Small-angle elastic scattering of 14.8 mev neutrons

2.L

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Nuclear Physics A212 (1973) 147--156; (~) North-Holland Publishing Co., Amsterdam

I

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

SMALL-ANGLE ELASTIC SCATTERING OF 14.8 MeV NEUTRONS R. E. B E N E N S O N , K. R I M A W I , E. H. S E X T O N t a n d B. C E N T E R t t

State University of New York, Albany, N Y 12222 Received 26 M a r c h 1973 Revised 29 J u n e 1973 Abstract: T h e 14.8 M e V n e u t r o n elastic scattering differential cross sections o f U , Pb, Hg, Ta, Sn a n d A1 have been m e a s u r e d for angles extending f r o m 10 ° dowrL to 1.8 ° a n d for U a n d Pb d o w n to 0.35 °. Nuclear cross sections extrapolated to 0 ° have been c o m p a r e d with t h e W i c k limit. T h e U nuclear cross sections did n o t rise as s h a r p l y t o w a r d 0 °, a n d were n o t in as serious disagreement with t h e spherical optical model, as in earlier m e a s u r e m e n t s . T h e smallest-angle data verified t h e Schwinger prediction. E

[

NUCLEAR

R E A C T I O N U, Pb, Hg, T a , Sn, Al(n, no), E = 14.8 MeV, m e a s u r e d ~(0), 0.35 ° < 0 < 1 0 °. D e d u c e d ~(0°). N a t u r a l targets.

L

1. Introduction

As neutron elastic differential cross section measurements are extended downward in angle toward 0 °, the dominant interaction is predicted to change from nuclear to electromagnetic 2). The nuclear amplitudes at 0 ° obtained by extrapolation from larger angles can be compared with the optical theorem, and then the sharp rise of the cross sections at smaller angles may be compared with the behavior predicted for the electromagnetic interaction 1. At some neutron de Broglie wavelength, the interference of the two types of amplitudes could in principle supply information about the nuclear spin-orbit interaction, which has not been included in the treatment of ref. 2). The first (group I) set of experiments to be described were made at scattering angles between 1.8 ° and 10 ° on samples of Pb, Hg, Ta, Sn and A1. These measurements extend comparisons with the Wick lower limit 2) to smaller angles than those obtained in the previous investigation by Coon et al. 3) on Pb, Sn, A1, Fe and Cu. The group II measurements were intended primarily to reinvestigate the nuclear cross sections for uranium 4, s) which have been measured down to 3 ° [ref. 4) only] and found to be considerably in excess of spherical optical model predictions. These cross sections were apparently successfully explained on the basis of strong nuclear deformation using coupled channels calculations 6, 7), but the data appeared to be still rising rapidly toward 0 °. t Present address: R o c h e s t e r Institute o f Technology, Rochester, N Y 14623. *t N a t i o n a l Science F o u n d a t i o n U n d e r g r a d u a t e R e s e a r c h Participant. t T h e influence o f n e u t r o n polarizability [see ref. 10)l will n o t be considered in this paper, except

for a remark in sect. 5. 147

148

R . E . B E N E N S O N et aL

The group III experiments on U and Pb were an extension down to mean scattering angles of 0.35 ° in a search for possible significant deviations from the Schwinger prediction 1): for unpolarized incident particles and spin-independent nuclear forces,

a(O) = ao(O)+ ?z cot 2 ½0,

(1)

where ao(O) is the specifically nuclear cross section, and ~ = ½#n(Ze2/Mc 2) with p, and M the neutron magnetic moment (n,m.) and mass, respectively. The predicted rise in cross section as 0 ~ 0 ° has been observed at E n = 0.6-1.6 MeV [refs. 8, 9)], 4 MeV [ref. lo)], a portion of the reactor spectrum 11), and 100 MeV [ref. 12)], but has not been reported near E , = 15 MeV. Extensions of the original PWBA treatment of ref. 2) have included an electromagnetic term of spin-orbit form in the scattering potential (i) to obtain perturbed wave functions based on a hard-sphere interaction 13), and (ii) in DWBA calculations [refs. 14, 15)] which explained appreciable neutron polarizations at angles larger than predicted by ref. 1) and stimulated the present work. 2. Experimental method and data reduction 2.1. G E N E R A L

METHOD

The associated particle time-of-flight method was used to select elastically scattered 14.8 MeV neutrons which originated from the 3H(d, n)4He reaction at angles near 0 ° with respect to a 150 keV deuteron beam. The experimental arrangement is shown in fig. 1. The electronically collimated neutron cone remained completely inside the 10 cm dia. hole joining the two rooms shown in fig. 1. The choice of forward angle neutrons eliminated kinematic shifts associated with target aging 16), and the use of an analyzed D + beam permitted more efficient use of the Ti-T targets. A scaler connected to the e-particle detector served as beam current integrator. Data were recorded as the net number of true coincidences in the time window of a time-to-pulse height converter (TPHC) gated by e-particle and neutron detector bias levels. Both detectors were of N E 102 (Nuclear Enterprises, Ltd). The time resolution of the system was < 1.4 ns, and the full coincidence peak was included in a 5.6 ns time window. Accidental coincidence were recorded simultaneously; the accidental to true coincidence ratio was usually << 1. The geometrical arrangements for the groups I-III measurements are shown in table 1. The steel shield placed in the hole as indicated in fig. 1 was needed to define the edge of the direct neutron beam and to reduce room background. The shape of the steel shield and of the scatterer for each of the three groups of measurements is shown as an insert in fig. 1. Horizontal beam profiles established the 0 ° reference direction; vertical profiles were interspersed, but less frequently. The steel shield defined a very sharp rise in coincident counting rate, which then bounded a profile having an approximately Gaussian shape. Decreasing the 1° defining aperture in front of the e-counter did not reduce the electronically collimated beam width [see ref. 16)].

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SCATTERING

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Fig. I. E x p e r i m e n t a l a r r a n g e m e n t s h o w i n g the two concrete-lined r o o m s connected by a 10.1 cm dia. hole. T h e scatterers or a t t e n u a t o r s a n d t h e m o v a b l e detector could be placed in position from t h e control r o o m . Supplemental external shielding was used in t h e target r o o m to reduce airscattered b a c k g r o u n d . T h e insert s h o w s t h e areas o f t h e steel shield a n d o f t h e s a m p l e seen w h e n l o o k i n g t o w a r d t h e tritium target. T h e d a s h e d area for t h e g r o u p III a r r a n g e m e n t indicates the scatterer size relative to t h e n e u t r o n channel. TABLE 1 Experimer~tal a r r a n g e m e n t s Group

I

II

III

Scattering sample

Pb Fig Ta Ta Sn Sn A1 Pb b) AI b)

Angular range center to center

1.5°-10 °

5 °, 10 ° 5o

U Pb Fig

1.9°-4.8 °

U Pb Cu

0.35°-2.10 °

Sample dimensions, width x height (cm)

Sample transmission

2.9 x 10 2.9 x 10 3.2x10 2.9 X 10 2.5 x 10 2.2 x 10 2.9 x 10 10 dia.

0.850 0.806 0.742 0.910 0.738 0.849 0.766 0.779 0.723

2.54 x 2 . 5 4 2.54 x 2 . 5 4 2.54 x 2 . 5 4 1 x 2 c) 1 x2 1 x2

Ti-T target Scatterer Neutron to scatterer to n e u t r o n detector distance detector dimensions, center to distance width x height center (era) (cm) (cm)

130.8

163 2.5 x 3.8 a)

130.8

159.8 147.4

0.637 0.678 0.637

139

143.5

0.37 0.37 0.37

220

233

3.8

2.5x2.5

0.32 × 5.10

") T h e axis o f t h e 3.8 c m dia. cylindrical detector was perpendicular to the 0 ° reference direction. b) Calibration runs. ¢) Set by c h a n n e l in steel shield. T h e actual s a m p l e cross section d i m e n s i o n s were 2.5 c m ×2.5 cm.

150

R.E. BENENSON

et al.

Plexiglass attenuators were used in the groups I I and I I I background measurements to compensate for background reduction by the scattering sample. Care had to be taken that neither sample nor attenuator ever barely overlapped the edge of the steel shield. Correction for scattering by plexiglass was by calculation. 2.2. GROUP I MEASUREMENTS Scattering from Pb, Hg, Ta, Sn and A1 was used initially to obtain relative cross sections normalized to Pb after correction for attenuation and multiple scattering. An absolute scale factor was provided in a separate measurement on Pb at 5 ° and 10 ° and A1 at 5 ° using associated a-particle counting first to calibrate the neutron detector, and then to measure the flux incident on large diameter scattering samples which intercepted the full neutron cone (with the steel shield removed). Backgrounds were taken with the sample removed, and background depression by the sample was calculated. Numerical integration of the beam profile over scatterer area was used to obtain the centroid of the incident neutron flux at the line of detector travel. 2.3. GROUP II MEASUREMENTS Measurement of U scattering was the primary purpose of the group II experiments (see sect. 1), but scattering by Pb was included in order to compare the absolute cross section calibration with that described in subsect. 2.2. In addition, Hg was remeasured because the cross sections seemed low. Absolute cross sections were measured by direct comparison of the incident flux at the scatterer position with the scattered flux. The neutron detector and sample cross sectional areas were identical, and at the beginning and end of each single or double sequence of scattering and background counting, the detector was placed in the sample position. In the latter position the large dead-time correction for the T P H C was carefully measured. The detector position for minimum sample transmission was taken as the 0 ° reference line. 2.4. GROUP III MEASUREMENTS Mean scattering angles well below 1° were required to observe the second term of eq. (1) relative to the large Cro(0) term. The problem of excessive background was solved by: (i) reducing the opening in the steel shield to a neutron channel 1 cm wide by 2 cm high, (ii) using samples of low transmission ( ~ e - 1), and whose cross sectional area exceeded that of the channel, and (iii) the increase of distances to those listed in table 1. A computer program was written to perform the averaging over cot 2 ½0 in eq. (1) for finite sample and detector areas [see ref. 8)] in order to optimize the design parameters needed to observe the predicted sharp rise t. The result included t For equal neutron source-scatterer and scatterer-detector distances, and with sample and detector widths as narrow as practicable, the calculated average of cot 2 ½0was found to be a maximum when the detector height equaled twice the sample height.

SMALL-ANGLE SCATTERING

151

a correction for electron screening calculated according to the treatment of ref. 17). The measured cross sections were relative. For purpose of normalization, one angle overlapped the group II range. The two points measured for Cu were intended only as a check on possible systematic errors. The 0 ° reference l i n e was taken as the center of symmetry of the beam profile defined by the neutron channel. 2.5. MULTIPLE AND INELASTIC SCATTERING A Monte Carlo program especially adapted for scattering samples in the shape of rectangular parallelepipeds was written in order to make the multiple in-scattering correction. Elastic scattering cross sections needed for the program were calculated using the program D W U C K 18) with reasonable optical model parameters. The contribution of the ~2 cot 2 ½0 term of eq. (1) when'modified by the electron screening correction was found to make a negligible contribution to multiple scattering. The time window permitted inelastically scattered neutrons corresponding to excitation energies of approximately 4 MeV to give valid counts. Since forward inelastic scattering differential cross sections are typically three orders of magnitude lower than elastic for E n ~ 15 MeV, no correction for the former was included.

3. Experimental results The measured nuclear cross sections for groups I and II are shown in fig. 2 after applying the standard procedure [see refs. 4, s-lO)] of subtracting the electromagnetic term of eq. (1). The error bars represent the statistical uncertainty. The ref. 4) results for U and Pb are also shown for comparison. Optical model calculations for neutron elastic scattering cross sections calculated from the program D W U C K 18) using two sets of well-known parameters 19,20) which provide good fits to larger angle data are also shown on fig. 2. For the purpose of extrapolating the measured cross sections o-exp(0) to 0 °, the assumption was made that the ratio a(O°)/aoxv(O) is the same as the ratio obtained from a calculated optical model curve. The basis of the assumption is that DWBA relative cross sections are not sensitive to the choice of a particular set of optical model parameters in order to give a good representation of the angular distribution forward maximum. For each experimental point o-~xp(0) a value of a(0 °) was obtained from a(0 °) -

~exp(O) aDWUCK(0°),

(2)

%wucK(0) where 0"DWUCK was calculated using the ref. 19) parameters. Applying this procedure to each experimental point generated a set of 0 ° cross sections for each sample, which was then averaged to obtain the mean and standard deviation given in table 2 and shown on fig. 2.

152

R . E . BENENSON et al.

• This Experiment o ref.4) . Wick's Limit

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Fig. 2. Experimental results from the groups I arid II measurements. The 0 ° experimental point was obtained by averaging 0 ° points from optical model curves successively normalized to pass through each actual experimental point. The solid and dashed curves are optical model calculations using, respectively, ref. ~9) and ref. 2o) parameters. The open squares at 0 ° are based on the optical theorem and published total cross sections. Ref. 4) data for U and Pb have also been plotted. TABLE 2

Comparison of extrapolated ~(0 °) with Wick limit Sample

~r(0°) (b/sr)

U Pb Hg Ta Sn A1

14.654-0.14 14.024-0.19 12.644-0.23 12.954-0.23 10.004-0.22 1.49 4-0.06

O'wi~k(0 °) (b/s0 ") 15.2 4-0.5 13.7 4-0.4 13.6 4-0.5 13.3 -1-0.5 8.9 4-0.3 1.28 :I=0.05

a) Calculated from ref. 2t). Errors correspond to uncertainties in reading fiT from graphs, but the uncertainty in aT amounts to less than 2~. T a b l e 2 c o m p a r e s a ( 0 °) w i t h t h e W i c k i n e q u a l i t y g i v e n by o%1(0°) =>

= [ I m f ( 0 ° ) l 2, \4~1

(3)

SMALL-ANGLE SCATTERING

153

40

50

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I

Pb

30 b 20

10

0

I

l

1

T Cu

I0

0

l

Q5

1

1.0

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1.5

2.0

2.5

0°C M Fig. 3. Experimental results for the group III measurements. The ordinate scale is based on the 2.1 ° measurement. The solid curve is obtained from eq. (1) after suitable correction for scatterer and detector areas and for electron screening. where a¢~(0 °) is the differential elastic cross section a t 0 ° a n d a T is the t o t a l cross section. Values o f a T were t a k e n f r o m BNL-325 [ref. 21)]. The experimental results o f g r o u p I I I m e a s u r e m e n t s corrected for multiple scattering a n d a t t e n u a t i o n are c o m p a r e d in fig. 3 with eq. (1) a d j u s t e d f o r finite sample a n d d e t e c t o r areas a n d for electron screening. The p o i n t s are n o r m a l i z e d to the n u m e r i c a l value o f the cross section at 2.1 o o b t a i n e d f r o m g r o u p s I a n d II. The e r r o r bars o f the smaller angle p o i n t s include the statistical u n c e r t a i n t y o f t h a t at 2.1 °. 4. Discussion

of results

4.1. C O M P A R I S O N W I T H T H E W I C K L I M I T A N D O P T I C A L M O D E L F I T S

The c o n t r i b u t i o n o f the real scattering a m p l i t u d e to the 0 ° cross section can be e x t r a c t e d using the o p t i c a l t h e o r e m :

EReI(O°)l 2 =

--(4~zaq2 / "

\

(4)

154

R.E. BENENSON et al.

For the four heavier nuclei, U, Pb, Hg and Ta, fig. 2 and table 2 indicate that the extrapolated 0 ° cross sections barely achieve the Wick limit, or even appear to be slightly below it. A similar trend can be found in ref. 3) and for U data at 18 MeV [ref. 22)], implying that in this energy region IRe f(0°)] 2 is essentially zero. Use of eq. (4) requires that the subtraction of the electromagnetic (e.m.) scattering be correct. According to ref. 1), for an unpolarized beam e.m. and nuclear amplitudes do not interfere, hence cross sections rather than amplitudes (sect. 3) are subtracted prior to extrapolating Go(0°). In addition, the e.m. amplitude is expected to vanish at 0 ° both because of electron screening and for reasons of symmetry [the ~r" n term 1) in the amplitude becomes undefined]; otherwise the effect of the e.m. term on the optical theorem becomes unclear. The parameter sets used to make the optical model curves in fig. 3 as a whole do not take into account the deformation or shell closure in special regions of mass number. Both potentials include surface absorption terms; small changes in volume absorption could easily make either set pass through the Wick limit. In a general sense, the ref. 19) parameters give better agreement for the heavier, and the ref. z0) parameters better agreement for the lighter nuclei. 4.2. URANIUM CROSS SECTIONS The present U cross sections lie appreciably below those of ref. 4). The data can be fitted using an optical model for a spherical nucleus. Were a systematic error present, the Pb cross sections shown in fig. 2 might also have been expected to lie below those of ref. 4). The data for Ta, also a deformed nucleus, again give good agreement with the conventional optical model calculation. 4.3. SEARCH FOR NUCLEAR SPIN-ORBIT AND ELECTROMAGNETIC INTERACTION INTERFERENCE When the scattering amplitude is separated into the spin-independent and spindependent amplitudes, in the usual notation: f ( O ) = 9N(O)+hN(O)(~r " n)+hs(O)(~; " n),

(5)

where the subscripts N and S refer to nuclear and electromagnetic (Schwinger), respectively, interference between the hN and h s terms will modify eq. (1). When theoretical curves generated according to ref. 14) using the ref. 19) parameters are compared with eq. (1), the difference at the smallest angles achieved in this experiment amounts to about 0.5 b, and a similar number appears when the interference term is calculated according to a simplified treatment which generates hN(O ) from a square well potential in the PWBA 23). Any such effect on cross section lies within the limits of experimental uncertainty; within these limits, the agreement between experiment and the calculated curves is excellent.

SMALL-ANGLE SCATTERING

155

5. Conclusions N o evidence for a strong interference between the electromagnetic and nuclear spin-orbit (or other) interaction has been found at the smallest angles studied. At slightly larger angles for which non-zero spin nuclei were used, no other significant interference effects (such as a spin-spin interaction) appeared. Extrapolation of nuclear cross sections to 0 ° indicates that Re f ( 0 °) << I m f ( 0 °) at this energy; one consequence is that evidence for a neutron polarizability amplitude is very unlikely from differential cross section measurements in this energy region 24), because the latter amplitude is multiplied by Re f ( 0 °) in the appropriate expression 1o) for a(0). Taken with other data 3, 22), a strong suggestion exists that for heavy nuclei cross sections obtained with a typical method of extrapolating a(0 °) can lie below the Wick limit. Further theoretical and experimental study of this contradictory point would be desirable. Uranium cross sections can be fitted with the spherical optical model without the need for invoking a coupled channels approach 6, 7). The theoretical curves supplied by Drs. J. Monahan and A. Elwyn and their continued and stimulating interest during the course of the experiment are gratefully acknowledged. Special thanks are due to J. Kowalchyk, A. Stein and C. Houghton for building and assembling the several shields and positioning mechanisms and to A. Horigan and H. Makowitz for help in taking data. William Kinney ( O R N L ) was very helpful with regard to the Monte Carlo technique. Thanks are also due to Dr. Richard Brown who participated in the early stages of the experiment and Stephen Ward who carried out a preliminary in-scattering calculation. The State University of New Y o r k Construction Fund generously supplied all the equipment used in the experiment.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)

J. Schwinger, Phys. Rev. 73 (1948) 407 G. C. Wick, Phys. Rev. 75 (1949) 1459 J. H. Coon, R. W. Davis, I~. E. Felthauser and D. B. Nicodemus, Phys. Rev. 111 (1958) 250 Y. V. Dukarevich and A. H. Dyumin, ZhETF (USSR) 44 (1963) 130 [English transl.: JETP (Soy. Phys.) 17 (1963)] A. Adam, P. Hrasko and G. Palla, Phys. Lett. 22 (1966) 475 G. Palla, Phys. Lett. 35B (1971) 477 C. J. Slavik, private communication A. J. Elwyn, J. E. Monahan, R. O. Lane, A. Langsdorf, Jr., and F. P. Mooring, Phys. Rev. 142 (1966) 758 F. Kuchnir, A. J. Elwyn, J. E. Monahan, A. Langsdorf, Jr., and F. P. Mooring, Phys. Rev. 176 (1968) 1405 G. V. Gorlov, N. S. Lebedeva and V. M. Morozo, Yad. Fiz. 8 (1968) 1086 [English transl.: Soy. J. Nucl. Phys. 8 (1969) 630] Y. A. Aleksandrov and I. L Bondarenko, ZhETF (USSR) 31 (1965) 726 [English transl.: JETP (Soy. Phys.) 4 (1956) 612] R. G. P. Voss and R. Wilson, Phil. Mag. 1 (1956) 175 J. T. Sample, Can. J. Phys. 34 (1956) 36

156 14) 15) 16) 17) 18) 19) 20) 21)

R . E . BENENSON e t al.

J. E. Monahan and A. J. Elwyn, Phys. Rev. 136 (1964) B1678 W. S. Hogan and R. G. Seyler, Phys. Rev. 177 (1969) 1706 H. Marshak, A. C. B. Richardson and T. Tamura, Phys. Rev. 150 (1966) 996 V. M. Koprov, Z h E T F (USSR) 38 (1960) 639 [English transl.: JETP (Soy. Phys.) 11 (1960)459] P. D. Kunz, Univ. of Colorado report C00-535-613, unpublished L. Rosen, J. G. Peery, A. S. Goldhaber and E. H. Auerbach, Ann. of Phys. 34 (1965) 96 D. Wilmore and P. E. Hodgson, Nucl. Phys. 55 (1964) 673 Neutron cross sections, 2nd ed., BNL-325 (1965) (Clearinghouse for Federal Scientific and Technical Information, NBS, Springfield, Va.) 22) P. H. Bowen, G. C. Cox, G. B. Huxtable, J. P. Scanlon, J. J. Thresher, A. Langsford and H. Appel, Nucl. Phys. 40 (1963) 186 23) R. F. Redmond, Phys. Rev. 136 (1964) B l I 2 24) G. V. Anilcin and I. I. Kotukhov, Soy. J. Nucl. Phys. 14 (1972) 152