- Email: [email protected]
Plural scattering of electrons at 1.00 Mev, 1.75 Mev, and 2.50 Mev. II
ANNALS
OF
PHYSICS:
Plural
6,
8689
Scattering
of Electrons
1.75
and
V. SPIEGEL, Department
(1959)
Mev, JR.,t
of Physics,
W. University
2.50
C. MILLER, of Notre
at 1.00 Mev.
Mev,
II.*
AND B. WALDMAN Dame,
Notre
Dame,
Indiana
Monoergic electrons were scattered from thin foils of aluminum, nickel, silver and gold. The scattered electrons were analyzed by a magnetic spectrometer. The electron-nuclear cross sections were measured as a function of foil thickness and for scattering angles of 30°, 60°, 90°, 120°, and 150’. The data presented show the onset of plural scattering and may be used as a convenient guide for single scattering.
In the measurement of the cross section for single scattering of electrons by the coulomb field of nuclei (1), it was necessary to recognize and correct for the presence of plural scattering. The recent interest in the detection of electron polarization by coulomb scattering suggeststhe separate publication of these data as a convenient guide for single scattering. The foremost criterion for single scattering is the observance of the linear dependence of the number of scattered electrons with the scatterer thickness. Any deviation from linearity is an indication of plural scattering. Extrapolation to zero scatterer thickness reduces the data to the correct value for single scattering. As Reich (2) has shown, it is convenient to plot the number of scattered electrons per unit scatterer thickness as the ordinate and the scatterer thickness in atoms per cm2 times 27 as the abscissa. The Z2 factor helps in normalizing the data so that scatterers of all 2 values can be plotted on the same scale. On this graph a line of zero slope indicates no plural scattering. Another indication of plural scattering is the comparison of the scattering from the transmission and the reflection positions of the scattering foil. These positions are illustrated in Fig. 1. The onset of plural scattering will affect the reflection data very much more than the transmission data because of the increased probability of two small angle scatterings. This phenomenon has been observed by * Supported in part by the joint program of the Office of Naval Research Atomic Energy Commission. t Now at the National Bureau of Standards, Washington, D. C. 86
and the
U. S.
PLURAL
SCATTERING
OF
‘, I \ ‘\ 1
FIG. 1. Transmission and reflection scattering angle in transmission. The flection.
ELECTRONS
87
REFLECTION
\‘\
TRANSMISSION
positions at 90’. plane of the foil
The normal to the foil bisects the bisects the scattering angle in re-
Chase and Cox (3) in experiments on electron polarization. Goertzel and Cox (4) calculated the relative scattering cross sections for a single 90” scattering compared to two 45” scatterings. Similar calculations have been made by Ryu (5) and Hammermesh and Monahan (6). The details of the experimental arrangement, procedure and treatment of data are described by Spiegel et al. (1). The results are plotted inFig. 2. The transmission position is used for the 30”, 60”, and 90” angles. The reflection position is used at 90”, 120”, and 150”. If the reflection position were used at the small angles the effective thickness would be too large. This is also true for the transmission position at the large angles. At 90” both reflection and transmission data were taken. The abscissa refers to the actual foil thickness, not the effective thickness due to the inclination of the foil. The general shapes of the curves, the trends with energy and with atomic number are all in agreement with the qualitative theory of plural scattering. Unfortunately no quantitative calculation is available for a better comparison. However, the calculation of Hammermesh and Monahan (8) predicts a reflection to transmission ratio of 1.05 f 0.01 for the 90” scattering of 1.7-Mev electrons on an aluminum foil 7 mg/cm2 thick. This foil thickness corresponds to 26 X 1021 Z2 atoms/cm2 and from Fig. 2 we find a ratio of 1.10 f 0.01. In the older literature, Wenzel’s (7) criterion has been used extensively to
88
SPIEGEL,
JR.,
WV--@
MILLER,
AND
WALDMAN
.
0
1.00
60.T
.
1.00 120* R 1
,> 2.50 1.75
150.R 1.75I1.00
FIG. 2. Compilation of all data. The curves have been shifted vertically for convenience in plotting. Each curve intercepts the ordinate axis at 1.0 and each unit of the ordinate is 0.1.
the maximum foil thickness for single scattering. This criterion is (O/W>> 1 (‘p is the angle at which one wishes to observe single scattering and w is a minimum deflection angle determined by the foil thickness). For cp = HOW, the curves of Fig. 2 indicate that the plural scattering at, cpwill be lessthan 10 % of the single scattering. calculate
RECEIVED:
October 14, 1958
PLURAL
SCATTERING
OF
ELECTRONS
89
REFERENCES I. 8.
3. 4.
5. 6’. 7.
V. SPIEG:EL, JR., T. F. RUANE, D. J. ANTHONY, B. WALDMAN AND W. C. MILLER, paper [Annals of Physics 6, 70 (1959)]. H. REICII, 2. Physik 130, 144 (1951). C. T. CHASE AND R. T. Cox, Phys. Rev. 68, 243 (1940). G. GOERTZEL AND R. T. Cox, Phys. Rev. 63, 37 (1943). N. RYU, J. Phys. Sot. Japan 6, 423 (1950). M. HAMMERMESH AND J. MONAHAN, Phys. Rev. 93,963 (1954). G. WENZEL, Ann. Physik 69, 335 (1922).
preceding
OF
PHYSICS:
Plural
6,
8689
Scattering
of Electrons
1.75
and
V. SPIEGEL, Department
(1959)
Mev, JR.,t
of Physics,
W. University
2.50
C. MILLER, of Notre
at 1.00 Mev.
Mev,
II.*
AND B. WALDMAN Dame,
Notre
Dame,
Indiana
Monoergic electrons were scattered from thin foils of aluminum, nickel, silver and gold. The scattered electrons were analyzed by a magnetic spectrometer. The electron-nuclear cross sections were measured as a function of foil thickness and for scattering angles of 30°, 60°, 90°, 120°, and 150’. The data presented show the onset of plural scattering and may be used as a convenient guide for single scattering.
In the measurement of the cross section for single scattering of electrons by the coulomb field of nuclei (1), it was necessary to recognize and correct for the presence of plural scattering. The recent interest in the detection of electron polarization by coulomb scattering suggeststhe separate publication of these data as a convenient guide for single scattering. The foremost criterion for single scattering is the observance of the linear dependence of the number of scattered electrons with the scatterer thickness. Any deviation from linearity is an indication of plural scattering. Extrapolation to zero scatterer thickness reduces the data to the correct value for single scattering. As Reich (2) has shown, it is convenient to plot the number of scattered electrons per unit scatterer thickness as the ordinate and the scatterer thickness in atoms per cm2 times 27 as the abscissa. The Z2 factor helps in normalizing the data so that scatterers of all 2 values can be plotted on the same scale. On this graph a line of zero slope indicates no plural scattering. Another indication of plural scattering is the comparison of the scattering from the transmission and the reflection positions of the scattering foil. These positions are illustrated in Fig. 1. The onset of plural scattering will affect the reflection data very much more than the transmission data because of the increased probability of two small angle scatterings. This phenomenon has been observed by * Supported in part by the joint program of the Office of Naval Research Atomic Energy Commission. t Now at the National Bureau of Standards, Washington, D. C. 86
and the
U. S.
PLURAL
SCATTERING
OF
‘, I \ ‘\ 1
FIG. 1. Transmission and reflection scattering angle in transmission. The flection.
ELECTRONS
87
REFLECTION
\‘\
TRANSMISSION
positions at 90’. plane of the foil
The normal to the foil bisects the bisects the scattering angle in re-
Chase and Cox (3) in experiments on electron polarization. Goertzel and Cox (4) calculated the relative scattering cross sections for a single 90” scattering compared to two 45” scatterings. Similar calculations have been made by Ryu (5) and Hammermesh and Monahan (6). The details of the experimental arrangement, procedure and treatment of data are described by Spiegel et al. (1). The results are plotted inFig. 2. The transmission position is used for the 30”, 60”, and 90” angles. The reflection position is used at 90”, 120”, and 150”. If the reflection position were used at the small angles the effective thickness would be too large. This is also true for the transmission position at the large angles. At 90” both reflection and transmission data were taken. The abscissa refers to the actual foil thickness, not the effective thickness due to the inclination of the foil. The general shapes of the curves, the trends with energy and with atomic number are all in agreement with the qualitative theory of plural scattering. Unfortunately no quantitative calculation is available for a better comparison. However, the calculation of Hammermesh and Monahan (8) predicts a reflection to transmission ratio of 1.05 f 0.01 for the 90” scattering of 1.7-Mev electrons on an aluminum foil 7 mg/cm2 thick. This foil thickness corresponds to 26 X 1021 Z2 atoms/cm2 and from Fig. 2 we find a ratio of 1.10 f 0.01. In the older literature, Wenzel’s (7) criterion has been used extensively to
88
SPIEGEL,
JR.,
WV--@
MILLER,
AND
WALDMAN
.
0
1.00
60.T
.
1.00 120* R 1
,> 2.50 1.75
150.R 1.75I1.00
FIG. 2. Compilation of all data. The curves have been shifted vertically for convenience in plotting. Each curve intercepts the ordinate axis at 1.0 and each unit of the ordinate is 0.1.
the maximum foil thickness for single scattering. This criterion is (O/W>> 1 (‘p is the angle at which one wishes to observe single scattering and w is a minimum deflection angle determined by the foil thickness). For cp = HOW, the curves of Fig. 2 indicate that the plural scattering at, cpwill be lessthan 10 % of the single scattering. calculate
RECEIVED:
October 14, 1958
PLURAL
SCATTERING
OF
ELECTRONS
89
REFERENCES I. 8.
3. 4.
5. 6’. 7.
V. SPIEG:EL, JR., T. F. RUANE, D. J. ANTHONY, B. WALDMAN AND W. C. MILLER, paper [Annals of Physics 6, 70 (1959)]. H. REICII, 2. Physik 130, 144 (1951). C. T. CHASE AND R. T. Cox, Phys. Rev. 68, 243 (1940). G. GOERTZEL AND R. T. Cox, Phys. Rev. 63, 37 (1943). N. RYU, J. Phys. Sot. Japan 6, 423 (1950). M. HAMMERMESH AND J. MONAHAN, Phys. Rev. 93,963 (1954). G. WENZEL, Ann. Physik 69, 335 (1922).
preceding