- Email: [email protected]
Proton proton bremsstrahlung at 20 MeV
Volume
26B, number
PHYSICS
9
PROTON
PROTON
LETTERS
1 April
BREMSSTRAHLUNG
AT
20
MeV
1968
*
A. BAHNSEN and R. L. BURMAN University
of Rochester, Received
Rochester, 12 March
New
York,
USA
1968
The proton proton bremsstrahlung has been investigated at 20 MeV beam energy. The outgoing protons were detected at equal angles of 35’ to the beam, and the cross section d2ddqd% was found to be This values is in agreement with theoretical calculations, and with other experimental 1.3 + 0.4 pb/sr2. data at low energies.
We have measured the proton proton bremsstrahlung (hereafter ppy) cross section at 20 MeV beam energy. A hydrogen gas target was bombarded with protons from the University of Rochester MP tandem Van de Graaff, and the two outgoing protons were detected in coincidence. The photon was not detected; instead, the ppy reactions were identified by the kinematic restrictions on the proton momenta. The detectors were placed at equal and opposite angles 8 with respect to the beam, choosing 0 = 35O such that 28 < 90°, to avoid direct elastic scattering coincidences. This is the so called “Harvard” geometry used in the majority of the ppy experiments, and the result is expressed by the laboratory cross section d2u/d01dC12, where 521 and a2 are the proton angles. Having fixed the polar angles 8, the azimuthal angle $J between one proton and the plane of the other proton and the beam is restricted by the kinematics to a range of a few degrees around 1800. In the present experiment, this range was 4.20. The result of the measurement is: d2, = 1.1 f 0.4 pb/sr2 dSlIdS22
,
averaged
over r$ .
The variation with 4 was measured with position sensitive detectors oriented perpendicular to the horizontal scattering plane. The angular resolution was ilo for both e and 4. The effective solid angle appropriate to any given range of $ was determined from a separate measurement of the random coincidence distribution, which has an isotropic +-dependence. The measurement of the distribution with $J of ppy events suffers from * Work supported
by the National Science
Foundation.
poor statistics; it may be used to derive a coplanar cross section from the averaged cross section with the result: = 1.2 f 0.5 pb/sr2
.
Most experiments obtain the coplanar cross section by assuming the $-variation to be deter mined by phase space [3]. This assumption leads to the result: = 1.3 f 0.4 pb/sr2 . oplanar In order to decrease the random coincidence rate from elastic protons, two anticoincidence counters were used, each set at 90’ to a solid state detector. The efficiency in vetoing the elastic protons was about 9570, and the resulting random coincidence rate was 1570 of the bremsstrahlung count rate. The main sources of background were then true coincidences from (p, 2p) reactions on gas contaminants and from multiple scattering of protons. The result of a representative run is shown on fig. 1. The random (delayed) coincidences were accumulated simultaneously with the true events. They have been subtracted out in fig. 1. The principal gas contaminant was deuterium. The hydrogen used contained 10-4 parts of deuterium, giving an equivalent cross section of 0.2 pb/sr2 in the region of interest. This number of events was determined on the basis of D(p, 2p)n events registered in an adjacent area and of a short run made with 20$&deuterium in the chamber. Those events in fig. 1 that are not accounted for by ppy or by D(p, 2p)n can be ascribed to multiple scatterings in the target gas and collimator slits. The yield of such coincident events 585
Volume 26B. number
9
PHYSICS
LETTERS
1 April
1968
.
“$/E
‘r
. .*
.
-
8 .
7
6
-
.
.
5
,.
.
.
.
..
,El
5 6 7 8 9 MeV Fig. 1. Experimental data. Coincident events are plotted with the two proton energies as axes. Random coincidences were subtracted out before plotting this figure. The area between the two curves is the kinematically allowed bremsstrahlung region, taking into account the finite energy resolution.
was calculated; for the particular geometry of this experiment, it was found that slits made of tantalum would give a yield in the ppy region equivalent to 1.1 pb/sr2, whereas beryllium, which was used here, gives 0.03 pb/sr2. The coincidence spectra obtained in initial runs using tantalum slits were in agreement with the calculations. Frequent checks were made of the coincidence timing and the energy calibration of the detectors by recording elastic protons in coincidence for a variety of incident beam energies and detector angles. The uncertainty of 32% on the measured ppy cross section is mainly due to statistics, with a few percent coming from uncertainties in coincidence efficiency, dead time, and target thickness. The volume of the gas target was calculated numerically on a computer. The measured rate of single counts constituted a check on the target volume calculations. Two runs were made to determine the cross section. A third run showed radiation damage to the position sensitive detectors to an extent that made this run useless. The result of the present measurement is compared to other results in fig. 2. The coplanar cross section d2c/dSZfdCL2 at 8 = 30° and 35’ is shown as a function of energy; calculations are represented by curves, the experimental points are given with their uncertainties. All low energy 586
Fig. 2. Survey of calculations and measurements of pw. The experimental data are plotted with their uncertainties. Data taken at 0 = 35O and 30° are shown; references are indicated on the figure. The coplanar cross section is plotted; for the low-energy data, a phase space variation has been assumed, whereas the high energy data (Gottschalk et al. [ll] at 160 MeV and Rothe et al, [ 121 at 200 MeV) are the measured coplanar cross sections. The curves are theoretical results at 30’ and 35O, as follows: a, 30°[5]; b, 30°[10]; c, 30’ [6]; d, 30’ [7]; e, 35O [lo]; f, 30° [9]; g, 300 [8].
data are normalized by phase space. The agreement with the other 35O data at 30 and 48 MeV is seen to be very good. The only available calculation at 35’ is that of Nyman [lo], which is in excellent agreement with the experimental data. This calculation on the other hand, is in agreement with most of the other calculations as evidenced by curve b. We can therefore assume that, essentially, all calculations are in agreement with the experiments within their uncertainties.
References 1. J.C.Thompson,
2. 3. 4. 5. 6. 7. 8.
S.I.H.NagviandR.E.Warner, Phys. Rev. 156 (1967) 1156. I. Slaus, J. W. Verba, J.R. Richardson, R. F. Carlson, W.T.H.van Oers and L.S.August, Phys. Rev. Letters 17 (1966) 536. R.E. Warner, Can. J. Phys. 44 (1966) 1225. M. L. Halbert, D. L. Mason and L. C. Northcliffe, Oak Ridge Natl. Lab. Preprint. I. M. Duck, W.A. Gale and W.A. Pearce, Nucl. Phys. B3 (1967) 241. D. Drechsel and L. C . Maximon, Natl. Bur. of Standards, Preprint. V.R.Brown, Phys. Letters 25B (1967) 506. A.H.Cromer and M.I.Sobel, Phys. Rev. 158 (1967) 1157.
Volume 26B, number
9
PHYSICS
LETTERS
1 April
1968
W. J. Shlaer and K. H. Wang, Phys. 11. B.Gottschalk, Letters 16 (1965) 294; Nucl. Phys. 75 (1966) 549; Nucl. Phys. A94 (1967) 491. P.F.M.Koehler and E.H.Thorndike, 12. K.W.Rothe, Phys. Rev. 16 (1966) 1118; 157 (1967) 1247.
9. J. E. Brolley and L. K. Morrison, Los Alamos Scient. Lab., Preprint. 10. E.Nyman, Phys. Letters 25B (1967) 135, and private communication. *****
587
26B, number
PHYSICS
9
PROTON
PROTON
LETTERS
1 April
BREMSSTRAHLUNG
AT
20
MeV
1968
*
A. BAHNSEN and R. L. BURMAN University
of Rochester, Received
Rochester, 12 March
New
York,
USA
1968
The proton proton bremsstrahlung has been investigated at 20 MeV beam energy. The outgoing protons were detected at equal angles of 35’ to the beam, and the cross section d2ddqd% was found to be This values is in agreement with theoretical calculations, and with other experimental 1.3 + 0.4 pb/sr2. data at low energies.
We have measured the proton proton bremsstrahlung (hereafter ppy) cross section at 20 MeV beam energy. A hydrogen gas target was bombarded with protons from the University of Rochester MP tandem Van de Graaff, and the two outgoing protons were detected in coincidence. The photon was not detected; instead, the ppy reactions were identified by the kinematic restrictions on the proton momenta. The detectors were placed at equal and opposite angles 8 with respect to the beam, choosing 0 = 35O such that 28 < 90°, to avoid direct elastic scattering coincidences. This is the so called “Harvard” geometry used in the majority of the ppy experiments, and the result is expressed by the laboratory cross section d2u/d01dC12, where 521 and a2 are the proton angles. Having fixed the polar angles 8, the azimuthal angle $J between one proton and the plane of the other proton and the beam is restricted by the kinematics to a range of a few degrees around 1800. In the present experiment, this range was 4.20. The result of the measurement is: d2, = 1.1 f 0.4 pb/sr2 dSlIdS22
,
averaged
over r$ .
The variation with 4 was measured with position sensitive detectors oriented perpendicular to the horizontal scattering plane. The angular resolution was ilo for both e and 4. The effective solid angle appropriate to any given range of $ was determined from a separate measurement of the random coincidence distribution, which has an isotropic +-dependence. The measurement of the distribution with $J of ppy events suffers from * Work supported
by the National Science
Foundation.
poor statistics; it may be used to derive a coplanar cross section from the averaged cross section with the result: = 1.2 f 0.5 pb/sr2
.
Most experiments obtain the coplanar cross section by assuming the $-variation to be deter mined by phase space [3]. This assumption leads to the result: = 1.3 f 0.4 pb/sr2 . oplanar In order to decrease the random coincidence rate from elastic protons, two anticoincidence counters were used, each set at 90’ to a solid state detector. The efficiency in vetoing the elastic protons was about 9570, and the resulting random coincidence rate was 1570 of the bremsstrahlung count rate. The main sources of background were then true coincidences from (p, 2p) reactions on gas contaminants and from multiple scattering of protons. The result of a representative run is shown on fig. 1. The random (delayed) coincidences were accumulated simultaneously with the true events. They have been subtracted out in fig. 1. The principal gas contaminant was deuterium. The hydrogen used contained 10-4 parts of deuterium, giving an equivalent cross section of 0.2 pb/sr2 in the region of interest. This number of events was determined on the basis of D(p, 2p)n events registered in an adjacent area and of a short run made with 20$&deuterium in the chamber. Those events in fig. 1 that are not accounted for by ppy or by D(p, 2p)n can be ascribed to multiple scatterings in the target gas and collimator slits. The yield of such coincident events 585
Volume 26B. number
9
PHYSICS
LETTERS
1 April
1968
.
“$/E
‘r
. .*
.
-
8 .
7
6
-
.
.
5
,.
.
.
.
..
,El
5 6 7 8 9 MeV Fig. 1. Experimental data. Coincident events are plotted with the two proton energies as axes. Random coincidences were subtracted out before plotting this figure. The area between the two curves is the kinematically allowed bremsstrahlung region, taking into account the finite energy resolution.
was calculated; for the particular geometry of this experiment, it was found that slits made of tantalum would give a yield in the ppy region equivalent to 1.1 pb/sr2, whereas beryllium, which was used here, gives 0.03 pb/sr2. The coincidence spectra obtained in initial runs using tantalum slits were in agreement with the calculations. Frequent checks were made of the coincidence timing and the energy calibration of the detectors by recording elastic protons in coincidence for a variety of incident beam energies and detector angles. The uncertainty of 32% on the measured ppy cross section is mainly due to statistics, with a few percent coming from uncertainties in coincidence efficiency, dead time, and target thickness. The volume of the gas target was calculated numerically on a computer. The measured rate of single counts constituted a check on the target volume calculations. Two runs were made to determine the cross section. A third run showed radiation damage to the position sensitive detectors to an extent that made this run useless. The result of the present measurement is compared to other results in fig. 2. The coplanar cross section d2c/dSZfdCL2 at 8 = 30° and 35’ is shown as a function of energy; calculations are represented by curves, the experimental points are given with their uncertainties. All low energy 586
Fig. 2. Survey of calculations and measurements of pw. The experimental data are plotted with their uncertainties. Data taken at 0 = 35O and 30° are shown; references are indicated on the figure. The coplanar cross section is plotted; for the low-energy data, a phase space variation has been assumed, whereas the high energy data (Gottschalk et al. [ll] at 160 MeV and Rothe et al, [ 121 at 200 MeV) are the measured coplanar cross sections. The curves are theoretical results at 30’ and 35O, as follows: a, 30°[5]; b, 30°[10]; c, 30’ [6]; d, 30’ [7]; e, 35O [lo]; f, 30° [9]; g, 300 [8].
data are normalized by phase space. The agreement with the other 35O data at 30 and 48 MeV is seen to be very good. The only available calculation at 35’ is that of Nyman [lo], which is in excellent agreement with the experimental data. This calculation on the other hand, is in agreement with most of the other calculations as evidenced by curve b. We can therefore assume that, essentially, all calculations are in agreement with the experiments within their uncertainties.
References 1. J.C.Thompson,
2. 3. 4. 5. 6. 7. 8.
S.I.H.NagviandR.E.Warner, Phys. Rev. 156 (1967) 1156. I. Slaus, J. W. Verba, J.R. Richardson, R. F. Carlson, W.T.H.van Oers and L.S.August, Phys. Rev. Letters 17 (1966) 536. R.E. Warner, Can. J. Phys. 44 (1966) 1225. M. L. Halbert, D. L. Mason and L. C. Northcliffe, Oak Ridge Natl. Lab. Preprint. I. M. Duck, W.A. Gale and W.A. Pearce, Nucl. Phys. B3 (1967) 241. D. Drechsel and L. C . Maximon, Natl. Bur. of Standards, Preprint. V.R.Brown, Phys. Letters 25B (1967) 506. A.H.Cromer and M.I.Sobel, Phys. Rev. 158 (1967) 1157.
Volume 26B, number
9
PHYSICS
LETTERS
1 April
1968
W. J. Shlaer and K. H. Wang, Phys. 11. B.Gottschalk, Letters 16 (1965) 294; Nucl. Phys. 75 (1966) 549; Nucl. Phys. A94 (1967) 491. P.F.M.Koehler and E.H.Thorndike, 12. K.W.Rothe, Phys. Rev. 16 (1966) 1118; 157 (1967) 1247.
9. J. E. Brolley and L. K. Morrison, Los Alamos Scient. Lab., Preprint. 10. E.Nyman, Phys. Letters 25B (1967) 135, and private communication. *****
587