Rad. and Environm. Biophys. t2, 157--168 (1975) © by Springer-Verlag 1975
Neutron Scattering and Energy Deposition Spectra* 1~I. Coppola and J. Booz Biology Group, Ispra, Italy; G. D. Research, Seience and Education, C.E.C. Received April «, 1975
Summary. The influence of neutron scattering in the wall of a spherieal proportional counter on the energy deposition spectra and the absorbed dose is investigated. Event probabilities, and frequency and dose-averaged d•posited energies are calculated with and without seattering contribution and compared. The change of absorbed dose due to attenuation of the primary neutron flux is also evaluated. Introduction I t is well known t h a t measurements of X - r a y and 7-ray exposure b y means of gas eounters involve a correction for the attenuation of the primary photon flux b y the chamber wall. The wall thiekness necessary for complete s]owing-down of the electrons of m a x i m u m energy will diminish somewhat the intensity of the prim a r y radiation and therefore an extrapolation to zero wall thickness has to be made (ICRU 23, i973). I n rLeutron dosimetry this problem has been bypassed b y the introduction of the quantity X E R M A which can be ea]culated from the knowledge of the neutron cross sections, and neglects purposely the ranges of the different recoil particles (ICRU i3, 1969). However, these particle ranges 'are very importartt for the microdosimetry of fast neutrons. I n microdosimetry one is interested in the spatial distribution of energy deposition b y eharged particles in gas chambers whieh simulate sensitive volumes of biologieal eells (Rossi and Rosenzweig, t955 ; Booz, 1974). Microdosimetric detectors are propoßional counters with walls of tissue-equivalent plastic of suflleient thickness for the complete slowing-down of the recoil particles of maxim u m energy. Hence the measurement of an energy deposition spectrum of fast neutrons in free air involves again the problem of attenuation of the primary neutron flux by the wall. I n addition there is the problem of deformation of the measured energy deposition spectrum due to the distortion of the primary particle spectrum in the wall. The proportional counters used in microdosimetry studios are generally classified into two groups with respect to their external configuration, i.e., counters with wall, or walled, and counters without wall, or wall-less. Since a gas counter necessitates of an external enelosure, the term wall-less indicates simply t h a t in this type of eounters the sensitive volume is limited only to a part of the total geo* Contribution No. 1157 of the Biology Programme, Direetorate General XII of the Commission of the European Communities.
•58
M. Coppola and J. Booz
metrieal volume. The boundary between the sensitive volume and the remaining part of the eounter is obtained without any mechanieal partition, bnt using an appropriate electrie field-line configuration. I n a walled counter, on the eontrary, the sensitive volume coincides praetically with the total internal volume and its boundary is represented by the interface gas-solid. Aa important experimental limitation to the use of ideal wall-less configurations arises when the counter is used in eonjunction with high-energy radiations, e.g. fast neutrons. I t is immediately seen t h a t if the macroseopic sensitive zone of the counter has to simulate a mieroscopie volume, the pressure of the filling gas has to be very low. Therefore, in the absence of a solid wall, the dimensions of the gaseous region surrounding the sensitive zone and necessary to establish charged particle equilibrium eould be in most eases prohibitively large. For instance if the sensitive zone is a eylinder of 3 cm diameter and the equivalent mieroseopie dimension is i ~zm, one should use an external gas thiekness of 63 cm, for neutrons of 1 MeV. For 5.8 MeV neutrons the depth ofthis zone should amount to about 13 m. Therefòre the so-ealled wall-less counters whieh are used for fast neutrons have always an outer enclosure of plastie material suffieiently thick to ensure the equilibrium of the high-energy seeondary charged partieles. I n other words, the problem of neutron scattering in the counter wall is still present also in the case of the so-called wall-less eounters. I n this paper we investigate the neutron scattering in the wall material, the related distributions of the energy deposition spectra, and the influence of nentron scattering on the measnrement of absorbed dose with a l~ossi-counter.
Neutron Scattering in the Counter Wall As was explained before, the equilibrium of charged particles has to be assured in general by a suffieient thickness of an external tissue-equivalent plastie wall. I f a terrain thickness of the wall is appropriate in this respect for a certain m a x i m u m neutron energy it is also good at lower energies. This is dne to the fact t h a t on the average the fange of neutron-produced eharged particles decreases rapidly with deereasing neutron energy. This sume fact, however, eauses t h a t a eertain thiekness of wall material appropriate for a given m a x i m u m neutron energy is more redundant the lower the energy of the irradiating nentrons. The consequence is that the eontribution to the shape of the measured spectra due to neutron seattering collisions in the wall material is unnecessarily increasing the lower the aetual neutron energy. This ean be easily seen from Table l where neufron mean free path-lengths and average interaetion probabilities in the Shonka plastie (Shonka et al., 1958) are reported for three nêutron energies. Let us eonsider a spherieal proportional eounter of the type developed by Rossi and eoworkers (Rossi and Rosenzweig, i955). I n partieular we assnme t h a t this eounter has an internal diameter of 5.08 cm (2"-eounter) and an external diameter of 6.35 cm. The inner volume is supposed to be filled with the tissue-eqnivMent gas of Rossi-Failla (Rossi and Failla, 1956). The amount of gas in the inner volume is thonght to be continuously adjustable in order to allow the simulation of any desired diameter. The eomposition in pereent of weight of the plastie and the gas taken in this theoretieal study are given in Table 2.
Neutron Scattering and Energy Deposition Spectra
159
Table 1. Neutron interaction parameters En [MeV]
,~ [cm]
1/A ~
• -- exp (-l/A)
5.8 1.0 0.1
6.83 2.55 0.98
0.302 0.8t0 2.108
0.261 0.555 0.878
a l = 2.066 cm Table 2. Composition of wall and gas in percent of weight Ma~eriM
H
C
N
O
F
S
Ca
Shonka-plastic T.E.-gas
t0.26 t0.19
76.10 45.62
3.50 3.51
5.12 40.68
1.96
1.00
2.06
Table 3. Cross-section of neutron-induced reactions in the Shonka-plastic [barn] Nucleus
En [1V[eV]
n, n
n, p
H
5.85 t.02 0A0
t.46 4.11 t2.65
.
5.85 1.02 0.10
1 . 1 0
- -
2.62
.
.
4 . 3 9
.
.
0.09 0.006
0.10
t.54 2.29 4.52
5.85 t.02 OAO
1.55 5.90 3.50
C
N
0
5.85 1.02
n, t .
.
.
n, o¢ .
.
. .
.
.
0.18
- -
.
.
.
0.0t ---
--
.
.
- -
0.001
n, n'
--
.
0A4 0.0002 --
----
0.03
--
.
.
.
.
.
.
.
.
A n e u t r o n b e a m i m p i n g i n g on the c o u n t e r m a y produce several reactions with the nuclei in t h e wall material, t h e reaction eross-sections being d e p e n d e n t on t h e n e u t r o n energy a n d on t h e t a r g e t n u c l e u s involved. T a b l e 3 indicates the possible n e u t r o n - i n d u c e d reactions for t h e four most a b u n d a n t a t o m s i n t h e wall, a n d t h e corresponding cross sections used a t t h e three n e u t r o n energies eonsidered in t h e p r e s e n t investigation. F r o m Tables 2 a n d 3 it can be seen t h a t at t h e chosen energies the most f r e q u e n t t y p e of n e u t r o n i n t e r a c t i o n i n the Shonka m a t e r i a l is seattering on hydroger~. Therefore most of the recoiling particles are protons. A recoiling particle g e n e r a t e d i n the c o u n t e r wall has a certain chance of e n t e r i n g t h e irreer volume. F o r this to h a p p e n it is necessary t h a t t h e recoiling particle be o r i e n t e d towards t h e i n n e r v o l u m e a n d t h a t its energy be high enough so t h a t t h e r a n g e be larger t h a a the distance from t h e i n t e r a c t i o n site to the gas zone, caleulated along the recoil direction. I t is easily seen t h a t in the case of the energies considered here the recoil ions from first collisions of p r i m a r y n e u t r o n s can e n t e r the sensitive vo]ume only from a v e r y small zone of the wall n e a r to t h e
160
M. Coppola and J. Booz
C
neuFrons
Fig. t. Schematie representation of a spherica! counter. Charged particles fi'om first neutron collisions created outside the darker region in the wall eannot enter the inner sphere inside cavity. T h a t is schematically represented by the darker area in Fig. t. There the re]ations between the aetual dimensions are not respected, however, the distance BA corresponds to the m a x i m u m range of recoil protons. I n general such a zone shrinks rapidly by decreasing the neutron energy, due to the rapid deerease of the charged particle ranges. Of course, e r e n in this region of the wall m a n y recoils are generated which de not fulfil the conditions mentioned before and therefore are not measured by the counter. I f in addition one cõnsiders the further interactions undergone b y a neutron in the counter wall before escaping from er being absorbed in it, it is possible t h a t the conditions given above for the penetration of a charged particle in the gas volume are Inet by one er Inore of the ions generated in these interactions, e r e n if the fast neutron collision does not take place in the active zone described before. Therefore the lilnitation of Fig. i for the potentially active part of the wall does not apply any longer. Method of Caleulation I n order to investigate the influence of neutron scattering on the shape of the energy deposition spectra b y fast neutrons, and on the Inagnitude of quantities of microdosilnetric relevance such as frequency er dose-averaged deposited energies, neutron histories in the above described Rossi-counter were silnulated using the Monte-Carlo code E.NS.PHERE 2 (Coppola and Booz, 1973). For the calculations the energy spread of the source neutrons was assulned to be negligible, as it is in most cases when neutrons are created b y well stabilized charged particle accelerators usiag thin targets. Calculations for a given neutroa energy and for a certain gas pressure corresponding to Olm particular effective diameter in the simulation were performed in two steps, making use of a facility in the program t h a t allows either to stop the neutron trackir~g after the first interaction in the counter wall, er to follow the complete ehaia of probability of neutron iuteraction in the wall until the statistieal weight of the followed-up neutron has fallen below a certain threshold. Therefore for euch energy and diameter two speetra were obtaiaed including respectively the contribution from the first collisior~s only and t h a t from all eol]i-
Neutron Scattering and Energy Deposition Spectra
161
sions. In the calculations the first part of the neutron histories until the first eollision, the emission of the first recoil ion and its energy deposition in the sensitive volume was always identical in the two cases, and that eliminated the greatest part of the statistica] uncertainty of the differenee between the two energy depositions. From the two caleulated spectra the differenees in shape can easily be detected visuMly. In addition the so-called frequency and dose-averaged lineal energies co
oo
~F = .[ Y/(Y) dy / .[/(y) dy 0
(1)
0
and co
~D = .[ y2/(y) dy / .[ y/(y) dy, 0
(2)
0
can be evMuated giving quantitative information on the influence of neutron scattering in the wall. The lineal energy y = «~el is the deposited energy, also called imparted energy, normMized to the average pathlength in the counter gas volume (ICRU 19, 1971), and the function [(y) represents the probability density. The qnantity YF gives therefore the mean lineal energy per event, and ~D is related to the variance of the energy deposition spectrum by the expression 0"2 -yD 92~ 9F (3) and plays an important role in the microdosimetric interpretation of the doseeffeet relationship (Kellerer and Rossi, 1972). Calculations and Results Actual calculations were pefformed at neutron energies of 5.8, t.0, and 0.t MeV. An example of the comparison of energy deposition spectra with and without neutron scattering contribution is showa in Fig. 2, for a diameter of 6.5 ~m and a primary neutron energy of 0.1 MeV. I-Iere both spectra are normalized to unit neutron fluence. The comparison shows clearly that the presence of scattering increases the number of energy deposition events, and therefore the absorbed dose, for a given neutroa fluence. This can be seen also from Table 4 presenting the ca]cu]ated event probability in the imler gas volume per unit neutron fluence, for the various types of ions resulting from neutron interactions. Small differences appearing in some cases between the vMues in the last but one and the last row derive from the fact that two simu]taneous events are counted in the complete spectrum as one event only, whereas they are recorded as two independent events in the single spectra and therefore in the sum spectrum. Spectra of the type showa in Fig. 2 al]ow to obtMn directly the value of YF by the expression (l). I t eomes more and more in use, however, to present the energy deposition spectra in the form of y2/(y). This type of spectra permits to establish a direct correspondence between the areas under the curve and the absorbed energy. Figs. 3 to 7 present the comparison of several calcu]ations of this kind. From these curves the vMues of ~D can easily be obtained using the expression (2).
162
M. Coppola and J. Booz
lo-"
10-E
B ~._
/~ jd
10 .6
0.1 M,:V
I
1ffZ
\/
f
6.5 AJr'~ 10-1
10-2
10 0
102
Id
103
Fig. 2. Lineal energy deposition specbra including neutron scattering (full line), and neglecting neutron scattering (dashed line)
Table 4. Observed event probability per unit neutron fluence [i0-~]. (a) without scattering and (b) with scattering En [~~eV]
Protons C-ions O-ions Qther ions Sum All ions
0.t0 a
b
1.02 a
b
5.85 a
b
3.34 0.41 0.21 0.03 3.99 3.99
7.79 0.68 0.46 0.03 8.96 8.97
4.45 0.47 0.59 0.02 5.53 5.54
6.27 0.6t 0.69 0.05 7.62 7.62
24.73 0.36 0.19 0.06 25.34 25.24
26.68 0.45 0.22 0.03 27.38 27.37
t
5.85MeV 6.5 ,Jm
B 8.~o-
ù,o-~ 0
r '
1~
~
102
103
104
Fig. 3. Comparison of the ealculated y2](y) for the complete event distributions at a primary neutron energy of 5.85 MeV. Full line includes scattering. Dashed line is without scattering
Neutron Scattering a n d Energy Deposition Spectra
163
e. 1~ 1.02 MeV 5.5 /Jm
6 '10-
"~4
A
- 10
u...
%.,
j
2 .lo~
1¢
#
/ s s a'
lfl
10:3
lO~ Y
Fig. 4. The same as in Fig. 3, a t En
0.1 M.eV 6.5 turn
2.10 a
/
1 "10";
= 1.02
MeV
/
~s
o
loo
10 z
• 10 ~
10 ~
Y Fig. 5. The s~me as in Fig. 3, ~t E~
6.10":
>"
=
0A0 MeV
i. n ,,J ~ r_ ,~~eV 6.5 ~m
4 .ler!
u_..
%. 2.10; I sS 0 ¸
.10 o
101
10 2
Fig. 6. The same as in Fig. 3 for pro~ons at E . = 1.02 MeV
10 3
M. Coppola and J. Booz
164 6 -10-3
1.02 MeV 6 . 5 /um 4.10 ~
~~,
. 2 "lõ ~
i
,Y
oi i¢
ld
j 10~
Fig. 7. The same as in Fig. 6 for carbon ions Table 5. Frequency and dose averaged lineal energies, ~F and ~D [keV/Fm]. (a) without seattering and (b) with seattering En [MeV]
~~-,p ?~D,p ?~F,c ?)D,c ?)F,o ~D,O ~r" ~D
0.10 a 9.85 t3.94 3,39 4.50 2.56 3.39 8.77 13.38
b 6.69 12.30 2.72 4.15 1.80 2.93 6.12 11.88
t.02 a
b
5.85 a
b
38A2 53.73 27.85 40.15 26.44 39.60 35.98 51.67
35.24 53A2 24.48 37.84 24.00 37.45 33.30 51.14
17.98 28.87 123.46 210.78 77.45 155.05 20.03 49.38
18.04 29.19 114.00 2t0.05 70.34 147.02 20A2 50.47
The indioes p, C and O refer to values from partial spectra due to single protons, earbon ions and oxygen ions only. The last two rows refer to the total energy deposition caused bya 10rimary neutron. T h e calculatiolls of t h e s p e c t r a shown in Figs. 2 to 7 were done w i t h 30 channels p e r e n e r g y decade. T h e curves were o b t a i n e d using a smoothing procedure. The r e m a i n i n g oscillations m a i n l y in Fig. 2 are due to p o o r s t a t i s t i c s in these calculations. The results of t h e calculations of ?TF a n d YD from t h e p r e s e n t w o r k are summ a r i z e d a n d c o m p a r e d in T a b l e 5 for t h e m o s t f r e q u e n t l y g e n e r a t e d ions a n d for t h e c o m p l e t e e v e n t distributions. H e r e t h e m e a n e n e r g y u n d e r a certain ton t y p e refers to e n e r g y t r a n s f e r r e d b y single ions of t h a t t y p e . The values for t h e c o m b i n e d e v e n t r e p r e s e n t i n s t e a d t h e t o t a l e n e r g y d e p o s i t i o n caused b y a p r i m a r y neutron. F o r d o s i m e t r i c p u r p o s e s it is c o n v e n i e n t to consider a q u a n t i t y D~ given num e r i c a l l y b y t h e expression D~ = 7 . 9 0 5 . 1 0 -9 ~~Pn
(i = a, b),
(4)
h a v i n g t h e dimensions of r a d p e r n e u t r o n / c m 2. t i e r e 771~is t h e f r e q u e n c y - a v e r a g e d lirmal e n e r g y of expression (1) a n d T a b l e 5, in keV/[zm, a n d Pn is t h e o b s e r v e d e v e n t
Neutron Seattering and Energy Deposition Spectra
t65
Table 6. Neutron doses D,, wRhout scattering, and Db, with seattering in mrad per I0 s neutrons/cm 2 En [l~IeV]
D~
Db
Db/D~
0A0 1.02 5.85
0.277 1.576 3.996
0.434 2.006 4.353
t.567 i.273 1.089
1.0
1.8
~
O.S
/ 0.6
- . ~ 0.4
ù / 1.2
tO
/J
0.0
~,./"
0.5
0.2
1.0
1,5
2.0
2.5
0.0 3.0
Fig. 8. Increase of neutron dose due to neulbron scattering (solid line). Decrease of primary neufron fluence (dotted line). I~et decrease of neutron dose due to combination of neutron sca~tering and neutron fluence attenuation (dashed line) probability per unit neutron fluence, as in Table 4. I n case the scattering is included, the quantity D, represents the absorbed dose in a sphere of tissue of unit density, equivalent to the Rossi-counter, when the primary neutron fluence is of one neutron/em ~. This quantity is denoted in this paper b y the s y m b o l / ) » , when the contribution of neutron scattering to the absorbed dose is included. The corresponding quantity without contribution of neutron scattering, i.e. the energy absorption per unit mass and unit neutron fluence for the primary fast neutrons only, is denoted b y Da. Table 6 presents the values of Da and Db at the three energies of the present work for the complete event spectra, i.e. the "all ions" spectra, in the uaits of m r a d per l06 neutrons/cm 2. The ratios between the values with and without seattering are also given in Table 6 and are plotted in Fig 8 as a funetion of the quantity i/~, which for small values of Z/~ is equal to the average neutron interaction probability in the counter wall. The values of 1/2 ean be found in Table I. B y the assumption t h a t the ratio Db~Da be equal to i for Z/~ = 0 and approach 1 + A for Z/2-~~, one ean deseribe it by a saturation eurve of the form Db D--~---- i + A [ i - - e x p ( - - B / / ~ ) ] .
(5)
t66
M. Coppola and J. Booz
This function is the solid line shown in Fig. 8. The values of the pararaeters A = i.054 and B = 0.3702 have been obtained b y a best fit to the calculated points. Fig. 8 shows in addition the funetion exp(--7/2,~) and the produet Db~Da. exp (--Z/22). The function exp (--Z/2st) represents the average attenuation of the priraary neutron fluenee duo to the first half of the eounter, and Db~Da. exp(--i/2,~) describes the influence of both effects, the inerease due to scattering contribution and the deerease due to the primary fluenee attenuation.
Discussion The results of the present investigation show that the presence of neutron scattering in the wall of a Rossi-type proportional counter, used to deterraine energy deposition spectra, raodifies the shape of the raeasured spectra and changes the event probability per neutron/cm 2. A raodification of the speetrura shape reflects itself in a variation of the values of ??F and YD. Frora the results of Table 5 it is seen that this wziation is negligible at 5.85 MeV for both ~?Fand ??D.At 1.02 MeV the values of ??F in the absence of scattering appear to be soraewhat higher than those with scattering for all ion types, whereas for ??D the only noticeable ehange is present for the heavier ions. The effect of neutron scattering is rauch more appreciable at the lowest energy considered here, i.e. at 0.1 MeV. At this priraary neutron energy the ~F for the eoraplete event distribution increases by about 43 % and the ??D b y about t3 % when negleeting the neutron scattering. Discussing the statistical significance of the values in Table 5 one taust eonsider that, because of the procedures followed to ealculate the speetra with and without neutron scattering contribution, the relative variations of these values are to be attributed raainly to a real effeet and only to a negligible extent to statistical uncertainties. Table 5 shows in addition t h a t for protons the average deposited energies YF and YD are !arger at 1.02 MeV than at the two other energies eonsidered, whereas for the heavier ions they increase with increasing priraary energy. A reasonable explanation is that for protons the recoil distribution corresponding to a priraary nentron energy of about t MeV is raostly in an energy region nearer to the Bragg peak than in the two other eases. Therefore the stopping power and consequently the deposited energies are larger on the average. This is not true for the heavier ions, for whieh the recoil distributions stay below the Bragg peak region and therefore in a region of increasing raass stopping power with inereasing ion energy. Considering the event probability per unit neutron fluence, here too the effeet of neutron seattering is most reraarkable at the lowest energy of 0.i MeV, as shown in Table 4. However, eontrarily to the average deposited energies, the event probability inereases when scattering is considered. For the explanation of such an opposite tendency in the influence of the neutron scattering it is necessary to consider t h a t the presence of neutron seattering inereases the total nuraber of neutron eollisions in the wall, because of the relatively small raean free p a t h of low energy neutrons in a hydrogenous material. As a consequence, the nuraber of those eollisions resulting in a eharged particle entering the rneasuring volnme of the counter, and therefore the probability of event observation, increases. On the other hand reeoil ions generated in further eollisions of scattered neutrons are, on the
Neutron Scattering and Energy Deposition Spectra
167
average, of lower energies than from primary neutron collisions. And since the large majority of absorption events at a primary neutron energy of 0.i MeV and for a diameter of 6.5 ~m is due to stoppers and insiders as already proved by us, the presenee of neutron seattering will result in an increase of events in the lower energy portion of the energy deposition spectrum. Therefore the average absorbed energies decrease when neutron scattering is included. The previous eonsiderations show also why the ehange of ~s is generally larger than the change of YD. I t is clear that the function y~f(y) is rauch more depending on higher y values than the function Y1(Y), due to the quadratic term. Therefore, from the expression (2) it is immedia,tely understood that the quantity ~D does not depend as rauch as the quantity ~r on the lower portion of the energy absorption spectrum, which is mostly affected by neutron scattering, as we have already shown, at least at low neutron energies. I f the primary neutron energy inereases these considerations become less and less stringent. Final]y at 5.85 MeV the relatively large neutron mean free path in the Shonka p]astic makes the irtfluence of neutron scattering not very marked on the observed event probability. On the other hand the large presence of crossers and starters among the energy-depositing ions makes the values of .YF and yD praetically insensitive to the scattering effect. The product of ~r, mean lineal energy per event, and Pn, mean number of events per unit neutron fluence, is proportional to the dose. The quantity Db, which includes neutron scatteI~ng, is therefore the absorbed dose in a Rossicounter per unit neutron fluence. The relation Db~Da shown in the last column of Table 4 describes how the absorbed dose is inereased due to neutron seattering, when the attenuation of the primary neutron is not taken into cortsideration. The funetional dependence of Db~Da on i/A, which was assumed in Eq. (5) and is shown in Fig. 8, can be eonsidered a good approximation for large values of i/A, because Db~Da for l/A» i taust approaeh a eonstant value. For i/2 < 0.5, instead, the assumption that also in this region Db~Da follows the same saturation curve having a slope of 0.39 at the zero point is somewhat more arbitrary. I f orte attaches any sense to the enrve in this region orte can say that the seattering effeet does not vanish at 14 MeV, i.e. at an Z/2 of about 0.22, where it produces still an inerease of absorbed dose of about 8 %. So rar, only the relative increase of absorbed dose with increasing seattering was eonsidered. In the method of calculation of Da and Db the same primary neutron flux attenuation is present and therefore the resulting relation does not eontain the deerease of the primary nentron flux, whieh is given by exp (--i/2 2) and is shown in Fig. 8 by the dotted line. The two effects ~re working in opposite direetions: the scattering of neutrons inereases the number of neutrons in the eounter and inereases the dose, the attenuation of the primary nentron flux decreases it. The combination of both effects results in a ner decrease of the absorbed dose, as shown by the dashed line in l~ig. 8. Again it has to be pointed out that the initial slope of this curve might be incorreet. Conclusions The presence of neutron scattering in the wall of a Rossi-counter affects the total probability of energy deposition as well as the shape of the energy deposition
t 68
M. Coppola and J. Booz
s p e c t r a in t h e gas. F r o m t h e m i c r o d o s i m e t r i e p o i n t of view this m e a n s t h a t t h e values of t h e f r e q u e n c y a n d d o s e - a v e r a g e d d e p o s i t e d energies o b t a i n e d from s p e e t r a m e a s u r e d w i t h a walled p r o p o r t i o n a l c o u n t e r d e p e n d to a certain e x t e n t on t h e t h i c k n e s s of t h e wall. I n t h e case of t h e 2 " - c o u n t e r eonsidered in t h e p r e s e n t i n v e s t i g a t i o n such a d e p e n d e n e e becomes e v i d e n t for p r i m a r y n e u t r o n s below 1 MeV, whereas it is negligible a t a b o u t 6 l~{eV. The considerations o f t h e previous p a r a g r a p h induee, therefore, to infer from t h e p r e s e n t results t h a t for t h e counter u n d e r c o n s i d e r a t i o n t h e effect of n e u t r o n s e a t t e r i n g on t h e a b o v e q u a n t i t i e s should be i r r e l e v a n t a t t 4 MeV. F r o m a d o s i m e t r i c v i e w p o i n t a change in t h e e v e n t p r o b a b i l R y p e r u n i t neut r õ n fluenee m e a n s t h a t , if u s e d as a dosimeter, a walled spherical e o u n t e r t e n d s to give a r e a d i n g which is d e p e n d e n t on t h e thickness of t h e o u t e r shell in r e l a t i o n to t h e n e u t r o n m e a n free p a t h - l e n g t h . The a b s o r b e d dose which ean be m e a s u r e d w i t h a R o s s i - e o u n t e r is m a i n l y influenced b y t h e a t t e n u a t i o n of t h e p r i m a r y neuf r o n fluencë in t h e c o u n t e r wall. T h e increase in dose due to t h e n e u t r o n s c a t t e r i n g is r e l a t i v e l y small, however it c a n n o t be neglected. The resnlts of t h i s w o r k were o b t a i n e d for a 2" R o s s i - c o u n t e r of c o n s t a n t wall thickness a n d for n e u t r o n s of various energies. Therefore t h e results e a n n o t be a p p l i e d s t r a i g h t - f o r w a r d l y to o t h e r d e t e c t o r s h a v i n g a ver:( different mass or a v e r y different g e o m e t r y of t h e s c a t t e r i n g b o d y . I n general one ean s a y t h a t t h e choice of o p t i m u m wall thiekness t a u s t p a y due e o n s i d e r a t i o n to t h e m o d e o f u t i l i z a t i o n of t h e eounter. I n o t h e r words, for m e a s u r e m e n t s s i m u l a t i n g surface d o s i m e t r y t h e c o u n t e r should h a v e t h e thinnes~ possible wall, c o m p a t i b l y w i t h all o t h e r p h y s i c a l requirements, whereas for i n t e r n a l simulation, e.g. dose m e a s u r e m e n t s a t c e r t a i n positions in animals, an a m o u n t o f tissue-like m a t e r i a l of t h e same o r d e r as in t h e real case t a u s t be p r o v i d e d a r o u n d it. Referenees Booz, J.: Energy deposition on a microseopic scale, relevant to the biological effects of fast neutrons. In: Biological effects of neutron irradiation, pp. 1i9--130. Vienna: IAEA 1974 Coppola, M., Booz, 5. : Influenee of energy straggling on the shape of neutron-produced single event spectra. Biophysik 9, 225--236 (t973) International Commission on Radiation Units and Measurements: Neutron fluence, neutron spectra and kerma. ICRU Report t3, Washington, D.C. 1969 International Commission on Radiation Units and 5Ieasurements: Radiation quantities and units. ICRU Report 19, Washington, D.C. 1971 International Commission on Radiation Units and )/Ieasurements: Measurement of absorbed dose in a phantom irradiated by a single beam of X or gamma rays. ICRU Report 23, Washington, D.C. 1973 Kellerer, A. M., Rossi, H. H. : The theory of dual radiation action. Curr. Top. Radiat. Res. 8, 85--158 (1972) Rossi, H. H., Failla, G. : Tissue-equivalent ionization chambers. Nucleonics 14, 32--37 (1956) Rossi, I-I. ~., Rosenzweig, W. : A deviee of the measurement of dose as a function of speeifie ionization. Radiology 64, 404--411 (1955) Shonka, F. R., Rose, J. E., Failla, G. : Conducting plastic equivalent to tissue, dir and polystyrene. In: Proeeeding of the Seeond United Nations International Conference on Peaeeful Uses of Atomic Energy, Vol. 21, pp. 184--187. Geneva: United Nations 1958 Prof. Dr. M. Coppola Biology Group CCR-Euratom 1-21020 Ispra (Va), Italy
Neutron Scattering and Energy Deposition Spectra* 1~I. Coppola and J. Booz Biology Group, Ispra, Italy; G. D. Research, Seience and Education, C.E.C. Received April «, 1975
Summary. The influence of neutron scattering in the wall of a spherieal proportional counter on the energy deposition spectra and the absorbed dose is investigated. Event probabilities, and frequency and dose-averaged d•posited energies are calculated with and without seattering contribution and compared. The change of absorbed dose due to attenuation of the primary neutron flux is also evaluated. Introduction I t is well known t h a t measurements of X - r a y and 7-ray exposure b y means of gas eounters involve a correction for the attenuation of the primary photon flux b y the chamber wall. The wall thiekness necessary for complete s]owing-down of the electrons of m a x i m u m energy will diminish somewhat the intensity of the prim a r y radiation and therefore an extrapolation to zero wall thickness has to be made (ICRU 23, i973). I n rLeutron dosimetry this problem has been bypassed b y the introduction of the quantity X E R M A which can be ea]culated from the knowledge of the neutron cross sections, and neglects purposely the ranges of the different recoil particles (ICRU i3, 1969). However, these particle ranges 'are very importartt for the microdosimetry of fast neutrons. I n microdosimetry one is interested in the spatial distribution of energy deposition b y eharged particles in gas chambers whieh simulate sensitive volumes of biologieal eells (Rossi and Rosenzweig, t955 ; Booz, 1974). Microdosimetric detectors are propoßional counters with walls of tissue-equivalent plastic of suflleient thickness for the complete slowing-down of the recoil particles of maxim u m energy. Hence the measurement of an energy deposition spectrum of fast neutrons in free air involves again the problem of attenuation of the primary neutron flux by the wall. I n addition there is the problem of deformation of the measured energy deposition spectrum due to the distortion of the primary particle spectrum in the wall. The proportional counters used in microdosimetry studios are generally classified into two groups with respect to their external configuration, i.e., counters with wall, or walled, and counters without wall, or wall-less. Since a gas counter necessitates of an external enelosure, the term wall-less indicates simply t h a t in this type of eounters the sensitive volume is limited only to a part of the total geo* Contribution No. 1157 of the Biology Programme, Direetorate General XII of the Commission of the European Communities.
•58
M. Coppola and J. Booz
metrieal volume. The boundary between the sensitive volume and the remaining part of the eounter is obtained without any mechanieal partition, bnt using an appropriate electrie field-line configuration. I n a walled counter, on the eontrary, the sensitive volume coincides praetically with the total internal volume and its boundary is represented by the interface gas-solid. Aa important experimental limitation to the use of ideal wall-less configurations arises when the counter is used in eonjunction with high-energy radiations, e.g. fast neutrons. I t is immediately seen t h a t if the macroseopic sensitive zone of the counter has to simulate a mieroscopie volume, the pressure of the filling gas has to be very low. Therefore, in the absence of a solid wall, the dimensions of the gaseous region surrounding the sensitive zone and necessary to establish charged particle equilibrium eould be in most eases prohibitively large. For instance if the sensitive zone is a eylinder of 3 cm diameter and the equivalent mieroseopie dimension is i ~zm, one should use an external gas thiekness of 63 cm, for neutrons of 1 MeV. For 5.8 MeV neutrons the depth ofthis zone should amount to about 13 m. Therefòre the so-ealled wall-less counters whieh are used for fast neutrons have always an outer enclosure of plastie material suffieiently thick to ensure the equilibrium of the high-energy seeondary charged partieles. I n other words, the problem of neutron scattering in the counter wall is still present also in the case of the so-called wall-less eounters. I n this paper we investigate the neutron scattering in the wall material, the related distributions of the energy deposition spectra, and the influence of nentron scattering on the measnrement of absorbed dose with a l~ossi-counter.
Neutron Scattering in the Counter Wall As was explained before, the equilibrium of charged particles has to be assured in general by a suffieient thickness of an external tissue-equivalent plastie wall. I f a terrain thickness of the wall is appropriate in this respect for a certain m a x i m u m neutron energy it is also good at lower energies. This is dne to the fact t h a t on the average the fange of neutron-produced eharged particles decreases rapidly with deereasing neutron energy. This sume fact, however, eauses t h a t a eertain thiekness of wall material appropriate for a given m a x i m u m neutron energy is more redundant the lower the energy of the irradiating nentrons. The consequence is that the eontribution to the shape of the measured spectra due to neutron seattering collisions in the wall material is unnecessarily increasing the lower the aetual neutron energy. This ean be easily seen from Table l where neufron mean free path-lengths and average interaetion probabilities in the Shonka plastie (Shonka et al., 1958) are reported for three nêutron energies. Let us eonsider a spherieal proportional eounter of the type developed by Rossi and eoworkers (Rossi and Rosenzweig, i955). I n partieular we assnme t h a t this eounter has an internal diameter of 5.08 cm (2"-eounter) and an external diameter of 6.35 cm. The inner volume is supposed to be filled with the tissue-eqnivMent gas of Rossi-Failla (Rossi and Failla, 1956). The amount of gas in the inner volume is thonght to be continuously adjustable in order to allow the simulation of any desired diameter. The eomposition in pereent of weight of the plastie and the gas taken in this theoretieal study are given in Table 2.
Neutron Scattering and Energy Deposition Spectra
159
Table 1. Neutron interaction parameters En [MeV]
,~ [cm]
1/A ~
• -- exp (-l/A)
5.8 1.0 0.1
6.83 2.55 0.98
0.302 0.8t0 2.108
0.261 0.555 0.878
a l = 2.066 cm Table 2. Composition of wall and gas in percent of weight Ma~eriM
H
C
N
O
F
S
Ca
Shonka-plastic T.E.-gas
t0.26 t0.19
76.10 45.62
3.50 3.51
5.12 40.68
1.96
1.00
2.06
Table 3. Cross-section of neutron-induced reactions in the Shonka-plastic [barn] Nucleus
En [1V[eV]
n, n
n, p
H
5.85 t.02 0A0
t.46 4.11 t2.65
.
5.85 1.02 0.10
1 . 1 0
- -
2.62
.
.
4 . 3 9
.
.
0.09 0.006
0.10
t.54 2.29 4.52
5.85 t.02 OAO
1.55 5.90 3.50
C
N
0
5.85 1.02
n, t .
.
.
n, o¢ .
.
. .
.
.
0.18
- -
.
.
.
0.0t ---
--
.
.
- -
0.001
n, n'
--
.
0A4 0.0002 --
----
0.03
--
.
.
.
.
.
.
.
.
A n e u t r o n b e a m i m p i n g i n g on the c o u n t e r m a y produce several reactions with the nuclei in t h e wall material, t h e reaction eross-sections being d e p e n d e n t on t h e n e u t r o n energy a n d on t h e t a r g e t n u c l e u s involved. T a b l e 3 indicates the possible n e u t r o n - i n d u c e d reactions for t h e four most a b u n d a n t a t o m s i n t h e wall, a n d t h e corresponding cross sections used a t t h e three n e u t r o n energies eonsidered in t h e p r e s e n t investigation. F r o m Tables 2 a n d 3 it can be seen t h a t at t h e chosen energies the most f r e q u e n t t y p e of n e u t r o n i n t e r a c t i o n i n the Shonka m a t e r i a l is seattering on hydroger~. Therefore most of the recoiling particles are protons. A recoiling particle g e n e r a t e d i n the c o u n t e r wall has a certain chance of e n t e r i n g t h e irreer volume. F o r this to h a p p e n it is necessary t h a t t h e recoiling particle be o r i e n t e d towards t h e i n n e r v o l u m e a n d t h a t its energy be high enough so t h a t t h e r a n g e be larger t h a a the distance from t h e i n t e r a c t i o n site to the gas zone, caleulated along the recoil direction. I t is easily seen t h a t in the case of the energies considered here the recoil ions from first collisions of p r i m a r y n e u t r o n s can e n t e r the sensitive vo]ume only from a v e r y small zone of the wall n e a r to t h e
160
M. Coppola and J. Booz
C
neuFrons
Fig. t. Schematie representation of a spherica! counter. Charged particles fi'om first neutron collisions created outside the darker region in the wall eannot enter the inner sphere inside cavity. T h a t is schematically represented by the darker area in Fig. t. There the re]ations between the aetual dimensions are not respected, however, the distance BA corresponds to the m a x i m u m range of recoil protons. I n general such a zone shrinks rapidly by decreasing the neutron energy, due to the rapid deerease of the charged particle ranges. Of course, e r e n in this region of the wall m a n y recoils are generated which de not fulfil the conditions mentioned before and therefore are not measured by the counter. I f in addition one cõnsiders the further interactions undergone b y a neutron in the counter wall before escaping from er being absorbed in it, it is possible t h a t the conditions given above for the penetration of a charged particle in the gas volume are Inet by one er Inore of the ions generated in these interactions, e r e n if the fast neutron collision does not take place in the active zone described before. Therefore the lilnitation of Fig. i for the potentially active part of the wall does not apply any longer. Method of Caleulation I n order to investigate the influence of neutron scattering on the shape of the energy deposition spectra b y fast neutrons, and on the Inagnitude of quantities of microdosilnetric relevance such as frequency er dose-averaged deposited energies, neutron histories in the above described Rossi-counter were silnulated using the Monte-Carlo code E.NS.PHERE 2 (Coppola and Booz, 1973). For the calculations the energy spread of the source neutrons was assulned to be negligible, as it is in most cases when neutrons are created b y well stabilized charged particle accelerators usiag thin targets. Calculations for a given neutroa energy and for a certain gas pressure corresponding to Olm particular effective diameter in the simulation were performed in two steps, making use of a facility in the program t h a t allows either to stop the neutron trackir~g after the first interaction in the counter wall, er to follow the complete ehaia of probability of neutron iuteraction in the wall until the statistieal weight of the followed-up neutron has fallen below a certain threshold. Therefore for euch energy and diameter two speetra were obtaiaed including respectively the contribution from the first collisior~s only and t h a t from all eol]i-
Neutron Scattering and Energy Deposition Spectra
161
sions. In the calculations the first part of the neutron histories until the first eollision, the emission of the first recoil ion and its energy deposition in the sensitive volume was always identical in the two cases, and that eliminated the greatest part of the statistica] uncertainty of the differenee between the two energy depositions. From the two caleulated spectra the differenees in shape can easily be detected visuMly. In addition the so-called frequency and dose-averaged lineal energies co
oo
~F = .[ Y/(Y) dy / .[/(y) dy 0
(1)
0
and co
~D = .[ y2/(y) dy / .[ y/(y) dy, 0
(2)
0
can be evMuated giving quantitative information on the influence of neutron scattering in the wall. The lineal energy y = «~el is the deposited energy, also called imparted energy, normMized to the average pathlength in the counter gas volume (ICRU 19, 1971), and the function [(y) represents the probability density. The qnantity YF gives therefore the mean lineal energy per event, and ~D is related to the variance of the energy deposition spectrum by the expression 0"2 -yD 92~ 9F (3) and plays an important role in the microdosimetric interpretation of the doseeffeet relationship (Kellerer and Rossi, 1972). Calculations and Results Actual calculations were pefformed at neutron energies of 5.8, t.0, and 0.t MeV. An example of the comparison of energy deposition spectra with and without neutron scattering contribution is showa in Fig. 2, for a diameter of 6.5 ~m and a primary neutron energy of 0.1 MeV. I-Iere both spectra are normalized to unit neutron fluence. The comparison shows clearly that the presence of scattering increases the number of energy deposition events, and therefore the absorbed dose, for a given neutroa fluence. This can be seen also from Table 4 presenting the ca]cu]ated event probability in the imler gas volume per unit neutron fluence, for the various types of ions resulting from neutron interactions. Small differences appearing in some cases between the vMues in the last but one and the last row derive from the fact that two simu]taneous events are counted in the complete spectrum as one event only, whereas they are recorded as two independent events in the single spectra and therefore in the sum spectrum. Spectra of the type showa in Fig. 2 al]ow to obtMn directly the value of YF by the expression (l). I t eomes more and more in use, however, to present the energy deposition spectra in the form of y2/(y). This type of spectra permits to establish a direct correspondence between the areas under the curve and the absorbed energy. Figs. 3 to 7 present the comparison of several calcu]ations of this kind. From these curves the vMues of ~D can easily be obtained using the expression (2).
162
M. Coppola and J. Booz
lo-"
10-E
B ~._
/~ jd
10 .6
0.1 M,:V
I
1ffZ
\/
f
6.5 AJr'~ 10-1
10-2
10 0
102
Id
103
Fig. 2. Lineal energy deposition specbra including neutron scattering (full line), and neglecting neutron scattering (dashed line)
Table 4. Observed event probability per unit neutron fluence [i0-~]. (a) without scattering and (b) with scattering En [~~eV]
Protons C-ions O-ions Qther ions Sum All ions
0.t0 a
b
1.02 a
b
5.85 a
b
3.34 0.41 0.21 0.03 3.99 3.99
7.79 0.68 0.46 0.03 8.96 8.97
4.45 0.47 0.59 0.02 5.53 5.54
6.27 0.6t 0.69 0.05 7.62 7.62
24.73 0.36 0.19 0.06 25.34 25.24
26.68 0.45 0.22 0.03 27.38 27.37
t
5.85MeV 6.5 ,Jm
B 8.~o-
ù,o-~ 0
r '
1~
~
102
103
104
Fig. 3. Comparison of the ealculated y2](y) for the complete event distributions at a primary neutron energy of 5.85 MeV. Full line includes scattering. Dashed line is without scattering
Neutron Scattering a n d Energy Deposition Spectra
163
e. 1~ 1.02 MeV 5.5 /Jm
6 '10-
"~4
A
- 10
u...
%.,
j
2 .lo~
1¢
#
/ s s a'
lfl
10:3
lO~ Y
Fig. 4. The same as in Fig. 3, a t En
0.1 M.eV 6.5 turn
2.10 a
/
1 "10";
= 1.02
MeV
/
~s
o
loo
10 z
• 10 ~
10 ~
Y Fig. 5. The s~me as in Fig. 3, ~t E~
6.10":
>"
=
0A0 MeV
i. n ,,J ~ r_ ,~~eV 6.5 ~m
4 .ler!
u_..
%. 2.10; I sS 0 ¸
.10 o
101
10 2
Fig. 6. The same as in Fig. 3 for pro~ons at E . = 1.02 MeV
10 3
M. Coppola and J. Booz
164 6 -10-3
1.02 MeV 6 . 5 /um 4.10 ~
~~,
. 2 "lõ ~
i
,Y
oi i¢
ld
j 10~
Fig. 7. The same as in Fig. 6 for carbon ions Table 5. Frequency and dose averaged lineal energies, ~F and ~D [keV/Fm]. (a) without seattering and (b) with seattering En [MeV]
~~-,p ?~D,p ?~F,c ?)D,c ?)F,o ~D,O ~r" ~D
0.10 a 9.85 t3.94 3,39 4.50 2.56 3.39 8.77 13.38
b 6.69 12.30 2.72 4.15 1.80 2.93 6.12 11.88
t.02 a
b
5.85 a
b
38A2 53.73 27.85 40.15 26.44 39.60 35.98 51.67
35.24 53A2 24.48 37.84 24.00 37.45 33.30 51.14
17.98 28.87 123.46 210.78 77.45 155.05 20.03 49.38
18.04 29.19 114.00 2t0.05 70.34 147.02 20A2 50.47
The indioes p, C and O refer to values from partial spectra due to single protons, earbon ions and oxygen ions only. The last two rows refer to the total energy deposition caused bya 10rimary neutron. T h e calculatiolls of t h e s p e c t r a shown in Figs. 2 to 7 were done w i t h 30 channels p e r e n e r g y decade. T h e curves were o b t a i n e d using a smoothing procedure. The r e m a i n i n g oscillations m a i n l y in Fig. 2 are due to p o o r s t a t i s t i c s in these calculations. The results of t h e calculations of ?TF a n d YD from t h e p r e s e n t w o r k are summ a r i z e d a n d c o m p a r e d in T a b l e 5 for t h e m o s t f r e q u e n t l y g e n e r a t e d ions a n d for t h e c o m p l e t e e v e n t distributions. H e r e t h e m e a n e n e r g y u n d e r a certain ton t y p e refers to e n e r g y t r a n s f e r r e d b y single ions of t h a t t y p e . The values for t h e c o m b i n e d e v e n t r e p r e s e n t i n s t e a d t h e t o t a l e n e r g y d e p o s i t i o n caused b y a p r i m a r y neutron. F o r d o s i m e t r i c p u r p o s e s it is c o n v e n i e n t to consider a q u a n t i t y D~ given num e r i c a l l y b y t h e expression D~ = 7 . 9 0 5 . 1 0 -9 ~~Pn
(i = a, b),
(4)
h a v i n g t h e dimensions of r a d p e r n e u t r o n / c m 2. t i e r e 771~is t h e f r e q u e n c y - a v e r a g e d lirmal e n e r g y of expression (1) a n d T a b l e 5, in keV/[zm, a n d Pn is t h e o b s e r v e d e v e n t
Neutron Seattering and Energy Deposition Spectra
t65
Table 6. Neutron doses D,, wRhout scattering, and Db, with seattering in mrad per I0 s neutrons/cm 2 En [l~IeV]
D~
Db
Db/D~
0A0 1.02 5.85
0.277 1.576 3.996
0.434 2.006 4.353
t.567 i.273 1.089
1.0
1.8
~
O.S
/ 0.6
- . ~ 0.4
ù / 1.2
tO
/J
0.0
~,./"
0.5
0.2
1.0
1,5
2.0
2.5
0.0 3.0
Fig. 8. Increase of neutron dose due to neulbron scattering (solid line). Decrease of primary neufron fluence (dotted line). I~et decrease of neutron dose due to combination of neutron sca~tering and neutron fluence attenuation (dashed line) probability per unit neutron fluence, as in Table 4. I n case the scattering is included, the quantity D, represents the absorbed dose in a sphere of tissue of unit density, equivalent to the Rossi-counter, when the primary neutron fluence is of one neutron/em ~. This quantity is denoted in this paper b y the s y m b o l / ) » , when the contribution of neutron scattering to the absorbed dose is included. The corresponding quantity without contribution of neutron scattering, i.e. the energy absorption per unit mass and unit neutron fluence for the primary fast neutrons only, is denoted b y Da. Table 6 presents the values of Da and Db at the three energies of the present work for the complete event spectra, i.e. the "all ions" spectra, in the uaits of m r a d per l06 neutrons/cm 2. The ratios between the values with and without seattering are also given in Table 6 and are plotted in Fig 8 as a funetion of the quantity i/~, which for small values of Z/~ is equal to the average neutron interaction probability in the counter wall. The values of 1/2 ean be found in Table I. B y the assumption t h a t the ratio Db~Da be equal to i for Z/~ = 0 and approach 1 + A for Z/2-~~, one ean deseribe it by a saturation eurve of the form Db D--~---- i + A [ i - - e x p ( - - B / / ~ ) ] .
(5)
t66
M. Coppola and J. Booz
This function is the solid line shown in Fig. 8. The values of the pararaeters A = i.054 and B = 0.3702 have been obtained b y a best fit to the calculated points. Fig. 8 shows in addition the funetion exp(--7/2,~) and the produet Db~Da. exp (--Z/22). The function exp (--Z/2st) represents the average attenuation of the priraary neutron fluenee duo to the first half of the eounter, and Db~Da. exp(--i/2,~) describes the influence of both effects, the inerease due to scattering contribution and the deerease due to the primary fluenee attenuation.
Discussion The results of the present investigation show that the presence of neutron scattering in the wall of a Rossi-type proportional counter, used to deterraine energy deposition spectra, raodifies the shape of the raeasured spectra and changes the event probability per neutron/cm 2. A raodification of the speetrura shape reflects itself in a variation of the values of ??F and YD. Frora the results of Table 5 it is seen that this wziation is negligible at 5.85 MeV for both ~?Fand ??D.At 1.02 MeV the values of ??F in the absence of scattering appear to be soraewhat higher than those with scattering for all ion types, whereas for ??D the only noticeable ehange is present for the heavier ions. The effect of neutron scattering is rauch more appreciable at the lowest energy considered here, i.e. at 0.1 MeV. At this priraary neutron energy the ~F for the eoraplete event distribution increases by about 43 % and the ??D b y about t3 % when negleeting the neutron scattering. Discussing the statistical significance of the values in Table 5 one taust eonsider that, because of the procedures followed to ealculate the speetra with and without neutron scattering contribution, the relative variations of these values are to be attributed raainly to a real effeet and only to a negligible extent to statistical uncertainties. Table 5 shows in addition t h a t for protons the average deposited energies YF and YD are !arger at 1.02 MeV than at the two other energies eonsidered, whereas for the heavier ions they increase with increasing priraary energy. A reasonable explanation is that for protons the recoil distribution corresponding to a priraary nentron energy of about t MeV is raostly in an energy region nearer to the Bragg peak than in the two other eases. Therefore the stopping power and consequently the deposited energies are larger on the average. This is not true for the heavier ions, for whieh the recoil distributions stay below the Bragg peak region and therefore in a region of increasing raass stopping power with inereasing ion energy. Considering the event probability per unit neutron fluence, here too the effeet of neutron seattering is most reraarkable at the lowest energy of 0.i MeV, as shown in Table 4. However, eontrarily to the average deposited energies, the event probability inereases when scattering is considered. For the explanation of such an opposite tendency in the influence of the neutron scattering it is necessary to consider t h a t the presence of neutron seattering inereases the total nuraber of neutron eollisions in the wall, because of the relatively small raean free p a t h of low energy neutrons in a hydrogenous material. As a consequence, the nuraber of those eollisions resulting in a eharged particle entering the rneasuring volnme of the counter, and therefore the probability of event observation, increases. On the other hand reeoil ions generated in further eollisions of scattered neutrons are, on the
Neutron Scattering and Energy Deposition Spectra
167
average, of lower energies than from primary neutron collisions. And since the large majority of absorption events at a primary neutron energy of 0.i MeV and for a diameter of 6.5 ~m is due to stoppers and insiders as already proved by us, the presenee of neutron seattering will result in an increase of events in the lower energy portion of the energy deposition spectrum. Therefore the average absorbed energies decrease when neutron scattering is included. The previous eonsiderations show also why the ehange of ~s is generally larger than the change of YD. I t is clear that the function y~f(y) is rauch more depending on higher y values than the function Y1(Y), due to the quadratic term. Therefore, from the expression (2) it is immedia,tely understood that the quantity ~D does not depend as rauch as the quantity ~r on the lower portion of the energy absorption spectrum, which is mostly affected by neutron scattering, as we have already shown, at least at low neutron energies. I f the primary neutron energy inereases these considerations become less and less stringent. Final]y at 5.85 MeV the relatively large neutron mean free path in the Shonka p]astic makes the irtfluence of neutron scattering not very marked on the observed event probability. On the other hand the large presence of crossers and starters among the energy-depositing ions makes the values of .YF and yD praetically insensitive to the scattering effect. The product of ~r, mean lineal energy per event, and Pn, mean number of events per unit neutron fluence, is proportional to the dose. The quantity Db, which includes neutron scatteI~ng, is therefore the absorbed dose in a Rossicounter per unit neutron fluence. The relation Db~Da shown in the last column of Table 4 describes how the absorbed dose is inereased due to neutron seattering, when the attenuation of the primary neutron is not taken into cortsideration. The funetional dependence of Db~Da on i/A, which was assumed in Eq. (5) and is shown in Fig. 8, can be eonsidered a good approximation for large values of i/A, because Db~Da for l/A» i taust approaeh a eonstant value. For i/2 < 0.5, instead, the assumption that also in this region Db~Da follows the same saturation curve having a slope of 0.39 at the zero point is somewhat more arbitrary. I f orte attaches any sense to the enrve in this region orte can say that the seattering effeet does not vanish at 14 MeV, i.e. at an Z/2 of about 0.22, where it produces still an inerease of absorbed dose of about 8 %. So rar, only the relative increase of absorbed dose with increasing seattering was eonsidered. In the method of calculation of Da and Db the same primary neutron flux attenuation is present and therefore the resulting relation does not eontain the deerease of the primary nentron flux, whieh is given by exp (--i/2 2) and is shown in Fig. 8 by the dotted line. The two effects ~re working in opposite direetions: the scattering of neutrons inereases the number of neutrons in the eounter and inereases the dose, the attenuation of the primary nentron flux decreases it. The combination of both effects results in a ner decrease of the absorbed dose, as shown by the dashed line in l~ig. 8. Again it has to be pointed out that the initial slope of this curve might be incorreet. Conclusions The presence of neutron scattering in the wall of a Rossi-counter affects the total probability of energy deposition as well as the shape of the energy deposition
t 68
M. Coppola and J. Booz
s p e c t r a in t h e gas. F r o m t h e m i c r o d o s i m e t r i e p o i n t of view this m e a n s t h a t t h e values of t h e f r e q u e n c y a n d d o s e - a v e r a g e d d e p o s i t e d energies o b t a i n e d from s p e e t r a m e a s u r e d w i t h a walled p r o p o r t i o n a l c o u n t e r d e p e n d to a certain e x t e n t on t h e t h i c k n e s s of t h e wall. I n t h e case of t h e 2 " - c o u n t e r eonsidered in t h e p r e s e n t i n v e s t i g a t i o n such a d e p e n d e n e e becomes e v i d e n t for p r i m a r y n e u t r o n s below 1 MeV, whereas it is negligible a t a b o u t 6 l~{eV. The considerations o f t h e previous p a r a g r a p h induee, therefore, to infer from t h e p r e s e n t results t h a t for t h e counter u n d e r c o n s i d e r a t i o n t h e effect of n e u t r o n s e a t t e r i n g on t h e a b o v e q u a n t i t i e s should be i r r e l e v a n t a t t 4 MeV. F r o m a d o s i m e t r i c v i e w p o i n t a change in t h e e v e n t p r o b a b i l R y p e r u n i t neut r õ n fluenee m e a n s t h a t , if u s e d as a dosimeter, a walled spherical e o u n t e r t e n d s to give a r e a d i n g which is d e p e n d e n t on t h e thickness of t h e o u t e r shell in r e l a t i o n to t h e n e u t r o n m e a n free p a t h - l e n g t h . The a b s o r b e d dose which ean be m e a s u r e d w i t h a R o s s i - e o u n t e r is m a i n l y influenced b y t h e a t t e n u a t i o n of t h e p r i m a r y neuf r o n fluencë in t h e c o u n t e r wall. T h e increase in dose due to t h e n e u t r o n s c a t t e r i n g is r e l a t i v e l y small, however it c a n n o t be neglected. The resnlts of t h i s w o r k were o b t a i n e d for a 2" R o s s i - c o u n t e r of c o n s t a n t wall thickness a n d for n e u t r o n s of various energies. Therefore t h e results e a n n o t be a p p l i e d s t r a i g h t - f o r w a r d l y to o t h e r d e t e c t o r s h a v i n g a ver:( different mass or a v e r y different g e o m e t r y of t h e s c a t t e r i n g b o d y . I n general one ean s a y t h a t t h e choice of o p t i m u m wall thiekness t a u s t p a y due e o n s i d e r a t i o n to t h e m o d e o f u t i l i z a t i o n of t h e eounter. I n o t h e r words, for m e a s u r e m e n t s s i m u l a t i n g surface d o s i m e t r y t h e c o u n t e r should h a v e t h e thinnes~ possible wall, c o m p a t i b l y w i t h all o t h e r p h y s i c a l requirements, whereas for i n t e r n a l simulation, e.g. dose m e a s u r e m e n t s a t c e r t a i n positions in animals, an a m o u n t o f tissue-like m a t e r i a l of t h e same o r d e r as in t h e real case t a u s t be p r o v i d e d a r o u n d it. Referenees Booz, J.: Energy deposition on a microseopic scale, relevant to the biological effects of fast neutrons. In: Biological effects of neutron irradiation, pp. 1i9--130. Vienna: IAEA 1974 Coppola, M., Booz, 5. : Influenee of energy straggling on the shape of neutron-produced single event spectra. Biophysik 9, 225--236 (t973) International Commission on Radiation Units and Measurements: Neutron fluence, neutron spectra and kerma. ICRU Report t3, Washington, D.C. 1969 International Commission on Radiation Units and 5Ieasurements: Radiation quantities and units. ICRU Report 19, Washington, D.C. 1971 International Commission on Radiation Units and )/Ieasurements: Measurement of absorbed dose in a phantom irradiated by a single beam of X or gamma rays. ICRU Report 23, Washington, D.C. 1973 Kellerer, A. M., Rossi, H. H. : The theory of dual radiation action. Curr. Top. Radiat. Res. 8, 85--158 (1972) Rossi, H. H., Failla, G. : Tissue-equivalent ionization chambers. Nucleonics 14, 32--37 (1956) Rossi, I-I. ~., Rosenzweig, W. : A deviee of the measurement of dose as a function of speeifie ionization. Radiology 64, 404--411 (1955) Shonka, F. R., Rose, J. E., Failla, G. : Conducting plastic equivalent to tissue, dir and polystyrene. In: Proeeeding of the Seeond United Nations International Conference on Peaeeful Uses of Atomic Energy, Vol. 21, pp. 184--187. Geneva: United Nations 1958 Prof. Dr. M. Coppola Biology Group CCR-Euratom 1-21020 Ispra (Va), Italy
