Recently, new calculations were made of the direct Coulomb pair cross section that rely less in arbitrary parameters. More accurate calculations of the cross section down to low pair energies were made. New measurements of the total direct electron pair yield, and the energy and angular distribution of the electron pairs in emulsion were made for O-16 at 60 and 200 GeV/amu at S-32 at 200 GeV/amu which give satisfactory agreement with the new calculations. These calculations and measurements are presented along with previous accelerator measurements made of this effect during the last 40 years. The microscope scanning criteria used to identify the direct electron pairs is described. Prospects for application of the pair method to cosmic ray energy measurements in the region 10 (exp 13) to 10 (exp 15) eV/amu are discussed

Dake, S.

Derrickson, J. H.

Dong, B. L.

Eby, P. B.

Fountain, W. F.

Fuki, M.

Gregory, J. C.

Hayashi, T.

Iyono, A.

King, D. T.

English

NASA Technical Reports Server

HE3.1-_6
NEW CALCULATIONS AND MEASUREMENTS OF THE COULOMB CROSS-SECTION FOR
THE PRODUCTION OF DIRECT ELECTRON PAIRS BY HIGH ENERGY NUCLEI
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J.H. Derrlckson, a S. Dake, e B.L. Dong, c P.B. Eby, a W.F. Fountain, a M. Fuki, f
J.C. Gregory, c T. Hayashi, c A. Iyono, e D.T. King, b , O. Miyamura, g T. Ogata, d
T.A. Parnell, a F.E. Roberts, a T. Tabuki, a Y. Takahashi, c T. Tomlnaga, d
J.W. Watts, a
aspace Science Laboratory, NASA Marshall Space Flight Center,
Huntsville, Alabama 35812, USA t
bDepartment of Physics and Astronomy, University of Tennessee,
Knoxville, Tennessee 37996, USA
CSchool of Science, University of Alabama in Huntsville,
Huntsville, Alabama 35899, USA
dInstitute for Cosmic Ray Research, University of Tokyo, Tokyo 188, Japan
eDepartment of Physics, Kobe University, Kobe 657, Japan
fMatsusho Gukuen Junior College, Matsumoto 390-12, Japan
gDepartment of Applied Mathematics, Osaka University, Osaka 560, Japan '
Abstract
Recently, new calculations have been made of the direct Coulomb pair cross-
section that rely less on arbitrary parameters. More accurate calculations
_, of the cross-section down to low pair energies have been made. New
o measurements of the total direct electron pair yield, and the energy and
angular distribution of the electron pairs in emulsion have been made for
160 at 60 and 200 GeV/amu and 32S at 200 GeV/amu which give satisfactory
agreement with the new calculations. These calculations and measurements are
presented along with previous accelerator measurements made of this effect
during the last 40 years. The microscope scanning criteria used to identify
the direct electron pairs is described. Prospects for application of the
pair method to cosmic ray energy measurements in the region 1013 - 1015
eV/amu are discussed.
Introduction The original motivation for this work was to develop a method
to measure the energy of cosmic rays above 10 TeV/amu which employs only the
electromagnetic interaction [I]. The method would use the energy-dependent
cross section for the production of electron-positron pairs from the virtual
photon field of a relativistic heavy ion in the field of a stationary
nucleus. This requires the measurement of the number of electron pairs
occurring along a segment of the primary ion track in nuclear emulsion or
other high spatial resolution detectors. The method for measuring primary
particle energy above 10 TeV/amu is "ionization calorimetry" which depends
on the strong interaction. However, there has been some concern about
possible changes in the behavior of nuclear interactions at these high
energies. Part of this concern is due to conflicting results of air shower
experiments which, by various analysis techniques, have indicated that
cosmic rays are either mostly protons or mostly iron near 1015 eV. In fact,
some central nucleus-nucleus interactions have exhibited unusual features,
such as high transverse momentum and high energy density that may indicate a
departure from the simple superposition models. A technique for energy
measurement that does not depend upon nuclear interactions would be most
desirable in this energy regime.
Some of the previous measurements of the electromagnetic pair yield reported
in the literature were not consistent with calculations. The calculations
https://ntrs.nasa.gov/search.jsp?R=19900013055 2020-03-19T23:13:12+00:00Z
H£3.!-16
converge at the highest energies, but predict different cross-sections below
1015 eV/amu. Furthermore the reported experimental results varied widely.
We report here the results of our recent calculations and experimental
measurements which appear to resolve most of the previous discrepancies.
Accelerator Exposures The CERN EMU04 experiment exposed nuclear track
emulsion to oxygen ions at 60 and 200 GeV/amu and sulfur at 200 GeV/amu.
The basic configuration was a stack of thick emulsion plates (800 U acrylic
substrate with 500 u of Fuji 7B emulsion coated on both sides) oriented
parallel to the beam and housed in a light-tight box with a thin window
facing the beam. The beam intensity was -3 thousand ions/cm 2. After the
exposure, a reference grid was photographed on one side of each emulsion
plate. This grid contained a pattern of numbers that allowed unique
identification of the primary tracks.
Microscope Scanning A total of 50 meters of heavy ion tracks have been
examined under the microscope with a magnification of 1000 [2]. The primary
ion track was scanned at a rate of less than I cm/hr, focusing over a depth
of field of 40 microns centered on the primary ion. Every electron
emanating from the primary track with an energy ) 2 MeV was recorded. First
the emission angle was measured. Then the energy of the observed electron
was measured by taking at least three deflection readings for the multiple-
scattering angle over a track typically several hundred microns in length.
The average multiple-scattering angle is known to be inversely proportional
to the electron's momentum. Having found an energetic electron, the
surrounding region was examined for an associated track with energy ) I MeV.
This energy is a practical lower limit because the energy uncertainty
approaches 50%. For a bonafide electron pair the first distinguishable
grain of the electron (positron) track must be within I U of the boundary of
the primary track and both candidate electron (positron) tracks, when
extrapolated to the primary track, should be coincident within 2 U. Most of
the false pairs arising from a chance coincidence of a delta ray of energy
I MeV and a fast knock-on electron of energy ) 2 MeV will be eliminated.
With this scanning procedure, it is estimated that I-2% of the accepted
pairs (e. ) I MeV, e_ ) 2 MeV) will be false, we use the kinematic]
relationship for fas_ knock-on electrons to establish a basis for checking
the energy and angle measurements made by various scanners. Observing and
recording the direct electron pairs and the knock-on electrons above a
prescribed energy threshold provides a data log that can be reviewed for
consistency among scanners.
Calculations New calculations have been performed that predict the total
yield, the energy transfer during collision, and the angular distribution of
the pairs [3]. This work has incorporated the Weizsacker-Williams (WW)
method of virtual quanta as described in [4], including corrections for pair
production by low-energy photons (Racah formula [5]) and higher order
corrections [6, 7]. The latter include higher-order terms in target atomic
number. This approach is accurate if the Lorentz factor 7 for the heavy ion
satisfies the condition 7 >> I and the energy transfer e = e I + e 2 is such
(e/me c2 ) << _. The WW method has an undeterminedthat parameter
corresponding to the minimum impact parameter. The Kelner and Kotov (KK)
calculation of the direct pair production cross section [8] has no
undetermined parameters but is valid only in the relativistic energy
transfer region. If the KK results are matched wiLh the WW calculations in
transfer region where bQth are va lid, i.e., meC 2 << ean
energy
<< _meC , then the minimum impact parameter is determined.
HE3.1-16
Results and Discussions The total calculated yield is show_n in figure I and
has been compared to a standard lowest-order quantum electrodynamic
evaluation of the yield by Hurota-Ueda-Tanaka (HUT) [9]. Previous
measurements of the direct electron pair yield produced by monoenergetic
beams of electrons, muons, pions, and protons [10-15] are displayed along
with the results of this work. Wlth the exception of the muon and proton
data, the measured palr frequency matches the most _recent calculations [23]
rather well. The calculated energy transfer for the y - 200 case is
compared to the CERN oxygen and sulfur electron pair _ata (Figure 2).
Although there is general agreement between theory and experiment, it is
true that there is a measured over abundance of the low-energy pairs for
sulfur coupled with a slight depletion of the high-energy pairs. When
comparing a previous pair energy transfer distribution [13] from protons
with the corresponding ones for oxygen and sulfur, a softening of the energy
spectrum for the produced pairs with higher projectile charge is noticed.
Figure 3 depicts the energy sharing distribution with the data being split
into low and high energy pair groups for protons, oxygen, _nd
sulfur (y = 200). All the distributions appear to be normal except for t2_e
high energy pair data for sulfur. There is a greater disparity in the
energy division for these sulfur pairs. The opening angle distributions in
Figure 4 indicate that a fraction of the sulfur pairs have larger opening
angles compared to the oxygen data. A possible explanation is that those
electron (positron) tracks that are emitted nearly parallel to the heavy
primary ion are obscured for a sufficient distance to bias the
observations. This may lead to a lower energy electron being selected over
an energetic (positron) due to the uncertainty in the location of the first
distinguishable grain of the forward track. Therefore, it is possible that
a chance association of a lower energy electron occurs reducing R and e and
increasing 4@i, 2 •
More accelerator data from CERN will be scanned to study these
systematlc errors with higher statistical accuracy. When the systematic
errors are clearly understood, this energy measuring technique will be
applied to cosmic rays provided a long path length in emulsion is
available () I cm) and the dip angle of the track is not too steep.
References
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Jackson J.D. 1962 "Classical Electrodynamics". Wiley: New York.
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Overbo I. et al 1973 Phys. Rev. A, 8 668.
Davies H. et al 1954 Phys. Rev. 93 788.
Kelner S.R. et al 1968 Soy. J. Nucl. Phys. 7__,237°
Murota T° et al 1956 Prog. Theor. Phys. 16.__,482.
Cary A.S. et al 1971 Phys. Rev. D 4_, 27.
Jain P.L. et al 1974 Phys. Hey. Lett. 32___,1460.
Kinzer R.L. et al 1968 Phys. Hey. Left. 20, 1050.
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New calculations and measurements of the Coulomb cross-section for the production of direct electron pairs by high energy nuclei

New calculations and measurements of the Coulomb cross-section for the production of direct electron pairs by high energy nuclei

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