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Volume 18, number 3

P HYS ICS

LETTERS

1 September 1965

PROTON SCATTERING FROM A TUNGSTEN SINGLE CRYSTAL A. F. TULINOV, V. S. KULIKAUSKAS and M. M. MALOV
Institute of Nuclear Physics, Moscow University, Moscow, USSR Received 26 July 1965

Usually amorphous or polycrystalline targets are u s ed fo r stu d y in g n u c lear reactio n s in itiated by accelerated particles. It has been shown [1,2] th at if a sin g l e crystal targ et is u s ed , clip s in th e d i rectio n o f th e crystallin e ax es ap p ear in th e angular distribution of charged reaction products. Th e in ten s ity d ecrease in th e d i p was attrib u t ed to th e Coulomb scattering of th e reaction products b y th e r e lev a n t n u c lear ch ain . Th is ef f ect w a s found experimentally in studying th e elastic scatter i n g o f prot ons from a t ungst e n si ngl e cr ystal. Th e present paper cont ai ns a st udy on t h e in f lu en ce o f different factors on th e effect in question. 304

The m easurem ents were carried out using the 120 cm cyclotron of the Institute of Nuclear Physics at Mo scow Univ ersity. The proton energy was changed with absorbers; a 2 mm th ick tungsten single crystal was used as a target. The crystall i n e axi s correspondi ng t o t h e short e st di st ance bet w een l a t t i ce si t e s was used. Si nce t ungst e n has a body centered cubic lattice the axis [111] m eets this condition (l = 2 . 7 A). The direction of the a x i s was det e rm i n ed wi t h an X-ray m e t hod. The s a mp l e was fast ened t o a copper rod connect ed to a cryostat. The beam diam eter was 1 m m . T h e a ngl e between the crystal surface and the direction of the beam was 30°, with the [111]


Volume 18, number 3

P HYS ICS

LETTERS

1 September 1965

CRYSTAL

COUNTER

F i g . 1. General sketch of the experiment.

measured near th e direction of th e [111] ax is ax is i n t h e hori z ont al pi ano, formi ng an angl e = 15° to the normal on the surface (fig. 1). The a ngul ar di st ri but i on of el ast i cal l y scat t e red proto n s w as. The prot ons were det ect ed by a sy st em of tw o junction detectors, each of them 4 mm in di am et er. The count ers were at a di st ance of 4 5 era from the target. One of them could be r o ta te d i n t h e hori z ont al pl ane and t h e ot her i n th e v er tical plane, without breaking th e vacuum. A th ir d junction detector placed at a fixed angle with respect to the direction of the beam was u s e d a s a m o n ito r. Pu lses fro m th e d e tecto r s were l e d t o a 100-channel amplitude analyser. F o r co n t r o l m easurem ents the sam p le could be replaced by a polycrystalline target without disturbing the vacuum. Shown in fig. 2 is the proton angular distribution corresponding to a beam ener g y o f E P = 3 M e V. Pl ot t e d as t h e ordi nat e are t h e numbers of pul ses correspondi ng t o t h e hi gh energy part of t h e cont i nuous spect rum (t he threshold was at 80% of the maximum signal). T h e ci rcl e s denot e t h e resul t s obt ai ned when a p o l ycrystallin e targ et was u s ed . To m a k e su re that the dip thus obtained was associated with the crystallin e ax is, th e targ et was ro tated in th e hori z ont al pl ane, whi c h ma de t h e di p shi f t accordingly. The m easurem ent s descri bed above were carried out at room tem p erature (T ~ 300°K). Th e heating of th e target under th e in fluence o f th e beam was i n si gni fi cant . In order t o st udy t h e temp erature dependence of the effect, the crystal was cooled down to liquid nitrogen tempera t u r e (T ~ 80°K). The angul ar di st ri but i on for t h i s c a s e i s shown i n fi g. 3. It i s seen t h at , as th e temp er atu r e falls , both th e depth and th e width of th e dip increase.

Fig. 2. Angular distribution of protons elastically scattered from a tungsten single cry stal near the [111] axis at EP = 3 MeV. - poly c ry stalline target. · - single cry s tal target.

A change in the proton energy causes a change in the width of the dip without any significant change in its general form. Thus, at EP = 6 MeV,

Fig. 3. Temperature dependence of the angular dist ribution of protons elastically scattered from a tungsten single cry s tal.

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LETTERS

1 September 1965

the half-width of the hole was about 1.2° and the distance between the side maxima was about 3 . Since a thick target was used for the m easurem e n t s, it was o f in terest to ex am in e th e in flu ence of the depth of the layer where the scattering was taking place. To th is end, pulse spectra were t a ken at di fferent angles. These spectra were divided into regions of 10 channels each. Evidently, every region can be associated with a certain d e p t h o f th e crystal layer cau sin g th e scattering. Shown in fig. 4 is th e dependence of t h e dept h of t h e di p on pul se si ze. The l o wer curve i s for room t e m p erat ure, t h e upper one for liquid nitr ogen temp erature.. Apparently, th e di p get s broader and shal l o wer wi t h i n creasi ng dept h of t h e scat t e ri ng l a y e r. In order t o est i mat e t h e wi dt h of t h e di p t h e angles and were used in refs. 1 and 2. The first o f th ese v a lu es, , is th e m i n i m u m scatteri ng angl e of a charged part i c l e , when t h e nucl e i of the scattering chain are fixed at the lattice sites. Th is v a lu e m a y b e sh o w n to d e term in e th e ext e ri or di m e nsi ons of t h e hol e; i t i s cl ose t o t h e distance between the side m a xim a . Let the interact i on pot ent i a l of t h e react i on product (charge Z 1 e) and t h e scat t e ri ng nucl e us (charge Z 2 e) be

function. Assuming that a = 0.5/Z1/3 A and EP = 3 MeV we obtain 2 = 3.3°. From fig. 2 one obt a i n s 2 exp 4 o . The second value is the average scattering an g l e. It ap p lies to p a rticles em itted b y n u c lei on th e ch ain ax is, with th e nuclei of the chain formi ng a sy st em of i ndependent t h ree-di me nsio n a l classical o s cillato rs. Th is v a lu e g i v e s some idea of the average width of the dip. It may b e calcu lated fro m th e fo llo win g relatio n

. Then it can be shown that

, where b = Z 1 Z 2 e /a , l is the distance between the nuclei of the scattering chain, E is the energy of the particle, Ko is the modified Hankel
2

where g i s t h e ampl i t ude of nucl ear vi brat i ons, which may be estimated using a Debye model of the tungsten lattice. At room tem p erature g 1.2 x 10-9 cm. Hence 2 = 2 ° which is in q u a litativ e ag reemen t with fig . 2 . At T ~ 80°K, g ~ 0.7 x 10 -9 cm hence 2 theor = 2.6° which is also in qualitative agreement with the data of fig. 3 The above rel a t i on ma y al so be used t o see how the width of the dip depends on the proton energy EP. At EP = 6 MeV, one obtains 2 = 2.5° and wh ich v alu es are co n s isten t with th e data given above. The fact that the width of the dip increases wi t h t h e dept h of t h e scat t e ri ng l a y e r ma y be understood as follo ws. Protons emerging from t h e i n t e rnal part of t h e sam p l e pass t h rough a t h i c k layer an d su ffer m u ltip le scatterin g . How the depth of the dip depends on the posit i on of t h e refl ect i ng l a y e r i s not qui t e cl ear yet. It is p o ssib l e th at th e effect o f p a rticle c h a n n e l i n g shows up here [3] . If t h i s i s t h e case, th e p ar ticles may be accumu lated in the channels. T h is s e e ms to be consi s t e nt wi t h fi g. 4. These p r o b l e m s a r e under st udy at present . It would also be of in terest to investig ate th e decay of nuclei inserted in to the lattice of a si ngl e cry s t a l . The correspondi ng ani s ot ropy has been described recently [4]. The aut hors are i ndebt ed t o a number of workers of the Department of Physics of Moscow State University, especially to N. B. Bran d t , V. K. Zubenko, G. A. Iferov, E. V. Kolontsova and V. E. Urasova. Addendum Recently, som e experim e nts were carried o u t using nuclear emulsion for th e detection of scat t e red prot ons. The pl ane of t h e em ul si on was perpendicular to the [100] axis of a tungsten sin g le crystal. Th e in ten s ity p attern o b tain ed at Ep = 200 keV is shown in fig. 5. The dots and l i n e s correspond t o t h e i n t e rsect i ons of t h e

Fig. 4. Relative minimum counting rate in the dip as a function of pulse size, at two different target temperatures. 306


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Fig. 5. Angular distribution of protons elastically scattered from a tungsten single cry stal at P = 200 keV. The photoplate was placed perpendicular to the [100] axis.

Fig. 6. The solid lines ar e the intersections of the cry stallographic planes with the plane which is perpendicular to the [100] ax is. The numbers are indices of the cry s tallographic axes .

crystallographic axes and planes, respectively, with the plane of the emul sion. Some of the axes are indicated schem a tically in fig. 6. The details of the experimental method will be published elsewhere [5]. Apparent l y , t h i s phot ographi c me t hod i s a straightforward and promising way of investig ating com p lex crystal structures. 1. A.F.Tulinov, Report at the XV Annual Nuclear Spectroscopy and Nuclear Structure Conference, January,
1965, Minsk (USSR).

2. A.F.Tulinov, Dokl.Akad.Nauk USSR 162 (1965) 546. 3. I.Lindhard, Phy s ics Letters 12 (1964) 126; E.Bogh, I.A.Davies and K.O.Nielsen, Phy s ics Letters 12 (1964) 129; M.W.Thompson, Phy s. Rev. Letters 13 (1964) 756. 4. B.Domeij and K.Bjorkqvi st, Phy s ics Letters 14 (1964) 127. 5. A.F.Tulinov, .G.Akhmetova, A.A.Pusanov and A. A.Bednjakov, submitted to Zh.Eksperim. i Teor. Fiz. (USSR).

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