Measurement of proton inelastic cross sections between 77 MeV and 133 MeV

Nuclear Physics 29 (1962} 47£

£95; (~) North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission front the publisher

MEASUREMENT

OF P R O T O N

INELASTIC

CROSS

SECTIONS

B E T W E E N 77 MeV A N D 133 MeV R. G O L O S K I E ? A N D K. S T R A U C H

Cyclotron Laboratory, Harvard University, Cambridge 38, Massachusetts tt Received 20 M a y 1961 A b s t r a c t : The p r o t o n inelastic cross sections of carbon, a l u m i n i u m , coppcr, silver a n d lead have bccn mcasurc
1. I n t r o d u c t i o n To understand the interaction of high energy nucleons with complex nuclei, it is desirable to have detailed information on total, absorption and ditferential cross secUons. Absorption cross section measurements with protons between 77 MeV and 133 MeV are reported in this paper. Neutron absorption cross section measurements are available in this energy region 1). The only other available proton measurements 2) were made at the upper limit of the energy region. Measurements at 61 MeV have been reported s) and the present measurements cover an energy interval not previously available for protons. 2. E x p e r i m e n t a l E q u i p m e n t The proton inelastic cross sections a a are measured with a specially designed range telescope placed directly into the external beam of the cyclotron. The general setup of the beam is shown in fig. 1 and a schematic view of the telet P r e s e n t address: D e p a r t m e n t of Physics a n d A s t r o n o m y , Colgate University, Hamilton, N e w York t? W o r k s u p p o r t e d b y the joint p r o g r a m of t h e Office of N a v a l Research and t h e U. S. Atomic E n e r g y Commission 474

PROTON INELASTIC CROSS SECTIONS

475

scope is shown in fig. 2. The cross sections are measured by counting the number of protons entering the target and then counting the number of protons leaving the target which have not lost energy in an inelastic collision. The difference between the two numbers represents the number of protons which have suffered a collision in which the internal energy state of the target nucleus is changed. Care must be taken not to consider the large angle elastic nuclear and Coulomb scatterings as inelastic.

! TS

Fig. 1. The e x t e r n a l p r o t o n b e a m us e d in t h i s e x p e r i m e n t .

The cyclotron is set up to give a well defined external, unpolarized beam ~) using slits A, B and C. The size of the beam is about 1 cm in diameter in the experimental area. Slit C does most of the defining and is closed down to 0.25 cm by 0.25 cm. Slit D serves as an antiscattering slit. The bending magnet removes from the beam low energy particles produced in the various materials inserted into the beam between slits B and C. This magnet, slit C and the size of the telescope limit the total spread in energy of the beam to 1.1 ~/o.

'476

STRAUCH

R. GOIOSKIE AND K.

The intensity of the beam passing through the telescope must be reduced by a factor of about 10~ from normal operation to ke~p the electronic circuits from overloading. This reduction is controlled by a carbon clipper placed inside the cyclotron at a small radius of 26.7 cm. A lead scatterer, placed between slits B and C and 10 MeV thick, reduces the intensity sufficiently to permit operation of the carbon clipper in a non-critical region.

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F i g . 2. T h e p r o t o n t e l e s c o p e .

Flat brass degraders are attached to this lead scatterer to reduce the beam energy to permit the measurement of ~ in different energy ranges. The first two counters use plastic scintillators and are discs 1.3 cm in diameter by 0.64 cm thick. These counters, operated in coincidence, define a well collimated beam striking the target and serve as the beam monitor. As a compromise between the desire for good energy resolution and reasonable counting time the targets are made 15 MeV thick which results in a 1.5 % to 3 % nuclear absorption in the target, depending on the target and the energy

PRo~o~ mRL^s~m CROSSs~cTIo~s

477

of measurement. The targets, carbon, aluminium, copper, silver and lead, are made from commercially pure stock. Counters 3, 4 and 5 with the specially shaped brass absorbers comprise the energy analyzer and detector for elastically scattered protons. This section is shown in detail in fig. 3. The geometry is made very "poor" to keep the systematic error due to large angle elastic scatterings to a few per cent or less. All elastic scatterings up to 45 ° can be detected except for nuclear absorption in the material of this section of the telescope. Some scattering up to 60 ° can be detected. The weighted average between these two angles is called the cut off

wbJ ZZ

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Fig. 8. Details of telescope showing the limiting angles within which elastically scattered protons are accepted by the telescope.

angle and is found to be 50°. The telescope absorbers must be shaped so that a proton elastically scattered through a large angle in the target will not come to the end of its range in the absorbers, while at the same time an inelastically scattered proton will be stopped. The absorbers are shaped so that a proton after passing through { of t h e target "sees" the same amount of material in all directions at a "cut off energy" of 10 MeV (see sect. 3.) Counter 3 is placed immediately behind the target. This counter when operated in coincidence with counter 4 or counter 5 keeps target generated neutrons from producing appreciable numbers of false coincidences. Only a high energy, target generated neutron which suffers a headlong collision with a proton in counter 3 can produce false counts. The error introduced into ~a by this effect is less than 0.1 °/o and has been neglected. Counter 3 has been found to b e necessary for the heavier elements.

478

R.

GOLOSKIE

AND

K.

STRAUCI-I

Counters 3, 4 and 5 are made with plastic scintillators and have a diameter of 6.98 cm, 15.2 cm and 20.3 cm, respectively, to accommodate the desired cut-off angle. The nuclear absorption of the beam protons in the telescope absorber~ is larger than in the target. Thus a measurement of the detection efficiency of the energy analyzing portion of the telescope must be made with protons having the same energy as when the target is in place. For this purpose pieces of polyethylene having the same stopping power as the targets can be remotely n.n~

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Fig. 4. Block diagram of the electronic circuits.

inserted into the beam behind slit B. These pieces of polyethylene are called the " C H 2 equivalents". In operation the CH 2 equivalent is in the beam when the target is out of the beam, or out of the beam when the target is in. These arrangements are known as the " t a r g e t - o u t " configuration and the "target-in" configuration, respectively. The bending magnet is readjusted whenever a CH z equivalent is inserted or removed. Shielding is placed in the area to reduce the single counting rates in the counters. Particularly useful are the two brass shielding blocks 3.8 cm thick which are placed immediately behind counters 1 and 2. All the plastic scintillators are viewed b y R. C. A. 6810 or 6810A photomultipliers. The pulse is taken off the last dynode and fed to a fast E F P 6 0 discriminator. The discriminator output pulse is negative and 5 × 10-8 sec in

PROTON I N R L A S T I C CROSS SECTIONS

479

width. The dead time of this E F P 6 0 circuit has been measured to be less than 2 × 10-7 sec, depending on the input pulse size. A block diagram of the electronic circuits is shown in fig. 4. These are arranged to count all protons going through the first two counter {monitor), all protons going through the first four counters and all protons going through counters 1, 2, 3 and 5. The cross sections are thus measured simultaneously with two different levels of energy discrimination. The coincidence cricuits are a U. C. R. L. modification 5) of the Garwin coincidence circuit which work in the nsec region. The fast amplifiers and the fast scalars {dead time 0.1 #sec) are made b y the Hewlett Packard Corporation. The use of the discriminators produces exceedingly flat and wide counting plateaus for all adjustable voltages and delays. Extreme stability is necessary for this experiment because only a few per cent of the beam protons are absorbed in the target.

3. E x p e r i m e n t a l Method Let M o and Mt be the number of beam protons entering the telescope in the target-out and target-in configurations, respectively. Call N O and N t the number of these protons which do not suffer an inelastic nuclear collision in the telescope for the target-out in target-in configurations, respectively. Thus, Mo and Mt equal the number of (1, 2) coincidences, N o and Nt equal, after small corrections, the number of (1, 2, 3, 4) or (1, 2, 3, 5) coincidences. The inelastic cross section of the target material is given b y

A "n (N°mt) where A is the atomic mass number of the target, N Avogadro's number and p the areal density of the target. In operation the telescope is aligned along the external beam axis to an accuracy of + 0 . 5 °. A range curve is taken at each energy of interest. These curves are useful for checking possible systematic errors due to range straggling as explained in sect. 4. To take into account correctly the telescope efficiency it is very important that the average energy and energy distribution of the protons entering the energy analyzing section of the telescope in the target-in and target-out configuration be equal. The reason is as follows: if any appreciable number of protons stop in the telescope absorber because of range straggling and/or low energy tail in the incident beam, this number must be the same in the target-in and target-out configurations. To insure that each target and its CH s equivalent have the same stopping power, the following procedure is used. Additional absorbers are placed into the telescope until about half of the protons

480

R. GOLOSKIE AND K. STRAUCH

reaching counter 4 stop before reaching counter 5. The (1, 2, 3, 4) to (1, 2, 3, 5) counting ratio is then a very sensitive function of the energy of the protons passing through the telescope. Energy changes of magnitude 0.05 MeV can easily be detected in relatively short counting times. The thickness of the CH~ equivalents is determined experimentally for each target b y adjusting the thickness of polyethylene until the same ratio of (1, 2, 3, 4) to (1, 2, 3, 5) counts is found in both the target-in and target-out configurations. Final small energy adjustments are made using the energy dispersion of the bending magnet. The cut-off energy is defined as the amount of energy a beam proton can lose in an inelastic collision in the target and still be counted as an elastic proton. Its value is determined b y the thickness of the telescope. No measurements are practical at a cut-off energy of less than 8 MeV because of the sensitivity of telescope efficiency to range straggling as just explained. To s t u d y the dependence of ~a on the value of the cut-off energy three Values of 8 MeV, 16 MeV and 24 MeV are used in this experiment. Because aa can be measured at two values of the cut-off energy simultaneously and to check the operation of the telescope the cross sections are measured, in general, with three different absorber configurations: (1) the "standard energy" corresponds to counters 4 and 5 at cut-off energies of 16 MeV and 8 MeV, respectively; (2) the "low energy" corresponds to counters 4 and 5 at cut-off energies of 24 MeV and 16 MeV, respectively; (3) finally, the "high energy" corresponds to counter 4 at a cut-off energy of 8 MeV and counter 5 at too low a cut-off energy to be used. To check that the geometry of the telescope does not affect appreciably the cross sections measurements the following changes were tried: (1) the distance between the first two counters was decreased b y a factor of 2.5; (2) counters 4 and 5 were moved back b y 5 cm; (3) the target was moved 0.3 cm upstream; (4) the bending magnet current was changed b y 4-1 ~ . No effect due to these changes was noticable within 3 °/o statistics. Measurements indicate that aa does depend on the thickness of the CHg. equivalent in a linear manner. This situation introduces an error of 0.4 % into as because of the uncertainty in the correctness of the thickness of the CH 2 equivalent. The rate effects are believed to be negligible at rates below 400 counts/sec from calculations based on the measured singles counting rates in the counters. Inelastic cross sections measured to 3 ~/o precision at counting rates of 100, 175 and 300 (1, 2) coincidence/sec all agree within statistics. Hence, for the cross sections measured at 175 counts/sec the errors associated with the rate affects are assumed to be much less than 1 °/o and are neglected. The actual data are taken in at least 6 pairs of runs of 128000 (1, 2) coincidences each for each setting of the absorbers, for each element, at each energy of measurement.

481

PROTON I N E L A S T I C CROSS SECTIONS

4. C a l c u l a t i o n s a n d C o r r e c t i o n s The absorption cross section is given b y eq. (1). Since No and N t are distributed binomially from 0 to Mo and Mt, respectively s), the standard deviation in aa, Aaa is evaluated as 1

Acra = - ~ { [(Mo--No) /NoMo] + [(Mt--N,) /M, Ni]} ½.

(2)

The values of aa calculated with the measured value of Na have to be corrected for (1) large angle elastic scattering and (2) the inclusion of "near-elastic" TABLE 1 Experimental r e s u l t s Energy (MeV)

"6

o

a&

uncorrected

(b)

"Near elastic" scattering

Large angle scattering

(b)

(b)

% final

(b)

1334-5 1134-5 95+5 774-5

1.22034-0.0022 0.21934-0.0047 0.23204-0.0041 0.22174-0.0044

+ 0.0033 +0.0010 +0.0021 +0.0000

--0.0005 --0.0009 --0.0016 --0.0030

0.22314-0.0063 0.21944-0.0072 0.23254-0.0073 0.21874-0.0077

I

1334-5 1134-5 954-5 774-5

0.41804-0.0050 0.40664-0.0081 0.41244-0.0081 0.44644-0.0088

+0.0062 +0.0020 +0.0037 +0.0000

--0.0003 --0.0006 --0.0011 --0.0024

0.424

I

133-4-5 1134-5 954-5 774-5

0.768 0.748 0.786 0.749

4-0.010 4-0.016 4-0.011 4-0.013

+0.011 +0.004 +0.007 +0.000

--0.000 --0.001 --0.003

0.779 0.751 0.774 0.746

4-0.023 4-0.025 +0.022 4-0.021

1334-5 1134-5 954-5 77+5

1.061 1.120 1.042 0.994

4-0.022 4-0.023 4-0.023 4-0.025

+0.016 +0.006 +0.009 +0.000

--0.000 --0.001 --0.001 -- 0.005

1.077 1.125 1.050 0.989

4-0.041 4-0.038 4- 0.036 4-0.038

1334-5

1.807 1.707 1.741 1.667

4-0.034 ±0.037 4-0.045 4-0.042

+0.027 +0.009 +0.001 +0.000

-- 0.000

1.834 -4-0.062 1.716 -4-0.056 1.756 -4-0.067 1.665 4-0.060

1134-5 95-4-5 77±5

-- 0.001

-- 0.000

--0.001 --0.002

~0.013 0.408 ~:0.013 0.415 4-0.013 0.444 4-0.014

scattering events as elastic events. The first correction is made b y extrapolating the elastic scattering data ,.s) at 95 MeV and 160 MeV to 180 ° and obtaining the total cross section for elastic scattering beyond 50 ° b y integration. The estimate of this cross section at other energies is found b y assuming that the differential elastic scattering cross section at energy E 1 and angle 01 is approximately equal to the cross section measured at energy E s and angle 0~, where ~ 1 0 x ----- ~/~020~ . This relationship is fairly well verified b y the data ,-11).

4s2

R. GOLOSKm AND X. S T ~ U C S

The magnitude of this correction is shown in table 1. The error is taken as equal to the magnitude of the correction. Because the cut-off energy is greater than 0 some inelastic events are counted as elastic events. To estimate the magnitude of this error, called near elastic scattering, the cross sections are first calculated at a particular value of the cut-off energy. Within relatively poor statistics, the per cent change in cr~ per MeV of cut-off energy is found to be nearly equal for all elements in a given energy range. Using this result and examining the differential inelastic scattering data 1~) the estimate for the correction for near elastic scattering is taken as { the average relative change in a~ between cut-off energies of 16 MeV and 8 MeV. The error range of this correction is taken as equal to the estimate of the magnitude. No corrections are made for the effect of small differences in range distribution of protons passing through the telescope in the target-in and target-out configurations. These arise because the CH~ equivalent is placed upstream from the bending magnet in order to remove low energy protons (produced in the CH 2 equivalents) from the beam passing through the monitor counters 1 and 2. The magnitude of the effect (as a function of cut off energy) can be calculated on the basis of the energy resolution of the bending magnet system and the theory of range straggling is). The calculation predicted an exponential drop off as the cut-off energy is increased. Cross sections measured at low values of cut-off energy are in quantitative agreement with the calculated results. The calculations show that for cut-off energies greater than 8 MeW, the cross sections are affected b y less than 0 . 1 % . The absorption cross sections measured with counter 5 are on the average 2 °/o higher than the cross sections measured with counter 4 at a specific cut-off energy. This figure is 221 standard deviations larger than the expected value of 0 ~o, indicating a definite discrepancy. The error is believed due to an inefficiency of counter 5 caused b y excessive light absorption at a glue point in the light pipe. The situation was not detected until after the present measurements had already been made. Still it is not certain that this discoloration is the cause of the difference in the measured values of ~a. Lacking further information 1 °/o has been added linearly to the final error of the quoted results. All other errors (statistical counting errors, measurement errors and the estimated errors in the corrections) have been combined in the usual manner for Gaussian errors. 5.

Results

and

Discussion

The final value for the inelastic cross sections is taken as the average of all ~a measured at a cut-off energy of 8 MeV corrected for the effects of large angle elastic and of near elastic scattering. The results are shown in table 1 with the errors computed as explained in sect. 4.

PROTON

INELASTIC

CROSS

SECTIONS

483

It is desirable to compare these results with the results of other experiments. This is done in fig. 5 which displays published 1,,, 14-1~) absorption cross sections values betseen 60 and 300 MeV. The proton cross sections have been divided by (1-W/E) to correct for effect of the Coulomb field 1, ~). (W is the Coulomb barrier energy and E is the energy of the bombarding proton.) The results for silver and cadmium are not plotted because there are not enough data to make direct comparisons between proton and neutron results.

0281

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THIS WORK

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Ref. 14) Ref 16)

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NEUTRON a Ref. 15) o Ref. t) o Ref. 17}

Fig. 5. S u m m a r y of measured absorption cross sections of C, A1, Cu and Pb b e t w e e n 50 M e V and 320 MeV.

Where available, the agreement at 133 MeV with the results of ref. 2) is satisfactory. For energies above 90 MeV the proton and neutron results for carbon and aluminium seem to be the same within the experimental error. Below this energy the Coulomb correction factor is probably in error. The copper and lead results are more interesting. In the region from 90 to 150 MeV the adjusted a~ for protons is as much as 8 % higher than the a= for neutrons, which number is well outside the quoted errors. For lead the discrepancy in this region is about 15 % at the maximum. No attempt has been made to make an overall optical model analysis using all of the available data. Rather calculations have been made to try to explain the difference between the neutron and proton absorption cross sections. The

4~

R. GOLOSKIE AND K. STRAUCH

calculations have been made with both the square well and the Saxon well, the phase shifts being calculated in W K B approximation ls-~) and neglecting the spin-orbit term. We have tried to explain the difference b y assuming first that the radius (and the taper) of the well is the same for both protons and neutrons incident. The assumption requires that the depth of the imaginary part W of the potential well be considerably greater for protons than for neutrons a factor of 1.7 or 2.0 for lead, a factor of 1.2 or 1.3 for copper and a factor of 1.3 or 1.5 for cadmium and silver for the Saxon well and the square well approximations, respectively. The silver and cadmium results are compared indirectly assuming a A} dependence for cra. The form of the Saxon potential used is expressed as

V+iW Vsw ----- 1 + e (~-~0)/~"

(3)

The starting values of the parameters used for incident protons are V = 16 MeV W ----- 15 MeV, r 0 = 1.20×A½ fm and a = 0.57 fm. These values were quite successful in fitting the 160 MeV elastic proton scattering data 8). A second attempt to explain the differences in a a for protons and neutrons was made b y allowing the radius of the imaginary part of the potential well to depend on the nature of the incident particle, keeping the depth (and the taper) of the well constant. A change in the radius of less than 10 ~/o can explain the difference in the neutron and proton results for lead. A smaller variation would be required for the lighter elements. Taking the optical potential as representing a sum of individual nucleonnucleon interactions 19), it is not possible to explain the large difference in the value of W required b y the first assumption. Consequently we conclude that it seems unlikely that both proton and neutron scattering results for high A elements can be fitted with the same size of the potential well permitting reasonable variations in potential depth only. It seems more likely that the size of the potential well depends on the nature of the incident particle. This possibility was suggested b y Voss and Wilson 23) on the basis of much less complete data. If the potential well is looked on as a sum of individual nucleon-nucleon interactions, this difference in the size of the well implies that the distribution of neutrons in high A nuclei is different from the distribution of protons. To make this conclusion more definite, exact calculations based on the optical model are required which would fit the cross sections and angular distributions and polarization for neutron and proton scattering. More precise experimental data of the latter would certainly be helpful in such an analysis. We wish to thank Mr. John Bahcall, Mr. Gordon Baym, Mr. Richard Gunther

PROTON INELASTIC CROSS SECTIONS

485

Mr. Costas Papaliolios and Mr. Popatlal Patel for help in preparing the equipment, taking data and calculating the cross sections. This work would not have been possible without the fine cooperation of the entire staff of the Cyclotron Laboratory. We should also like to thank Colgate University for assistance in preparing this paper. References I) R. G. P. Voss and R. Wilson, Proc. Phys. Soc. 236 (1956) 41 2) J. M. Cassels and J. D. Lawson, Proc. Phys. Soc. 67 (1954) 125 3) R. F. Carlson, R. M. Eisenberg and V. Meyer, Univ. of Minnesota annual progress report (Nov. 1959) p. 2 4) G. Calame, P. F. Cooper, Jr., S. Engelsberg, G. L. Gerstein, A. M. Koehler, A. Kuckes, J. w . Meadows, Jr., K. Strauch and R. Wilson, Nucl. Instr. 1 (1957) 169 5) Univ. of California, Lawrence Radiation Laboratory, drawing no. 1 x 6554D 6) H. Margenau and G. M. Murphy, The mathematics of physics and chemistry (D. Van Nostrand Co., New York, 1943) 7) G. Gerstein, J. Niederer and K. Strauch, Phys. Rev. 108 (1958) 427 8) G. Gerstein, thesis, Harvard University (1958) 9) J. H. Williams, Phys. Rev. 114 (1959) 525 lO A. J. Marls and H. Tyre, Nuclear Physics 4 (1957) 662 11 J. Dickinson and D. Salter, Nuovo Cim. 6 (1957) 235 12 K. Strauch and F. Titus, Phys. Rev. 104 (1955) 191 13 B. Rossi, High energy particles (Prentice-Hall, New York, 1952) p. 37 14 A. J. Kirshbaum, University of California, Lawrence Radiation Laboratory report 1967 (1954) 15 W. P. Ball, Univ. of California, Lawrence Radiation Laboratory report 1938 (1952) 16 G. P. Milburn, W. Birnbaum, W. E. Crandall and L. Schecter, Phys. Rev. 95 (1954) 1268 17 J. DeJuren and N. Knable, Phys. Rev. 77 (1950) 606 18 H. A. Bethe, Phys. Rev. 57 (1940) 1125 19 M. L. Goldberger, Phys. Rev. 74 (1947) 1114 20 S. Pernbach, R. Serber and T. B. Taylor, Phys. Rev. 75 (1949) 1352 21 R. M. Sternheimer, Phys. Rev. 97 (1955) 1314 22 G. A. Snow, R. M. Steraheimer and C. N. Yang, Phys. Rev. 94 (1954) 1073 23 R. G. P. Voss and R. Wilson, Proc. Phys. Soc. 236 (1956) 52