Frequency distributions of event size in deposition of energy over small pathlengths measured after penetration of 44.3 MeV protons through thicknesses of tissue-like materia

Baily, N. A.

Hilbert, J. W.

Steigerwalt, J. E.

English

NASA Technical Reports Server

https://ntrs.nasa.gov/search.jsp?R=19710021617 2020-03-11T20:23:37+00:00Z
G/?LLEY PZOOF TO: Norman A. Baily, professor of Radio!oCiy 
University of Cu\ i fo rn iu ,  Sari Dicgo 
Schco! of hl iedic i i -~  - Dcpt-. of Ro:?ioiogji 
504-6 Basic S~fei-tc~.:  Buf fdii.zg 
[.a Jol la, Ccrlifor~?ia 92037 
Norn~un .A. Eaily, f ~ ! i i ?  E .  S~.eioerwcij, arid Jei-ald \V. !-Eilbcl-t 
Department- of 2adioiogZ/, l!i?Yvc~sii-)r of  Ccjlifoi-nia, San Diego  
La Jollcr, CatiFori?ia 92037 
AC.51;'RACT 
The fi-equency disi:rib:~:ians of eveni- size i r ?  the deposition of ei7ergjr over s!-:-!.>i i 
pathieng:h: hcve heel-, measured aFi.er pcnrztr~fion of 44.3 Me\/ protons througi,i \,oi-iocis 
i-l-~icltriesses of ;issue-~:c~ulvci[en.i. material , Il,less dlsi-1-ibations have been measui-:;::,! o.,.~.i 
a range of prnetratiorr e:ctendii?g f rom zero ii-iic:i<r?ess to t1:icl:nesses of r!?vsc!e-ec;i;i~sajerii. 
plastic close to i-holi- corrssponding to  the total rci:?e of file psoi-ens. These di~ii.;li~:tii?!..r~ crc 
3 , .  ' flloie ~ s s o c i n ~ r d  wi fk l  i-iq-: passo(,; 0.r th; yioi-i; f i : l i lugh 0.667 ;; i()-'d g/ci,l-- or c. i i i f i ~ - -  
equivai~:nt gos. The trar,sl;.ion frc>i?i rzgior~ \ / , J ~ ~ T C - :  ~fcj t is t i~cj!  +'I~:CI.U~!FC~!.IS d~;:-:;!-.:!;i.? i.3
tl- at where a signiflcai?t spread ir: hearrr ei?i?i-gy I-,i:~s taken place is clearly d4zmcnsii-n~?d. 
In  n o  iijstcrnce docs i t  apcecar that f1-e corlcept o! do52 based upon CY ucrlue of file si~p;>T~:g 
powel- or civei-age enci.gy deiaosli-ed adequctfe?v defines the energy delivered to ci 5 t i  uciuic: 
1-invii~g t h e  d"if;?ensio~-is u sua \ l y  associated wi th  fl*io~e of bio\agical significai?ce \5: n:-rly a 
The possll3le conseqvcfic~s crr . id  pi-obcihle iiripol-i-cri~ce o F  ti?c s i - ~ t i s i i c a i  : i i ! c ; i : i ~ ;  ii:r:> (;' 
e;-iergy dei1osi~ioi-1 in snul i \ro(umes I-ici\\re beer? polnied o:~ i  by Rossi aird Rosenz\veYc -J (':) 21-id 
by f(el!ei-er (2, 3 ) .  T!le ;.heor;/ :?overi-liriy such F ~ L ~ c I . I ~ c ~ ~ . ~ G ~ ! P ;  is 5ei-i~i.a/IY felt 1.0 k t . ?  iic;r 
treated by t!?e woi-lc of \/a\/ilo\t (4.) as col-rcci-ed by the rriethod oF Efunck  and I-eF:-e:)c-;:.,:! (5). 
Tlie frequency disi-I ihuthons of enersy deposifioix associai.ed with the pa:,scgr of a 
monoenerg:?tic 4.3.7 /,t,eV p r ~ t o n  becnri? tl-irough \.raal-Feu t h i  cknssses of u i-issue - q : j i : , ~  !cn;- 
gas were  ii-ivesi.igai.ed by M i  ibert, Bcri ly, ar,d Lane (@,This work dei?ior.lsti.ai-ed, Fo;. i i:c: cc;<:.i 
whni-e the enrrgy Inss  i: very much sn-t:?ilc;r tlrrai? t i le particle energy, that firs.;, the: fu l l  
width a?. half rnaxii-ium (FVdl-IN\) Is \/cry lcirge and second, that si~nlficani- diFfcii:;~ctss 
bet~vc;c.r> th:? average e m r g y  loss and  rr!osi pi-obahle energy loss exist d u e  to the slrc:v,~i-:~:,.-:. 
causc:d hy il-ii: !arge nurniser of evenis ha\~Fng high energy losses. The spread ai?~: v I - i . 2  :i:e!i,ti:r:; 
boj-ii arc :'vi?ci.ioi:s of i!.ie rr:Lai-i eilergy lost., ij.5 reicrjive ,!cilue wii-I? respeci. i.0 the sr,ckjn 
binding energy of tile sfomi c e!eci.ronr! F;i i-he rrrei.>rial ui?dcr C G ~ ~ C ~ ~ E ? ! - C T ~ ~ D I ? ,  cii?ci i ts  \r:!!ue 
ro!ai-ive to i-l~ti: mcsxir:-ium possible erC:eryy "ircii?sr'ei. ~vhich the incidet>t pari-icle c~i-i  r irts ' . - . -  ,.A,., t to 
rrn elzc.i.ron i n  a single coilision. Good cori-elcttioi? bztween theory a d  e>;pcrirn:~i?i ihas ls;:~? 
fourlct when comparisons nre mude b ~ s e d  o n  the f u l l  vf'ia'iir ci- imir' mwxinluni (FvJI.-;":A) (J.? i-:,:: 
disi-rii- 2ui;an ..- func.bions, SiinIlctr clistribui-iiins for electrons hcr\,e l2eel1 sepoj,i.~.,ci by Kc:g~yi.;-r~o, 
N i s h i ~ . i i ; l r ~ ,  r;;-:d Onai (7) .
A coi~?p:xisc,n of tk~cary and cspei-irrrenial c.?:,i.a acquired ~ ~ s i r ~ g  46,4 Me\/ p~'~io;.i:,. O\VC::I- 
rnost of ti.1:: i-ai-qe of er!r6!-gy deposli-icns i-ecordcd v4ii-h i-hat zt-~ergy protonr ~ Q S  En,2;;iz I~:CI:,:'!<: 
Ka j . I>r ,  S;-eig~?-wcrlt, cri?:! l--!iEbe;-f (8). Good ~ J $ ~ ~ C L L . : C I - ~ { -  was again f'ognd foi- l.i.,c! F\)'dj-!j\j\ ci!-:d 
I e r ,  Fcr the \:n!l~c.s of the avei-uge a!-~d nosf probal3la C:.ICI.QY losses. !-lowever, s~gi-11 i r cc ,~ t  
discr~.pa~-,~Ii::.; wi.:re ;~u!.:l trbovs (arid be!0\4/ tlii. i?7<;51. pr'oX:,::ble Ti-,~:se 
m a n i f e s t  rh;i..ry:sci vb.5 in cr deficiency cf low e:~??e~-~)r 105s  e\iet?ts and a12 excess of I - i i~ ! . !  ., i.'i',:?i.g\r J /
I I uccoui7i for fl!ese, sir-~cicl i i - 1 2 ~  c.ioti!d ~ ~ o ~ i u c e  cri~ excess oF st-i?ui~ energy losses crliti ~~;~,.. i i~-j ~15,: ' .  ;:?.ye 
a fargel- ciiscrepai-lc, r :-c appear It? i-he region of h i g h  enersy losses thnn Is found .. 
Son:e prefIminary drii-~r 013 il-IC C F ) C ! ~ C : C I % I  sf 1hi.j fi-ecuef?cy disi-ribupions \):hic!; nr,cril- In 
ct, !-I- <. small vo[r~:n?es aficr jsossag-. of a liorr~o~zriecius hecm i-l-ii.ough a lcxrge arr\our\'i 0.f ub ,,, ' L)'%:! (:ar,,c~ 
thus aii-es suffering various et?srgy Iossles was giver) by 1-iiibel-t and Bail)/ (9). Fn cJddli.is&: 'i.c 
statistical fluctuations such distributiorrs c;rz subject to perturbations due 1.0 tiic: 
inhzmogei-leity of i-he el-iei-gy dist~lbt . i .~.Eo~~ of i-1-~e chcrged pcrri-lcies (70, 17, 72). T!:sric: 
criithors hove shov;rr? that energy speci-l-mci of cx I.~oii;:ogeneous bean1 c f  c l~a rged  
beconizs skewed i.oward lower energies cific:. r;cisicru.g::. .ihroug!-f i.I.ii!> Q ~ ~ S C I T ~ C Y S .  <:)b.:c>rk>2r 
thicklizss becom.=s grecr.ier- the iiisfribvtfcrt-I cpfr?rc;oc.iies c guussiai?. This c h ~ ~ i ~ ~ a  oc:c~lr-s 
becaus3 of stajisticcil flucfucii.io;3s cf 1 . 1 ~ : ~  cn<?!-c\, iDSZ: i f l  t h e  cbsoi-ber cxl?d icrecav5E i-5- di"r,li-2r,i \J / 
ener-o:, paulc{es  lose en.l.gy gi diffclcr!t  a;.rrsr:j:. : i.:li-3~e The f l~s t r~bu. ; . ior - l  a o ~ i i - l  i42.,-;;,::i,~ ! 1 ~ 1 . ! . -  J /  .J ‘ 4 
~ a ~ s i c ~ ~  ~r.i.:>r i-he mcai-1 pai-;fcle e n e r s y  i s  ;.r:ducc;d i .3  jZss thal-: 3.5 per cc!-,t of tjic? 
particle energy.  This is .[he point where the fluc.ti.jati'31~s F~?troduced by statist; cs- t:lrs o . ~ ~ e :  corn.? 
by the spread in s toppi~>g powiers ~ ~ ~ r e s i > ~ ) i : d  i to i.1.i" part icle energy spocfra . ii> s,;ci-~ a 
si tuation,  the freqcrei-,cy dizfributioi? of eilcrgy Io:;.<:s ? n  a sinall pcr~-I-i\eng~h c0uii-i !:c s f ~ ~ i - ~ l r : . - - ~ . - ~ "  r ik ,Goi , l  :y 
al tered by {-!-I.. amount of n-iat-.riai f;.avei.scd kty the F>rrc.ticie before ei3terlny ih-. \ i ~ ! b i i : ~ !  
f he e;:pc~-imenf-a! results discussed i:! t!,:i:; p:!jsc! \,,ere oi-,,jriin@d ijsil-19 t'iic msi i-!-,d :;c5scrIl;,?ci 
i n  (5) excep't fisr i-he i12ircdvction of ~ i ~ i - ! o ~ j :  j.f,i'ic\:.n~sscs cf i-isjue-ecjuivcj]& pia:,iic i:r::j: fir 
c ,  < '  SI?o~~!tci r~nirscfs (12) . T'hese aLso;-b-rs \ye re piaczd i;! c o r ~ ~ c c t  wi -17 ti32 ~ : 3 ~ r 4 ~ ~ l ~ , ~  I:$ i,-:!c".&< i ; i .  i.1: : 
" .  !3ropori.ii?170( ~Cbiinter , 'illii prc;o.;.l heam u?: ~ ~ e ~ : j  i2:d ern (-?:-~ei.g)r 3f ~1.4~3 -i- 0 -2 i\'ir2\,/ crrlr: 7d, j (>~  
-. 
generci-ccl 13). i-h.t Secfci- Focosing Cyc!sii-on rii. :.I;:: i-ir,l\,,el-:i;-y of  Cn[iTcri?jc~, !..os 
-The j~roporj-ioi;al co~iriir;!- usad F I T  i-!.~is in\/cs{.l~cri.Yoi2 wtxs cyiir;dl-ica[ oi;d .fa[>i-lcc;i :i F;<\;I-: r ,c: 
saii~e ti  sire -*equ ivc! leni r?;ate.r-ial wh icit wc!s iis;:d for the a bsorbers . T!te i~i^ii.hi e
pariicles il-iro~!~Ir i-!?e co~rni-cl- Yr'Qs crccuratc;iy cf3finc;d bby t h ~  coii-iciclSsi?~e sysierr: 
r r  l i .  i !-I (6). li,i:2 + I  I 11173 gcjs \YOS an equir-r;o[u~" I-le-CC3.) n~isfcrrc at cr pressure of 2i' i.01 r ,  7/ ie  
L 
- 
eircii-on density of ihii gas is 3.01 x !a2' eizi~ronr/~. i 12s experimc-infa1 diiii  ~~~JI- IL- . ;  \;B:-- 
rne~sai-cd for a p~ti-i ier~gtI-~ ecjui i ,a i~nt  to 0 ..!;'13 x !0v-4 g/ '~!-~~f2 of u n i t  de;iiiiy t i i i ~ ; : ~ .  E>:i f  
and ei?j-rcrr~cc.: \vindciys were  fabricated from 0.OC325" aiurninifed mylar, S u F f i ~ i l > i  s t!~~. l ts  
were er,c?:rn:ii~ed to pi-avid rcc~sonc?bly good statistics over t h e  entire rai-ige of ei7i:i-9 C:,\!~ii:.:. 
/ L 
recorded. i n  each case appi-nrim~tcly lo4 eventi were co!iacied i;, ilia chonna: c~rcc. : ; . ;~r:<:i i~~ 
i-o the imost pi-obaLIe energy loss. 
Tl-te exlr?esirnantcii ~ i a t a  c>!>t.aEneri is skio\:,/n Iri Figs. I ,  2,  ornd 3. All eurv !22,3 :.; 
nor!~;aIizc:ci so tisat ti-ic t ~ > i - ~ l  proiinbi l i i y  For each is equal to u n i t y .  Fig . si-b~,,:is "I-,.:: .",.-," { I L -;'.J C.!D c:\' 
s dlstrii~lii-ion curves of ths energy deposri-co ti? the set-lsiftve volurzie aFtet- pcrssage '?!i:-,2:si: vc,;irus 
j-hficlcn-ssis of Sho~?!:a lnuicie va;-ying frar!~ zero 10 1 .54 y/c;ri~2 (1 .$O cm) . i u i ~ ; ~  /A i.;pi'2ents 
the dutc! obtc~ineol for the ui-Idegraded beam ci;d Cr~i-ves 8, C, U, E, and F are  oftc!. I . : ~ : C C ~ B C  .i 
C, 
ihrsvgii 0.2% c ~ / c i r ~ ~ ,  0.44- g/cm2, 0.66 9/~i:22, 0 -99 g/cn ?, and 1 '54 g/crn*, ~ c ~ ~ ~ z c ; . ~  i-vre!v I - 
After ptsssag? i . l- iro~~~h svFf?cient material, de~radatior:  of fhe b ~ i i i ~ i  (ei-rc-,rgy s;l~ ri;d OF 
e a t . ?  the prirncri-y protons et-j,te:*ing the sensitive voli:t~ic of the coi~ni-er), p-odi~ces a .,!GI-!!; icc:,-l'i 
cl.>cnge ii-1 ?I-~n, ensrgy dcposi!.ign i:,ai-:ern.. - r I~ ls :.:%suii-s it? cj, 12;-oader disi-rtl-?ukioi? T~:,-~c:"ior., :r/.>ur7 
wovlc! i~avf: heerr ~bi.crii;~d from c?, primary proton bearri \vl~ose energy wcs e q u a l  jic:, i ; & ~ r : -  
* 8 "... 
c u l c u l ~ t e d  fi-orx the i ' ~ 5 i ~ i l i C i i  rang-, of ihe 44.3 M e V  protons. This i s  iiiusi-rcuicd in :-:i.:. -, 2 2nd :i. 
s Curve i' of Fig. 1 Is repradr.!ced as C!i:-vc A, i !-I Fig . 2 atid represei7fs i-j?e 1Creoirei-I:~~ ls t i , r . ' - '  ,-. ~ ' ,  t i!>L:i ia2-i 
obiri!-l-ci of!;!- pas;onr ;!rirjugi,; 1 -54. cJ/crn? af S:,u~.\\o ii;u; tie. Cuivr:s 6 and C i,! i i c ;  - $ Gic 
r i  
tire Cist.i.ibui-io.-ts c?f ewi.ov d / [ a s  ::fi;et p~5:r;g.l ii!!~;~!: 1 .(A c~//ci;)2 cn.i 1 .63 s/c:l:!i,r 
In Fig. 3 \t!e have the F,-ec.ilc:?c:/ c{i_ctribuiior-,s ni>.;.c~;?ii:cd ~Fker pas:;c:-rgc of ti::: [>-.clli 
,".. 1 '03 c ~ / c r n ~ #  1 .74- S/crrt2, 1 .TI c~/c: i i~,  i:-d 1 .3i g/cnr? of S!;oiko muici;  ii~o\*;,:; ;:i :,.+u<v;:: 
A, O ,  C, and C, 
. I  , TI?.. F'\/\!i-;M deci;?crses frc;l-!i a ~~ci ; , : i r j?~m for  i.l-!c vildtigi-adcj beain ;-].l;.c!ic.,lq r/ ; : ,c i -  
@ ' r  ,- > 
vo1~1e obtilinr;d a i i e r  jwisogo thi ,cur!? . 7 -63 S / c m a  (Curve D of Fig. 2 and C I J ~ Y ~  .;, 3 .  : .  . (ii 
a ,  i-heil sfai.;.s 1.0 irici-t2ajc: again,  TIIP; " 15 CI !c2t ccri csnsaquence of \ 1 ~ r \ r i 1 1 ~  i i:irodil C C T ~  
spread of energies it? i he proton 1r;ecirui :,,~ith cr iocv energ., L) fa i l .  
1' r he p r t i i ~ e i i t  quanfita:t.i\.e data obic:ilr-led ore given i n  Pc:b!c i .  
, 2  * & 0 .  ihat i17is becoiq-ji.s ti-je d c ~ ~ i r - i ~ i - ? t  fcctor in c;ei.~:rn.r I ng i.{;e character  of the er~c:rgy tic p c ' : ~ )  isr-i 
pattern. These facto!-s arc evicieiqced by .i-he :j-eadi,i c'ecrease in {-fie v4idj.ki of ~/ICJ e~;;:!-c), iois 
func: ;c: i  i h s ~ u ~ l - ~  ihs$ f i r s f  I .&: c;,icm2 of r:l.iorl;is fI?ic[:r?esr end the subsequcili, 
of  ih%se w i t h  f;irji-!e;- c ; 2 g ! - o : d c r t i o n  of i-l:e t;esi-r~, Of p!-ii;?tz ir::pot.~cit~~e is ;he feet i - i - t i ~ )  F,: i-!; 
, ' ' i ! ~ s ; c i n c e  j.j~i:~:? f!.~~ici.ions njzprr:~isl-> the i..ii:.lri.~\Ai ~- ; ;~* : .JsT~~:~ : :  ~fL:!-ici.F~t:s C O : ~ I I ? O ; - ~ ~ ,  .. A , , I , ..I t . c; :O 
r . 1 lei coi:cc;ti.: of i-a'{foi c.:i.i ~ f f : ; . ~ i - . ;  c:;~d ~-cxdir;i;i<:ic~icd ii-iod.?fs wiilc[-r c;..? hasec! Q;) 
e " .^ 
0;' energy c!er;~i?si~ici? ii: srnciE I vo!ii:.r~cs oL; [:~;o~~c.J~co! S I C J ~ , ~ ! T ~ C B I ? C C  
A secol-id ii!-,pai.j-,li:i- us ,~e i f  of i-he cjzr;c; i s  i . 1~~;  fac[- fj lut  for 1 disj-;.ibij;ion; 
I i Prob;.'!3\C e:c~:-i.gy tois Is sigl-!ific~i?i!y lo \~ ,~er  iilai.; m\:c;i-ugh energy lc?ss, in s;,-\?/i 
or target- an:! fczr a:? eqfeci. cle:.?eficicni. or: i-i c j  nG,!c or  sma! i ;:vrn-ilser o f  ~-i-cr\,~erstrF~, : ii:.: c.c;:~c\ 
* ' 
closr deli \.ere:: \:,/Ii I Isle incoi-rectly inferr-cc\' i f  cbsorbcd c!ose (riiucroscopic) rs vzt:d ,. 
As ~ ~ e v i o i i ~ i ~ r  po nicd oiit by [ ~ c I ~ I ~ ,  --------- ei a ! .  ($), whcs! the !ogc:!-8ti:m of fI;s 
~veni -5 ii2 eacls c / ~ a i ~ ~ : . ~ ~ ~ [  or eil.crgy i n f -e r \ i ~ j  i s  i>!oi{-ed ci.gcil?s,b energy tile hfg!z er;?r.r b' .( J : ,a ; ;  
po!.i.lcn Ys \r(-71-y \veli  cujjjs;o;:irur:i.a.;: by a si-i-c.lgl.ij. l i r rn ,  En alj cases i~*!.~~ci;f i~ated b-1 !/IT.: sf.; cf 
eq'erini-3i-its (fable I ) ,  s i o p  of this jil-ie Is coi?s.i-a!-ii. in {he regior2 gove!-i;ed by 
f I ~ c , i i i ~ ~ i ~ > n s  occurring Frr the a~?~avi?f ofei.;~?i-gy deposited i r i  the ccu!.:i.cr ~ c s .  t i?  .i./.!~: ;r:c::ic>i-r ' . 
l l i -  
where the bc-:lmifior of ;-lie di: tribi.14-icn . ~ u : ~ c J . ~ ~ T ) s  is zr;;!uer\ced by ei-icrgy sj-ragCi:ijii ,:; ei' $7" 
t i - ~ i s  sjcp- beiidir j C! c ] i t , : ; . i ?~~s~ ,  Si SICG this i s  r j  i~"!g~,:j.i\fi? ~ I ~ i p f ;  it m ' i ~ l ; ~  CI re lalive 
the ni~rnber o r  i-lic~1-l energy ever~-:.s vqliich ore  due to the ;ow ennrgy :ails of  t i  
rrnd we  i-h~rta-F,:xe r-;:r-nuf u wii-h rather i~rcj3 d disiii  hu ?ions. There are Fndicatioi-is 
enai-gy lossec there is w s!-lorp decrease i r t  eve:-nts, prolmbfi' C ! U ~  to flla loss of /O\Y c,iz!-C:)i 
p r i i -~a : -~  pr-ofoi-!s which hcr\r~ st.!!ferc-ld larscr than a\fer:-igc erisrgy loses as a a f 
tl?e s i - r ~ ~ ~ l i n ~  phcnor~ic~on. 
\ille tire !lot abi;? rer.idiEY ascsss i:$luencc GF t \ ? ~ f  lass ~f /1igh er!erg)i (4;: !t:.j i.cp ctr 
out  expai Firtr:i:ic!! curves. ,4s pr.e\,rious ( ysTt?i,cd oui- @), sl,ecl~ Ios::~L; y,,oU IC: ~ a l i ~ ; '  (1 
bi-oadenirig coT cjur distrik;ai.ion I.;'~ii-~ctlo:-;s tl-lcin pret-:ertt!y oSserved n i ~ d  vircluId t h  
e\/eiJ gi-eaier discreparicles bci-~~geen i.i-rec;sy (?\;d e;:p,:riri1:2r.\t tl-i.;n a re  now fou;-ic(. v,/c: ~ j , ? :  
, * In:ei~dii..;~~ !.to il-!vesi,igate .i-I?c dlsi.!.i!>utic;? of ei?ei-gy iosscs I,:igh eiier-g>/ seccnc!;~i..Ii:s i.!?~.?!:,:.'; 
the !,Jsc.; of C l  ! I ? i , ) \ f i ~ i i " ~ :  i~ i .C>D0l. i i (>i i3 i  ~oi, i l i)~+i., ~ ' ~ ! I ~ ~ @  I:>i3i!j fl*te ~prii- it~! ]{$try/->(iiipp ! C : R < )  ,:;I,> <:I,;~Z).~T,, 
dr-;po:;ite:! i n  vurious ~_;eorrleiric. \roiun;es ~.i.lese pu;.ticjes u.i-e of inii-.,i.cs:- 
: C ptri-iltr.r?gi-hs of [cw ~i.on?ic: i-l~;.;1bar nc;.izriciis i-o rei~~oii-1 broad, even ilcoi- i . F . 2  ei?cs c;, 
tilt pcsri-icle range and ii? the regiorz of the Rragg peal<. 
2. En al I cases inves.~igei.ea' the ratio of ~nof;.! prob~lslc fo the aver-cgc: i.i?ai-y>, i~:':.i,:;$ 
llcis heei? signifi cui?i-l less i hail c r n t  t y .  
3 .  T h s  slopes of i.h-2 h i g h  ei;e;.gy tail j>oriio;-~s of freqi~eilcy disisi:ilsu~ici;~ i:i~r.lc:io.-lc; 
are col?si.anf for a l l  clisfribij[-ion fui~c~~ic>i?s \fi,,j?o~.c s I ? Q ~ $ s  are C * O V ~ I - ~ ; ~ C ~  J by . " ; i ~ t Y < t i ~ ~ ,  i 
FIucfu<xi.ions. 
,b,.M,!<ei[ei-ei-: hA,ici-odr:ir'!;;-ic!ir)l and t!13 i.i?eol-y of r ; - ~ c ? ~ ~ i i r i ~ ~ .  R::mri,  
Vienncr  (1 FG?) . 
* * P.\/.\/cviEo\,: jc.~~izc;i.iofi losses of i~ i~ :~ i ; - i .ne i~y  i?a:7vy parficles.. Zll. E:c;:t;l 
Fiz - 32/  923-923 (1957j, Ti-arlsi . JE.[T!. 5, 7,$9--7!;1 (7957). 
--.- .- 
-7 0. Eiuncl: ~ i - i d  S.L.ei~ega;-!c~: /_urn Eii<:;r-gie\ier!~i.~c;lmiii~e!ie~- Eiec i-oi*!-t: ir! 
%.  Pliys;k '/i/i'', 529.535 ('1"'" i J L ~ )  , 
-- 
.J . ~ J . ~ i l j c ; c i j . ,  1'4 .;A,. Baiiy, ci.id 2.G r.i.;i:il:: Stufisi-icc:l[ f i v c j -  
in  to\v-=a:.on.lf c: i?i!n:ber mclieri,c~:!f s by 4.3 .7 :\j\e\/ prz:oii.r. P \ ~ ) ( S  , :Ll;iV. 1 f t F 3 ,  
- 
5. i<ageyarna,- I,<, Nisi-iimuro, and Y'C?ir~;z.i;: si-i.c!cl:Ilng dd ol: fcs:- e!ect!-firl;, .i, S ( . i c .  
Japan 8, 692-683 (1 853) . 
- 
b! ,A. Bai I y ,  J .  E .Si-eigerv,io\:-, and J .\f\/.i-lilbcrf: Frecrhuen*\ /  b i disfi-ibv;tici?s 0' 
. . deposi i-!on by Fcst cllargsd particles i n  very smgI I i ~ ~ ~ ~ h i e i ~ g ~ - l l s .  Ph>/s. i? ev. n r  2 ,  
577-532 (7973) . 
J .W. tlf iilei-i cind P4 . A .  Rrrl l y  r Energy clei3osition i n  m i c r o s c o p i c  volc~rr?r.s by I - I I ~ ; I I  
protons. Rcid . Res . 39, 1 -1 4 (1 963). 
-
C . ~ s c i ~ c r l & r :  Struggling ciisi-ribiii-ioi?~ of e::i.~-emcE~ l a r g e  en'::r-gy loi;ses ktj/ 
7 lr-1 Rut!-ierforci Lcib, Report, r,i-!c.-,/&164 (1969) . 
1 . M . G. i )ayi~e: Energy ~ i . i . : i : i ; : ~ l i t i ~  .'a of iir,a\ly c,l.l:irc-ci p~i. i . i r ; /es is: ti.iic[: 
Ph;,s. Rev. 185, 611--625 (1969). 
--- 
pas;-icles i n  th ick ulrrsosbzrs. P l i j f s .  Re\/. B,, 1, 2863-2669 (1';"TC)j. 
- 
13. F.i:.ShoriIta, .I. E .Rose, and G .  Fa; !la: Co~-,d!.:crli?~ plas:-ic .u.qulvcricl-;:i j . 3  ii::::u::,. -:I-; 
and p o l y ~ ! - ~ i - e n e .  Proc. %!-,d l i ? i ' l  Conf. [ ' eace f~ l  Uses At. Energy 21, 184.-1",'- 
-- 
,/ 
TABLE I 
E p r o ~ o n  = -44-3-t 0,2 MeV 
- - 
Akraorbei Ti-ickness - j Aveioga Energy Lois, h I MosiProhabic  Energy Loss, ,bPp Amp/ " { S l o p e  of' High-E,crgy Tai l  j FWSiil, 
I (keVj S honkcr i./?vsc!e ji<eV) f I 1 i (Frob . /~c~ : i /ke \ /  I 940 (2/c K 15:) 1 I i j 
! i j 1 i 
-- - i I i i 
I 1 8 ? C I 9 -899 0 . .43 1 0.53 0 -86 1 133 1 I E 1 
i f 13r . 22 1 0.856 o .a0 1 j 0.54 i 0.85 133 i 1 
I j 1 1 j 0 .Lf4 i 0.919 
4 1 0 -52 : 0.53 i 9 .S6 I "'6 i 1 ? i 0 .C.5 ! 0 .SP7 3 .$7 i i 1 1 0.01 0.27 I 1 118 1 J i 
i 9 .';? j 1-17 j 0.72 i 6.62 I 3 .Sf$ i ! : ,  
i 1 8 i 4 i i 1 $ 
j 1.54 j 1.95 I 1 1.30 0.67 0.86 
1 
I l i s  
! 
I 
I 1 2 1 ! T .6,3 2.20 1.50 : C.63 f 8.88 j 
I I i C4" I I 1 1 1 ..5.:3 1 2.9A 2.15 ' 0.73 j 0.55 r 
f 
I i ! ! 100 i 1 1 I 
1 .T4  1 4.13 1 3.00 i ! 0273 I 0.55 1 113 I 1 f i f I j i i * 
1 5.67 0,47 1.73 3.90 i 0,69 i i 1 23 1 1 f j 
--4 , 8 ,  
Fig. 1:  Frequency disti-i5vtio1?s of ener-g)! 10s:; i n  a pai.l,ili7nCT!fh 01' 0 -667 >: S s / ' c ; Q - i a '  
- .---" --.-- 
of Fic.--CfJ2 by 4.4.3 Me\/ pi::fcjfic. rir.cc~o';: ,...td2 C4 3 ' .  r t l i .~i;gh va:-ious 
of Sf-ionl:~ rili~scle. Curve A I s  Tor ti-12 u1?:4egr;~deci bnat-9. Cur-ves E;, C, D, 
E, atid F ore clitci pcrrzg-. l i i i ~ ~ ~ ! ,  0.22 C Y / C I ~ ~ ~ ,  C .44 g/csn2; 0.61. i;/::~.,"2f 
0 -99 CJ/CIR'~ arid i "54 CJ/<;~R', sesp':c:iveiy. 
, '  Fig. 2: PcithEc:ngi-h, pi-oion energy, onci absorhi!~g ~??aiei-ial ctse scn;c: CIS c;;;;,:er! To;- 
--- 
Fig. 1.  Curvcs A, Ff, c;nd C \~$ere  o5tained after possage uf thr: 
,-," L,>>t"L;\di\l,'<:! .,,.*., .,<. 7,: 1.54. g'cr2, 1,60 CJ/CIR', atid 1.63 $/on2 of S h c i ~ ! < ~  mgicic, )" 
Fig. 3:  Pai-hlangth, proion erjr-rcjy, a r d  abzo!.blng c-icii.srSal ore t!:e sai:-lc$ us 
+-.- 
Fig. 1 . Curves h,, B, C, aid D we:e O ~ ~ ~ F I - I F J , ~  cifj.er p ~ 1 s s ~ ~ i e  L, of t I ~ ~  
through 1.63 g"cm2, 1 *71- g/crn2, 1.79 cy'crn2, nnd 1.85 g/ci;i2 r e ~ , ; ~ c ; i \ i d ~ ~  
of Shonka ~-nc!scle, 





Changes in the frequency distribution of energy deposited in short pathlengths as a function of energy degradation of the primary beam

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