Total neutron cross-sections of Na, K, and Ca between 4 and 6 MeV

Nuclear Physics 62 (1965) 165--171; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or m i c r o f i l m without written permission from the publisher

TOTAL NEUTRON CROSS-SECTIONS

OF Na, K, and Ca B E T W E E N 4 A N D 6 MeV D. STOWERt, H. GENZ and M. BORMANN L Institut fiir Experimentalphysik, Hamburg, Germany Received 17 July 1964

Abstract: Total neutron cross-sections in the energy range from 4.2 to 6.2 MeV are measured for sodium, potassium and calcium using the transmission method. Mono-energetic neutrons are produced via the reaction D(d, n)He s in a deuterium gas target with the deuteron beam of a 3 MeV Van de Graaff generator. A neutron energy resolution of about 30 keV is achieved. The transmission is measured with a stilbene scintillation spectrometer in steps of about 50 keV. The cross-sections clearly exhibit pronounced structures with widths of 100-150 keV which are very probably due to statistical fluctuations of the compound nucleus level density. E I

I

NUCLEAR REACTIONS Na ~s, K, Ca (n), E = 4.2-6.2 MeV; measured O'nT(E). Natural targets.

1. Introduction T o t a l n e u t r o n cross-sections a r e n o t o n l y o f interest to test nuclear r e a c t i o n m o d e l s such as the o p t i c a l m o d e l b u t they a r e also n e e d e d in r e a c t o r physics 1) for energies u p to several MeV. T h e w o r k d e s c r i b e d here r e p o r t s m e a s u r e m e n t s o f t o t a l n e u t r o n cross-sections for N a , K a n d C a in the energy r e g i o n f r o m 4.2 to 6.2 M e ¥ using the t r a n s m i s s i o n m e t h o d . These m e a s u r e m e n t s were p e r f o r m e d with an energy r e s o l u t i o n o f a b o u t 30 k e V so t h a t detailed v a r i a t i o n s o f the cross-sections with n e u t r o n energy could be followed.

2. Experimental Method 2.1. NEUTRON SOURCE T h e r e a c t i o n D ( d , n ) H e 3 was u s e d as n e u t r o n source. D e u t e r o n s were accelerated to energies b e t w e e n 1 a n d 3 M e V b y a 3 M e V V a n de G r a a f f generator, m a g n e t i c a l l y a n a l y s e d a n d focussed on a d e u t e r i u m gas target o f a b o u t 1 c m 3 volume. T h e e n t r a n c e w i n d o w o f this gas t a r g e t was a nickel foil o f 0.6 c m d i a m e t e r a n d a b o u t 1.5 m g / c m 2 thickness. This nickel foil was s o l d e r e d to the t o p o f a d o u b l e - w a l l e d h o l l o w c y l i n d e r w h i c h was w a t e r cooled. A gas pressure o f a b o u t 180 T o r r a n d a b e a m c u r r e n t o f 3 # A were used. T a k i n g into a c c o u n t the energy r e s o l u t i o n o f the a n a l y s e d d e u t e r o n b e a m ( a b o u t 0.1 ~ ) , the straggling in the e n t r a n c e foil, a n d the thickness o f the d e u t e r i u m gas target, a n energy r e s o l u t i o n o f n e u t r o n s in the f o r w a r d d i r e c t i o n (only n e u t r o n s in this d i r e c t i o n were used in the m e a s u r e m e n t s ) o f a b o u t 30 k e y was achieved. t Present address: AEG Research Laboratories, Frankfurt/Main, Germany. 165

166

D. STUWERe t

al.

2.2. NEUTRON DETECTION The transmission was measured with a 2.5 c m x 2 . 5 cm stilbene scintillation spectrometer, placed at 60 cm from the neutron source in the direction of the deuteron beam. Discrimination against g a m m a radiation was achieved by the method of space charge limitation of the pulses between the last dynode and the anode in the photomultiplier (Philips 56 AVP) as first described by Owen 2). Fig. 1 shows the block diagram of the electronic circuitry. The voltage between the anode and dynode 14 was set such that the space charge limited pulses of the recoil protons taken from dynode 14 became positive after a short negative spike whereas the pulses of g a m m a radiation remained negative. The positive part of the proton pulses then were used to open a gate on the input of which the total pulse spectrum taken from dynode 12 was admitted. Thus the multi-channel analyser registered only the recoil proton spectrum. Anode

~ I I

i !

I

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56AVP HV negative

Dyn.13

Transitron-D=odes

Dyn.12

Fig. 1. Block diagram of the electronic circuitry.

The energy resolution of this spectrometer was about 12 ~o for 5 MeV neutrons so that it was always possible in our case to discriminate against neutrons falling on the stilbene crystal which had interacted inelastically with nuclei of the sample. However, it was not possible to distinguish neutrons which were elastically scattered into the counter. This so-called inscattering effect causes an error in the transmission which must be taken into account. In each measurement, at least two of the three available neutron monitoring systems were used simultaneously. The three monitoring systems available were a long counter, a scintillation counter with plastic N E 150 scintillator and a scintillation counter with a lithium glass scintillator enriched in Li 6 and surrounded by a polyethylene moderator. 2.3. SAMPLES Thin-walled brass cylinders of 10 cm length and 2.5 to 3.5 cm diameter were filled with the samples. For measuring the effect of the cylinders themselves on the trans-

TOTAL

NEUTRON

CROSS-~CTION$

167

mission, empty cylinders of the same size were used. The samples were situated in the middle between the neutron source and the stilbene crystal and were held there by a nearly massless assembly which also allowed a quick interchange of the filled and empty cylinders during the measurements. 3. Measurements and Results

At each neutron energy the recoil proton spectra in the stilbene crystal were measured with the multi-channel analyser for the same counting rates of the neutron monitors for the filled cylinder, the empty cylinder and a lead cone of vanishing transmission placed between the neutron source and the crystal, respectively. The spectra measured with the lead cone gave the neutron background at the position of the neutron detector, arising from scattering from the surroundings. The spectra were summed above a given threshold to give the counting rates No, N1 and N B for empty cylinder in, filled cylinder in, and background, respectively. The background counting rate N B always amounted to less than 1 % of the other counting rates. From these data the transmission T is calculated to be

T-

N1-NB No - N s '

and the total cross-section a x then can be obtained from T = exp ( - aT nl), where n is the number of sample nuclei per cm 3 and I is the sample length. At each energy the transmission has been measured independently two or three times with good statistics in order to test for long term drifts in the electronics o f the counting and monitoring systems. The threshold above which the proton recoil spectra were summed was set 2 MeV below the proton energy corresponding to the incident neutron energy. Therefore, since the first excited states of K 39 and Ca 4° lie at 2.53 and 3.35 MeV, respectively, inelastically scattered neutrons were excluded. The assumption also was made that contributions from the other stable isotropes of K and Ca which only have small abundances in the natural elements can be neglected. In Na 23 there is one excited level in the region below 2 MeV, namely at 0.44 Me¥, so that the neutron scattered from this level and falling on the stilbene crystal may also be registered causing an additional error in the transmission. But the differential cross-section for neutron scattering from this 0.44 MeV level has been measured by Towle and Gilboy 3) at somewhat smaller neutron energies than we are dealing with in this work and this cross-section turns out to be smaller by more than one order of magnitude in the forward direction than the differential cross-section for elastic scattering. Thus the error caused by the elastic forward scattering (the in-

D. STf3WER e t al.

168

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TOTAL NEUTRON CROSS-SECTIONS

169

scattering effect) can be assumed to be much larger than the error coming from the inelastic scattering. The error in a T caused by the inscattering effect was estimated using a formula. given by Bratenahl et al. 4) Aa T

(R 1 "3L-R2)2 Fael (0)

aT

R 2 R 2 aT

Here R1 and R 2 a r e the respective distances of the gas target and the stilbene crystat from the middle of the sample, F is the geometric cross-section of the sample, and ae~(0) is the differential cross-section for elastic neutron scattering in the forward direction. As only a few measurements of ae~(0) for the nuclei and energy region considered in the present work are known the results given by Towle and Gilboy 3) for Na, by Kent et al. 5) for K and by Caswell 6) for Ca were used as a hint for the order of magnitude of a~(0) in the error estimations. The errors so calculated from the above formula amount to about 1 70 for K and Ca and 1 to 2 70 for Na. The only other error in aT, is the statistical one, which was held to 1 to 1.5 ~ in all measurements. Consequently all cross-sections in the present work are determined within about 2 to 3 70. The results of our measurements are shown in figs. 2-4. For K and Ca the crosssections of two different runs taken several months apart are given. On the average the cross-sections slowly decrease with increasing neutron energy but at the same time exhibit clearly pronounced structures which lie outside of the error limits. 4. Discussion On the average, the cross-sections for K and Ca are smaller, for Na, however, higher than the semi-empirical values given by Howerton 7) which he derives from the systematic behaviour of a T for neighbouring elements. For K and Ca these deviations may be connected with the fact, that K 39 has magic neutron number N = 20 and Ca 4° has double magic structure. Average total neutron cross-sections in the energy region considered here can often be approximately described by the formula of Feshbach and Weisskopf s) aT = 2 n ( R + ~ ) 2, using 1.35 A ~ (fm) for the nuclear radius R. In figs. 2-4 these calculated cross-sections also have been drawn. In K and Ca the measured cross-sections are considerably larger than the calculated ones. These deviations very probably are connected with the well-known giant resonances in the total neutron cross-sections, which are understood on the basis of the optical model. For nuclei with mass numbers around A = 40 such a giant resonance maximum does in fact just appear near the energy region considered in this work (see for example Peterson 9)).

170

D. ST~W~R et al.

Our results can be compared with total cross-sections measured for Na by Leroy et al. lo) and for Na, K and Ca by Glasgow and Foster 11). All of these results are

shown together in fig. 5. However, a comparison is possible only with respect to the averaged behaviour of the cross-sections because the energy resolution with which the measurements by Leroy et al. and by Glasgow and Foster were performed are much poorer than in the present work. In Na, good agreement of the averaged cross-sections of all three measurements exists. For K and Ca, however, the values of Glasgow and Foster are systematically larger than our values by about 6 %. 251/~

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Fig. 5. Comparison of the total neutron cross-sections for Na, K and Ca as measured by Leroy et al. xo), Glasgow and Foster ~) and in the present work.

Considering the cross-section fluctuations observed in the present work it should be noted that these fluctuations are certainly not of the type discussed by Ericson 12) in the frame of the statistical theory for excitation energies of the compound nuclei at which the average level width F is much larger than the average level spacing D. These Ericson fluctuations exhibit widths which are of the same order of magnitude as the level width F. For incident neutron energies of 4 to 6 MeV and for the nuclear mass region considered in the present work, the compound nuclei are excited to the region of 11 to 14 MeV. Now it is well-known from slow neutron resonances (see for example Bilpuct. et al. 13)) that in this mass region F is of the order of a few keV at 7-8 MeV excitation energy (neutron binding energy). From the analysis of crosssection fluctuations on the basis of the Ericson theory, it turns out that F is of the order of 150 keV at about 20 MeV excitation energy 14~. So one may expect that in the excitation energy region of 11 to 14 MeV F amounts to about a few tens of keV. The widths of the total cross-section fluctuations observed in the present work, however, are of the order of 100-150 keV, so that we are certainly not dealing here with Ericson fluctuations.

TOTAL NEUTRON

CROSS-SECTIONS

171

T h e C a t a n i a g r o u p also has r e p o r t e d t o t a l n e u t r o n cross-section m e a s u r e m e n t s f o r m e d i u m - w e i g h t nuclei in n e a r l y the s a m e energy r e g i o n considered in the present w o r k ~5-17). I n these investigations it is also f o u n d t h a t the cross-sections exhibit f l u c t u a t i o n s with widths o f a b o u t 100-200 k e V a n d it is s h o w n t h a t this b e h a v i o u r o f the cross-sections can be e x p l a i n e d on the basis o f statistical fluctuations o f the c o m p o u n d nucleus level density ~6-1s). T h e r e f o r e we believe t h a t this e x p l a n a t i o n a l s o applies to the present results. W e w o u l d like to t h a n k P r o f e s s o r H. N e u e r t for suggesting this investigation a n d his e n c o u r a g e m e n t d u r i n g the experiments. W e also t h a n k the V a n de G r a a f f g r o u p e f the II. I n s t i t u t fiir E x p e r i m e n t a l p h y s i k , H a m b u r g a n d Dr. S. S k o r k a for m a k i n g t h e facilities o f the g e n e r a t o r available a n d for the assistance d u r i n g the m e a s urements. F u r t h e r , grateful t h a n k s are d u e to D r . J. L. Leroy, and to D r . D. W. G l a s g o w a n d D r . D. G. F o s t e r for m a k i n g results available p r i o r to publication. T h e s u p p o r t o f this w o r k b y the Deutsches B u n d e s m i n i s t e r i u m fiir wissenschaftliche F o r s c h u n g is gratefully a c k n o w l e d g e d . N o t e A d d e d in Proof" T o t a l n e u t r o n cross-sections f o r N a have also been m e a s u r e d b y Calvi et aL in t h e e n e r g y r a n g e 2.8 to 5.2 M e V with a n energy r e s o l u t i o n w h i c h is c o m p a r a b l e w i t h t h a t in the present w o r k . I n the o v e r l a p r e g i o n o f t h e e n e r g y r a n g e s c o n s i d e r e d b y these a u t h o r s a n d b y us g o o d a g r e e m e n t o f the exp e r i m e n t a l results exists also with respect t o the cross-section fluctuation.

References 1) R. P. Perret and R. A. Selby, compilation of EANDC requests, EANDC 25 "L", EANDC 26 "L" and EANDC 27 "L" (1963) 2) R. B. Owen, I.R.E. Trans. Ns-5, No. 3, 198 (1958) 3) J. H. Towle and W. B. Gilboy, Nuclear Physics 32 (1962) 610 4) A. Bratenahl, J. M. Peterson and J. P. Stoering, Phys. Rev. 110 (1958) 927 5) D. W. Kent, S. P. Puri, S. C. Snowdon and W. P. Bucher, Phys. Rev. 125 (1962) 331 6) R. S. Caswell, J. Res. Nat. Bur. St. 66A (1962) 389 7) R. J. Howerton, UCRL-5351 (1958) 8) H. Feshbach and V. F. Weisskopf, Phys. Rev. 76 (1949) 1550 9) J. M. Peterson, Phys. Rev. 125 (1962) 955 10) J. L. Leroy, F. C. Berthelot and E. Pomelas, J. Phys. Rad. 24 (1963) 826 and private communication 11) D. W. Glasgow and D. G. Foster, Jr., private communication 12) T. Ericson, Ann. of Phys. 23 (1963) 390 13) E. G. Bilpuch et al., Ann. of Phys. 14 (1961) 387 14) L. Colliet al., Energ. Nucl. 9 (1962) 439 15) P. Cuzzocrea, S. Notarrigo, R. Ricamo and F. Vince, Nuovo Cim. 18 (1960) 671 16) A. Agodi, G. Pappalardo, R. Ricamo and D. Vinciguerra, Nuovo Cim. 23 (1962) 1136 17) G. Calvi, R. Potenza, R. Ricamo and D. Vinciguerra, Nuclear Physics 39 (1962) 621 18) A. Agodi and G. Pappalardo, Nuclear Physics 47 (1963) 129 n9) Calvi et al. Nuclear Physics 48 (1962) 408