restricted angular interval or it is extended uniformly over the whole
44 solid angle. Instead of performing a rather tedious direct angular- -distribution measurement the energy spectra dn/dE of the recoil protons have been measured at different neutron energies E ranging from 2.7 MeV to 5.3 MeV as in one of our previous measurements.
The differential cross-section in center-of-inass system is given Ьуб'(ер )= E (dn/dJp)E ^ /(41</>N ) where is the c.m. angle of proton emission,P p e fPe ^ = E cos2 6^/2 is tfie corresponding proton energy /in lab.system/, ф is the integral neutron flux /in neutron per cm2/ at a thin scatterer which contains N hydrogen atoms. Any energy- -dependent departure from the isotropy in the angular distribution can be traced as a corresponding distortion of the proton energy-distribu
tion dn/dE . In practical cases, however, the true shape and the intensity of the energy spectra is uncertain to some extent because of distortion factors to be discussed lateb and of difficulties, respec
tively, which arise in connection with a reliable determination of the neutron flux. Fortunately, all distortion factors depend smoothly and slowly on the neutron energy, therefore quickly varying distortions, if can be developed by a suitable comparison of the spectra measured.
The proton energy distributions have been measured by means of a scintillation counter consisting of a small trans-stylben crystal viewed by a DuMont 6292 photomultiplier. The crystal was of cylindrical shape /0.8 cm in diameter and 1.0 cm long/ and it was mounted in a thin copper housing, surrounded by MgO as reflector. In the energy region investigated
any distortion due to /n, charged particle/ reactions of the surrounding elements and to the carbon content of the crystal was found negligi
ble. Care was taken of minimizing the proportion of neutrons in-scat
tered from the surroundings. The neutron-source target arrangement was the same as previously and the neutron energy was varied again by changing the angle /see Fig 4./ , at a fixed bombarding d e u t e r o n
energy. The source-crystal distance was 25 cm.
In such an experiment it is very important to eliminate the Г -background which may distort the measured spectra seriously and, in addition, the 1 -intensity may fluctuate quite rapidly with the neutron energy. We made use of the pulse-shape-discrimination technics in its space-charge controlled version [31]• The separation threshold for protons and fast electrons was found as somewhat below O .5 MeV electron energy /equivalent to about 1,8 MeV proton energy/, in good agreement with Owen’s result [31].
After sunplification, both the separation— and the energy—pulses were analyzed simultaneously by a 4096 channel analyser /NTA-4096 typ./
working in two-dimensional /52x128/ setting. Fig 7« 3hows an illustrative example i'or how this system operates,at E = 5 MeV neutron energy. Hie S- and U-axises correspond to the separation and the energy-pulse amplitudes, respectively. The discrimination line lies along the middle of the valley between the mountains. In such a way the best possible proton-gamma
discrimination could be established.
The amplitude-resolution in the energy-channel was 15 % for neutrons of 5„2 MeV energy and followed the rule (U in channels)
Л и / и ~ 1.5 l T 1/2 + o . O l
Proton amplitude-distributions have been measured in three runs each ranging over the same ten neutron energies from 2.72 MeV to 5.24 MeV. The total number of counts detected above the p ~ V dis
crimination threshold was in the order of 10^ in each of the spectra and this could be accomplished in about 50 minutes. The overall sta
bility of the measuring system proved to be satisfactory and. the spectra measured at the same neutron energy but in different runs were rSairly
consistent.
The response-energy function of our crystal could be determined with a considerable accuracy by means of the spectra themselves in the following way. Assuming a Gaussian-distribution to express the finite resolution of the detector, and an isotropical angular-distribution for
“ 31
-F i g . 7
T w o - d i m e n s i o n a l /axonometric and intensity-modulated/
r e p r e s e n t a t i o n s o f the channel content of the analyser
w h e n m e a s u r i n g recoil-proton energy distribution at 5 MeV
n e u t r o n energy. For details see text
the recoil protons in c.m. system /i.e. dn/dEp = constant for 0 < E p < E / the amplitude distribution takes the form
i - U ( * ) ' % „
P — 1/2
where E ^ u -) is the inverse response-energy function, ^ ( x ) = 2 1 £rf x is the error-integral with the argument x = (E-E )• aV? and
a"1 2 ^ is the full-width at half-maximum at E « E . P
First, an approximate derivated response-function (dU/dE^ ) 0 was determined and, to compensate the edge-shifts caused by the non- -linear response, all spectra were multiplied by this common function
|^(du/dEp)oJE ^ , The spectra so corrected approximate the ideal shape and the edge-positions could be determined .
The response-energy data fit the quadratic expression
U W 2.52 E + 2 . 3 6 5 E + 0 . 0 0 8
v P P /49/
as determined by a weighted least square analysis. The function agrees reasonably well with the response-function calculated from Birks*s expression t30]» assuming there kB = 0.0120.
Fig 8. shows the deviations of our measured response data from the best fitting quadratic form /51/» in the function of the energy.
c h a n n e l U - U ( E )
+ 1
-и --- 1--- .
4 5 M e V
Fig 8.
The deviations of the measured response data from a best fitting quadratic expression as given by Eq/51/ at dif
ferent proton /neutron/ energies. Note the occurence of maximum deviations where fluctuation-maxima are expected
33
-The c.m. differential cross-section was calculated using the expression uncorrected spectra measured at the same neutron energy0
Because of the p - Y discrimination threshold only a limited angular region as seen in Table could he evaluated. In Table 4.
the relative cross-section 6"(e) /5(50°) is given for different neu
tron energies since this ratio is independent of the /undetermined/
neutron flux. If the limits U-^ and U2 often happened to fall far from an integer number, in such cases the corresponding fraction of the channel content was taken into account. The errors of the cross-sec
tion data refer to the assumption that each sum s e 2) can be determined with an uncertainty corresponding to + 1/2 of one channel content. Compared with this, the statistical errors are negligible.
Fig 9' ♦ shows the energy-dependence of the differential cross
section at fixed angles 9 . A s for the angles 9 > 30°, no significant energy-dependence can be found and the angular distribution is isotropic, as it was known.
An entirely different behaviour can be observed, however, in the forward angular region О < e < 20°. At these low angles the differen
tial cross-section fluctuates with the energy just in the same way as
® n p ( E ^ d °es. Apart from some slight shift the maxima and minima shown in Figs 5c., 9., and also in Fig 1. correspond to each other quite closely, though they were measured in a completely different way. Even in Fig. 8 where the response-energy data are compared to a smooth
quadratic function, shows the same structure indicating that at forward angles and in fluctuation maxima there should be an excess of protons with respect to their average intensity.
& / d e g r e e s / 1 0 3 0 7 C 8 5
£
(MeV)
6" (9 ) / o ( S C ° ) ± A [ 0 (6)/о (50°)]2 . 7 2 - 0 . 1 1 1 . 8 S 5 ± C . 1 9 5 0.909 ± 0.116 - — ■
3 . 0 1 ± C . l l 2 . 0 3 7 1 0 . 1 3 7 C . S 3 5 ± 0 . 0 9 3 -
-3 . -3 -3 1 o . l l 1 . 6 1 5 ± 0 . 1 5 2 . C . 3 9 6 - 0 . 0 7 9 1.008 ± C.055
-3 . 5 5 1 0 . 1 1 1.590 - 0 . 1 1 5 0 . 9 0 7 ± 0 . 0 6 4 0.975 ± 0 . 0 4 1 0.935 - 0 . 0 8 4 4 . C l .- 0 . 1 0 1.720 4 0.156 0 . 9 4 S - C . O55 C.952 ± 0 . 0 4 5 О.975 ± О . О92
4 . 3 4 ± 0 . 0 3 1.347 1 0.102 С .9О З * О . О54
. 0 . 9 7 5 t 0 . 0 3 7 0 . 9 8 4 '± 0 . 0 3 1 4 . 5 5 ± C . O S 1.376 — 0.100 0 . 9 0 5 ± 0 . 0 4 5 C.974 ± С . О З2 0 . 9 7 0 ± 0 . 0 3 3 4 . 9 1 ± C . 0 5 1.395 1 0 . 0 7 5 C.949 1 О . О З З 0 . 9 5 5 ± О . О25 0.933 ± 0.053
5 . 1 0 - 0 . 0 4 1 . 2 5 9 ± 0 . 0 3 2 0 . 9 7 7 - 0 . 0 4 0 O.919 ± О . О25 0 . 3 8 3 1 0 . 0 5 2 5 . 2 4 - C . 0 1
_________________________
1
I .32O ± 0 . 0 3 0
J
O .97I - О . О57 0 . 9 2 4 ± О . О23 С . З52 ± 0 . 0 4 6
Table 4 .
The measured relative differential cross-sections 6'(0)/6' (50°) f or neutron-proton scattering at different c.m. angles ® of proton emission and laboratory-energies E „ The energy errors are calculated from reaction kinematics, for the cross-section errors see text
35
-Fig 9
The measured differential cross-section data
6'(50°,E) plotted as a function of the neutron energy £ .
1
Unfortunately» this Mousui-ement could not bo extended to backward angles /in c.m. frame of reference/, because of technical difficulties, and we do not know whether similar phenomena exist in that region too.
5 S . Summary of the results and discussion
In the previous paragraphs evidences were put forward, for the exist
ence of cross-section fluctuations in neutron-proton scattering. There are more or less clear signes of these fluctuations up to neuti’on energies as high as 40 MeV. The fluctuating contribution to the total cross-section
turned out to be 9 % or less and the sequence of the fluctuation maxima and the forward c.m. hemisphere of proton emission and the differential cross- -section depends on the neutron energy, from 2.7 MeV to 5«3 MeV as it was expected on the base of the shape independent effective range theory. At
forward angles, however, a considerable excess of differential cross—
-section has been found showing fluctuations with maxima which correspond to those occuring in the energy-dependence of total cross-section.
The question, how these experiences are compatible with the measu
rements of other authors can be answered partly by quoting the results of half-maxima. Therefore a nearly homogenous set of data had been used.
Probably the presence of the fluctuations would explain why the error of rs could not be improved significantly in Noyes’s calculations when using 20 more data on 6"n
37
-As for the differential cross-section measurements in the MeV region, the situation is somewhat emharrasing for the first sight, since it is generally assumed that the angular distribution is isotropic in this energy region. However, no critical review or compilation of data, like that of Hess [14] for higher energies, could, be found. In an attempt [32] to have some better insight it has been pointed out that the experimental evidences for isotropy below 9 MeV are not unambiguous enough so as to be uncompatible with what has been found here.
Our experiences can be explained in terms of a quite simple model of charge-exchange processes outlined in the first two paragraphs of this paper. Quantitatively, when using a dipole approximation for the inter
action matrix-element to the analogy of that of electromagnetic transitions, one finds a realistic, chough a bit small value as 0.068 for the dimension- less pion-nucleon coupling constant f /he if = 24.9 MeV ' is
assumed, and 0.090 for the somewhat less significant value d = 28.9 M e V ^ ^ /see Eq/33//.
A less definite statement can be given about the amplitude К of the fluctuations. In the MeV region, they are probably higher than suggested originally in § 2. /see Eq/34//, a quantitative rule, however, has not been found as yet.
The authors wish to express their thanks to Mrs. A.Simon for taking responsibility for most of the numerical calculations, and also for her help
ful assistance during the experimental work. The authors are also indebted to Dr. I.Borbély, Dr. L.Eócs and Br. M.Ziraányi for their invaluable helps and to Dr. L.Keszthelyi for his encouraging support from the very beginning of this work.
t
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Printed in the Central Research Institute for Physics, Budapest Kiadja a Könyvtár- és Kiadói Osztály. O.v.: dr. Farkas Istvánná Szakmai lektorr dr. Keszthelyi Lajos. Nyelvi lektor: Kovács Jenőné Példányszám; 170 Munkaszám: 4-34-9 Budapest, 1969. március 21? Készült a KFKI házis sokszorosítójában. F.v.: Gyenes Imre