in effective diameter as determined by the photon beam size and is
situated in the center of Igloo. This corresponds to the
geometry used in the actual performance tests described later.
For ‘*C the differential cross section in the y-nuclear cm frame is, to a good approximation, proportional to the quantity F’(Q) sin’@f where 0: is the
pion angle and F’(Q) is a nuclear factor which tends
to shift the angular distribution forward of the 90”
maximum. (Further details on the cross section are
given in Ref. [4].) The T” detection efficiency within
30 MeV of threshold (135.8 MeV) and with Igloo in the
closed mode is illustrated by the solid curve in Fig. 14.
The rapid decrease as one moves away from threshold
is simply reflecting the rapidly decreasing minimum
opening angle between the decay photons; at threshold they are back-to-back in the cm frame. For single
photons, the spectrometer subtends about 0.86 of the
47~ solid angle when the “soft edges” at the ends are
included.
Let us consider how the detection efficiency is
influenced by the pion angular distribution. As an
extreme alternative to the sin’Bz distribution. consider
the detection efficiency for pions emitted isotopically
in the y-nuclear cm frame, shown as the dashed curve
in Fig. 14. The divergence between the two curves
reflects the different degrees to which photons escape
through the open apertures of Igloo, as governed by
the differences in the pion angular distributions. The
significant point here is that the detection efficiency is
not a strong function of the angular distribution. In
other words, the total (y, v”> cross section deduced
from Igloo is not unduly compromised by the incomplete 4~ coverage and the presumably-unknown
angular distributions encountered in other measurements.
‘H( y. rr”) for example.
Information on pion angular distributions is gained
by reconfiguring Igloo to the open mode. as shown in
Fig. 1. Each arm is retracted 424 mm, which means the
perpendicular distance between opposing walls is now
about 1020mm. The pion detection efficiency for “C
is of course now somewhat reduced, spanning the
range E = 28-10% over the incident photon energy
range E, = 136-165 MeV In fact, the retraction of
424mm was chosen as a compromise between a
rapidly decreasing detection efficiency versus improvement in the pion angular resolution. The angular
resolution will be described later.
In the open mode, the overall pion detection efficiencies for the sin’0: versus isotropic distributions
are slightly more divergent than the results portrayed
in Fig. 14. but even at EY = 16.5MeV they are within
5% of each other. However, the angular (i.e. 0,“)
dependence
of the efficiencies becomes more enhanced with increasing E., as illustrated in Fig. 15. The
apparent contradiction
between the angular dependence of the detection efficiency on the one hand, and
the relative insensitivity of the gross efficiency to the
160
5-
7t’
35
I
I
140
145
I
1
150 155
Ey (MeV)
,
I
I
160
165
170
0’0
TARGET : CARBON
’
20
’
40
’
’
60
80
0;
Fig. 14. Total rr” detection
efficiency as a function
of the
incident photon energy ET, for Igloo in the closed mode. The
target is a carbon disk situated
in the center of the spectrometer.
The solid curve is based on the physical angular
distribution
which is proportional
to sin’0:. For comparison,
the dashed curve derives from an isotropic pion distribution.
’
100
I
I
!
120
140
160
180
(de@
Fig. 15. Angular dependence
of the pion detection
efficiencies for Igloo in the open mode, for a carbon target situated
in the center of the spectrometer.
These results are independent
of the actual pion angular distribution.
The angle
03 is the pion polar angle in the y-nuclear
cm frame.
J.M. Vogt et al. I Nucl. Instr. and Meth. in Phys. Res. A 366 (1995)
two angular distributions on the other hand, is resolved when one realizes that P” spectrometers of this
geometry directly yield de/de,*, not dcAd(cos 13:) (i.e.
not the physical cross section da/da:).
The sine,*
factor relating these quantities effectively “damps out”
the pion population at the extreme angles in du/dez,
precisely where the detection efficiency is lowest (Fig.
15). Note that the sin 19: factor is not intrinsically
contained in our definition of the pion detection
efficiency, so the results in Fig. 15 apply to any pion
angular distribution. In the closed mode, the angular
variations of the efficiencies are much milder than this,
as one might expect.
For very light target nuclei, recoil effects cause the
efficiencies shown in Fig. 15 to become skewed with
respect to 0: = 90” (cm). Symmetry is restored by
shifting the target position upstream with respect to
the incident photons. Thus for hydrogen, the target
center is situated 100 mm from the geometric center of
Igloo.
P,* = P, )
7.3. Pion angular resolution (open mode)
tan 0: = [Pl + P~]“‘lP~
The cm pion angles 0: and cp,* are reconstructed
from the measured n” decay photon energies E,,, and
their respective laboratory angles 0, ,Z and (p,,: as
defined with respect to the target center. There are
several ways of doing this, depending on the particular
weight one wishes to give the individual photon
parameters, and we refer the reader to Ref. [5] for a
review of the various options. The particular algorithm
we employ here strikes a balance between the limited
resolutions in photon energy and angle as measured by
Igloo in the sense that each contributes
roughly
equally to the reconstructed pion angular resolution.
The photon angles 0, and p, are defined only to
within the finite angular domains subtended by the
square faces of the PbG blocks. Therefore, each
photon is assigned angular coordinates within these
domains by choosing ‘p and cos e,, with uniform
probability, between the corresponding
angular extremes defined by the appropriate block. The alternative is to place each photon dead-center of the block
face, but this yields a discontinuous structure in the
reconstructed distributions due the large facial dimensions of the blocks.
The pion angles are deduced as follows. In the
laboratory frame the Cartesian components of the
pion momentum are given by
P., = E, sin 0, cos ‘p, + E, sin 0,
Pf = P,
(2)
PT =+;
‘
where
The incident photon energy in the lab frame is E,, and
M is the target nuclear mass (we employ c = 1). The
pion total energy in the cm frame is given by
E:=
W2fm”
2;
-M’
.
where
W’ = 2EYM + M2
describes the invariant mass. Finally, the pion angles in
the cm frame are reconstructed using the expressions
,
(3)
tan cp,*= P?lP, .
(4)
Only Eq. (3) is of interest for the present application.
The angular response following from Eq. (3) has
been investigated using the Monte Carlo simulation.
The reconstructed O,* distributions for pions emitted
with unique values of 0: (but arbitrary cpz) exhibit
roughly gaussian shapes. The half-widths rFWHM,
which are a measure of the angular resolution, are
displayed in Table 1 as a function of the incident
photon energy EY for some representative
initial
angles S_*. Two features of I&,,
are of note here:
the resolution is relatively insensitive to S,*, and the
resolution improves quickly as one moves away from
threshold (135.8 MeV for ‘*C). The latter effect can be
traced to the increasing asymmetry in E, versus Ez
away from threshold. However, the angular depenTable 1
The angular resolution of Igloo in the open mode, as deduced
by Monte Carlo simulation.
The resolution
is defined as the
half-width
f,,,,,
(degrees) of the distribution
function of 02
as given by Eq. (4a). for specific values of the emitted pion
angle 0: (but arbitrary
~05). The target is “C whose n”threshold is EI = 135.8 MeV, where EY is the incident photon
energy in the lab frame
cos cpz
Pv = E, sin 0, sin ‘p, + E, sin e2 sin q2
P_ = E, cos e,
109
100-114
+ Ez cos e, .
A Lorentz transformation to the y-nuclear
indicated by asterisks, gives
20
50
90
130
160
140
45”
1.50
160
170
29”
22”
20”
45”
28”
24”
22”
48”
32”
28”
27”
46”
29
23”
21”
45”
27”
23”
19”
(1)
cm frame,
110
J.M. Vogt et
al.
I Nd.
lmtr.
md
Mrth.
dence of I;-WHM is a more subtle phenomenon and
requires comment. From the Monte Carlo simulations
one may readily discover how c,v,,, is influenced by
the uncertainties in the photon energies E, as returned
by Igloo, as well as the corresponding uncertainties in
the lab angles 0, and ‘p. The results are as follows:
1) The resolutions in E, and cp,have little influence
on I&+, at 0: = 90” but both display increasing
influence as the extremes in 0: are approached.
2) The resolution in 0, has a profound influence in
r FWHM at 0: = 90” and least influence at the
extremes in 0:.
The uncertainties in E,, 0, and ‘p are such that these
two opposing trends tend to complement each other
across the whole angular range of 6:.
7.4. Pion angular distribution (open mode)
Finally. we address the pion angular distribution
measurements. specifically how to recover information
on the differential cross section da/da,*
in the 7~nuclear cm frame. Given the limits on energy and
angular resolution, one cannot expect to reconstruct
an accurate representation of da/do,* in the threshold
region without resorting to a complicated deconvolution procedure. Instead, we will rely on the Monte
Carlo code to provide a replication of the observed
Igloo response by optimizing the input-model angular
distribution. Comparison with the data is made on two
levels: through the reconstructed
angle 0,*, and
through the *‘belt-hit” patterns.
For purposes of illustration, let us suppose the cross
section of interest can be expressed as
in P/IJ.\.
Res. A 366 (lYY_i)
100-11-l
First. consider the cross section as given by the Hz
reconstruction
algorithm Eq. (3) and converted to
du/dS2:.
The reconstructed
partial cross sections
corresponding to the A, B and C terms of Eq. (5) are
displayed in Fig. 16. No efficiency corrections have
been applied to these simulations. so each curve
represents the convolution of the input cross section
with the angular resolution and the angular efficiency.
The input cross sections are portrayed by the dashed
curves. Each simulation has been renormalized to the
same total cross section as given by the dashed curves.
Ultimately, it is the coefficients A, B and C that one
wishes to extract from the experimental
data. In
principle this could be accomplished by treating each
simulation in Fig. 16 as a “template”.
One then
weights each template by the appropriate coefficient
A-C until a fit to the experimental data over a small
energy region is achieved. In practice one must fit
1.5
I
1
0.5
II
1.5 -
B=l
k da
--=AAB(l-cos8,*)+Csin’B,*,
9 da,*
where A, B and C are constants for a given energy.
This expression is appropriate
for describing the
reaction ‘H(y, 7~“). and in fact we will use this particular reaction as our model since it represents a
worst case scenario because of recoil effects. Writing
the cross section in the above rather unconventional
form has the advantage that, for hydrogen, all three
coefficients are positive at low energy. Thus Eq. (5)
can be considered as the sum of three positive-definite
cross-section components which greatly simplifies the
analysis.
Let us now examine the Igloo response to each
component of Eq. (5). The “target” cell will be
assumed 100mm in length, 30mm in effective diameter, and is shifted 100 mm upstream from the center
of the spectrometer. In order to display a “typical”
response (i.e. neither the best nor worst), we will
assume an energy 5 MeV above v5’ threshold, which for
hydrogen corresponds to E, = 149.67 MeV
o.5c
/
o//’
0
20
\
”
40
60
’
80
6;
’
’
I
’
‘._
100 120 140 160 160
Ws)
Fig. 16. Simulated
reconstructions
of the three components
of the cross section Eq. (5). for ‘H(r, a”) at an energy 5 MeV
above threshold
with Igloo in the open mode. The reconstruction algorithm
is defined by Eqs. (l)-(3).
The angle 0;
is the pion polar angle in the y-nuclear cm frame. The dashed
curves describe the “input” to the Monte Carlo code used to
simulate
the “data“.
while the solid lines are the reconstructed
results. normalized
to the total “input”
cross sections. No detection
efficiency corrections
have been applied
to the solid lines.
J.M. Vogt et al. I Nucl. Imtr.
and Meth. in Phys. Res. A 366 (199-T) 100-114
several energies simultaneously
to maintain energy
continuity in the coefficients, but that is beyond the
scope of the present article.
The second method for retrieving information on
da/da_*, which requires no 0: reconstruction at all. is
based on “belt-hit” patterns. Through a series of
coplanar cuts made perpendicular to z-axis, one can
conceptually dissect the active volume of Igloo into a
set of five square rings or belts. These belts are
situated side by side, and each consists of eight active
PbG blocks and four corner guard-blocks. In the open
mode these belts naturally contain dead sections, but
the concept remains intact.
The method relies on the fact that the relative
distribution of photon hits across the five belts is a
function of the pion angular distribution du/dnz.
To
illustrate, we again turn to the model cross section Eq.
(5), with the same target geometry as before, and
again observed 5 MeV above threshold. Let us consider the cross section under two extreme physical
situations. S-wave dominance and P-wave dominance:
a) S-wave dominance: A = 0,B = 1,C = 0.
b) P-wave dominance: A = 1,B = 0,C = 1S.
The corresponding distributions of belt-hits for these
two cases, in the open mode of Igloo, are displayed in
Fig. 17. We discern from this figure our ability to
distinguish between symmetric and highly asymmetric
cross sections, realizing that these indeed represent
physical extremes and that physical reality would lie
somewhere in between. Nevertheless,
there is a
0.8 -
0.6 -
0.4 -
I
L
A-
(4
Om2- i
Fig. 17. Simulated
belt hit patterns
for ‘H(y, n”) based on
Eq. (5). evaluated
5 MeV above threshold
with Igloo in the
open mode. Pattern (a) represents
the extremely
asymmetric
pion angular
distribution
given when A = 0, B = 1, C = 0,
while pattern (b) reflects the symmetric
pion distribution
for
A = 1, B = 0, C = 1.5. In both patterns, the forward belt is the
left-most bin.
111
statistical advantage in this method in that all events
are distributed over only five bins, and furthermore
since no reconstruction
is involved, the measured
photon energies E,,,play no direct role.
Finally, we will complete this discussion of belt-hit
patterns on a technical note. For the method to be
reliable, it is clearly important that the simulation code
replicates the actual behavior of Igloo in situations
where the initial shower in a given belt is subthreshold. in which case the photon hit might then be
subscribed to the adjacent belt. The net effect is to
transfer events outward, away from the target, to the
outermost belts. This problem was previously alluded
to in Section 7.1. The simulation code incorporates this
leakage by resorting to the same conversion efficiency
look-up table described therein, and employs a similar
algorithm. Note that photons can be “lost” only to the
extreme outer belts, otherwise they are simply transferred to the next-outermost belt. The transfer effect is
not negligible, for example it can increase the population of the outer belts by 10% or more. The algorithm
has proved to be reliable, as will be demonstrated
when we discuss the spectrometer performance test.
8. The commissioning
experiment
The commission of Igloo was made using the reaction “C(y, n”) with an end-point energy of 206 MeV
We chose this target for two reasons. First, there is an
ample supply of total cross section data in the literature which provides a check on detection efficiencv.
Second, the pion angular distribution can be predicted
reliably at low energy and this provides a mechanism
for gauging the angular response of the spectrometer.
We report here some preliminary results of the commissioning runs.
The photon tagging rate for these runs was about
100 kHz per tagger channel, or about 200 kHz per
MeV of tagged photon energy. This modest rate was
not limited by the singles rates in the tagger detectors,
nor by the trigger rate from Igloo, but rather by
random coincidences with the copious number of
untagged pions due to the high end-point energy of
the bremsstrahlung. With the installation of a new
“end-point” tagger at SAL in the near future, the pion
background should be further reduced because of the
associated reduction in the bremsstrahlung end-point
energy. Since the n” spectrometer employs no charged
particle veto counters, another major source of background derives from efem pair production in the
target, followed by large-angle rescattering within the
target material. The random rate was exacerbated by
the poor timing stability of the Igloo PMTs and the
resulting compromise in coincidence resolving time.
These backgrounds are a particular nuisance close
J.M. Vogt et al. I Nucl. Instr. and Meth. in Phw. Res. A .166(199-T)lOC11-1
112
the pion threshold, where the cross sections are
quite small. To deal with this problem we have devised
a software technique we call “masking” which eliminates much of the background. It is most effective in
the threshold region, precisely where needed. It is also
most effective when Igloo is closed. Actually, the
background is substantially reduced in the open mode
in any case.
The technique is based on the fact that the angular
correlation between the decay photons becomes more
tightly constrained as the pion energy decreases, and
this reduces the available “phase space” for a background event that otherwise could pass as a legitimate
event. Using the Monte Carlo simulation code, we
compile a list of all combinations of detector pairs
which fire in a simulated photopion run of several
million pions. This is repeated for each tagged photon
energy (typically 50-60 values), and for each target.
From this we extract all pair combinations that did not
fire, and these form the “masks” for background
rejection in an actual Igloo run. Thus, any event that
triggers a detector pair in the null-hit region of the
masks is rejected, and this is done on a channel-bychannel basis of the photon tagger detector array, i.e.
for each tagged photon energy.
Because of the statistical nature of the maskgenerating procedure, there is always the possibility
that certain block combinations, which are accessible
to
3
t
t
=2
Ri
T
aJ
‘5
1
0
130
l*,*(1***1)
’
photon pairs but with very small probability. receive
no hits in the Monte Carlo simulation and are assigned
to the null-hit region of the mask. This in turn could
lead to the rejection of legitimate pions. In order to
reduce the chances of such an occurrence, we compute
each mask 2MeV above the actual tagged photon
energy, in effect reducing the number of null-hit
patterns in the thinly populated regions. Of course. the
price of this extra caution is an increase in the amount
of background permitted to slip through the masks.
Fig. 18 demonstrates the effectiveness of the background rejection technique, showing the raw yield
curves within 10MeV of threshold, uncorrected for
detection efficiencies, etc. The upper and lower curves
represent the data without masking and with masking,
respectively. A direct measure of the background
contamination
can be seen in the region below n”
threshold, and here the masking has reduced the
background to about l/7 of its original strength.
As one moves to higher energies above threshold,
the background rejection gradually becomes less effective, as is evident from Fig. 18. This simply reflects the
increase in the available “phase space” for legitimate
n” events and therefore a corresponding reduction in
the null-hit patterns. Thus, unlike the unmasked situation, the residual target related background under the
yield curve will now display an energy dependence.
This dependence is readily deduced from the difference between the unmasked and masked data, together with the knowledge that the unmasked background is flat.
In Fig. 19 we compare the total cross section for
“C(y,n”),
measured with Igloo in the closed mode,
with a montage of available data from Mainz and
Saclay (references are given in Ref. [4]). The visual
agreement indicates that Igloo is operating according
to expectations; in particular, the pion detection efficiencies from the Monte Carlo simulations are reliable.
Turning to the open mode configuration, which tests
the angular response, there are two quantities to be
considered, the invariant-mass
distribution
and the
belt-hit patterns.
The invariant-mass
distribution
reconstructs
the
pion mass according to the general relation
to
t
tt+,
,
,
Ey
,
,
140
135
,
,
,
m,
,
=
[2E,&(l
- cos @Ycy)]l”
14!
WV
Fig. 18. Preliminary
yield curves
for “C(y,n”)
within
10 MeV of threshold,
demonstrating
background
rejection
using the software
“masks”
as described
in the text. The
upper data are the raw yields, while the lower data have been
masked.
Threshold
is E, = 135.8 MeV. Near threshold,
the
procedure
reduces the background
by roughly a factor of 7.
These data were taken with Igloo in the closed mode.
where GY.,is the opening angle between the rr” decay
photons, and E,, are the photon energies, This relation is useful because it incorporates all the measured
quantities in a single quality factor, namely the
FWHM of the distribution r_. To give an example, for
EY = 160 MeV we obtain
r (Igloo) = 47 MeV ,
J.M. Vogt et al. I Nucl. Instr. and Meth. in Phys. Res. A 366 (1995) 100-114
175
while the Monte Carlo simulation
I
I
I
I
1
113
predicts
Tm(M. Carlo) = 44 meV,
150
in satisfactory agreement.
As noted in Section 7.4, the belt hit patterns do not
rely on the measured energies El,? to give information
on the pion angular distribution, but they do rely on a
correct understanding
of the “shower leakage” phenomenon which can adversely effect the distribution.
In Fig. 20 we compare the observed pattern for
“C(y. n”) at E, = 160 MeV (solid line) with the simulated pattern (dashed line), normalized to the same
total number of events. The model cross section
includes excitation of the 4.43 MeV state of “C in the
manner described in Ref. [4]. This comparison, while
preliminary,
is further confirmation
that Igloo is
operating according to design.
i
125
9$LgwQm
i
I
4
140
145
9. Conclusion
I
I
I
150
155
160
16!5
Ey We’4
Fig. 19. Total cross section for ‘*C(y, P”). Solid circles are
the present
results. Open squares
are a montage
of four
measurements
from Saclay and Mainz, as cited in Ref. [4].
I
I
I
I
I
I
__I
Fig. 20. Belt hit patterns for “C(y. PO) at E, = 160 MeV with
Igloo in the open mode. The solid line is the experimental
pattern, where the vertical bars indicate the statistical errors
for each belt. The dashed line is the Monte Carlo prediction,
normalized
to the same total number of events. The contribution of the 4.43 MeV (2’) state has been included
in the
simulation
with strength
as deduced
in Ref. [4]. Note the
distinction
between these patterns and those of Fig. 17.
A large-acceptance
m” spectrometer, for taggedphoton measurements of nuclear photoproduction, has
been constructed and commissioned. The instrument
was designed to permit both total and differential
cross section measurements
in the low excitation
region, roughly O-25 MeV above threshold.
The pion detection efficiency, as well as the angular
and energy resolutions,
have been studied using
Monte Carlo simulations based on a carefully modelled description of the spectrometer.
Preliminary
analysis of the commission of “C(y, -‘I) confirm the
predicted efficiencies and energy resolution, while the
belt-hit patterns have demonstrated the required angular sensitivity for future differential cross section
measurements.
Background from high energy (untagged) pions and
genuinely tagged e+e- pairs are evident in the experimental data. In lieu of veto counters, the chargedparticle background was rejected in software by means
of Monte Carlo generated “masks”. While this rejected much of the background, there is still room for
improvement, particularly with respect to the untagged pion background. This situation should improve
with the installation of the “end-point” tagging spectrometer in the near future.
Acknowledgement
We gratefully acknowledge the support given this
project by Professor Ed Booth of Boston University,
whose material assistance was instrumental
to its
successful completion.
This work was supported in part by the Natural
Sciences
Canada.
and
Engineering
Research
Council
of
[Z] J.M. Vogt et al.. Nucl. Instr. and Mcth. A324 ( 1993) IYX
[3] C.R. Wuest et al.. Nucl. Instr. and Meth. A239 (19X5) 467.
[4] J.C. Bergstrom.
Phys. Rev. C50 (1991) 2979.
1-51 H. Strciher et al., Nucl. Instr. and Meth. A269 (1988) 56X
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