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Stopping power and range of relativistic and non-relativistic heavy ions in different materials including solid state nuclear track detectors
Nuc/. Tradu pa,4~,n Meal., Vol. 22, Nm I-4, pp. 81-84, 1993 Ebevter Scieace Lid Prmmi in Grim Bnt-,n. 096940"/8/94 $6.00+ 00
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STOPPING POWER AND RANGE OF RELATIVISTIC AND NONRELATIVISTIC HEAVY IONS IN DIFFERENT MATERIALS INCLUDING SOLID STATE NUCLEAR TRACK DETECTORS S. K. StUUXM&*SB~AM KUMAR*and A. P. SHAgMAT *Department of Phymcs, KmukshetraUmvemty, Kuru~he~ 132119, Indut; and l"Depmment of Physics, Ahgarh Mushm Untver~ty, Aiigagh 202001, Ind-ABSTRACT Calculations of stopping p o w e r a n d r a n g e o f yam-zeus heavy zone of both the relativistic and n o n - r e l a t i v i s t l c e n e r g i e s have been done i n v a r i o u s elemental as w e l l as comple:( media a d o p t i n g the formulations of ~enton and Honks, Mukherjee and Nayak, Z l e g l o r s t . a l . and H u b e r t ~ t . ~ ; . Finally a comparison has been made w i t h t h e e ~ p e r l m e n t a l r e s u l t s . I~EYWORDS Heavy zone, s t o p p i n g power, r a n g e ,
solid
state nuclear track
detector.
INTRODUCTION The s t u d y o f i n t e r a c t i o n s o~ heavy ions with matter Is of great Importance to many scientific fields su~h as nuclear physics, astr-oph),sxcs, elementary particle physics, radiation doelmetry, materials science, radiation biology and c h e m i s t r y , h e a l t h p h y s i c s e t c . (Rhlen, 1980) and has a l w a y s been a subjec~ of v i t a l i n t e r e s t o f i n v e s t i g a t i o n s due t o t h e complex n a t u r e of the phenomenon. Charged p a r t i c l e detectors have been m a i n l y responsible for most of the experimental results in hight medium and low energy Physics and the knowledge of exact stopping power and range relations for- chat-god particles xs one of the e s s e n t i a l requirements f o r the c a l i b r a t i o n and use of any charged particle detector. (Benton and Honks; 1969). In the present work, a comparative study of the various stopping power and range formulations e.g. Benton and Honks (1969), l~.tkherJee and Nayak (1979), Z l e g l e r s t . al. (1985,1991) and Hube~'t St. al~ (1989) ~as been done by comparing the calculated stopping power and range values for different projectile-target combinations at different energies adoptxn 9 these f o r m u l a t i o n s w i t h the c o r r e s p o n d i n g e x p e r i m e n t a l v a l u e s . The. t h e o r e t i c a l c a l c u l a t i o n s o f s t o p p i n g power and Pangs h a v Q ~oen done utilL=Ing the ND-IO SUPER-32, computer facilities of Kuru~shetra University, )¢urukshetra. The e x p e r i m e n t a l s t o p p l n 9 power d a t a of Dlan~ s~. ~, 1990; Dtmbot ~ta~., 1978,1980,198a; 8 a u v i n s t . a l . 1987,1990; H e c k m a n et~ ~I~, 1987 have been utili=ed. The N o r t h c l i f f and S c h i l l i n g (1970) t a b u l a t e d stopping power ~alues wherever a v a i l a b l e have a l s o been t a k e n . RESULTS
AND DISCUSSION
Table-1 presents the experimental values of stopping po~er" f o r " dLfferent heavy ions -n different solid targets at varLous enet-g l e e along with the c o r r e s p o n d Ing theoretically computed values adopt,rig the above mentioned f o r m u l a t i o n s . The p e r c e n t a g e d e v i a t i o n s o f t h e c a l c u l a t e d s t o p p i n g power v a l u e s from t h e e x p e r i m e n t a l v a l u e s a r e a l s o p r e s e n t e d i n t h e t a b l e . From T a b l e - l , it is clear t h a t "the Zlegler mr. al. formulat,on highly undsrestlmates the stopping power values for heavy projectile and l i g h t target combinations (e.g. U, Pbw Xe, Me p r o j e c t i l e s in Be t C, AI targets etc.) whereas for" heavy projectile and h e a v y t a r g e t combinations ( e . 9 , U, P b , X e , Me p r o ~ e c t x l e s In Au, B i t U t a r g e t s e t c . ) the f o r m u l a t i o n o v e r e s t i m a t e s the ~topping power values. With t h e i n c r e a s e I n t h e ' e n e r g y o f t h e p r o j e c t i l e , these d e v l a t z o n s reduce and i t seems t h a t above t h e p r o j e c t i l e e n e r g y 50 MeVln, t h e s e devtatzon's disappear and t h e r e s u l t s a r e I n agreement w i t h t h e e x p e r i m e n t a l r e s u l t s . For all other p r o j e c t i l e and t a r g e t c o m b i n a t i o n s a t a l l e n s r g , e s up t o a b o u t 400 P1eV/n, the Z x e g l e r e~, ~ , f o r m u l a t i o n p r o v i d e s the r e s u l t s In good agreement w . t h the e x p e r i m e n t a l r e s u l t s . The c o m p a r l s o n o f t h e calculated stopping power" values from t h e Benton and Honks f o r m u l a t i o n w i t h t h e e : c p e r i m e n t a l v a l u e s shows that t h i s f o r m u l a t i o n g e n e r a l l y p r o v i d e s r e s u l t s I n agreement w l t h the experimental r e s u l t s e x c e p t f o r heavy p r o j e c t i l e s l i k e U, Fb, Xo, e t c . I n dxff~r~f~t targets f o r p r o j e c t i l e e n e r g i e s up t o S MeV/n, where t h i s f o r m u l a t i o n under'ms*lea*ms t h e experimental stopping power. Further, from table it is Qvxdent that the C a l c u l a t e d s t o p p i n g power v a l u e s from Mukhef'jee and Nayak*s f o r m u l a t i o n deviate from t h e e x p e r z m e n t a l v a l u e s e x c e p t foe~ p r o j e c t i l e s I x ~ e i : r , Ca, A r , O etc in
81
S.K. SHARMA et oZ.
82
d i f f e r e n t t a r g e t s zn t h e e n e r g y ;,ange ~ 20-100 MeV/n ~*hePe t h e foPmulatzon p r e y , d e s a e'easonable agreement ~ i t h t h e e:(pePzmental r e s u l t s . Noe-thcllffe and 8 h l l l i n e ' s data also shows large d a y ( a t ~ons from the e:¢per,I m e n t a I values e s p e c z a l l y f o r heavy p r o j e c t : l e e . F u r t h e r z n e p e c t z o n o f t h e table shows thatthe c a l c u l a t e d s t o p p i n g power v a l u e s the from the Hubert s t . e l , f o r m u l a t i o n a r e a l w a y s zn b e s t agreement w~th t h e e~pee-imental r e s u l t s (ma:¢zmum-dev~ation ~ 5% )~ most o f t h e txme w i t h z n t h e e:4pePzmen~al errors for all proje~tzle-taPget ¢ombznatzons znclud~ng t h o s e where t h e o t h e r f o r m u l a ( z o n e sho~ l a r g e " d e v t a t z o n s a t a l l e n e r g x e s c o n s i d e r e d (maximum 400 MeV/n). T h i s fomulation also provxdes agreement wzth comple:c t a r g e t media, In a d d i t z o n t o t h e s t o p p i n g power ¢ a l c u l a t z o n s , we have also calculated the range v a l u e s o f d i f f e r e n t p c - e j e c t ( l e e zn d : f f e r e n t s o l ; d e at vaPlous energx~s a d o p t i n g a l l t h e a b o v e mentzoned f o r m u l a t i o n s ( r e s u l t s a r e n o t p r e s e n t e d h e r e ) . Aga;n t h e compaPzson of calculated ~ange v a l u e s wzth the coPPespondzng e~perzmental v a l u e s shows that the Benton and Honks and Hubee-t ~t, ~,~ f o r m u l a t i o n s p r o v i d e t h e b e s t ageement w i t h the e:(perxmental r e s u l t s (8harma a t . a 1 . , 1992).
TABLE-1. E:(per~mental and computed s t o p p i n g power v a l u e s t h e i r percentage dev~atzons (~-esented in the p~ranth~s~s) ft'~m values. ION TAR- £NEGET
RGY
CALCUL~TEO z
t(r
KP KP Ca Ca Ca Ca Ca Ar
Be C A1 Be A1 Be C C Bz U Au Au Ta Be Bo Ta Au Ta Au Au Au Au Au C Nx Ag A1 Ni Au Be A1 Sz Nz Ag Au Au Be C A1 N~ Au Be
3.99 3.13 4.60 3.9/` 4.58 4.10 4.58 ~.20 4.92 4.85 4.89 4.95 4.62 24°07
OF
STOF'PING POWER~
Szxe.
(MeV/n) (Mev/n~/¢m) Hubert ~t~ al~ U U U Pb Pb XO Xe KP U U Pb Xe KP Xe .0 Xs Xe Mo Me Au AU Au AU Ar AP AP 0 0 0 KP Kr K~ KP
VALUE .UES
along wzth ~:¢pee'~mental
200~7" 15/`±5* 125~+3~ 175~/`~ 110±3" 103~ * 89.0~3 ~ 57.73±1,5/`f 43.0~4 ~ 41,5±2.5 ~ 4 0 . 0 ± 2 . 5~ 25.7~1.5~ 2/-,9±0.7" 44./-±0,9 e
23.14 294~08:
22.39 2 0 . 9 ~ 0 . 4 ~ 23.23 20,4~0.8 e 20.24 14,7~0,2 e 23,39 17&1±0,5 e 25.0 7 6 . 2 5 0 . 0 27.58o 75.0 23.4 150.0 16.20 ° 3.4/` 20-0~0-7 ! , 5.21 10.81¢0,2~" 5,36 8.02~0.45; /`.10 2.99±0.12 ! 6.06 2.48±+0,2o 4.39 1.72±0,0~ T 24.14 2 1 . 3 ± 0 . 3 42.78 13.~±0.6 e 2 5 . 4 2 19.5~0.4 e 42.50 11.1~0.4 e 4 1 . 7 7 9 . 6 ± 0 . 0 2a 2 4 . 0 2 10.3±0,~ e 43,01 7 . 5 ± 0 . 7 " = 70.09 3.08~0.0~ : 7 0 . 5 2 3.44~0.04m~ 75.60 2.74±0.06~e 75.28 2 . 4 9 ~ 0 . 0 6 72.98 1 . 8~+ ~ _ 0 . 0~em ~ 25.94 5 . 7 5 ± 0 . 1 0 ~
Benton & Henke
2P0.77(0) 142.1(-29) 154.2(-1) 140.7(-I0) 1 2 1 . 6 1 ( - ~ ) 105.4(--16) 176.79(I) 126.2(-28) 109.54(0) 9~,60(-15) 101.89(-1) 83,12(-19) 91.20(2) 84,48(-5) 57.74(0) 54,92(-5) 45.28(5) 79,77(-8) 42./-2(3) 36,/`2(-12) 41.79(4) 3/`,70(-8) 27.39(7) 25,21(-2) 17,43(3) 16,8(-1) 43.14(--3) 44,57(O) 28.3~(-4) 29,22(-1) 21.49(3) 21.25(2) 20.43(0) 20,25(-1) 15.11(3) 14,82(1) 13./-B(4) 13,4/-(3) 34.b0(-4) 35,09(-3) 2/-.78(3) 27,56((}) ~.~ 2 9 ( - 5 ) ~,~ 8 5 ( - 2 ) 15.74(-3) 1/`,01(-1) 20,49(2) 21.03(5) 10,79(0) 10,81(0) 8.2/`(3) 8.19(2) 3.02(+1) 3.11(4) 2.50(1) 2.58(4) 1.73(1) 1.79(4) 20.82(-2) 21,44(1) 12,91(--3) 13,10(-1) 18./-3(-4) 19,07(-2) 11.35(2) 11,44(3) 9.52(-1) 9.49(-1) 10.46(2) 11.26(9) 7./-7(2) 7.50(0) 3.09(1) 3.11(1) 3.35(-~) 3.3/-(-2) 2.78(2) 2.78(2) 2.49(0) 2.48(0) 1.79(-2) 1.7/-(-4) 5.38(1) 5,51(3)
Zleglar ~t,
Mukherjoo a~ • Na~ak
S eel. Not~thcllYf & Shilzn9
124.8(-38) 1/-2./-9(-19) 125.74(-34) 127.2(-18) 149.7(-4) 127.23(-18) 105.O(-1/-) 130.88(~) 113. ( - 3 5 ) 106.2(-39) 108,38(--381 94.50(-14) 118.10(7) 74.45(-28) 67,70(-34) 64.19(-38) 77.03(-1~) 94,29(6) 50.99(-12) 57,/`3(0) 44.4(--23) 50.5/`(18) 5~,03(28) 4&.83(13) 49.81(20) 4/-.b5(12) 45,78(14) 51.7/`(29) 29.49(15) 33,0/`(29) 18,52(I0) 20,34(20) 39.81(-11) 42,~2(15) 2/-.58(-10) 23, 46(12) 23.21(11) 22.43(10) 21,97(8) 1/-.30(11) 1/-. 17 (10) 14.81(13) 14, 4 7 ( 1 0 ) 38.93(8) 39,02(8) 29.40(7) 27,44 (0) 24.00(7) 21,29(-9) 1 A- 4/` ( 2 ) 13, 17(-19;) 19.43(--3) 19,/-3(-2) 10./-9(-1) 11,/-4(8) 8.21 (2) 9. 4/- (18) 2.94(-1) 3. 17(/-) 2.45~-I) 2.79(12) 1.72(0) 2.05(19) 20,43(-4) 20, 4 3 ( - 4 J 12.89(-3) 1-.,31 ( - 7 ) 19.05(--2) 18,35(--6) 11.45(7) 12,17(1) 9.75(2) 9.72(1) 10.97 (&) 7 . 9 5 (6) 7, 65 (2) 3. 11 (1) 2.89(--b) 3.38(-2) 3.07(--II) 2.79(2) 2.57(-6) 2 . 49 ( 0 ) 2.7b (-5) 1.D1(-1) 1.77(-5) 5.48(2) 5.43(I) contd..
RELATIVISTIC AND NON-RELATIVISTIC HEAVY IONS
contd.,
table
83
1.
'iUN TA~-- ~ 4 ~ (MeV/n) ~v~ml~,,~ . . . . . . . . . . . . . . . . - -
Ar Ar Ar Ar Ar 0 0 0 0 0
C AI Tz A9 Au Be C 8x Ti Ta O Au U Mylae" Au (CH~
75.70 23.66 74.35 25.92 73.93 23.59 91.86 88.06 45.~8 90.83 84.38 4.74 15.0
Au (CH~
150.0 ~ 0 . 4
Hubert eC......al. ::
2.50¢0.07 5.~3~0.05=e 2.04÷0.04~- e 3.59~0.06_~ 1.44~0.02 ~ 1.22~.002 ~ 0.45±0.01 # 0.417~.005: 0.594~.008 0.257~.006~ 0.2~3~.00~ # 176¢1~ ~ 119.0
Benton & . Hen kI
Zzegler ....... ~
a~.~
Mukher#ee& Nayak _
2.58(3) 5.34(0) 2.06(1) 3.56(0) 1.45(0) 1.19(-2) 0.446(-1) 0.413(-I) 0.595(0) 0.259(1) 0.262(0) 177.20(0) 117.25(-1)
2. SB(~) 5.42(2) 2.0~(-1) ~.59(0) 1.41(-2) 1.19(-2) 0.441(-2) 0.409(-2) 0.558(-6) 0.248(-4) 0.255(--~) 156.0(-12) 125(5)
2.59(4) 5.41(2) 2.07(2) 3.~9(~) 1.46(1) 1.21(-1) 0.443(-1) 0.414(-1) 0.599(1) 0.255(-1) 0.262(0) 1~B.83(-22) 10~.42(-13)
Z.~ o, 5.38(1) 1.B6(-6) 3.S9(9) 1.39(--4) 1.1B(-~) 0.39(-13) 0.317(-11) 0.549(-8) 0.237(-B) 0.246(--~) 178.77(0) 123.31(4)
30.~8(2)
~2.&2(7)
31.77(5)
25.25(--17)
33.~2(&) 31.23(0) 31.17(0) M y l a r ~2 . 76 3 1 . ~ 0 . 7 e 3 1 . 5 ~ ( 1 ) M y l a r 24.95 1.26±0.0~# 1 . 2 9 ( 1 ) 1.30(2) 1.31(2) 1.26(-2) M y l a r 93.10 .45¢0.04-- 0 . 4 6 ( 2 ) 0.46(2) 0.4&(2) 0.41(-9) • (Stopping p o w e r zn u n x t s of MeV/nucleon) Ar C 400.~3 20.28±.2~ $ 19.71(-3)~19. b4(-~) 19.40(-4) 12.00(-41) (thickness of C target'~ 8~0 m9/cm ) P Al 362.14 100.96~.22 ° 9 9 . 1 B ( - 2 ~ 9 9 . 2 7 ( - 2 ) 99.60(-1) b4.3b(-3&) (thxckness of Al target ~ ~787 mg/ce ) N C 146.67 26.&8±0.10" 28.79(0)x28.68(0) 29.20(2) 23.54(-18) (thickness o~ C target ~ 1~73. mg/cm ) Li A1 1~1.1& 2~.71~0.09 ° 23.61(0) ~3.47(1) 2~.88(1) 20.09(-15) (thxckneee of C target ~ 5747. mg/¢m ) Me 0 0
• Heckma~ it. #~,. (19B7)I* Bxmbot It. al...(19BO)11Bzmb o t ~t. ~,. (197B)~ • 6auvln e~e F~T. ( 1 9 9 0 ) ; o * Bimbot I t . a l . . ( 1 9 8 6 ) ; # Gauv~n ~ t . a l . . (1987)! $ Blank I t . a l . . (1990); 6¢x P E x p e r l m e n t a l s t o p p : n 9 power v a l u e . ACKNOWLEDGEMENTS One o f t h e a u t h o r s (S. K. Sharma) zs thankful to the Councxl of 6¢lentlfi¢ and [ndustrzal Research, Government of India, New D e l h z f o r p r o v x d ~ n g fznenc;al support. The authors are also thankful to Dr. F. Hubert for many useful suggestions and to Dr. J . F. Z i e g l e r for kxnd co-operatLon.
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6 . P. ( 1 9 8 0 ) " T h e theoretical and experimental aspects of the energy loll of relativistic heavily ionizing particles** R e v . Mod P h y s . . 52~ 121-173. 73. Benton £.V. and R.P. Henke (1969) "Heavy partzcle range-energy rmlatzons for dielectric nuclear track detectors'~ Nut1. Znstrum. M e t h o d s 09"~ 6 7 - - ? 2 . Bimbot R., 6. Della N e g r a t D. G a r d e s ~ H. G a u v i n ~ A. F l e u r y a n d F. H u b e r t (1978) Stopping Power Measurements of 4-5 MeV/Nu¢leon s d ~ a ~ A ; % d l C u AND laKP i n Ct AI~ N I , A 9 a n d Au N u t 1 . [nstrum. Methods. lg3, 1b1-169. B l m b o t R . , D. S a r d i s , H. G e i s s e l , T. Kitaharat P. A r m b r u s t e P , A., Fleury : ~ XF ' ~e , ~ert (198~ "Stopping Power Measurements o~ 3-5 MeV/Nucleon e~Kr, - -Pb and "''U in Solid~ Nut1. Znstrum. Methods. 174, 231-2~4. Bimbot R . , H. Gauvln, I . O r l l a n 9 e ~ R. Annet S. B a s t i n and F. H u b e r t (19Sb) •' 6 t o p p x n g Powers of Solids f o r aOAp a n d 4 ° C a I o n s a t I n t e r m e d z a t e Energxea (20-80 MeV/u)" Nut1. Instrum. M ~ t h o d s 8 1 7 e 1--10. B l a n k B . , J . J . G a x m a r d ~ H. G e t e s e l t 8. MQn:enbergt K.-H. 6chmidt, H. 6 t e l = e r ! and 6Qmmerer (1990).'*Energy--loss measurements wzth heavy lens at relattvxstlc energies"~ Nut1 u Inetrum~ M e t h o d s BS~p 8 5 - 8 6 . S a u v i n H.~ R. b ; m b o t , J. H~aultt R . Anne ~ G. B a s t x n , F. H u b e r t (1987) "St(=qDptn 9 Powers of Solids ~or 0 Ions at Intermedxate Energzes (20-95 MeV/u)Nu¢l, Instrum~ M e t h o d s . B2B, 1 9 1 - 1 9 4 . Gauvxn H . , R. Bzmbot~ J . H e r a u l t t B. Kubzca, R. Anne, 6. B a s t i n ~ F H u b e r t (1990) " 6 t o p p z n 9 Power o f S o l i d s f o p Kr, Me and Xe zoos a t I n t a r m e d ~ a t e energies (20--45 MeV/u) and the charged state dxntrxbutzons at equxlibrlum " N u c ~ I n s t r v m I M e t h o ~ . B 4 7 , 339-~50. Heckman H.H.~ H.R. Bowman, Y . J . K a r a n t t J . O . Rasmussen, A . I . N a r w l c k and Z . Z ~ X u (1987). "Range-Energy Relation f o r Au I o n s , E / A ~ 150 MeV. P h y s . R ~ v . ,_~
NTAItM22/I-t.--H
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36~4-3668. H u b e r t F , R. B L m b o t a n d H. G a u v L n ( 1 9 8 9 ) " S e m i - e m p z r z c a | fot-mulae for- heavy ion s t o p p i n 9 p o w e r s Ln s o l i d s Ln t h e i n t e r m e d z a t e energy f*ange*' N~cl. [nstrum. t t J f t h o d s , B3Q, 3 = 7 - 3 6 3 . M u k h e t . J e e S. And A . K . N a y a k ( 4 9 7 9 ) " C a l c u l a t i o n o f h e a v y i o n i . a n g e zn c o m p l e x medi~" Nut1. Instrum. Hethods. 25g, 421-431. Northcliffe L.C. and R.F. 8htl|Lng (1970) '*Range and stoppzn 9 power" ~ablee for heavy ions A Atomic Data ~ ~ Data Tables 7, 233-463. Skal-ma S. I ( . , Shy~m K u m a , a n d A. P. Sharma (1992) Response of soda 91ass detector to -IIU and Fe Lens ~ R~dlat~ leo. 43, 1493-1498. ZLegler ~.F., J.P. B t e , 0 s a c k auld U . LLttmalok ( 2 9 8 S ) " T h e S ~ o p p L n 9 a n d R a n g e o f Z o n e zn 8 o l x d l . Vol. 1. ( P e r g a m o n P r e s s , New Y o r k ) . Ziegler J.F.(1991) TRXM-gXt The Transpor~ o f I o n s Ln M a ~ e ~ ' . I.B.M.-Research, 28-O~.Yorktown, New Y o r k ~ 0 S 9 8 U . S . A .
peglgllmoll
STOPPING POWER AND RANGE OF RELATIVISTIC AND NONRELATIVISTIC HEAVY IONS IN DIFFERENT MATERIALS INCLUDING SOLID STATE NUCLEAR TRACK DETECTORS S. K. StUUXM&*SB~AM KUMAR*and A. P. SHAgMAT *Department of Phymcs, KmukshetraUmvemty, Kuru~he~ 132119, Indut; and l"Depmment of Physics, Ahgarh Mushm Untver~ty, Aiigagh 202001, Ind-ABSTRACT Calculations of stopping p o w e r a n d r a n g e o f yam-zeus heavy zone of both the relativistic and n o n - r e l a t i v i s t l c e n e r g i e s have been done i n v a r i o u s elemental as w e l l as comple:( media a d o p t i n g the formulations of ~enton and Honks, Mukherjee and Nayak, Z l e g l o r s t . a l . and H u b e r t ~ t . ~ ; . Finally a comparison has been made w i t h t h e e ~ p e r l m e n t a l r e s u l t s . I~EYWORDS Heavy zone, s t o p p i n g power, r a n g e ,
solid
state nuclear track
detector.
INTRODUCTION The s t u d y o f i n t e r a c t i o n s o~ heavy ions with matter Is of great Importance to many scientific fields su~h as nuclear physics, astr-oph),sxcs, elementary particle physics, radiation doelmetry, materials science, radiation biology and c h e m i s t r y , h e a l t h p h y s i c s e t c . (Rhlen, 1980) and has a l w a y s been a subjec~ of v i t a l i n t e r e s t o f i n v e s t i g a t i o n s due t o t h e complex n a t u r e of the phenomenon. Charged p a r t i c l e detectors have been m a i n l y responsible for most of the experimental results in hight medium and low energy Physics and the knowledge of exact stopping power and range relations for- chat-god particles xs one of the e s s e n t i a l requirements f o r the c a l i b r a t i o n and use of any charged particle detector. (Benton and Honks; 1969). In the present work, a comparative study of the various stopping power and range formulations e.g. Benton and Honks (1969), l~.tkherJee and Nayak (1979), Z l e g l e r s t . al. (1985,1991) and Hube~'t St. al~ (1989) ~as been done by comparing the calculated stopping power and range values for different projectile-target combinations at different energies adoptxn 9 these f o r m u l a t i o n s w i t h the c o r r e s p o n d i n g e x p e r i m e n t a l v a l u e s . The. t h e o r e t i c a l c a l c u l a t i o n s o f s t o p p i n g power and Pangs h a v Q ~oen done utilL=Ing the ND-IO SUPER-32, computer facilities of Kuru~shetra University, )¢urukshetra. The e x p e r i m e n t a l s t o p p l n 9 power d a t a of Dlan~ s~. ~, 1990; Dtmbot ~ta~., 1978,1980,198a; 8 a u v i n s t . a l . 1987,1990; H e c k m a n et~ ~I~, 1987 have been utili=ed. The N o r t h c l i f f and S c h i l l i n g (1970) t a b u l a t e d stopping power ~alues wherever a v a i l a b l e have a l s o been t a k e n . RESULTS
AND DISCUSSION
Table-1 presents the experimental values of stopping po~er" f o r " dLfferent heavy ions -n different solid targets at varLous enet-g l e e along with the c o r r e s p o n d Ing theoretically computed values adopt,rig the above mentioned f o r m u l a t i o n s . The p e r c e n t a g e d e v i a t i o n s o f t h e c a l c u l a t e d s t o p p i n g power v a l u e s from t h e e x p e r i m e n t a l v a l u e s a r e a l s o p r e s e n t e d i n t h e t a b l e . From T a b l e - l , it is clear t h a t "the Zlegler mr. al. formulat,on highly undsrestlmates the stopping power values for heavy projectile and l i g h t target combinations (e.g. U, Pbw Xe, Me p r o j e c t i l e s in Be t C, AI targets etc.) whereas for" heavy projectile and h e a v y t a r g e t combinations ( e . 9 , U, P b , X e , Me p r o ~ e c t x l e s In Au, B i t U t a r g e t s e t c . ) the f o r m u l a t i o n o v e r e s t i m a t e s the ~topping power values. With t h e i n c r e a s e I n t h e ' e n e r g y o f t h e p r o j e c t i l e , these d e v l a t z o n s reduce and i t seems t h a t above t h e p r o j e c t i l e e n e r g y 50 MeVln, t h e s e devtatzon's disappear and t h e r e s u l t s a r e I n agreement w i t h t h e e x p e r i m e n t a l r e s u l t s . For all other p r o j e c t i l e and t a r g e t c o m b i n a t i o n s a t a l l e n s r g , e s up t o a b o u t 400 P1eV/n, the Z x e g l e r e~, ~ , f o r m u l a t i o n p r o v i d e s the r e s u l t s In good agreement w . t h the e x p e r i m e n t a l r e s u l t s . The c o m p a r l s o n o f t h e calculated stopping power" values from t h e Benton and Honks f o r m u l a t i o n w i t h t h e e : c p e r i m e n t a l v a l u e s shows that t h i s f o r m u l a t i o n g e n e r a l l y p r o v i d e s r e s u l t s I n agreement w l t h the experimental r e s u l t s e x c e p t f o r heavy p r o j e c t i l e s l i k e U, Fb, Xo, e t c . I n dxff~r~f~t targets f o r p r o j e c t i l e e n e r g i e s up t o S MeV/n, where t h i s f o r m u l a t i o n under'ms*lea*ms t h e experimental stopping power. Further, from table it is Qvxdent that the C a l c u l a t e d s t o p p i n g power v a l u e s from Mukhef'jee and Nayak*s f o r m u l a t i o n deviate from t h e e x p e r z m e n t a l v a l u e s e x c e p t foe~ p r o j e c t i l e s I x ~ e i : r , Ca, A r , O etc in
81
S.K. SHARMA et oZ.
82
d i f f e r e n t t a r g e t s zn t h e e n e r g y ;,ange ~ 20-100 MeV/n ~*hePe t h e foPmulatzon p r e y , d e s a e'easonable agreement ~ i t h t h e e:(pePzmental r e s u l t s . Noe-thcllffe and 8 h l l l i n e ' s data also shows large d a y ( a t ~ons from the e:¢per,I m e n t a I values e s p e c z a l l y f o r heavy p r o j e c t : l e e . F u r t h e r z n e p e c t z o n o f t h e table shows thatthe c a l c u l a t e d s t o p p i n g power v a l u e s the from the Hubert s t . e l , f o r m u l a t i o n a r e a l w a y s zn b e s t agreement w~th t h e e~pee-imental r e s u l t s (ma:¢zmum-dev~ation ~ 5% )~ most o f t h e txme w i t h z n t h e e:4pePzmen~al errors for all proje~tzle-taPget ¢ombznatzons znclud~ng t h o s e where t h e o t h e r f o r m u l a ( z o n e sho~ l a r g e " d e v t a t z o n s a t a l l e n e r g x e s c o n s i d e r e d (maximum 400 MeV/n). T h i s fomulation also provxdes agreement wzth comple:c t a r g e t media, In a d d i t z o n t o t h e s t o p p i n g power ¢ a l c u l a t z o n s , we have also calculated the range v a l u e s o f d i f f e r e n t p c - e j e c t ( l e e zn d : f f e r e n t s o l ; d e at vaPlous energx~s a d o p t i n g a l l t h e a b o v e mentzoned f o r m u l a t i o n s ( r e s u l t s a r e n o t p r e s e n t e d h e r e ) . Aga;n t h e compaPzson of calculated ~ange v a l u e s wzth the coPPespondzng e~perzmental v a l u e s shows that the Benton and Honks and Hubee-t ~t, ~,~ f o r m u l a t i o n s p r o v i d e t h e b e s t ageement w i t h the e:(perxmental r e s u l t s (8harma a t . a 1 . , 1992).
TABLE-1. E:(per~mental and computed s t o p p i n g power v a l u e s t h e i r percentage dev~atzons (~-esented in the p~ranth~s~s) ft'~m values. ION TAR- £NEGET
RGY
CALCUL~TEO z
t(r
KP KP Ca Ca Ca Ca Ca Ar
Be C A1 Be A1 Be C C Bz U Au Au Ta Be Bo Ta Au Ta Au Au Au Au Au C Nx Ag A1 Ni Au Be A1 Sz Nz Ag Au Au Be C A1 N~ Au Be
3.99 3.13 4.60 3.9/` 4.58 4.10 4.58 ~.20 4.92 4.85 4.89 4.95 4.62 24°07
OF
STOF'PING POWER~
Szxe.
(MeV/n) (Mev/n~/¢m) Hubert ~t~ al~ U U U Pb Pb XO Xe KP U U Pb Xe KP Xe .0 Xs Xe Mo Me Au AU Au AU Ar AP AP 0 0 0 KP Kr K~ KP
VALUE .UES
along wzth ~:¢pee'~mental
200~7" 15/`±5* 125~+3~ 175~/`~ 110±3" 103~ * 89.0~3 ~ 57.73±1,5/`f 43.0~4 ~ 41,5±2.5 ~ 4 0 . 0 ± 2 . 5~ 25.7~1.5~ 2/-,9±0.7" 44./-±0,9 e
23.14 294~08:
22.39 2 0 . 9 ~ 0 . 4 ~ 23.23 20,4~0.8 e 20.24 14,7~0,2 e 23,39 17&1±0,5 e 25.0 7 6 . 2 5 0 . 0 27.58o 75.0 23.4 150.0 16.20 ° 3.4/` 20-0~0-7 ! , 5.21 10.81¢0,2~" 5,36 8.02~0.45; /`.10 2.99±0.12 ! 6.06 2.48±+0,2o 4.39 1.72±0,0~ T 24.14 2 1 . 3 ± 0 . 3 42.78 13.~±0.6 e 2 5 . 4 2 19.5~0.4 e 42.50 11.1~0.4 e 4 1 . 7 7 9 . 6 ± 0 . 0 2a 2 4 . 0 2 10.3±0,~ e 43,01 7 . 5 ± 0 . 7 " = 70.09 3.08~0.0~ : 7 0 . 5 2 3.44~0.04m~ 75.60 2.74±0.06~e 75.28 2 . 4 9 ~ 0 . 0 6 72.98 1 . 8~+ ~ _ 0 . 0~em ~ 25.94 5 . 7 5 ± 0 . 1 0 ~
Benton & Henke
2P0.77(0) 142.1(-29) 154.2(-1) 140.7(-I0) 1 2 1 . 6 1 ( - ~ ) 105.4(--16) 176.79(I) 126.2(-28) 109.54(0) 9~,60(-15) 101.89(-1) 83,12(-19) 91.20(2) 84,48(-5) 57.74(0) 54,92(-5) 45.28(5) 79,77(-8) 42./-2(3) 36,/`2(-12) 41.79(4) 3/`,70(-8) 27.39(7) 25,21(-2) 17,43(3) 16,8(-1) 43.14(--3) 44,57(O) 28.3~(-4) 29,22(-1) 21.49(3) 21.25(2) 20.43(0) 20,25(-1) 15.11(3) 14,82(1) 13./-B(4) 13,4/-(3) 34.b0(-4) 35,09(-3) 2/-.78(3) 27,56((}) ~.~ 2 9 ( - 5 ) ~,~ 8 5 ( - 2 ) 15.74(-3) 1/`,01(-1) 20,49(2) 21.03(5) 10,79(0) 10,81(0) 8.2/`(3) 8.19(2) 3.02(+1) 3.11(4) 2.50(1) 2.58(4) 1.73(1) 1.79(4) 20.82(-2) 21,44(1) 12,91(--3) 13,10(-1) 18./-3(-4) 19,07(-2) 11.35(2) 11,44(3) 9.52(-1) 9.49(-1) 10.46(2) 11.26(9) 7./-7(2) 7.50(0) 3.09(1) 3.11(1) 3.35(-~) 3.3/-(-2) 2.78(2) 2.78(2) 2.49(0) 2.48(0) 1.79(-2) 1.7/-(-4) 5.38(1) 5,51(3)
Zleglar ~t,
Mukherjoo a~ • Na~ak
S eel. Not~thcllYf & Shilzn9
124.8(-38) 1/-2./-9(-19) 125.74(-34) 127.2(-18) 149.7(-4) 127.23(-18) 105.O(-1/-) 130.88(~) 113. ( - 3 5 ) 106.2(-39) 108,38(--381 94.50(-14) 118.10(7) 74.45(-28) 67,70(-34) 64.19(-38) 77.03(-1~) 94,29(6) 50.99(-12) 57,/`3(0) 44.4(--23) 50.5/`(18) 5~,03(28) 4&.83(13) 49.81(20) 4/-.b5(12) 45,78(14) 51.7/`(29) 29.49(15) 33,0/`(29) 18,52(I0) 20,34(20) 39.81(-11) 42,~2(15) 2/-.58(-10) 23, 46(12) 23.21(11) 22.43(10) 21,97(8) 1/-.30(11) 1/-. 17 (10) 14.81(13) 14, 4 7 ( 1 0 ) 38.93(8) 39,02(8) 29.40(7) 27,44 (0) 24.00(7) 21,29(-9) 1 A- 4/` ( 2 ) 13, 17(-19;) 19.43(--3) 19,/-3(-2) 10./-9(-1) 11,/-4(8) 8.21 (2) 9. 4/- (18) 2.94(-1) 3. 17(/-) 2.45~-I) 2.79(12) 1.72(0) 2.05(19) 20,43(-4) 20, 4 3 ( - 4 J 12.89(-3) 1-.,31 ( - 7 ) 19.05(--2) 18,35(--6) 11.45(7) 12,17(1) 9.75(2) 9.72(1) 10.97 (&) 7 . 9 5 (6) 7, 65 (2) 3. 11 (1) 2.89(--b) 3.38(-2) 3.07(--II) 2.79(2) 2.57(-6) 2 . 49 ( 0 ) 2.7b (-5) 1.D1(-1) 1.77(-5) 5.48(2) 5.43(I) contd..
RELATIVISTIC AND NON-RELATIVISTIC HEAVY IONS
contd.,
table
83
1.
'iUN TA~-- ~ 4 ~ (MeV/n) ~v~ml~,,~ . . . . . . . . . . . . . . . . - -
Ar Ar Ar Ar Ar 0 0 0 0 0
C AI Tz A9 Au Be C 8x Ti Ta O Au U Mylae" Au (CH~
75.70 23.66 74.35 25.92 73.93 23.59 91.86 88.06 45.~8 90.83 84.38 4.74 15.0
Au (CH~
150.0 ~ 0 . 4
Hubert eC......al. ::
2.50¢0.07 5.~3~0.05=e 2.04÷0.04~- e 3.59~0.06_~ 1.44~0.02 ~ 1.22~.002 ~ 0.45±0.01 # 0.417~.005: 0.594~.008 0.257~.006~ 0.2~3~.00~ # 176¢1~ ~ 119.0
Benton & . Hen kI
Zzegler ....... ~
a~.~
Mukher#ee& Nayak _
2.58(3) 5.34(0) 2.06(1) 3.56(0) 1.45(0) 1.19(-2) 0.446(-1) 0.413(-I) 0.595(0) 0.259(1) 0.262(0) 177.20(0) 117.25(-1)
2. SB(~) 5.42(2) 2.0~(-1) ~.59(0) 1.41(-2) 1.19(-2) 0.441(-2) 0.409(-2) 0.558(-6) 0.248(-4) 0.255(--~) 156.0(-12) 125(5)
2.59(4) 5.41(2) 2.07(2) 3.~9(~) 1.46(1) 1.21(-1) 0.443(-1) 0.414(-1) 0.599(1) 0.255(-1) 0.262(0) 1~B.83(-22) 10~.42(-13)
Z.~ o, 5.38(1) 1.B6(-6) 3.S9(9) 1.39(--4) 1.1B(-~) 0.39(-13) 0.317(-11) 0.549(-8) 0.237(-B) 0.246(--~) 178.77(0) 123.31(4)
30.~8(2)
~2.&2(7)
31.77(5)
25.25(--17)
33.~2(&) 31.23(0) 31.17(0) M y l a r ~2 . 76 3 1 . ~ 0 . 7 e 3 1 . 5 ~ ( 1 ) M y l a r 24.95 1.26±0.0~# 1 . 2 9 ( 1 ) 1.30(2) 1.31(2) 1.26(-2) M y l a r 93.10 .45¢0.04-- 0 . 4 6 ( 2 ) 0.46(2) 0.4&(2) 0.41(-9) • (Stopping p o w e r zn u n x t s of MeV/nucleon) Ar C 400.~3 20.28±.2~ $ 19.71(-3)~19. b4(-~) 19.40(-4) 12.00(-41) (thickness of C target'~ 8~0 m9/cm ) P Al 362.14 100.96~.22 ° 9 9 . 1 B ( - 2 ~ 9 9 . 2 7 ( - 2 ) 99.60(-1) b4.3b(-3&) (thxckness of Al target ~ ~787 mg/ce ) N C 146.67 26.&8±0.10" 28.79(0)x28.68(0) 29.20(2) 23.54(-18) (thickness o~ C target ~ 1~73. mg/cm ) Li A1 1~1.1& 2~.71~0.09 ° 23.61(0) ~3.47(1) 2~.88(1) 20.09(-15) (thxckneee of C target ~ 5747. mg/¢m ) Me 0 0
• Heckma~ it. #~,. (19B7)I* Bxmbot It. al...(19BO)11Bzmb o t ~t. ~,. (197B)~ • 6auvln e~e F~T. ( 1 9 9 0 ) ; o * Bimbot I t . a l . . ( 1 9 8 6 ) ; # Gauv~n ~ t . a l . . (1987)! $ Blank I t . a l . . (1990); 6¢x P E x p e r l m e n t a l s t o p p : n 9 power v a l u e . ACKNOWLEDGEMENTS One o f t h e a u t h o r s (S. K. Sharma) zs thankful to the Councxl of 6¢lentlfi¢ and [ndustrzal Research, Government of India, New D e l h z f o r p r o v x d ~ n g fznenc;al support. The authors are also thankful to Dr. F. Hubert for many useful suggestions and to Dr. J . F. Z i e g l e r for kxnd co-operatLon.
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~
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