Neutron-proton analyzing power at 12 MeV and inconsistencies in parametrizations of nucleon-nucleon data

0.28 MB·English

by  R. T. Braun

Neutron-Proton Analyzing Power at 12 MeV
and Inconsistencies in Parametrizations of Nucleon-Nucleon Data
R.T. Braun, W. Tornow, C.R. Howell, D.E. Gonz´alez Trotter, C.D. Roper, F. Salinas, H.R. Setze, and R.L. Walter
Department of Physics, Duke University, Durham, North Carolina 27708-0308
Triangle Universities Nuclear Laboratory, Durham, North Carolina 27708-0308
G.J. Weisel
Department of Physics, Penn State Altoona, Altoona, PA 16601
We present the most accurate and complete data set for the analyzing power Ay(θ) in neutron-
protonscattering. Theexperimentaldatawerecorrectedfor theeffectsofmultiplescattering, both
in the center detector and in the neutron detectors. The final data at En = 12.0 MeV deviate
8 considerably from the predictions of nucleon-nucleon phase-shift analyses and potential models.
0 Theimpactofthenewdataonthevalueofthechargedpion-nucleoncouplingconstantisdiscussed
0
in a model study.
2

n PACSnumbers: 13.75.Cs,24.70.+s,25.40.Dn
a
J
0 INTRODUCTION and gπ2±/4π = 13.54±0.05 [11]) and of the VPI group
3 (g2 /4π = 13.3 and g2 /4π = 13.9 from NN scattering
π0 π±
[12, 13] and g2 /4π = 13.75±0.15 from π±p scattering
] There are reasons why low-energy (EN ≤ 20 MeV) [14]). π0
x Nucleon-Nucleon (NN) scattering data might appear to
e In principle, this inconsistency can be reduced by as-
beoflimiteduseinconstrainingNN phase-shiftanalyses
- suming a charge-splitting of the pion-nucleon coupling
l (PSAs) [1, 2] and potential models (PMs) [3, 4, 5, 6, 7].
c constant, i.e., one could assume that the neutral pion
u For one thing, the deuteron bound-state properties al-
couples to the nucleonwith a different strengththan the
n ready provide a fairly stringent constraint for any NN
chargedpion. InRefs.[9,10]itwasshownthatthe com-
[ PM, and might seem sufficient. For another, low-energy
1 scatteringdatacanprovideconstraintsonlyforthelower bination of gπ20/4π = 13.6 and gπ2±/4π = 14.4 creates a
sufficientlylargevalue forthe quadrupolemomentofthe
v partial wave NN interactions and, even then, can not
0 determine individual partial waves. For example, the deuteron, and reproduces the low-energy p-p 3P0 phase
0 shifts.
low-energy analyzing power, A (θ), is governed by the
y
.46 athnrdee3Pa2n.guAllatrhomuogmheNntNumdaLta=pr1ovinidteercaocntisotnras,in3tPs0o,n3tPh1e, weAretptehrefosrammede,ttihmeeretwhaertetihnediacantailoynssesthoaftRne-pfs.di[ff9e,re1n0-]
1 3P phaseshifts takentogether,it cannotdetermine each tial cross-section data at intermediate energies favored
0 a larger value for g2 /4π. On this, see Ref. [15] for
parameter unambiguously [8]. π±
8 a comprehensive overview of recent determinations of
0 Despite the very small magnitude of NN A (θ), its 2 2
y g /4π and especially Ref. [16], which quotes g /4π =
: π π±
v importance derives from the fact that it is possible ex- 14.50±0.26 obtained from n-p differential cross section
i perimentallytomeasuresuchdatatogreatprecision. As
X data at En = 162 MeV. However, the recent n-p differ-
a result, NN A (θ) can provide a crucial test of our un-
y ential cross section data obtained at IUCF at 194 MeV
r
a derstanding of the NN interaction and of the nuclear [17] do not support this larger value of g2 /4π.
π±
force in general.
Although it seems likely that there is no significant
Perhaps the most important controversy surround- charge splitting in the pion-nucleon coupling constants
ing current NN interaction models concerns the pion- atintermediateenergies,thequestionremainsunresolved
nucleon coupling constant, g2/4π. In Ref. [9], Machleidt atlowenergies. Onthe onehand,the theoreticalmodels
π
and Slaus point out that low-energyproton-proton(p-p) used to account for the charge dependence of the singlet
Ay(θ)dataareverysensitivetotheneutralpion-nucleon NN scattering lengths, 1S0, do not allow for any large
2 2
couplingconstant,implyingavalueofg /4π≤13.4(see chargesplitting ofg /4π. Onthe otherhand,manylow-
π0 π
also Ref. [10]). At the same time, the correct descrip- energy data suggest a significant charge splitting. We
tion of the quadrupole moment of the deuteron andlow- reporthereonthe resultsofanewn-pA (θ)experiment
y
energy neutron-proton (n-p) A (θ) data requires meson- carried out at E = 12.0 MeV utilizing improved data-
y n
exchange based NN potential models to have values for taking and data-analysis techniques. For references to
the neutralandchargedpion-nucleoncouplingconstants previous n-p A (θ) measurements see Refs. [18, 19, 20].
y
g2 /4π and g2 /4π, respectively, of 14.0 or larger. The Our results confirm the inconsistencies between low-
π0 π±
latter finding is clearly inconsistent with the results of energy analyzing power and available theoretical models
the Nijmegen group’s NI93 PSA (g2 /4π = 13.47±0.11 of the NN interaction.
π0
EXPERIMENTAL SETUP (between up and downrelative to the horizontalscatter-
4
ing plane). The n-p and n- He data were accumulated
simultaneously in six runs, each lasting about 250 data-
The experimental setup is shown in Fig. 1. Polarized
taking hours.
neutrons with mean energy of 12.0 MeV and total en-
The data-acquisition electronics recorded the center
ergy spread of about 400 keV were produced via the
detectorpulseheight(CDPH),the neutrontime offlight
polarization-transferreaction2H(d~,~n)3He at0◦. The po-
(NTOF) between the CD and the NDs, and spectra for
larizeddeuteronbeamwasacceleratedtoE =9.40MeV
d each ND, including pulse-shape information. Since the
andenteredthrougha4.6µmHavarfoilintoasmall(3.14
energy of the scattered neutrons varied from En′ = 11.1
cm long, 0.48 cm radius) gas cell filled with 7.8 atm of MeV at θlab = 16◦ to En′ = 1.1 MeV at θlab = 72◦,
deuteriumgasandcappedwitha0.1cmthickgoldbeam-
different hardware thresholds were used for the NDs. In
stop. The gascellwasmountedinside a 1.8m-thick wall
addition, three different gains were used for the CD sig-
made of concrete, paraffin, iron, copper, and lead, to
nals (using different dynodes).
shield the neutron detectors from the direct flux of the
Software cuts were set on the CDPH and the pulse
neutron source. Typical deuteron beam intensities on
heightintheNDstoeliminatepulsesattheextremeends
target were 1.5 µA and typical values for the deuteron
ofthespectra. Gateswerealsosetontheneutronsinthe
vector polarization |p | were 0.65. The polarized neu-
z pulse-shape discrimination spectra and wide gates were
trons produced at 0◦ relative to the incident deuteron
set on the elastic peak of the NTOF spectrum. All four
beam passed through a collimation system to produce a
of these cuts (identical for spin-up and spin-down spec-
rectangular shaped neutron beam at the position of the
tra)were used to generate two-dimensional(2D) spectra
proton-containing active target labelled “Center Detec-
of CDPH versus NTOF, for scattering to the left and
tor” in Fig. 1. The center detector (CD) consisted of
right NDs and for neutron spin up and spin down. An
an upright cylinder made of the plastic scintillator ma-
example ofsuch a spectrumis shownin Fig. 2 where the
terial NE102Awith dimensions 1.9 cm diameter and 3.8
CDPH scale has been temporarily compressed in order
cm height. The CD was located at a distance of 172 cm
to fit within 64 channels. Tight NTOF gates were set
from the neutron source and was mounted via a short
in these 2D spectra eliminating the tails of the peak, as
light guide onto a 5 cm diameter photomultiplier tube
showninFig.2,inordertoidentifytheelasticscattering
(PMT).
events of interest (again, identical for spin-up and spin-
Neutrons scattered to the left or right were detected downspectra). ThesenewNTOFgateswereusedtosort
by five pairs of neutron detectors positioned symmetri- thefinalCDPHspectra(nowintheirfull512-channelres-
cally relative to the incident neutron beam direction in olution)correspondingtoeachneutrondetectorandspin
the horizontal scattering plane. The neutron detectors state. The CDPH spectra were used to determine the n-
(NDs) were filled with the liquid scintillator material p yields and scattering asymmetries, after applying the
NE213. These detectors had excellent neutron-gamma correctionsdescribedinthe followingsection. Theabove
pulse-shape discrimination capabilities and had an ac- process was also followed to sample the accidental (i.e.,
tive volume of 4.3 cm wide, 11.9 cm high and 7.5 cm time uncorrelated) background by using an NTOF cut
deep. Theywereviewedby5cmdiameterPMTsthrough located at times shorter than the gamma peak. The ac-
0.5 cm thick Pyrex glass windows and 7.5 cm long light cidental background proved to be extremely small.
guides. The neutron detectors were mounted onto (low-
mass)30cmhighstandsandplacedonanaluminumring
DATA ANALYSIS
surrounding the CD. The center-to-center distance be-
tween the CD and the neutron detectors ranged from 45
cmto 70cmdependingonscatteringangle. Theangular After the sorting procedure described above and the
separation between the neutron detectors was 12◦ (lab). subtraction of the accidental events, the data still
Inordertocovertheangularrangefromθ =16◦to72◦ contained a number of finite-geometry and multiple-
lab
in 4◦ steps, three settings of the five detector pairs were scattering effects. To remove these effects, Monte-Carlo
required. The absolute magnitude of the neutron polar- calculations were performed to simulate the experiment.
izationwasmeasuredwithaneutronpolarimeterlocated Two effects are due exclusively to the finite size of the
downstream of the n-p scattering arrangement. The po- center detector (CD) and the neutron detectors (NDs)
larimeterconsistedofa4Hegasscintillatorpressurizedto andhaveaslighteffectonsingle-scatteringevents. First,
100atm(95%He,5%Xe)andapairofneutrondetectors because there is a range of angles subtended by eachde-
positioned at θ = 58◦, which were identical to those tector set at each nominal angle and because the cross
lab
used for n-p scattering. In order to reduce instrumental sectionofn-pelasticscatteringvariesoverthisrange,we
asymmetries for the n-p and n-4He measurements, the must reportan effective angle. These were calculatedby
deuteron vector polarization p , and therefore the neu- our code and are listed in the first column of Table I.
z
tron polarization, was flipped at a frequency of 10 Hz This effect is small; the largest shift is no more than a
half of a degree. The second finite-geometry effect con- alsoconcludedthatthebackgroundwasunpolarized. For
cerns the value of A (θ) itself, again due to the range all ND angle settings we approximated the remaining
y
of angles subtended by each ND. Effective A (θ) values background by a linear function connecting the left and
y
werecalculatedby our Monte-Carlocode andthese were rightsidesoftheCDPHpeak(forexample,inFig.3from
comparedtothevaluesfromthecode’slibrary. Theratio channel 180 to 280). The remaining background seen
between these two values was then applied to the data. abovechannel290inthebottompanelofFig.3isdueto
Onceagain,thecorrectionissmall;onlythefirstfouran- cross-talk effects between two adjacent detectors, specif-
gleshadcorrectionsthatwerelargerthantheuncertainty ically neutron scattering from the detector positioned at
of the calculation (about 0.00012). a larger scattering angle (and shorter distance from the
In addition to elastic scattering, multiple scattering CD) to the detector of interest.
events occur in the CD. About 50% (depending on ND Three sets of gates were used to calculate the yields
angle) of these events were eliminated as a result of the andasymmetries,at10%(showninFig.3by the dashed
neutron time of flight (NTOF) gate. Nevertheless, the lines), 30%, and 50% of the CDPH peak maximum. In
centerdetectorpulseheight(CDPH)spectrumcontained Fig. 3, this is done for N↑, for spin up scattering to the
L
multiple scattering events amounting to approximately left ND at θ = 36◦. Similarly, the yields N↑, N↓,
2% ofall single scattering events. Our Monte-Carlosim- lab R L
and N↓ were obtained to calculate the asymmetry ǫ =
ulation showed that the only significant processes were R
those due to double scattering, specifically neutron dou- (α−1)/(α+1) with α = NL↑ NR↓. The nominal gates
ble scattering from hydrogen (1H-1H), neutron scatter- rNR↑ NL↓
were the 30% set. The other two gates (the 10% and
ing from hydrogen and subsequent scattering from car-
bon (1H-12C), and neutron scattering from carbon and 50%set)wereusedtocheckontheappropriatenessofthe
subsequent scattering from hydrogen (12C-1H). In per- background subtraction. Within statistical uncertainty,
the results for ǫ proved to be independent of the choice
forming these calculations, we used complete libraries of
1 of the gate width.
cross-sectionand polarizationdata for both n- H and n-
12Cscattering. Wewillreturntothesubjectofthen-12C In order to extract the n-p Ay(θ) from the measured
library in our discussion of the PDE correction. asymmetry ǫ(θ), the neutron polarization pny must be
We also removed edge-effect events from the data, known. For this purpose the n-4He asymmetry data ac-
whichresultwhenrecoilprotonsleavethe CDbefore de- quired with the neutron polarimeter referred to above
positingtheir fullenergy. Alongwiththe double scatter- were processed and analyzed in the same way as the
ing events, these counts elongate the tails of the CDPH n-p asymmetry data. In this case the 4He recoil pulse
peak, especially to the left (low-energy) side. height in the high-pressure gas scintillator plays the role
of the CDPH in the plastic scintillator used for the n-
A sample CDPH spectrum is shown in Fig. 3 (top
p asymmetry measurements. The neutron polarization
panel). The solid curve represents our Monte-Carlo sim-
ulation for a scattering angle of θ = 36◦, while the was obtained from ǫHe(58◦) = (αHe −1)/(αHe +1) =
lab A¯ (58◦)pn, where α is defined as above. Here, the ef-
smallopencirclesshowtheexperimentaldata. Agreatly y y He
expanded view is shown in the middle panel, where the fective analyzing power A¯y(58◦) for n-4He scattering at
open circles again indicate the experimental data. The En = 12.0 MeV was calculated for the present neutron
curveslabeled“double”arethecalculateddoublescatter- polarimetergeometryviaMonte-Carlocalculations. The
ingcontributions1H-1H,1H-12C,and12C-1H.Thedotted n-4He phase shifts of Stammbach and Walter [21] were
curve labled “edge” is the calculated pulse-height distri- used. All of the relevant multiple scattering processes
bution due to edge effects. Finally, the curve labeled were included. We obtained A¯y(58◦) = −0.554±0.008,
“single” is the calculated single scattering contribution where the uncertainty is mainly of a systematic na-
(plus the edge effects). All of the calculations are nor- ture reflecting the uncertainty associated with the n-
malized to the data. 4He phase shifts. The average neutron polarization was
Another expanded view is displayed in the bottom pny =0.563±0.008.
panelof Fig.3. Here,“data with subtraction”showsthe Atsuchahighlevelofprecision,asubtlesystematicef-
data after the removal of all counts due to double scat- fectcomesintoplay,whichdoesnotcancelbyreversalof
tering and edge effects (labeled “ms+edge”). Even after the neutronpolarization. Thisis the polarizationdepen-
thissubtraction,asmallbackgroundremains,amounting dent efficiency (PDE) [19] of the neutron detectors. The
to about 0.3% of the single-scattering events. A number NDs contain hydrogenand carbon in the ratio of 1.21:1.
of fits were used to estimate this remaining background, The double scattering process12C-1H in the NDs, which
ranging from a linear fit between channel numbers 150 accounts for about 10% of the total neutron detection
and 350 to a parabolic fit between channel numbers 180 efficiency, is sensitive to the n-12C A (θ). If the n-12C
y
and 280. Due to the smallness of the remaining back- A (θ) is not constant over the range of neutron energies
y
ground, the asymmetry provedto be independent of our En′ seenbyaparticularND,aninstrumentalasymmetry
background choice, within statistical uncertainties. We willoccur. Typicalvaluesfor∆En′ are800keV.Arealis-
ticcorrectionforthiseffectrequiresadetailedknowledge DISCUSSION
12
of the n- C A (θ), especially in the resonance region of
y
the n-12C total cross section between 2.0 and 8.5 MeV
Figure 4 shows the present n-p A (θ) in comparison
neutron energy. In this energy regime the n-12C A (θ) y
y to the NN phase-shift analysis prediction (solid curve)
changes rapidly and therefore causes sizeable PDE ef-
of the Nijmegen group, NI93. Clearly, NI93 provides a
fects.
larger A (θ) throughout the entire angular distribution.
y
Allofthepost-1985n-pA (θ)measurementshavebeen
y The accuracy of the neutron polarization determined in
correctedfor the PDE.However,due to the lackof a de-
the present work does not allow for a renormalization
12
tailed n- C A (θ) database, especially at low energies,
y of the A (θ) data beyond the error bars given in Fig.
y
the accuracy of the associated corrections was limited.
4. Furthermore, the present n-p A (θ) data are in good
y
In assembling our data library, we used the thirty-three
agreementwith the trendestablishedby previousTUNL
n-12C A (θ) angular distributions measuredby Roper et
y data where a different method was used for determining
al. [22] in the energy range from 2.2 to 8.5 MeV. From pn [20].
y
E =0to6.5MeV,weusedanR-matrixanalysisbyHale
n
As we have pointed out in the introduction, the un-
[23], which included the data from Ref. [22]. In certain
derlyingNN dynamicsthatcharacterizeA (θ)precludes
regions(especiallyforforwardanglesandforneutronen- y
us from extracting unambiguous information about the
ergiesbetween3.5and4.5MeV),theanalysisofRef.[23]
3P NN interactions. However,wecanconcludethatthe
missed the A (θ) data slightly and we therefore substi- j
y
NI93NN PSAoverestimatesthen-pA (θ)atE =12.0
tutedLegendrepolynomialfits tothe dataofRef.[22]in y n
MeV. This statement is of considerable importance con-
these regions. Between 6.5 MeV and 8.5 MeV, we used
sideringthe fact thatmostNN potentialmodelbuilders
fits to the data of Ref. [22] as well as the recent phase-
use the NI93 PSA results or the associated database for
shift analysis (PSA) of Chen and Tornow [24]. Above
determiningthefreeparametersoftheirmodels. Onehas
E = 8.5 MeV, we used the Chen-Tornow PSA exclu-
n
to conclude that all the recent so-called high-precision
sively. The new data by Roper et al. and the analyses
of Hale, Chen and Tornow improved the n-12C A (θ) NN potential models overestimate the n-p Ay(θ) at low
y
energies. This observationhasfar-reachingconsequences
database considerably, making corrections for the PDE
for nuclear scattering systems with A > 2, which are
more reliable.
3
much more sensitive to the P NN interactions than
WeranourMonte-Carlocodefor20separatelegs,each j
the NN system [25].
leg of three million events, and each leg starting from a
different random number. The PDE correction to the Valuableinformationcanbeobtainedfromthepresent
A (θ)datawastakenasthedifferencebetweentheA (θ) dataifthey arecomparedtovariationsofthe theoretical
y y
resultwithpolarizationeffectsturnedonintheNDs and predictions. Here we focus on the charged pion coupling
the result with the polarization turned off. The second constant [9, 10]. Figure 4 shows our data in compar-
column of Table I lists our final PDE corrections. Note ison to three theoretical predictions based on the CD-
that they vary greatly from one data point to the other Bonn NN potential, which use three different values of
due to the pronounced resonance features in n-12C scat- the charged pion-nucleon coupling constant, gπ2±/4π. In
tering at low energy. It is important also to note that these three models, only the S-wave NN interactions of
our present results agree well with the overall trend of CD-Bonn were refitted. All three predictions use the
the PDE corrections of Ref. [20], which used a different same neutral pion coupling constant, gπ20/4π = 13.6.
2
Monte-Carlo code and a different database. Our reason The curve using gπ±/4π = 13.6 is indistinguishable on
for having much greater confidence in the present PDE this scale from the prediction of NI93 (solid curve). The
results is due to our extensive and detailed work in re- dashedcurveinFig.4usesgπ2±/4π=14.0andthedotted
vising the data libraries, as outlined above. curve uses gπ2±/4π = 14.4. The values of χ2 per degree
of freedom associated with the solid, dashed and dotted
The third column in Table I summarizes our final re-
sultsforA (θ)inn-pscatteringatE =12.0MeV.Note curves are 6.0, 1.7, and 2.5, respectively. Therefore, this
y n
modelstudyconfirmsandputs onmoresolidgroundthe
the small overall uncertainty. The final results include
uncertainties in Ay(θ) due to statistics, the measure- findings of Refs. [9, 10] regarding low-energy n-p2Ay(θ)
ment of beam polarization, the multiple-scattering cal- data and their demand for a charge splitting of gπ/4π.
culation, the PDE calculation, and the remaining back- In summary, the present data represent the most ac-
ground (typically zero) all added in quadrature. The curate and complete n-p A (θ) angular distribution ever
y
finaluncertaintiesareabouthalfofthose ofthe previous reported. Our model study based on the CD-Bonn NN
TUNL n-p A (θ) measurement at E = 12.0 MeV [20]. potential model supports a substantial charge depen-
y n
This is partly due to the fact that the Atomic Beam Po- dence of the pion-nucleon coupling constant. Our re-
larized Ion Source used in the present study produced sults are inconsistent with the existing globalNN PSAs
aboutfour times the deuteroncurrentas the Lamb-Shift of the Nijmegen [11] and VPI [12, 13] groups and with
source used in the previous study. high-precision NN potential models. However, our re-
sults agree with inconsistencies previously noticed be-
tween data and predictions for the 3S1-3D1 mixing pa- TABLEI:Resultsofn-pAy(θ)experimentatEn=12.0MeV.
rameter ǫ1 in n-p scatteringat low energies[26] and also θ3c2.m.6. 0.P00D0E14co±rr0ec.0t0io0n16 0.00fi8n5a4l±res0u.l0t0s067
with requirements placed on the charged coupling con-
40.5 0.00004 ± 0.00016 0.01231 ± 0.00064
stant by the quadrupole moment of the deuteron [9]. Of 48.5 0.00006 ± 0.00015 0.01451 ± 0.00065
course, it is possible that neither of these scenarios is 56.5 0.00013 ± 0.00013 0.01443 ± 0.00063
the “correct” one. Perhaps the impasse comes because 64.4 -0.00005 ± 0.00015 0.01560 ± 0.00063
we are at the point where the precision of our data and 72.4 0.00294 ± 0.00022 0.01659 ± 0.00067
the development of our “low energy” theoretical models 80.5 -0.00185 ± 0.00014 0.01470 ± 0.00060
88.4 0.00019 ± 0.00017 0.01386 ± 0.00057
has pushed the paradigm of meson-exchange based NN
96.3 0.00072 ± 0.00018 0.01198 ± 0.00059
potential models beyond its limits.
104.2 -0.00136 ± 0.00018 0.01110 ± 0.00058
This work was supported in part by the U.S. Depart- 112.2 -0.00114 ± 0.00028 0.00662 ± 0.00062
120.2 0.00108 ± 0.00029 0.00558 ± 0.00065
ment of Energy, Office of Nuclear Physics, under Grant
128.2 0.00103 ± 0.00021 0.00483 ± 0.00056
No. DE-FG02-97ER41033. The authors would like to 136.0 -0.00018 ± 0.00036 0.00372 ± 0.00067
thank R. Machleidt for valuable contributions to this 143.8 -0.00029 ± 0.00040 0.00287 ± 0.00079
work.
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CONCRETE HEAVY METAL
PARAFFIN LEAD
GAS CELL Scintillator (NE102A)/Center Detector
58°
SCALE
Helium Polarimeter
50 cm
FIG. 1: Experimental setup for n-p Ay(θ) measurements in
TUNL’s Shielded Neutron Source area.
E = 12 MeV
n
θ = 64˚
lab
H
DP
C
TOF
FIG. 2: 2D spectrum of compressed CDPH versus NTOF
◦
for scattering to θ = 64 . A tight NTOF gate was set
lab
around the elastic neutron peak in order to remove as many
background eventsas possible.
60000 0.020
Monte-Carlo
50000
E = 12 MeV
n 0.015
40000 θ = 36°
lab
s
Count 30000 θA()y0.010
20000
0.005
10000
0
100 150 200 250 300 350 0.000
0 20 40 60 80 100 120 140 160 180
Channel θ
cm
600
500 data FIG. 4: Neutron-proton Ay(θ) data at En = 12.0 MeV in
edge comparison to theoretical predictions. The error bars asso-
ciated with the data represent the overall uncertainty of the
400
single data with statistical and systematic uncertainties added in
s
unt 300 quadrature. The solid curve is the Nijmegen NI93 PSA pre-
Co diction. The other curves are for the CD-Bonn based model
200 double studywhichvariesthechargedpioncouplingconstant. Here,
2 2
for gπ0/4π, all three curves use 13.6. For gπ±/4π, the cal-
100 culation using13.6 coincides on thisscale with theNijmegen
NI93PSAresult(solidcurve);thedashedcurveuses14.0and
0
thedotted curve14.4.
100 150 200 250 300 350
Channel
2000
E = 12 MeV data with
n subtraction
θ = 36°
lab
1500
ms+edge
unts 1000 data
o
C
500
0
100 150 200 250 300 350
Channel
FIG.3: Thetoppanelshowsacomparisonofcalculated(solid
curve)andmeasured(dots)CDPHspectrumforscatteringto
◦
θ = 36 . The middle panel shows an expanded view with
lab
focus on calculated multiple-scattering and edge effect con-
tributions. The bottom panel shows an additional expanded
view focusing on the remaining background. See text for de-
tails.