DEEP INELASTIC ELECTRON SCATTERING (#816)
FROM HYDROGEN AND DEUTERIUM
Presented by M. R. Sogard
Massachusetts Institute of Technology
Cambridge, Massachusetts
An experiment perfonned at the Stanford Linear Accelerator Center in
which the cross sections for inelastic electron-proton and electron-deuteron
scattering were measured at angles of 18°, 26°, and 34° has yielded preliminary results for the proton and deuteron structure functions.
results, infonnation about the neutron has been extracted.
Fran these
Earlier results
fran this experiment and prior small angles measurements (1) were reported
at the 1971 Cornell Conference (2).
This report therefore will be brief
and will concern itself with same additional features of the large angle
data revealed by further analysis.
The proton and deuteron structure functions WI and WZ ' obtained fran
this experiment are defined in the usual manner (2):
v
=E
- E'
where E and E' are the incident and scattered electron energies and
scattering angle, all measured in the laboratory system.
a
is the
WI and Wz are related
to as and at' the total photoabsoTption cross sections for longitudinal and
transverse virtual photons, by the expression
as
R
=-at
2
=
2
(~)
q
-98-
W2
1
• (w:-) - 1
R for the proton had previously been detennined (4) over a deep inelastic
kinematic region extending approximately fran q2 = 1.5 to 11.0 (GeV/c)2 and
fran W = 2.0 to about 4.0 GeV.
The quantity W is the mass of the final state
hadronic system and is given by
where m is the mass of the target particle.
scattering
exper~ents
Data fran earlier inelastic e-p
perfonned at 6° and 10° (5) and at 18°,26°, and 34°
(4) were employed for this detennination.
The measured values were in the
range 0.0 to O. 5 and had no apparent kinematic dependence.
Assuning R to
be a constant in this kinematic region, Rp was found to be
R = 0.18 + 0.10
P
1),
now has been detennined using the present large angle data over a
kinenatic range fran q2 = 2.5 to 13.0 (GeV/c)2 and fran W = 2.0 to approximately 4.0 GeV.
The resu1ts are in good agreenent with the earlier ones.
R for the deuteron has also been detennined over this same kinematic region,
and we can
the
n~
say that
exper~ental
1),
and Rd are consistent with being equal to within
errors.
Infonnation about the neutron is extracted fran our measurements on
deuterium using the impulse approximation.
The deuteron structure flDlctions
are expressed in tenus of free neutron and proton structure functions averaged over the Fenni motion of the nucleons wi thin the deuteron.
The method
used is that of West (7), with small modifications employed to study possible
-99 -
off-mass-shell corrections (8).
Wi th the exception of Glauber
corrections which are known to be quite
small, other corrections to the above picture cannot be estimated accurately
and are assuned to be small.
The results are quite insensitive to the choice
of wave function used to detennine the manentUll distribution of the bOWld
nucleons, as long as it is in satisfactory agreenent with other experimentally
detennined properties of the deuteron and the n-p interaction.
Our procedure
was to apply to the experimentally detennined proton structure ftmctions the
West method of averaging over the Fermi manentlDn thereby yielding a "smeared"
proton cross section.
Subtracting the smeared proton cross section fran the
deuteron cross section yielded by definition, the smeared neutron cross
section:
:: a
nsm = ad - aPsm
sm
/0
= ad/a
- 1 is plotted against x = l/w in Figure
nsrn Psm
Psm
1, where w is the Bjorken scaling variable, w = 2rnv/q2. The points were obThe quantity a
tained by calculating this ratio for all experimentally determined points
outside the resonance region and then fanning weighted averages of these
points over small intervals in x.
implies that R
p
rv
The approximate equality of Rp and Rd
R as well, which pennits us to equate (J
lap with
n
n~
~
It is meaningful to plot this ratio against a scaling variable because
the deuteron is observed to scale approximately, as well as the proton (2).
-1.00-
- - - - - - - - - - - - - ------
For values of q2, v in the scaling region, the smearing correctiOns are also
fOlIDd to scale, as they must in order to be consistent with the above results.
The Bjorken variable was chosen for the figures shown purely as a matter of
convenience.
Our preliminary results are insensitive to the choice of scaling
variable.
During the analysis perfonned in preparation for the Cornell Conference,
a preliminary version of the smearing procedure was enployed.
version has since been developed and applied to the data.
An improved
The corrected
results fran the large angle measurements shown in Figure 1 are largely
unchanged frClll the previous results t save for the last two points at the
largest values of x which are raised by approximately one and one half
standard deviations on the average.
The effect of smearing for the points shown can be significant.
Figure 2
illustrates the error that would be made, were no smearing correction applied.
The dashed line represents a curve drawn through the data shown in Figure 1,
while the solid line represents the quantity 0d/op - 1 (i.e. smearing is
ignored) • The difference between the two curves is about 40 per cent at
x = 0.79.
l-le are developing a nearly model independent program for removing the
effects of smearing on the neutron structure flDlctions.
The neutron to
proton ratio with the effects of smearing removed can then be obtained.
Preliminary results show that this ratio is essentially unchanged from
that shown in Figure 1 except at large values of x.
At x
lZ
o. 79,
unsmeared ratio is lower than the smeared ratio by about 0.02.
-101-
the
Figure 3 shows v(W 2
- W2n ) versus x. Again the points shown represent
Psm
sm
averages of data points over small intervals of x. Non-diffractive contributions to the cross sections are eVident.
References
1.
E. D. Bloom, eta a1., in PToceedi~S of 1970 International Conference on
High Energy Physics, Kiev, Septem~r 1970.
J. S. Poucher, MIT Thesis, 1971.
2.
11. W. Kendall in Proceedings of 1971 International Symposium on Electron
and Photon Interactlons at HIgh EnergIes, Cornell, August 1911.
3.
s.
4.
G. Miller, eta al., Phys. Rev., DS, 528, 1972.
G. Miller, Stanford Thesis, 1970, SLAC 129, 1971.
5.
E. D. Bloam, eta a1., Phys. Rev. Lett., 23, 930, 1969.
M. Breidenbach, MIT Thesis, 1970, MIT 2098-635.
6.
J. D. Bjorken, Phys. Rev., 179, 1547, 1969.
7.
W. D. Atwood and G. B. West, SLAG-PUB-lOBI, this conference (paper #539).
G. B. West, this conference (paper #317).
G. B. West, Phys. Lett. 37B, 509, 1971.
8.
A. Bodek, MIT Thesis, 1972, Wlpublished.
D. Orell and J. D. Wa1echka, Ann. of Phys. (N.Y.), 28, 18, 1964.
-to2-
W)2.0
0.20
o
0.40
)(=
Fig. 1.
I/w
Rate of smeared cross sections cr
0.60
/ cr
n sm
-i03-
P sm
vs scaling variable x.
1.0
9
/
,j
,
...u
"0
Q)
Q)
''0
.;
CD
bil
d
1£
0
.e
~
U
0
"'0
C
0
+-
c:
:::::>
"'0
Cl
+-
'+-
Q)
:t:::
Q)
0
u
''0
Q
c
d
Q,)
~
~
3
""'- ·cc
0
0
boO
E
:.J
U
~0
W
It
X
~
0
~
(1,)
S
UJ
ilI-I
...
0
0
~
~
N
bil
~
C\J
d
~L.....------L--....L..m--""'----w.&.-_-..L-_--.J..f()-_....L..-_-
d
d
0
(~-*H/a)
-104-
0
i
W)2.0
0.16
~
c
E0.14
U}
~ 0.12
~
I
~ 0.10
o
~
E0.08
CJ)
~ 0.0
~
:) 0.04
z
•• •
0.02
o
-0.02
0
0.40
0.20
0.60
•
0.80
X=f/w
Fig. 3.
Plot of v(W
2
- W
Psm
2n
) vs scaling variable x.
sm
-105-
1.0