oak ridge national laboratory operated by union carbide corporation nuclear division to ·...

Ile N0NAL OAK RIDGE NATIONAL LABORATORY

operated by 0 UNION CARBIDE CORPORATION

NUCLEAR DIVISION to for the

0 U.S. ATOMIC ENERGY COMMISSION

ORNL- TM- 3105

COPY NO. -

DATE - August 24, 1970

Neutron Physics Division

THE ABSORBED DOSE AND DOSE EQUIVALENT FROM NEGATIVELY AND POSITIVELY

CHARGED PIONS IN THE ENERGY RANGE 10 TO 2000 MeV

R. G. Alsmiller, Jr., T. W. Armstrong, and Barbara L. Bishop

Abstract

Nucleon-meson cascade calculations have been carried out for broad

beams of monoenergetic negatively and positively charged pions normally * 0

0 0 ncident on a semi-infinite slab of tissue 30-cm thick, and the absorbed

doses and dose equivalents as a function-of depth in the tissue are pre

sented. Results are given for incident energies of 10, 30, 84, 150, 500,

21000, and 2000 MeV. For the lower incident energies (<84 MeV), the pion

n " range is < 30 cm in tissue, and peaks in the absorbed doses and dose equiv

alents, due to the reaction products produced by the nuclear capture of the

" -4" stopped negatively charged pions and to the decay products of the stopped

<positively charged pions, are clearly evident.

Z09 WHOA AlDVA NOTE: This Work Partially Funded by NATIONAL AERONAUTICS 'AND SPACE ADMINISTRATION

Under Order H-38280A

NOTICE This document contains information of o preliminary- nature and was prepared primarily for internal use at the Oak Ridge National 6V Laboratory. It is subject to revision or correction and therefore does % not represent a final report.

*Submitted for journal publication.

https://ntrs.nasa.gov/search.jsp?R=19700033401 2020-03-09T12:26:12+00:00Z

LEGAL NOTICE

This report was prepared as an account of Government sponsored work. Neither the United States,

nor the Commission, nor any person acting on behalf of the Commission-

A. Makes any warranty or representation, expressed or implied, with respect to the accuracy,

completeness, or usefulness of the information contained in this report, or that the use of

any information, apparatus, method, or process disclosed in this report may not infringe privately owned rights, or

B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or process disclosed in this report.

As used in the above, "person acting on behalf of the Commission" includes any employee or

contracto, of the Commission, or employee of such contractor, to the extent that such employee

or contractor of the Commtssion, or employee of such contractor prepares, disseminates, or

provides access to, any information pursuant to his employment or contract with the Commission,

or his employment with such contractor.

3

iTSREf'7mT PACT. BLAJA!{ NOT FILMEW I. INTRODUCTION

In a previous paper, 1 hereinafter referred to as paper 1, the calcu

lated absorbed doses and dose equivalents from broad beams of high-energy

(< 3000 MeV) neutrons and protons were presented. In the present paper,

calculated results for the case of broad beams of incident negatively and

positively charged pions are presented. The results are of interest-not

only because of their applicability in the shielding of high-energy accel

erators but also because of the possible use of negatively charged pions in

- 4cancer radiotherapy.2 Since the results presented here are for the case

of incident beams of infinite width, they do not apply directly to cancer

therapy; that is, in cancer therapy the lateral spread of narrow beams of

negatively charged pions is of importance. The results do, however, include

reliable estimates of the absorbed dose and dose equivalent produced by the

reaction products that arise from the nuclear capture of negative pions

which come to rest in tissue.

In See. II the method of calculation is discussed. In Sec. III the

calculated results are presented and discussed.

II. METHOD OF CALCULATION

The method of calculation and the cross-section data used in obtaining

the results presented in this paper are in almost all respects the same as

those used in paper 1. The only notable difference between the calculational

method used here and that used in paper 1 is that here the electrons and

positrons from muon decay are transported, while in paper 1 these particles

were assumed to deposit their energy at their point of origin. The method

used to transport electrons and positrons is described later in this section.

All of the results were obtained using the nucleon-meson transport code

'4

written by Coleman. 5 The code is described in some detail in ref. 5, but,

for completeness, a description of the physical interactions that are in

cluded in the present calculations is given here.

Charged-Particle Energy Loss

The energy loss of protons, charged pions, and muons by the excitation

and ionization of atomic electrons is treated in the continuous slowing

down approximation using the well-established energy loss per unit distance

5'6of such particles. The density-effect correction to the energy loss of

all charged particles has been calculated using the asymptotic form of the

7 correction.

Nucleon-Nucleus and Pion-Nucleus Nonelastic Collisions

At energies > 15 MeV for nucleons and > 2.2 MeV for charged pions,

5

the differential cross sections for nucleon and pion emission from nucleon

nucleus and pion-nucleus nonelastic collisions are obtained from the intra-

This modelnuclear-cascade-evaporation model of nuclear reactions.8- 10

gives the energy and angular distribution of the emitted nucleons and pions.

The evaporation portion of the intranuclear-cascade-evaporation calcula

tions is carried out with the version of the code EVAP-3,11 which is suit

able for use-with the intranuclear-cascade code of Bertini.8'9 This evap

oration code gives an estimate of the energy of the emitted deuterons,

tritons, 3He's, alpha particles, and photons, as well as an estimate of the

kinetic energy of the recoiling residual nucleus from a nonelastic collision.

The differential cross sections for particle production from nucleon

and pion nonelastic collisions with hydrogen nuclei are the same as those

-1 0' 12

used in the intranuclear-cascade calculations of Bertini.

8

5

Proton-nucleus nonelastic collisions below 15 MeV and,pion-nucleus

nonelastic collisions below 2.2 MeV (except forth ecapture of negative pions

at rest) are neglected. Particle production from neutron-nucleus nonelastic

collisions below 15 MeV is obtained using the code EVAP-3 as described in

ref. 11 in conjunction with the total nonelastic cross-section data on the

05R master cross-section tape.a

Nucleon-Nucleus and Pion-Nucleus Elastic Collisions

The elastic collisions of protons and pions with all nuclei other than

hydrogen are neglected. The differential cross sections for the elastic

collision of neutrons with nuclei other than hydrogen are those given on

the 05R master cross-section tape.a The differential cross sections for

the elastic collisions of nucleons with energy > 15 MeV and pions with

energy > 2.2 MeV with hydrogen nuclei are taken from experimental data and

are the same as those used in the intranuclear-cascade calculations of

Bertini.8, 9 ,12 The differential cross sections for the elastic collisions

of neutrons with energy < 15 MeV with hydrogen nuclei are those given on

a the 05R master cross-section tape.

Charged-Pion Decay in Flight

Charged pions are unstable and may decay into muons and neutrinos.

Charged-pion decay in flight is taken into account using the known pion

lifetime. When a decay occurs, the energy and angular distribution of the

produced muon is obtained by assuming that the decay is isotropic in the

rest frame of the pion and by using the Lorentz transformation to transform

the distribution from the pion rest frame into the laboratory system. The

produced neutrino deposits no energy in the tissue and is therefore of no

interest here.

6

Charged-Pion Decay and Capture at Rest

Charged pions may come to rest in the tissue. When a positively charged

pion comes to rest, it will ultimately decay into a positively charged muon

and a neutrino, and the energy and angular distribution of the muon may be

obtained in the same manner as when a positively charged muon decays in

flight (see above). When a negatively charged pion comes to rest, it usually

will not decay but will be captured by a nucleus and will produce a variety

of secondary particles. In the calculations reported here, it is assumed

that all negatively charged pions that come to rest are captured, and the

energy and angular distribution of the particles produced as a result of

this capture is obtained from the intranuclear-cascade-evaporation model of

nuclear reactions, since it has previously been shown that this model de

scribes the capture process quite well.13

Neutral-Pion Decay

The neutral pion is very unstable and for practical purposes may be

assumed to decay into two photons at its point of origin. The two photons

have equal and opposite momenta in the rest system of the pion, and the

sum of their energies in this system is equal to the pion rest energy. The

energy and angular distribution of the photons in the laboratory system is

obtained by assuming that the decay is isotropic in the rest system of the

pion and by using the Lorentz transformation to transform from the rest

system to the laboratory system.

Muon Decay in Flight and at Rest

Muons are unstable and may decay into electrons or positrons, depend

ing on the charge of the muons, and neutrinos. Muon decay in flight is

taken into account using the known muon lifetime, and muons which come to

7

rest are assumed to decay. The energy and angular distribution of the

electron or positron in the muon rest system is known, 14 and the energy and

angular distribution of these particles in the laboratory system is obtained

by using the Lorentz transformation. In the work reported here, the asym

metric portion of the energy and angular distribution in the muon rest sys

tem due to the polarization of the muon has been neglected; that is, the

angular distribution of the electron or positron in the muon rest system has

been taken to be isotropic. 14

Electron-Photon Cascade From High-Energy Photons, Electrons, and Positrons

Photons from the decay of neutral pions, and electrons and positrons

from the decay of muons are relatively high in energy, and in passing through

matter they induce an electron-photon cascade. To obtain the energy deposited

by such cascades, results obtained from the cascade code written by Zerby

1 5and Moran 18 and the published results of Beck 19 and Claiborne and Trubey2 0

were used. The procedure followed was to construct curves of energy depo

sition as a function of depth and incident photon energy and to interpolate

in these curves to find the energy deposited in subslabs of the tissue by

each electron, positron, or photon produced in the Monte Carlo calculations.

This procedure is approximate in that it does not accurately account for

the lateral spread of the cascade, but the error is not thought to be large.

Thermal-Neutron Capture

Neutrons which become thermalized will be captured by hydrogen and

nitrogen if they do not escape from the system. The energy deposited by the

photons produced by thermal-neutron capture in hydrogen and by the protons

produced by thermal-neutron capture in nitrogen is included in the calcula

tions by using the capture cross sections from the 05R master cross-section

tape.a

8

Transport Details

In the calculations reported here, neutrons, protons, charged pions,

and muons are transported through the tissue taking into account the energy

Theand angular distributions with which these particles are produced.5

transport of electrons and positrons from muon decay and photons from neu

tral pion decay is carried out using the calculated results on electron

photon cascades as described above (see page 7). Heavy nuclei, that is,

nuclei with mass number greater than one, are not transported but are assumed

to deposit their energy at their point of origin. This assumption is quite

valid because these particles have a very short range. Photons from all

nonelastic nucleon-nucleus and pion-nucleus collisions are assumed to de

posit their energy at their point of origin. These photons are relatively

low in energy and could be transported without difficulty if their spectrum

was known, but for the higher incident nucleon and pion energies (0 15 MeV)

the spectrum cannot be calculated at all well.2 1 The assumption that these

photons deposit their energy at their point of origin is not entirely valid

but is somewhat justified here in that in most instances these photons con

tribute only a small amount to the absorbed dose and dose equivalent.

The geometry considered throughout this paper is that of a broad beam

of monoenergetic pions normally incident on a semi-infinite slab of tissue

30-cm thick. The composition of tissue is the same as that used in the

previous calculations 1'2 2 and is shown in Table I.

The calculation of the dose equivalent was carried out taking the

quality factor to be a function of the linear energy transfer as in the

previous calculations.1 In the case of protons, the damage curve given by

Turner et al.,23 which is based on the recommendations of the National

9

TABLE I

Composition of Tissue

Density of Nuclei

Element (nuclei/cm3)

H 6.265 x 1022

0 2.551 x 1022

C 9.398 x 1021

N 1.342 x 1021

10

Committee on Radiation Protection and Measurements, was used. In the case

of charged pions and muons, the quality factor as a function of linear energy

transfer was taken to be the same as that for protons, and damage curves for

charged pions and muons, constructed in a manner similar to the proton damage

A quality factor of 20 was assigned tocurve given in ref. 23, were used.

the energy deposited by all heavy nuclei and a quality factor of unity was

assigned to the energy deposited by electrons, positrons, and photons.

III. RESULTS AND DISCUSSION

Calculations have been carried out for incident negatively and posi

tively charged pions with energies of 10, 30, 84, 150, 500, 1000, and

2000 MeV.

In Figs. 1 and 2 the contribution to the absorbed dose and dose equiv

alent, respectively, from the various kinds of particles produced in tissue

by 8h-MeV incident negatively charged pions is shown.b The total absorbed

dose and the total dose equivalent are obtained by adding all of the con

tributions in each figure. In Fig. 1 the histogram labeled "primary ion

ization" gives the absorbed dose from the ionization and excitation of

atomic electrons by those incident pions that have not undergone nuclear

interaction. The histogram labeled "secondary protons" gives the absorbed

dose from the excitation and ionization of atomic electrons by protons pro

duced from nonelastic nucleon-nucleus and pion-nucleus collisions and from

the elastic collisions of nucleons and pions with hydrogen nuclei. The

histogram labeled "heavy nuclei" gives the absorbed dose from particles with

mass number > 1 produced from nonelastic nucleon-nucleus and pion-nucleus

collisions and the absorbed dose from the recoiling nuclei produced from

elastic neutron-nucleus collisions and from nonelastic nucleon-nucleus and

-_ ORNL-DWG 70-9971

0 _______

TS

- 1(:F9

0

0

S

S

co A-O

o PRIMARY IONIZATION * SECONDARY PROTONS A HEAVY NUCLEI A CHARGED PIONS

10-1 - PHOTONS FROM NEUTRAL PIONS n ELECTRONS, POSITRONS, PHOTONS

- v MUONS

0 5 10 15 20 25 30

DEPTH INTISSUE (cm)

Fig. 1. Absorbed Dose from the Various Kinds of Particles vs Depth in Tissue for 84-MeV Normally Incident Negatively Charged Pions.

12

ORNL-DWG 70-9972 =0 PRIMARY IONIZATION

SECONDARY PROTONS - HEAVY NUCLEI

10-6 CHARGED PIONS 0 PHOTONS FROM NEUTRAL PIONS * ELECTRONS, POSITRONS, PHOTONS v MUONS

08

sA ' - ' ...,1...r ,L - rr Ls

-'AO10-8O > iciy9

10-11

-io-l2

0 5 10 15 20 25 30

DEPTH IN TISSUE (cm)

Fig. 2. Dose Equivalent from the Various Kinds of Particles vs Depth

in Tissue for 84-MeV Normally Incident Negatively Charged Pions.

13

pion-nucleus collisions. The histogram labeled "charged pions" gives the

absorbed dose from the excitation and ionization of atomic electrons by

both negatively and positively charged pions produced from nuclear inter

actions. The histogram labeled "photons from neutral pions" gives the ab

sorbed dose from the electron-photon cascade produced by the photons that

arise from the decay of neutral pions. The histogram labeled "electrons,

positrons, and photons" gives the absorbed dose from the electrons and posi

trons that arise from the decay of muons and the absorbed dose from the

photons produced from nonelastic nucleon-nucleus and pion-nucleus collisions.

The histogram labeled "muons" gives the absorbed dose from the ionization

and excitation of atomic electrons by both negatively and positively charged

muons. In Fig. 2 the histograms have similar meanings but give the dose

equivalents from the various kinds of particles.

The range of 84-MeV pions in tissue is between 21 and 22 cm, and there

fore the primary-ionization histogram in Fig. 1 does not extend beyond 22 cm.

The increase in the absorbed dose from the primary particles near the end

of their range is due to the increase in the pion stopping power as the pion

energy decreases. The peaks in the absorbed doses from secondary protons,

heavy nuclei, and photons at the end of the pion range arise from the par

ticles that are produced by the nuclear capture of the negative pions which

come to rest. A large fraction of the pion rest energy is converted by the

capture process into charged particles (protons and heavy nuclei) which

have a sufficiently short range that they deposit their energy in the im

mediate vicinity of the capture event. The peak in the histogram labeled

"electrons, positrons, and photons" is primarily due to photons produced in

the capture process. This photon peak is overestimated somewhat in the

14

present calculations because these photons, that is, photons produced by

nonelastic collisions, are assumed to deposit all of their energy at their

point of origin.

In Fig. 2 the peaks in the dose-equivalent histograms at a depth of

21 to 22 cm have the same origin as the corresponding peaks in Fig. 1. In

Fig. 2, however, the peak in the dose equivalent from heavy nuclei is more

pronounced because of the large quality factor which is attributed to heavy

nuclei. It is, of course, the ability of negative pion beams to produce a

large dose equivalent in a small spatial region that seems to make them

ideally suited for cancer radiotherapy. It should be noted that in both

Figs. 1 and 2 the magnitudes of the peaks are determined by the somewhat

arbitrary 1-cm spatial interval over which the doses have been averaged;

that is, the shape of the dose equivalents within the 1-cm interval has not

It should also be noted that pion range straggling, whichbeen determined.

has been neglected in the calculations presented here, is probably not a

negligible effect in the vicinity of peaks such as those shown in Figs. 1

and 2. In Fig. 1 there is an appreciable contribution to the absorbed dose

from secondary protons at all depths. In fact, beyond the pion range the

major contribution to the absorbed dose is from secondary protons. In

Fig. 2 there is an appreciable contribution to the dose equivalent from

secondary protons and heavy nuclei at all depths.


alent from the various kinds of particles produced in tissue by 84-MeV in

cident positively charged pions are shown. The meanings of the various

histograms in these figures are the same as those in Figs. 1 and 2. The

pion range is between 21 and 22 cm and therefore in Figs. 3 and 4, as in

15

6 ORNL-DWG 70-9973o0_

5

2 40-7 __ __ __

5

All -' "., --

O~ 2

"0

0 5 0

m

< o PRIMARY IONIZATION * SECONDARY PROTONS

-A HEAVY NUCLEI40-40 A CHARGED PIONS

5 o-PHOTONS FROM NEUTRAL PIONS " ELECTRONS, POSITRONS, PHOTONS v MUONS

2

0 5 10 15 20 25 30


Fig-. 3. Absorbed Dose from the Various Kinds of Particles vs Depth

in Tissue for 8'-MeV Normally Incident Positively Charged Pions.

16

0-6

5

2

5 0--

E

o 2O25'La io7 E-

LLJ 2

LI 5

MH 2

1-1010A

5

12

0

Fig. 4.

in Tissue for

ORNL-DWG 70-9974

*-t-.'" -....-

-

I NALT '-MNE

NT

IONIZATIPRIMAY IN* SECONDARY PROTONS

a HEAVY NUCLEI CHARGED PIONS

o PHOTONS FROM NEUTRAL PIONS -

ELECTRONS, POSITIONS, PHOTONS-- __

1_

5 10 15 20 25 30 DEPTH IN TISSUE (cm)

Dose Equivalent from the Various Kinds of Particles vs Depth

84-MeV Normally Incident Positively Charged Pions.

17

Figs. 1 and 2, the primary ionization curve does not extend beyond 22 cm.

The peaks in the histograms labeled "muons" and "electrons, positrons, and

photons" in the 21- to 22-cm interval arise from the decay of these incident

pions that come to rest and then decay. A positive pion at rest will decay

into a positive muon with a kinetic energy of approximately 4 MeV.2 5 The

range of a muon with this kinetic energy is very small, and thus the muon

from the decay of a stopped pion will stop and decay very near its point of

origin. The positron from the decay of the positive muon will be relatively

high in energy and will deposit only a small portion of its energy in the

immediate vicinity of the point where the muon decays. By comparing Figs. 1

and 3, it can be seen that a larger fraction of the pion rest energy is de

posited locally when a stopped negative pion is captured than when a stopped

positive pion decays. Furthermore, by comparing Figs. 1 to 4, it can be

seen that the energy deposited locally when a stopped negatively charged

pion is captured has associated with it a much larger quality factor than

the energy deposited locally when a stopped positively charged pion decays.

In Fig. 3 there is an appreciable contribution to the absorbed dose at small

depths, but at the larger depths the major contribution to the absorbed

dose is from the electron-photon cascade produced from the positrons which

arise from positive muon decay. In Fig. 4 there is an appreciable contri

bution to the dose equivalent at small depths from secondary protons and

heavy nuclei, but the major contribution to the dose equivalent at the larger

depths is that from the electron-photon cascade induced by the positrons.


alent, respectively, from the various kinds of particles produced in tissue

by 2000-MeV incident negatively charged pions is shown. In Figs. 7 and 8

ORNL-DWG 70-9975O-7

5

i - -- t' • 0""

x 2

E _@,--L , -

- - I_ _A -A--A -A C']A

- EAY _A_UCE ' 10I 8 Ca

oo PRIMNARY IONIZATION *SECONDARY PROTONS

0 io0 HEAVY NUCLEI CoA

__9

CHARGED PIONS ____

< o PHOTONS FROM NEUTRAL PIONS a ELECTRONS, POSITRONS, PHOTONS

5 v MUONS

2

10-40

0 5 10 15 20 25 30


Fig. 5. Absorbed Dose from the Various Kinds of Particles vs Depth


19

ORNL-DWG 70-9976

= o PRIMAR4Y IONIZATION - PHOTOhS FROM NEUTRAL PIONS

-* SECONDARY PROTONS - ELECTRONS, POSITRONS, PHOTONS 5,HEAVY NUCLEI v MUONS

A CHARGED PIONS 2''

7 10

N. _____,...__r__ ,vL

'3 5

2

2

-IC 8 -A-____ *.r-A,.rrAe3A.r

0-

Uj L.-. .. L'

LiJ 2 .. J z&_ co

_

0 40-40~

c0 520 5 __

2

0 5 10 15 20 25 30 DEPTH IN TISSUE (cm)

Fig. 6. Dose Equivalent from the Various Kinds of Particles vs Depth


20

,10-7 ORNL-DWG 70-9977

5

°" 2 - ,jo -Oi

IiI

E -, o il X

.0 5 .. -6Fo 25 * SECONDARY PROTONS

5 ma A CHARGED PIONS 0 O a PHOTONS FROM NEUTRAL PIONS

0 tj~a3* ELECTRONS, POSITRONS, PHOTONS

0 5 40 15 20 25 30 DEPTH IN TISSUE (cm)

Fg. 7. Absorbed Dose from the Various Kinds of Particles vs Depth in Tissue for 2000-&eV NormAlly Incident Positively Charged Pions.

21

t0_6 ORNL- DWG 70-9978 - 0 PRIMARY IONIZATION

5- * SECONDARY PROTONS - HEAVY NUCLEI

- A CHARGED PIONS o PHOTONS FROM NEUTRAL PIONS 2 ELECTRONS, POSITRONS, PHOTONS v MUONS

Eo

2 E 1-0-8 ________ -__- .A. -A - --~ r" ... A.A,L-A

0 7

-1 5

w 2 co 0o t0-9__ __ __ _

5

2

t0-i0

0 5 10 15 20 25 30


Fig. 8. Dose Equivalent from the Various Kinds of Particles vs Depth in Tissue for 2000-MeV Normally Incident Positively Charged Pions.

22

similar results are given for 2000-MeV incident positively charged pions.c

At this energy, incident pions of both charges pass through the 30-cm tissue

slab unless they undergo nuclear interaction, and thus there are no peaks

due to stopped pions as in Figs. 1 to 4. In Figs. 5 and 7 the major con

tribution to the absorbed dose is from primary pion ionization and secondary

protons. In Figs. 6 and 8 the dose equivalent from heavy nuclei is the

largest contributor to the total dose equivalent, but there is also an

appreciable contribution from primary pion ionization and from secondary

protons.

In Figs. 9 and 10 the absorbed dose and dose equivalent, respectively,

for all of the incident energies considered here are shown as a function of

depth. In each figure, the solid-line histogram gives the results for nega

tive pions and the dashed-line histogram gives the results for positive

pions. For incident energies of 10-, 30-, and 84-MeV, the peaks in the

absorbed dose and dose equivalent occur at the -end of the incident pion range.

In the vicinity of the peak, the absorbed dose and particularly the dose

equivalent are always larger for negative pions than for positive pions.

For incident energies of 30 and 84 MeV, there is no appreciable difference

in the absorbed dose from positive and negative pions at the smaller depths,

that is, at the depths over which the incident pions are slowing down. At

incident energies of 150 MeV and above, the absorbed dose is relatively flat

as a function of depth. For incident energies of 500, 1000, and 2000 MeV

there is no appreciable difference between the absorbed doses from positive

and negative pions, but there is a significant difference for an incident

energy of 150 MeV. This difference at 150 MeV is probably due to the large

difference between the R+-proton and --proton elastic-scattering cross

23

ORNL-DWG 70-9979

-2000 MeV

2- __

jC-7 - - . 500MeV

2

5 -. 15MeV

10-8

o

---- 0 MeV

5

0

211

5

2

0 5 1 15 20 25 0

DEPTH (cm)

Fig. 9. Absorbed Dose vs Depth in Tissue for Monoenergetic Normally Incident Negatively and Positively Charged Pions.

24

ORNL-DG70-9980

105

2

c7M

2

,C7

5

2

5

0 52

& "

o '0 o -- -- -- -

5

.CF6 5 -30 MeV

5

2

5 0 5 10 I5 20 25 30

DEPTH(ten)

Dose Equivalent vs Depth in Tissue for Monoenergetic NormallyFig. 10. Incident Negatively and Positively Charged Pions.

25

d sections in this energy region. At the lower energies in Fig. 10, the

dose equivalents from negative pions are larger at all depths than the dose

equivalents from positive pions, but at the higher energies the dose equiv

alents from negative and positive pions are comparable at all depths.

In Fig. 11 the absorbed dose and dose equivalent averaged over the 30-cm

tissue depth are shown as a function of incident energy for negatively and

positively charged pions. The curves have been drawn by eye through the

plotted points which give the actual calculated values. The curves have not

been drawn between 84 and 150 MeV because the shape of the curves in this

energy region has not been determined. A rather abrupt change may be expected

to occur in the absorbed dose and dose equivalent for approximately 108-MeV

incident pions because at this energy the pion range is 30 cm in tissue, and

thus at slightly higher energies those pions that do not undergo nuclear

collisions will pass through the slab and no part of their rest energy will

be deposited in the tissue. The fact that the average dose equivalent from

positive pions increases as the incident energy changes from 84 to 150 MeV +

is probably due to the large +-proton elastic-scattering cross section in

the 100- to 150-MeV energy region.

For radiation protection purposes, the maximum absorbed dose and dose

equivalent which occur in the 30-cm slab of tissue are often used. There

fore, in Fig. 12 the "maximum" absorbed dose and dose equivalent are shown

as a function of incident pion energy for both negatively and positively

charged pions. It is very important to note that for incident energies of

: 84 MeV the values shown in the figure were taken directly from Figs. 9

and 10 and therefore correspond to an average over a particular 1-cm in

terval. The shape of the curves in Figs. 9 and 10 in the vicinity of the

ORNL-DWG 70-9984 -10-6 - ,_-__

5

T"E 2 __

1t0-7 " o

o AVERAGE DOSE EQUIVALENT i00f A AVERAGE DOSE EQUIVALENT 7r+

2 AVERAGE ABSORBED DOSE 7r-

A AVERAGE ABSORBED DOSE 7r+

40-8 1, I I I I 10t 1032 5 102 2 5 2

E (MeV)

Fig. 11. Absorbed Dose and Dose Equivalent Averaged Over 30-cm Tissue

Depth vs Incident Pion Energy.

27

ORNL-DWG 70-9982t0-5

i5

2

j0.6 I

-0 0

o "MAXIMUM" DOSE EQUIVALENT ir-A "MAXIMUM" DOSE EQUIVALENT "vr+

r2 * "MAXIMUM" ABSORBED DOSE DOSE Tr+

- "MAXIMUM" ABSORBED

110-8 1 -" i'I IIII I

tO 2 5 102 2 5 1O 2 E (MeV)

Fig. 12. "Maximum" (see discussion on pages 25 and 28) Absorbed Dose and Dose Equivalent vs Incident Pion Energy.

28

peaks is not known, and therefore quite different maximum values might be

determined if the average were performed over a smaller depth interval.

Furthermore, the position of the 1-cm interval over which the dose has been

averaged with respect to the end of the pion range also has a decisive effect

on the maximum value obtained; that is, the amount of energy that will be

deposited in the 1-cm interval is quite dependent on where the pion stops

within that interval. At energies of 150 MeV and greater, the values in

Fig. 12 were obtained by drawing smooth curves by eye through the histograms

in Figs. 9 and 10 and taking the maximum from each of these curves. As in

Fig. 11, no curves between 84 and 150 MeV have been drawn because of the

expected rapid variation of the dose values in the vicinity of 108 MeV. In

Table II the quality factor obtained by dividing the maximum dose equivalent

from Fig. 12 by the maximum absorbed dose from Fig. 12 is given as a function

of incident energy of pions of both charges. At the lower energies, the

quality factor is much larger for negative than for positive pions, but at

the higher energies ( 500 MeV) there is no appreciable difference between

the quality factor for negatively and positively charged pions. The fact

that the quality factor given in the table is larger for 30-MeV negative

pions than that for either 10- or 84-MeV negative pions may be due to the

somewhat arbitrary way in which the "maximum" is defined here and therefore

may not be meaningful.

29

TABLE II

Quality Factor as a Function of Incident Pion Energy

7+7- Quality Factor Quality Factor

Energy "Maximum" Dose Equivalent "Maximum" Dose Equivalent (MeV) "Maximum" Absorbed Dose "Maximum" Absorbed Dose

10 9.1 1.2

30 11.1 1.1

84 9.2 1.2

150 3.2 2.2

500 2.6 2.3

1000 2.4 2.3

2000 2.3 2.3

30

APPENDIX

In this appendix the contributions to the absorbed dose and dose equiv

alent from the various kinds of particles produced in tissue by incident

negatively and'positively charged pions with energies of 10, 30, 150, 500,

and 1000 MeV are given. In the figures to follow the individual contribu-

The totaltions are defined in the same manner as in the body of the paper.

absorbed dose and dose equivalent obtained by adding all of the contribu

tions in a given figure are shown in the body of the paper.

o-6

C

31

5

2b-9

S

110-I1i0

2

1611

"I@ 2b SEWCDLr PROIONS

162 -RVY+ PV2-wMEJ

10V PHIONS FflO4NEUnd. pij~s

® PP.iIY 1I2A11W

. FO5i1flONS. ?i1TmSt atEC1Ba

5.00 52 25 30 DEPIH IN TISSUE (CM.

Fig. A-1. Absorbed Dose from the Various Kinds of Particles vs Depth


32

-2

10 (-7 5

-

10

C,0, 2-

ElO 1

SEOOWPMN &S 2

2

+ KiVY NUCLEi2-

INa7 wmCAPCK-12Of 0T FROMU

Fig. A-2. Dose Equivalent from the Various Kinds of Particles vs Depth


33

10- X PRIKT IMJAZT1

2-A & MY PR6TftS

1CC 2+ HEW t&CLEJ X CFIEO PI@43 0 PMONS FROI NEUIJ:LPIONS + ntttrlFnmI rOSJ1k9N5. MnociS

2• X Ras

10"

L2 10

, 10

il10"

lO I I I I J 0 5.U 10 15 20 25 50

DEPTH IN TISSUE (CH.)


in Tissue for lO-MeV Normally Incident Positively Charged Pions.

34

S CD PRJI'Y JOIJZAT]N

& SECMT PMTMS - 2 .9- MV4-"NULI

FR04 P.0 F?187ONS NUAflSELEIRJS. POSjIMNS. p?1614S

-10

2

2

I

N10 E 10 Li

01

o10"

si- DET INTSUEfM

10 0 52 2 L Fig. -4. Dos Eqialn frmteVriu id o atcesv et

OEPTH IN TISSUE (CM.1


in Tissue for 10-M4eV Normally Incident Positively Charged_Pions.

35

10 -

s C) PRfllWY &SECOW

IORztiON MPONS

+ IERVYNUCEI 2 X M Pina Po

10 t ELECHMS. POSLIRNS. MPSSNS

5

2

110 25

2

101 I I I II 5.0 -10 15 20 25 30

OEPTHIN TISSUE (CM.)


in Tissue for 30-MeV Normally Incident Negatively Charged Pions.'

36

16-5

0 PRIMA ONmIZATONl A S(CU PRMOTNS

5 + IHEVYNUL.EI

2- x CHAGE aiMs F PIW$

I0 -aEECTRONS. *F POSJTRONS. 0 PMICMS NEUTRAL

P~FlTS x tiNs.

zld

2 -

1010

12

100 10 15 20 25 30

OEPTH IN TISSUE (CM.)



37

10' 2

( PRIiMAY IUOIZRTIOL A SCOMr PfflT S + Fr-RYYHUMlE X D4 PIOms 0 PHOTONS FRMtIMIL PIONS

*ELECRNS. PtSMflS. PHOTOS5

10F

10' SKOS

+ +

5

10

10

10

o10 1 0 5

DEPTH IN TISSUE (Cli.)

Fig. A-i'. Absorbed Dose from the Various Kinds of Particles vs Depth

in Tissue for 30-MeV Normally Incident Positively Charged Pions.

38

(D PRIff IMNIZTION

0 PIObSNS F1 HEWFL. PIONSPOSITRON,+, ELECTRONS. M407

10

-w 1 -

S

o" I I I ". 15 20 25 3 0 5.0 10

DEPTH IN TISSUE (CII.)


in Tissue for 30-41eV Normally Incident Positively Charged Pions.

39

o-.7 -a10

-10

2- xc'

&i SECOND5R20PROTON T SE. +, NR

- s D o Vo X PaION(D1 IONZTOPRIMARY

ose frm theVariou of& PartceFig. A9. Absrbed Kind vset

nDEPTHgai PSons.IhrNe Tisefr10 I0MVNral Incdn Neaivl Chre Pos

10

-5

2

2

2 - X ta IN

Fig, AVf Tissfr +n ei

+ DfL&0TM PIRNS. MT

IDpT INMFI TM,TISSUE

10 .0 10 15 20 25 30

DEPTHI IN TISSUE (CM.)

Fig. A-i0. Dose Equivalent from the Various Kinds of'Particles vs Depth

in Tissue for l50-MeV Normally Inciaent Negatively Charged Pions.

41

0-'

C

( PRIH FA¥IOt IZRIICN A SECONDARYPROTONS + HEVY WCLEI X CHAGEO PIONS

2- PHOTONS FROM4 WUlRPL ?TONS + ELECTRONS., POSITRONS. PHOTONS X MONS

0.0 10 20 25 30 IN TISSUE (OMS) *EPTH

Fig. A-Il. Absorbed Dose from the Various Kinds of Particles vs Depth in Tissue for 150-MeV Normally Incident Positively Charged Pions.

42

-

C-,

z

I

5

0 RIM BY ION17.RTION ,& SECONOM¥ PROTONI$

00 + HEWv NUCLEI X CHqRGEDPION5 0 PHOTONSPBO P.EUTRF-PIONS

2- + ELECTRONS.POSITRONS.PHOTONS

10 I I I I 5010 15 20 25 3

DEPTH INTISSUE (CM.)


in Tissue for 150-MeV Normally Incident Positively Charged Pions.

10'

-O105

0 PRIMAY IONIZATION

+ HEAVY NUCLEI

X CMAFGEO PIONS NEURAL PIONS

+" ELIECTRONS.POSITRONS. PHOTOS 11 PHOTONSMROM

X MONS2_

25 30Is 2010

IN TISSUE OEPTH NCM.I

Absorbed Dose from the Various Kinds of Particles -vs DepthFig. A-13. in Tissue for 500-eV Normally Incident Negatively Charged Pions.

44

1-7

5

2

iu

o PnIKiar IONIZATION A SECONOAYPROTONS

+ IEVY IXEJ x)COFRGEn PIONS * OTONSFMOM UNEIJ PIONS + a.ECTaiS. PFSITMS. PHOTONS

I I I I 5.0 10 15 20 25 30

nFPTH IN TISSUF (CM.)

Fig. A-14. Dose Equivalent from the Various Kinds of Particles vs Depth in.Tissue for 500-MeV Normally Incident Negatively Charged Pions.

10-D PRIWT ICIZRTIV &SECONDSY IWTM#S +- NEVY NUCLEI X CKIE PIMN

-- 0 FFMMKWUTPFLPMi'ONS PIONS

+" ELECTRMF3 PObSITWN. PM TOS x NOWs

C'

10

05. 10 15 20 25 DEPTH IN TISSUE (CN.)

Fig. A-15. Absorbed Dose from the Various Kinds of Particles vs Depth in Tissue for 500-MeV Normally Incident Positively Charged Pions.

46

d0-7

+ IERVT MUCLE! 10 x OW"O PONS

1F 0 P)CTeNS FMI NEUITFL PI03 F P tS+ ELECTfiS. TJS. MMtf,

0

lOD

D1 20 25 DEPTH IN TISSUE (CM.)

Fig. A-16. Dose Equivalent from the Various Kinds of Particles vs

Depth in Tissue for 500-MeV Normally Incident Positively Charged Pions.

10

51

2

10-

A

161C

PICf4S I"CSUT

A SECUOMMT MJCISI

1 I 1 X wa FJGONrmSI 061 +

IZIO0 PtMlOS MW§tmfRt ?IMt £LW1U4S. FaSuiRNS. P11610*42

a5.0 10 15 2 25 30 DEPI IN TISSUE (CH.)

-Fig.A-17. Absorbed Dose from the Various Kinds of Particles vs Depth


lo-b ( ) PRimiRT IONIIA71M

ASECONOffIT PMICNS 5 + IEAVYNL'U

X 0

CHAGO pIONS PHIONS R]OM N ULM. PIO s aiciONaS. rosxiRNaS. PNOIONS

x XUONS 2

j-7

N

S

5_

-J

o

160

5.0 10 15 20 25 30

OEPTH IN TISSUE (CM.)

Fig. A-18. Dose Equivalent from the Various Kinds of Particles vs Depth in Tissue for 1000-MeV Normally Incident Negatively Charged Pions.

49

ASECONDA RY PROTONS +t HEY RXLE1 X CHRGED PIONSRIM

-- PHOTONSFRO NWURAL.PIONS + ELECTRONS.POSITMM. PHOTONS

10

i'-3

2

2

10 15 20 2S 30 DEPTH IN TISSUE (CH.)


in Tissue for lO00-MeV Normally Incident Positively Charged Pions.

0

50

0 PRIMARYONIZATION A SECONDY PROTONS

+ HEAVYNJCLEI X CHARGEO PIONS

SPROTONS FROM PIONSNEUTRAL + ELECIRONS. PHOTONSPOSIIROJS. S tUONS

2

2-CF

t I ° IF1 x x X 1L4

1 05.0 tO eI 5

OEPTH IN,TISSUE (CH.)

Fig. A-20. Dose Equivalent from the Various Kinds of Particles vs Depth in Tissue for 1000-MeV Normally Incident Positively Charged Pions.

0

51

FOOTNOTES

a.

b.

c.

d.

This cross-section tape, together with references to all of the data

used, is available on request from the Radiation Shielding Information

Center of the Oak Ridge National Laboratory.

Experimental data for the absorbed dose from 84-MeV incident negatively

and positively charged pions are available, 2 4 but because the experi

mental geometry was not that of a very broad beam incident on a semi

infinite slab of tissue, a meaningful comparison between these data

and the results presented here could not be obtained.

Results similar to those shown in Figs. 1 to 8 for all of the incident

pion energies considered in this paper are given in the Appendix.

References to the experimental data used for these cross sections, as

well as graphs of the cross sections used in the calculations, may be

found in ref. 12.

52

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55

Internal Distribution

1-B. L. S. Abbott 41. D. Sundberg 4. F. S. Alsmiller 42. D. K. Trubey

5-24. R. G. Alsmiller, Jr. 43. J. W. Wachter 25-29. T. W. Armstrong 44. H. A. Wright

30. H. W. Bertini 45. W. Zobel 31. B. L. Bishop 46. E. R. Cohen (consultant) 32. C. E. Clifford 47. H. Feshbach (consultant) 33. T. A. Gabriel 48. H. Goldstein (consultant)

34. M. P. Guthrie 49. C. R. Mehl (consultant)

35. W. E. Kinney 50-51. Central Research Library

36. T. A. Love 52. ORNL Y-12 Technical Library, 37. F. C. Maienschein Document Reference Section

38. R. W. Peelle 53-54. Laboratory Records Department

39. R. W. Roussin 55. Laboratory Records ORNL RC 40. R. T. Santoro 56. ORNL Patent Office

External Distribution

57. P. B. Hemmig, Division of Reactor Development & Technology, U. S. Atomic Energy Commission, Washington, D. C.

58. W. H. Hannum, Division of Reactor Development & Technology, U. S. Atomic Energy Commission, Washington, D. C.

59. Kermit Laughon, AEC Site Representative. 60. W. A. Coleman, Science Applications, Inc., P. 0. Box 2351,

La Jolla, California, 92037. 61-185. Given NASA Space and AEC High-Energy Accelerator Shielding

Distribution* 186-200. Division of Technical Information (DTIE).

201. Laboratory and University Division (ORO).

*This distribution list is available upon request.

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