Elastic Compton Scattering from Deuterium at 40-110 MeV
The Compton@MAXlab Collaboration:
The University of Glasgow, Glasgow, Scotland
Contact: John R. M. Annand, [email protected]
The University of Göttingen, Göttingen, Germany
Contact: Martin Schumacher, [email protected]
The University of Illinois, Urbana-Champaign, Illinois, USA
Contact: Alan Nathan, [email protected]
The University of Kentucky, Lexington, Kentucky, USA
Contact: Michael A. Kovash, [email protected]
The University of Lund, Lund, Sweden
Contact: Bent Schröder, [email protected]
The Mount Allison University, Sackville, New Brunswick, Canada
Contact: David Hornidge, [email protected]
The University of Saskatchewan, Saskatoon, Saskatchewan, Canada
Contact: Rob Pywell, [email protected]
The George Washington University, Washington DC, USA
Contact: Gerald Feldman, [email protected]
Corresponding Authors: Gerald Feldman and Michael A. Kovash
We propose to significantly increase the world data set for elastic compton scattering on the
deuteron with the goal of extracting the neutron polarizabilities, and . Using a tagged beam
in the energy range from 40 to 110 MeV, scattered photons will be simultaneously detected in
three very large NaI spectrometers covering the angular range from 30 to 150 . Projected statistical errors on the measured differential cross sections are . The expanded energy and
angular coverage of these new data will provide significant constraints on the reaction models used
to extract the polarizabilities. We request a total of three 4-week running periods to complete these
measurements.
Submitted 5 November 2004
1
Introduction
The polarizability of the nucleon is a measure of its response to an applied electromagnetic field. In
the presence of an external electric field the nucleon acquires an induced electric dipole moment,
where is the electric polarizability. Similarly, in an applied magnetic field a
magnetic dipole moment is induced,
where is the magnetic polarizability. In
the magnetic case, the value of arises from two components, one which is paramagnetic (positive)
and another which is diamagnetic (negative). In the usual way,
derives from the orientation
of existing magnetic moments, while
is due to induced electric currents in opposition to the
externally applied field.
#"!$%
!
Even on the scale of nucleon dimensions, both and are known to be quite small, indicating
a relative ‘stiffness’ of the nucleon to external fields. The exact values of and are quite sensitive to the structure of the nucleon. In a quark model, for example, is most sensitive to the
polarization of the pion cloud surrounding the nucleon core, i.e. it is determined by the excitation
of quark-antiquark states. Conversely, is determined primarily by the valence quarks, and in
particular by the excitation of the resonance, which contributes to the paramagnetic response.
The diamagnetic response is thought to derive from
an asymptotic contribution. Because of the
near cancellation of these two terms the value of is predicted to be smaller than . Clearly, a
precise experimental determination of both and is of high intrinsic interest for testing models
of nucleon structure.
&
Because it is a second-order electromagnetic process, Compton scattering is sensitive to the nucleon polarizabilities in certain kinematic regions. Indeed, the first polarizability measurements
were made on the proton using the Compton process. In general,
the scattering cross sections are
rather low (typically 10 to 20 nb/sr) and the effects of and tend to be small. As a result, precise
data are required.
The first ‘modern’ experiments [1] arrived with the advent of high quality tagged photon beams
with a high duty factor at an energy near E MeV. Equally important was the availability
of NaI spectrometers capable of detecting these relatively high energy photons with good energy
resolution and low backgrounds. Other Compton experiments on the proton include: an earlier
(1975) bremsstrahlung measurement [2] at E from 70 to 110 MeV; a 180 experiment [3] (the
only such data in existence) at 98 and 132 MeV; and a measurement [4] above pion threshold,
extending from 136 to 289 MeV.
'
)(
'
Most recently, the group at Mainz has studied the proton at energies both below (55 - 165 MeV)
[5] and through the region of the resonance (200 - 490 MeV).[6, 7, 8, 9] The results of these
experiments provide both precise values of
and , as well as information on the higher-order
electromagnetic response functions of the proton, such as the backward spin polarizability and the
excitation of M1 and E2 multipoles.
&
*
There are three known methods for determining the neutron polarizabilities: neutron scattering
from high-Z targets, quasielastic Compton scattering from the deuteron, and elastic Compton scattering from the deuteron. A large number of experiments have been done in the field of neutron
scattering over a period of many years.[10, 11] Unfortunately, this process provides information
2
only on the value of , and is not without controversy [12] in determining its value. This is primarily due to the fact that exceedingly precise measurements are required, [13] i.e., the necessary
errors in the scattering data are of the order
. In a 1997 reanalysis of the existing
relevant neutron scattering data, Enik, et al., [14] are able to conclude only that the value of the
neutron’s electric polarizability lies in the range,
& ( Quasielastic photon scattering from deuterium has been studied theoretically to uncover the sensitivities of both the cross section and polarized-photon observables to the proton and neutron
polarizabilities.[15] In addition to the usual quasi-free scattering contributions, the calculations
have also included the effects of final state interactions, meson exchange currents, and isobar
, has been presented, these
currents. Since the triple-differential cross section,
results can be used to determine the most interesting kinematical ranges for coincidence experiments, i.e., those regions where the cross sections are both largest and most sensitive to the nucleon
polarizabilities. It should be noted that the quasielastic calculations for the neutron contribution
present some difficulties. For example, the vanishing neutron Thompson amplitude suppresses
the neutron polarizability contribution, so that this sensitivity first appears at order O(E ) in the
low-energy expansion. In contrast, the proton polarizability contributes at O(E ). Moreover, other
terms of O(E ) appear due to the spin-dependent parts of the scattering amplitude, and these additional terms cannot be evaluated in a model-independent way.[16] The net result is that neutron
polarizabilities extracted from quasielastic data carry model uncertainties of at least 2, even in
the absence of uncertainties in the nuclear environment corrections.
' '
'
'
Recently, the quasielastic reaction has been observed by groups at Mainz and SAL [17]. One set
of Mainz experiments was done in the energy range from 200 to 300 MeV and detected scattered
photons in coincidence with recoil protons [8]; another data set for photon-neutron coincidences
was reported in the range of photon energies from 200 to 400 MeV [18, 19]. One feature of these
data is that the proton polarizabilities from the quasielastic measurements can be compared with
the free-proton values. Pending a favorable comparison of the proton data, the neutron results can
be interpreted with more confidence. Overall, the Mainz results for the neutron are presented with
somewhat poorer statistical precision than those for the proton. A comprehensive review of the
quasielastic measurements appears in [20].
' ((
(
MeV (i.e., in an energy range accessiThe quasielastic n coincidence cross section for E
ble at Lund) has been given in ref. [15]. While the neutron energy spectrum does indeed show a
sensitivity to the value of , it is only for values for which this sensitivity appears. Moreover, the cross sections at this energy are approximately two orders of magnitude smaller than at
the energies previously studied at Mainz. For these reasons we feel that a quasielastic experiment
is not appropriate at Lund at this time.
Elastic Compton scattering from the deuteron offers a relatively unrealized opportunity for extracting the neutron polarizabilities. Here the coherence of both neutron and proton amplitudes leads
All polarizabilities are given in units of 10 fm
3
'
to a significant advantage. Namely, the O(E ) contribution of the neutron polarizability interferes
with the O(1) contribution of the proton’s Thompson amplitude, thus strongly enhancing the neutron polarizability contribution to the cross section. Further, the contribution from the t-channel
exchange diagram is isospin forbidden in d scattering. As a result, the nucleon spin polarizability – which derives largely from this source, and is already an O(E ) correction – is further
suppressed. Of course, it is still necessary to carefully account for two-body currents when interpreting the data. Both meson-exchange currents and meson-exchange seagulls are potentially
important and must be evaluated. One relatively minor complication in interpreting the d elastic
data derives from the fact
experimentsare sensitive only to the isospin-averaged combina that the
tions
and
. However, given the accuracy with which both
and
have been previously determined, the extraction of and is both straightforward and
potentially quite precise.
*
'
Model Calculations
Calculations of the elastic d cross
section below the pion threshold from
ref. [21] are shown in figure 1. These
results include the effects of both oneand two-body currents, and are intended to demonstrate the nucleon
polarizability sensitivity of the angular distribution of cross section. First,
we see that the cross section is rather
low, typically 15 nb/sr between 50
and 100 MeV. The dispersion in the
curves for various values of shows that all of the sensitivity to the
polarizability difference is at backward scattering angles, and that this
sensitivity increases with increasing
energy. At 100 MeV, and at an easily
accessible backward scattering angle,
a variation of by 3 changes
the cross section by about 5-10%. The
forward angle results are insensitive
to , but can be used to de termine the combination ,
which is independently determined
by total photoabsorption cross sec-
Figure 1. Calculated elastic d cross sections from ref. [21].
tion data through the Baldin sum rule.[21, 26]
4
A calculated angular distribution at 20 MeV is shown in figure 2.[21] As is apparent in this figure,
the lower energy cross sections evidence only a minimal sensitivity to the polarizability. This
general behavior of the cross sections – nearly independent of
at both forward angles
and low energies – is systematically observed in all of the model calcuations.[21, 22, 23, 24, 25,
26, 27, 28] As a result, an experiment that spans the energy range from 30 to 110 MeV, and
which includes data at both forward and backward angles, will provide a very stringent test of the
consistency of the models.
Figure 2 Low energy d cross section from ref. [21].
A comparison among these calculations shows that at present a realistic model uncertainty of about
3 should be assigned to a value of derived from an elastic d experiment. Currently, the error
in an extracted value of is probably somewhat smaller. The model error in is dominated by
the 4% variation observed in the calculated cross sections for a variety of NN potential models.
In recent years chiral perturbation theory has been used to study both p and coherent d scattering
up to order O(p ).[27, 28] The deuteron calculation contains two unknown parameters, which are
related to the isoscalar nucleon polarizabilities. In one scenario, the values of these parameters
can be determined by fitting the current data sets from SAL, Illinois, and Lund. Alternately, the
model allows one to predict the sensitivities of the elastic cross section to the polarizability values
in various kinematic regimes.
Such predictions are shown in figure 3 at four photon energies extending
from 55 to 115 MeV.[29]
The solid curves are calculated with the values (
; the dashed curves are with
; and the dotted use the values
. Note that the sum
is held fixed at 15 for these
5
calculations
so as to be consistent with the current Baldin sum rule value, while the difference
has been varied.
Figure 3 O(p ) chiral perturbation theory calculation of d elastic scattering.[29] Solid curves:
; dashed curves: ; dotted curves: .
Current Experimental Results
In the case of the free proton, the global set of low energy Compton experiments has determined
the polarizability difference rather accurately [20, 5],
( ( ( When combined with the polarizability sum as obtained from the Baldin sum rule [26, 20],
( we obtain the proton values
( ( ( ( ( (
6
For the neutron, the overall situation
is not nearly so clear. A compilation of the world data set for elastic d is shown in figure 4. Data
from Lund at 55 and 66 MeV are
shown as solid circles [30]; the open
circles show the energy-extrapolated
results, originally taken at 49 and 69
MeV, from the Illinois experiment [31];
and the open squares give the SAL
results.[32] The error bars shown on
this figure represent the quadratic sum
of statistical and systematic errors.
Overall, generally good agreement
is observed between the Lund and
Illinois data sets. The curves are from
the calculations of ref. [21]: the dashed
line is calculated without polarizabil
=
= 0), the solid line is
ities (
calculated with the values = 10.4
and
= 4.6, and the dotted line
used the values of , from the most recent global averages.
* Figure 4. The present d data set. Solid circles: Lund[30]; Open circles: extrapolated Illinois results[31]; Open squares: SAL results[32].
An analysis of the Illinois data alone using the model of ref. [21] provides the value
This value is not in agreement with the results of the analysis of the 94 MeV SAL data, which finds
the rather different value
It is clearly the two backward angle SAL data points which drive this result. A variety of dispersion
calculations [33, 34, 35] predict the general result
so that one would expect
* 7
(
The current Lund data set at 55 and 66 MeV has similarly been analyzed, extracting the values
( which gives the results for the neutron,
( Agreement is found between the Illinois and Lund neutron results, but not between the Lund and
SAL values.
For comparison, the values of and
extracted from the two most recent quasielastic experiments [17, 18] are in mutual agreement,
( ( but clearly disagree with the analyses of the elastic data. Note also that these results are consistent
with the prediction that .
(
As yet, no theoretical calculation has been able to reproduce the 94 MeV backward-angle elastic
cross sections from SAL. In a recent preprint [36], however, an extension of heavy baryon chiral
pertubation theory – one which explicitly includes the resonance – has been developed for elastic
d scattering. The parameters of the model have been fit to both the 69 and 94 MeV data, and now
show slightly better agreement with the back-angle 94 MeV results. However, the value of /d.o.f.
for the fit remains relatively high – in the range from 2.2 to 3.7, depending upon the number of fit
parameters and the potential model used. The neutron polarizabilities derived from this fit are,
&
(
( These values show good agreement with the measured values of the proton.
Experimental Details
We envision a series of Compton scattering experiments ranging from the maximum energy that is
consistent with the ability to resolve the elastic strength from the deuteron (which would be about
110-120 MeV) down to an energy where polarizability effects play a relatively minor role (about
30-40 MeV). These experiments will be carried out in energy ‘bands’, selected such that each run
will cover a limited range of beam energy. We anticipate a total of three energy bands: 90-110, 6095 and 40-65 MeV. These bands can be adjusted slightly, but they are designed to cover the entire
energy range of interest and to allow some overlap between adjacent energy bands. For the purpose
of calculating a count rate, we discuss the first stage of this series, which is our highest requested
8
energy range, 90-110 MeV. This energy is where the maximum sensitivity to polarizability effects
will occur, and this will also serve as a critical confirmation of the only other high-energy Compton
experiment [32], which was performed in the range 85-105 MeV using a single large energy bin.
In this proposal for the PAC, we are requesting approval of the full amount of time necessary to
complete our program of measurements.
We propose to utilize three large NaI detectors for this Compton scattering experiment. The detectors include the CATS detector from Mainz (48.3 cm diameter by 63.5 cm long), the BUNI detector
from Boston University (49.5 cm diameter by 55.9 cm long) and a new NaI detector recently obtained by the University of Kentucky (60 cm diameter by 50 cm long). All of these detectors
consist of a large central NaI core surrounded by a segmented NaI annulus which serves as an
anti-coincidence shield to veto cosmic-ray events as well as an extension of the core to re-sum
single-escape and double-escape events. The latter helps improve the resolution of these detectors
to a level typically below 2%, which is sufficient (at E MeV) to resolve the elastic Compton
peak in deuterium from the inelastic (breakup) strength that is separated by 2.23 MeV.
'
((
At present, the same liquid deuterium target that was used in an earlier Compton scattering experiment by Lundin et al.[30] resides at Lund, and would be used for the new proposed experiment.
This target has a cylindrical cell of length 16 cm and diameter 4.8 cm fabricated from 125 m thick
Kapton foil.
Another major variable is the geometry of the NaI detectors. We will be able to measure three
angles simultaneously, which is a significant advantage. The practical limitation, however, will
be managing to locate these large NaI detectors fairly close to the target without interfering with
each other. We can of course utilize both sides of the beamline, so one detector can sit by itself,
but invariably the other two detectors will have to be located on the same side of the beamline.
The Kentucky (UK) detector has a very large entrance collimator (25 cm diameter), so it could be
located at a greater distance from the target and still provide a reasonable solid angle. This would
be most helpful at the extreme forward (30 ) and backward angles (150 ), where the detector
shielding cannot overlap with the beamline. In fact, it might even allow for extending the range of
back angles, possibly to
. For measurements at
, one of the other NaI detectors
can be moved considerably closer to the target without interfering with the beamline.
(
(
One possible scenario (as shown in the figures below) is to locate BUNI on one side of the beamline
and the UK and CATS detectors on the other side. This would enable the UK detector to be used
at the extreme angles. In particular,
is arguably the most important angle, since the
sensitivity to
is the greatest there. On the same side, CATS could be used at 60 , as shown in
the left panel, when the UK detector is at the backward angle. The detectors should be sufficiently
separated so as not to interfere with each other. In the next set of angles, as shown in the right
panel, with the UK detector at the forward angle (and pulled back a bit), CATS could be pushed
close to the target to measure at 90 . Hopefully there is sufficient space to arrange the two detectors
in this geometry, where they are somewhat closer to each other. The CATS measurement at 90 would also serve as a reproducibility check of what BUNI had measured on the opposite side of
the beamline at the same angle.
(
9
An estimate of the count rate is discussed below. Average values are used and are intended to
represent (roughly) the count rate in all detectors. There will be some variations due to different
entrance collimators and target-detector distances, but for the most part the estimate below should
apply to the geometry that we expect to be able to achieve in most cases. This is based primarily on
our ability to achieve a solid-angle acceptance of at least 41 msr (see below) for all of the detectors
at any angle.
The count rate in the NaI detector is given by:
' & where
is the differential cross section at angle , ' is the photon beam intensity, is the
is the solid angle. To compute the count rate, we make the following
target thickness, and &
assignments for the various parameters:
( /MeV (taken to be a Lund standard value)
1) photon beam intensity, '
2) differential cross section,
nb/sr (rough average between 30 and 150 )
( cm (
3) target thickness,
x = 16.0 cm
= 0.167 g/cm
N = 6.02 ( (linear thickness of liquid deuterium target)
(density of liquid deuterium)
(Avogadro’s number)
A = 2.0 g/mole (atomic mass of deuterium)
4) solid angle,
& = 41 msr
NaI entrance collimator diameter = 16 cm
NaI distance of front face to target = 70 cm
Using these values in the above expression for the count rate, we obtain a rate of 1.42 counts/hour/MeV.
To increase the statistics, we propose to bin the tagger focal plane into 5 MeV bins, which should
give us 4 separate bins spanning a 20 MeV tagged photon energy range. This results in an overall
10
count rate of 7.1 counts/hour/(5 MeV), which is the foreground count rate used in the backgroundsubtracted estimate below.
For the purpose of estimating the background contribution due to the empty target, we assume that
75% of the yield in the elastic scattering region will be true Compton events from deuterium, and
25% will arise from the target cell walls. This is almost certainly an exaggeration of the possible
background, but using it allows us to get a conservative estimate of the required beamtime. If
we call F the foreground and B the background, and assuming that background running is given
one-half the time of full target running, we see that:
FULL Target Yield = F + B
EMPTY Target Yield = B/2
(F + B)
(B/2)
To obtain the foreground (F) yield, we subtract the normalized EMPTY target runs from the FULL
target runs, obtaining:
(F + B) - 2(B/2) = F
(F + 3B)
=F
(2F)
To obtain 5% statistics after background subtraction, it will be necessary to accumulate 800 foreground (F) counts. Using the count rate obtained above (7.1 counts/hour/bin), this requires 112.7
hours of FULL target running and then 56.3 hours of EMPTY target running (based on our estimate of half the time for EMPTY running). Thus, one set of angles will require 169 hours of
beamtime.
In order to measure a complete angular distribution at 5 angles (30 , 60 , 90 , 120 , and 150 ), we
plan to move the three NaI detectors to the remaining angle settings. With three detectors, this will
give us one repeat angle in the second setting (or, the option for a 6th angle). Based on the time
estimate for one setting calculated above, we see that two settings will require 338 hours (14.1
days) of beam on target for the actual data collection.
Note that if the EMPTY target background ends up being so small as to be able to be (almost) ignored, then the total of 169 hours per angle setting could be entirely used for collecting foreground
counts, which would give us 1200 total counts per detector, resulting in a measurement with 2.9%
statistics in each 5 MeV energy bin. This would reduce the error bar for this measurement by
almost a factor of two compared to the previous work of Hornidge et al. [32] in this energy region,
which is a significant improvement.
The limiting case of zero EMPTY target contribution is probably too optimistic, but the background
estimate in the above paragraphs (leading to our intended 5% level of precision) is also probably
too pessimistic. The truth will likely lie somewhere in between, so in any case, we should be
able to make a noticeable advance compared to Hornidge et al.[32] In that particular case, the best
angular point was 5.2% at 90 , followed by 5.9% at 60 and 150 , and then 7.0% at 120 . The most
forward angle (35 ), which is the most difficult experimentally, had a 9.8% statistical uncertainty.
For the overall time request, we must consider other issues besides beam on target. The mechanical
aspects of changing the geometry from the first angle configuration to the second will take about
half a day. Since the absolute cross section is a critical issue in this experiment, we also plan to
11
measure the tagging efficiency once per day, where each measurement requires about two hours.
This totals 28 hours over the course of the entire experiment. Finally, in order to get a definitive
handle on the detector response function of each of the three NaI detectors, it is necessary to put
each detector successively directly into the photon beam (at low flux) to measure the lineshape.
This is a considerable mechanical undertaking, and so it is estimated that each in-beam measurement would take about half a day, for a total of 1.5 days. We also request 7 days at the start of the
run for setup and commissioning of the three NaI detectors.
The various contributions to the beamtime request are listed in the table below:
Measurements in two angle configurations 14.1 days
Detector setup and commissioning 7.0 days
Change from 1st to 2nd angle configuration 0.5 days
Tagging efficiency measurements 1.2 days
Lineshape (in-beam) measurements 1.5 days
Total 24.3 days
TOTAL REQUEST AT 90-110 MeV 28 days
At the moment, we are assuming that a ‘standard’ Lund run period for nuclear physics will be
about 4 weeks at a time. Taking all of the above factors into account, we request the full 4-week
running period for this first part of the experiment. This includes some small contingency for
accelerator downtime or maintenance. In the case of an absolute cross section measurement over
a single range of tagged photon energies (90-110 MeV), there is a huge advantage to performing
the measurements all at one time, as opposed to being spread over two temporally separated run
periods that are several months apart. Given that we feel the estimates given above to be reasonable
(or a bit conservative), we believe that the Compton scattering data for this energy setting can be
acquired within the time frame described in this section.
The remaining two energy bands (60-95 and 40-65 MeV) are chosen based on the tagger energy
table given on the Lund web page. Both of these energy ranges utilize the Main Tagger at electron
energies of 150 and 100 MeV, respectively. The tagger setting and beam energy can be slightly
adjusted to tune this range, although it is clear that these two settings, in conjunction with our
highest energy setting, accomplish all of the goals set forth in this proposal. The overlap of 5 MeV
for each setting with its neighbor enable a direct comparison to be made between data sets taken
in separate run periods that may be months apart.
For each of these energy bands, we also request 28 days of beamtime. While the cross section
rises slightly as the energy drops (see figure 1, for example), this is not a big effect and will not
alter the count rate significantly. Moreover, with a wider tagged photon energy range for these
lower two settings, it is possible that the incident flux per MeV may be slightly lower, which
is roughly compensated by the increase in cross section. With this in mind, the 14.1 days of data
collection estimated above will still approximately hold in the other two cases. Since the sensitivity
to the polarizability decreases as the energy decreases, it will also therefore be necessary to obtain
greater statistics at the lower energies, so the increase in cross section will contribute favorably in
that regard.
12
The other items listed in the table above will mostly be unaffected in the case of the other energy
settings. It is possible that the setup time (7.0 days) might be reduced slightly for subsequent runs,
but we would still require at least 4-5 days of setup anyway, so this estimate is again still fairly
accurate.
In summary, we are requesting three periods of 28 days each for the elastic Compton scattering
program on deuterium. These experiments entail 5-point angular distributions to be measured in
two separate geometrical configurations using three large NaI detectors at each energy setting. We
are planning for a total of three separate energy settings: 90-110, 60-95 and 40-65 MeV. This range
of energies and angles will provide the most comprehensive and precise data set on deuteron elastic
Compton scattering to date.
13
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15