Shani G. Radiation Dosimetry: Instrumentation and Methods

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420 Radiation Dosimetry: Instrumentation and Methods

Figure 9.23a shows the effect of varying the cross-

linker fraction on , the maximum R

achievable by a

saturation dose, at three different temperatures. It can be

seen that increases with cross-linking and that this

dependence increases dramatically above approximately

30%C. In addition, this effect is clearly enhanced by cool-

ing the gels during the NMR measurment.

Figure 9.23b illustrates the dependence of on

temperature for several different values of cross-linker

fraction. appears to be more sensitive to temperature

changes as the cross-linker fraction increases.

Figure 9.24 shows how the dose-response curve for a

50%C BANG gel changes with temperature. It is clear that

it is the radiation-induced build-up of the cross-linked

polyacrylamide in the gel that enhances the solvent R

2 ,

well as rendering it more sensitive to temperature changes.

The spatial uniformity of gel sensitivity to radiation

was found to depend strongly on the presence of oxygen,

which must be eliminated for the gel dosimeter to be of

use. The gel formula used by Oldham et al. [21] is shown

in Table 9.3.

The 3D gel-image data produced by the NMR scanner

is in the form of calculated T

relaxation times. This image

must be converted to absorbed dose to allow veriﬁcation

of radiotherapy dose distributions. Conversion is achieved

by means of a calibration curve, obtained by measuring

FIGURE 9.22 (a) Dependence of the initial dose-response sen-

sitivity on the cross-linker content for three different temperatures

at which

was measured. (b) Dependence of the dose sensitivity

on the measurement temperature for several different proportions

of the cross-linker. (From Reference [20]. With permission.)

max

FIGURE 9.23 (a) Dependence of the maximum R

measured at

a saturation dose on cross-linker fraction for three dif-

ferent temperatures. (b) Dependence of on temperature for

several different values of cross-linker fraction. (From Reference

[20]. With permission.)

max

()

max

Ch-09.fm Page 420 Friday, November 10, 2000 12:04 PM

Gel Dosimetry 421

the T

relaxivity in regions of the gel that have been irra-

diated to known doses.

The ﬁnal step in forming the calibration curve was to

determine the dose actually delivered in the regions of

interest for which the T

values were measured. This deter-

mination was performed by ﬁlm measurement in a simu-

lated geometry. The required quantity is D

, the absorbed

dose delivered by a 2  2-cm

, 6-MV radiation ﬁeld to

the measurement plane after it has been attenuated through

a 6-mm Perspex plate and a 2-cm layer of gel. D

was

calculated according to

(9.26)

where D

is the dose in the measurement plane; MU is

the number of monitor units delivered; D

is the dose per

MU measured by a piece of ﬁlm placed in a Perspex

sandwich at the effective radiological path length (d) to

the measurement plane (

d  2.38 cm is the Perspex-equiv-

alent radiological path length of 6 mm of Perspex and 2 cm

of gel); ISC is an inverse-square law correction to allow for

the fact that the measurement plane is 2 mm further from the

source than the ﬁlm; and BSC is a backscatter correction to

account for the reduced backscatter radiation from the nitro-

gen space compared with solid Perspex. The ISC term is

(102.38102.6)

 0.9957. The BSC term for a 2-  2-cm

ﬁeld, from Perspex that is 2 cm from the measurement

plane, is negligible and was ignored.

Figure 9.25a shows the relationship between the stan-

dard deviation (SD) in a 1-cm-diameter region placed cen-

trally in the irradiated region and the pixel size. It is seen

that for a 2-mm slice thickness, little improvement in noise

TABLE 9.3

Chemical Composition of BANG–gel

Component Formula Weight Fraction Amol

Gelatin C

0.05 402.22

Acrylamide CH

CHCONH

0.06 71.04

Bis (CH

CHCONH)

0.06 154.1

Water H

O 0.83 18

From Reference [21]. With permission.

FIGURE 9.24 Effect of temperature on the R

dose-response

curve of the 50%C BANG. (From Reference [20]. With permis-

sion.)

MU D

ISC BSC()

FIGURE 9.25 (a) The relationship between noise (i.e., stan-

dard deviation on the mean) in small regions (

1 cm

) in the

(or R



1/T

) gel image and the pixel size. (b) The rela-

tionship between noise (i.e., standard deviation on the mean)

in the

(or R

 1/T

) gel image and R

. High R

corresponds

to high dose and high polymerization. (From Reference [21].

With permission.)

Ch-09.fm Page 421 Friday, November 10, 2000 12:04 PM

422 Radiation Dosimetry: Instrumentation and Methods

is gained by increasing the pixel size above 0.8 

0.8 mm

. The latter therefore represents a good tradeoff

between noise and spatial resolution. Figure 9.25b shows

the relationship between noise (SD on the mean) and R

The MR-imaging sequence parameters were chosen to

minimize the errors for ﬁtting the exponential decay of

short T

(i.e., high-dose regions 6–8 Gy, corresponding

to an R

of 5–6.0).

REFERENCES

1. Gore, J. C. et al., Phys. Med. Biol., 29, 1189, 1984.

Schreiner, L. J., in Proc. 1st International Workshop

on Radiation Therapy Gel Dosimetry,

1999, 1.

Appleby, A., in Proc. 1st International Workshop on

Radiation Therapy Gel Dosimetry,

1999, 9.

Audet, C., in Proc. 1st International Workshop on Radi-

ation Therapy Gel Dosimetry,

1999, 31.

Back, S. A. J. and Olsson, L. E., in Proc. 1st Interna-

tional Workshop on Radiation Therapy Gel Dosimetry,

1999, 47.

Maryanski, M. J., in Proc. 1st International Workshop

on Radiation Therapy Gel Dosimetry,

1999, 63.

Maryanski, M. J. et al., Phys. Med. Biol., 39, 1437,

1994.

Gore, J. C. et al., Phys. Med. Biol., 41, 2695, 1996.

Maryanski, M. J. et al., Med. Phys., 23, 699, 1996.

10.

Gambarini, G. et al., Phys. Med. Biol., 39, 703,

1994.

11.

Balcom, B. J. et al., Phys. Med. Biol., 40, 1665, 1995.

12.

Luciani, A. M. et al., Phys. Med. Biol., 41, 509, 1996.

13.

Olsson, L. E. et al., Phys. Med. Biol., 37, 2243, 1992.

14.

Schulz, R. J. et al., Phys. Med. Biol., 35, 1611, 1990.

15.

Gambarini, G. et al., Nucl. Inst. Meth., A422, 643, 1999.

16.

Gambarini, G. et al., Rad. Prot. Dos., 70, 571, 1997.

17.

Kelly, R. G. et al., Med. Phys., 25, 1741, 1998.

18.

Bero, M. A. et al., Nucl. Inst. Meth., A422, 617, 1999.

19.

Maryanski, M. J. et al., Phys. Med. Biol., 41, 2705,

1996.

20.

Maryanski, M. J. et al., Phys. Med. Biol., 42, 303,

1997.

21.

Oldham, M. et al., Phys. Med. Biol., 43, 1113, 1998.

22.

Parasad, P. V., Rad. Res., 128, 1, 1991.

Ch-09.fm Page 422 Friday, November 10, 2000 12:04 PM

423

Neutron Dosimetry

CONTENTS

I. Introduction ............................................................................................................................................................423

II. Kerma Calculation and Measurement....................................................................................................................425

III. Gas-Filled Neutron Dosimeters .............................................................................................................................436

IV. TLD Neutron Dosimetry........................................................................................................................................446

V. Superheated Drop Neutron Dosimeter...................................................................................................................451

VI. Solid-State Neutron Dosimeter ..............................................................................................................................460

VII. Bonner Sphere and Other Portable Neutron Monitors..........................................................................................466

References .......................................................................................................................................................................476

I. INTRODUCTION

Neutrons are non-ionizing particles and are thus identiﬁed

by detection of ionizing particles emitted in neutron interac-

tion. The most common reactions are (



), (



and proton recoil.The dosimeters can be gas-ﬁlled, scintilla-

tors, TLD, solid-state, track detectors, photographic ﬁlm, and

other types. Gas-ﬁlled neutron dosimeters are generally tis-

sue-equivalent ionization chambers. The properties required

for a neutron dosimeter are high efﬁciency for neutron detec-

tion, constant response per unit kerma in tissue as a function

of neutron energy, and the possibility to discriminate against



-radiation. It is important that the dose or the energy trans-

ferred to the dosimeter is similar to that transferred to the

human body irradiated, taking into consideration the body

composition, such as bone, tissue, etc.

Neutron dosimetry is done for medical purposes as well

as in nuclear research laboratories, reactor centers, nuclear

power stations, and industry. For routine radiation surveys,

the “rem-counters” have practically solved the problem of

measuring dose-equivalent rates without much information

on neutron spectra. Routine personnel neutron dosimetry is

done by TLD badges and pocket ionization chambers. The

requirements for accident dosimetry are different from those

for routine survey and dosimetry. Superheated drop detectors

are useful for environment dosimetry.

Most neutron dosimeters that exist for direct reading or

quick, easy evaluation are of the military or civil defense

type, such as tissue-equivalent condenser chambers, neutron-

sensitive diodes, or radiation elements, suitable for foolproof

operation. Accident dosimetry for neutrons is well-estab-

lished. The important systems are reliable critical alarms and

similar dosimetry systems that are partly worn by persons

and partly set up on ﬁxed positions in the controlled areas.

Fission-track dosimeters and activation-threshold detectors,

together with body counting for

Na by a simple body

counter, permit a reasonable quick evaluation of the severity

of exposures after an accident.

Standardization of neutron dosimetry procedures has

been established by drafting protocols for neutron dosim-

etry for radio therapy in Europe and the U.S. The use of

calibrated tissue-equivalent (TE) ionization chambers with

TE gas ﬁlling is recommended as the practical method for

obtaining the tissue kerma in air and the absorbed dose in

a TE phantom. The TE chamber should have a calibration

factor for photons applied to it.

Correction factors convert the reading of the chamber to

the charge produced in an ideal chamber at a reference tem-

perature and pressure. Also, correction factors account for

the ﬁnite size of the TE chamber, its build-up cap, and its

stem when measurements are made in air. For the conversion

of measured charge to absorbed dose, several parameters are

necessary, including the average energy required to create an

ion pair in the gas, the gas-to-wall absorbed dose conversion

factor, the neutron kerma ratio of reference tissue to that in

the wall material of the ionization chamber, and the displace-

ment correction factor.

The types of personnel neutron dosimeters commonly

used for radiation-protection purposes are neutron ﬁlm type

A (NTA ﬁlm), thermoluminescent albedo dosimeters

(TLD albedo), superheated drop detectors, and ﬁssion

track detectors. Deﬁcient energy response and sensitivity,

fading, use of radioactive material, and other limitations

prevent any of these dosimeters from being satisfactory

for universal application in a wide variety of radiation

environments.

A primary requirement for the personnel neutron

dosimetry system is that it be able to meet current regulatory

Ch-10.fm Page 423 Friday, November 10, 2000 12:04 PM

424

Radiation Dosimetry: Instrumentation and Methods

requirements. Neutron dosimeters should be worn if the

neutron whole-body dose equivalent exceeds 10% of the



- plus X-ray dose equivalent. The dosimeter is consid-

ered satisfactory for operation in mixed radiation ﬁelds

if it can measure 1 rem of fast neutrons in the presence

of 3 rem of



-rays with energy above 500 keV. The

dosimeter response must simulate the dose-equivalent

conversion factor, which varies by a factor of 40 over

that range. Radiation weighting factor is given below

for various kinds of radiation and for neutrons of various

energies.

Calculation of the radiation weighting factor for neu-

trons requires a continuous function; the following

approximation can be used, where

is the neutron energy

in MeV:

(10.1)

The rationale for fast neutron therapy (high LET radi-

ation) is based on radiobiological arguments: [1]

a. a reduction in the oxygen enhancement ratio

(OER) with high LET radiations; i.e., a selec-

tive efﬁciency against hypoxic cancer cells;

b. a greater selective efﬁciency against cells in the

most radio-resistant phases of the mitotic

cycle;

c. a smaller role of the sub-lethal lesions; i.e., less

importance of the dose per fraction.

These factors can bring an advantage or a disadvantage,

depending on the characteristics of the cancer cell popu-

lation and of the normal tissues at risk. This raises the

problem of patient selection. According to NCI, fast neu-

tron therapy should be the treatment of choice for

advanced-stage salivary gland tumors, and surgery should

be limited to cases where there is a high likelihood of

achieving a negative surgical margin and where the risk

of facial nerve damage is high.

A standard A-150 tissue-equivalent or graphite thim-

ble chamber having a standard

Co calibration factor is

the recommended reference dosimeter for clinical proton

dosimetry. The mean neutron energy or related parame-

ters such as the half-value thickness (HVT) have also

been used (Figure 10.1). The development of the micro-

dosimetric programs has shown that this approach is

indeed an oversimpliﬁcation and that several types of

secondary charged particles must be taken into account

(Figure 10.2).

In a given neutron beam, the RBE does not vary as a

function of depth (Figure 10.2). For proton beams, the

observed RBEs are lower, ranging from about 1.0 to 1.2.

This range is clinically signiﬁcant but only slightly larger

than the experiment uncertainties on RBE determinations

(Figure 10.3). The proton energy decreases with depth

and, thus, there is possible increase in RBE.

Type and energy range of radiation Radiation weighting

factor

Photons, all energies 1

Electrons and muons, all energies * 1

Neutrons, energy



10 keV 5

10 keV to 100 keV 10



100 keV to 2 MeV 20



2 MeV to 20 MeV 10



20 MeV 5

Protons, other than recoil protons, energy



2 MeV 5

Alpha particles, ﬁssion fragments, heavy nuclei 20

* Excluding Auger electrons emitted from nuclei to DNA, for which

special microdosimetric considerations apply.

517e

2E()ln()

---





FIGURE 10.1

Variation of RBE on different neutron beams as a function of energy. (From Reference [1]. With permission.)

Ch-10.fm Page 424 Friday, November 10, 2000 12:04 PM

Neutron Dosimetry

425

II. KERMA CALCULATION AND

MEASUREMENT

Kerma is deﬁned as the average kinetic energy released

in matter (per unit mass) and is the sum of all energy

transferred to light-charged particles and residual nuclei

in a reaction. The neutron kerma factor is the kerma pro-

duced per unit neutron ﬂuence. The absorbed dose is the

energy deposited per unit mass.

Neutron dose is obtained by calculating the kerma.

The kerma factor for neutrons of energy , for a given

material is deﬁned as the ratio of the neutron kerma

and

the neutron ﬂuence. The kerma factor is usually calculated

from the average energy transferred to kinetic energy of

FIGURE 10.2

Comparison of microdosimetric spectra measured at different depths in a phantom on the beam axis of the

(65)



Be neutron therapy beam of Louvain-la-Neuve (the highest energy used in neutron therapy). The curves represent the distributions

of individual energy deposition events in a simulated volume of tissue 2



m in diameter. The parameter

(lineal energy) represents

the energy deposited by a single charged particle traversing the sphere, divided by the mean cord length. Four peaks can be identiﬁed

in the

(65)



Be neutron spectra: the ﬁrst is at 8 keV





and corresponds to high-energy protons, the second is at 100 keV





and corresponds to low-energy protons, the third is at 300 keV





and is due to a-particles, and the last is at 700 keV





and is due to recoil nuclei. The (rather ﬂat) peak corresponding to the gamma component of the beam is at 0.3 keV





The differences between the spectra measured at differents depths are relatively small and no signiﬁcant RBE variation has been

detected. (From Reference [1]. With permission.)

FIGURE 10.3.

Variation of RBE with depth in the modulated 200-MeV proton beam produced at the National Accelerator Centre

(NAC), Faure (left ordinate, closed circles). The width of the spread-out Bragg peak is 7 cm (from 13 to 20 cm in depth). The error

bars indicate the 95% conﬁdence intervals. The open square corresponds to the RBE for the unmodulated beam. The depth-dose

curve in the modulated beam is superimposed for comparison (right ordinate, small open circles). The hatched areas indicate the

different positions where the mice were irradiated. The width of the shaded areas corresponds to the size of the mice abdomens.

(From reference [1]. With permission.)

Ch-10.fm Page 425 Friday, November 10, 2000 12:04 PM

426

Radiation Dosimetry: Instrumentation and Methods

charged particles in the various types of interactions and

the corresponding cross sections. For neutron energy

less than 20 MeV, the data can be taken from the

ENDF/B-V data ﬁle. For higher energies, the data is from

relied-on calculations only. Above 15 MeV the number of

nuclear reactions increases and substantially contributes

to the kerma, with strong uncertainty in the cross section.

Erroneous cross sections due to the use of inadequate

calculation models, in particular for light elements, leads

to large discrepancies in kerma factor calculations. More

experimental data are needed at energies above 20 MeV.

The kerma factor can be obtained by direct

dose measurement with ionization chamber or propor-

tional counter. Knowing the dose, the kerma

, and

the ﬂuence provides the necessary data. A-150 tissue-

equivalent plastic and graphite chambers are used for

this purpose.

The energy transferred (kerma per neutron per cm

)

for an incident neutron of energy

in the laboratory is

deﬁned by

(10.2)

where

identiﬁes the element,

identiﬁes the type of

nuclear reaction, is the number of nuclei of the

element per gram, and is the average amount of

energy transferred to kinetic energy of charged particles

in a collision whose cross section is . For elastic

scattering, the kinetic energy (laboratory system) of a

recoiling nucleus of mass

relative to that of the neutron

(10.3)

where is the angle of scattering of the neutron in the

center of mass system.

For inelastic scattering the energy transferred to a

recoil nucleus left in an excited state with energy above

the ground is

(10.4)

The kerma can be calculated by

(10.5)

where

is the secondary particle type produced by the

neutron interaction,

is the particle energy, and is

the intensity of the particle spectrum (particles per gram

per neutron per cm

is given by

(10.6)

For elastic scattering, if the neutron ﬂuence intensity is

and the atomic density in the material is

(atoms/g), the differential spectrum intensity of the recoil-

ing particle of mass

and energy is

(10.7)

The neutron mass is assumed to be unity, (cos )

is a Legendre polynomial of degree

, and is its coef-

ﬁcient. In the case of elastic scattering by hydrogen,

(10.8)

where

and

The total kerma induced by neutrons in the wall mate-

rial of the PC is derived from

(10.9)

where is the correction factor for the attenuation and

scattering caused by the wall, is the gas-to-wall

absorbed dose conversion factor, and is the average

-value (average energy required to produce an ion pair

in the gas) for neutron-induced secondaries. is the

value for the radiation used for calibration,

is the cali-

bration factor which relates pulse height

to energy

imparted (the energy deposited in the cavity),

is the

mass of the gas, and

(

) is the number of neutron-induced

events measured as a function of pulse height

KE() N





E()



E()







E()



E()



iel,



E,()

2AE

A 1()

----------------------



cos()



E



i inel,



E,()

2AE

A 1()

----------------------

E

A 1

--------------



2AE

A 1()

---------------------



cos

A 1()E

--------------------------





E()E Ed







E()

E()E Ed()



E()EWE()

[]













()

() N



()

1 A()

4AE

----------------------



()

2l 1()





()P



cos() particles/g.MeV



()

() N



E()

1 A()

4AE

---------------------



() ME

()

() 1 1/2



1/2bcos



cos() 1 b/6()

b 2 E

90()



mg,

()

W

()Cm()hn h() hd

min

max





mg,

()

Ch-10.fm Page 426 Friday, November 10, 2000 12:04 PM

Neutron Dosimetry 427

Kerma factors for carbon and A-150 tissue-equivalent

plastic were determined by Schuhmacher et al. [2] in two

nearly monoenergetic neutron beams. Kerma was mea-

sured with low-pressure proportional counters (PC) with

walls made of graphite and A-150 plastic. The neutron

ﬂuence was measured with a proton recoil telescope. The

corrections for the kerma contributions from low-energy

neutrons in the beams were determined by time-of-ﬂight

measurements with an NE213 scintillation detector and

with the PCs. For neutron energy of (26.3  2.9)MeV and

(37.8  2.5)MeV, the kerma factors for carbon were (35.5

 3.0)pGy cm

and (42.6  3.9)pGy cm

, respectively,

and for A-150 they were (75.6  5.4) pGy cm

and (79.0

 5.6) pGy cm

. At these energies the kerma factor ratio

for ICRU muscle tissue to A-150, calculated on the basis

of the new kerma factors, is 0.93.

A proton recoil telescope (PRT) was used for the

ﬂuence measurements; it was based on the detection of

recoil protons produced by elastic scattering in a hydro-

gen-containing radiator foil. This type of instrument

enables the neutron ﬂuence to be determined with uncer-

tainties of only 2.5% to 3% in the neutron energy range

from about 1 to 15 MeV and is therefore used as a primary

ﬂuence standard at various laboratories. The PRT

described by Schuhmacher et al. consisted of a polyeth-

ylene (PE) radiator foil (areal density 144.7 mg cm

2

)

mounted on a 1.0-mm thick Ta backing, two proportional

counters, a solid-angle deﬁning aperture, and two solid

state detectors, and (Figure 10.4). The proportional

counters were ﬁlled with isobutane at a pressure of 50

kPa. A 1.0-mm-thick Si surface barrier detector was cho-

sen for

S at 27 MeV and a 2.5-mm-thick one at 39 MeV,

while in both cases consisted of a 5.0-mm -thick Si(Li)

detector operated at room temperature. For the 39-MeV

neutron ﬁeld, a 0.5-mm-thick aluminum absorber was

inserted into the PRT between the aperture and S

, so that

protons of the maximum energy were stopped in the sili-

con detector . The signals from the four detectors were

analyzed with a multi-parameter data acquisition system

which allowed the protons to be discriminated from other

types of charged particles emitted from the radiator foil.

The PRT was used to determine the ﬂuence of neu-

trons of the nominal energy, i.e., within the main peak.

The probability of energy depositions by recoil protons in

the various detectors of the PRT for a given spectral neu-

tron ﬂuence at the position of the radiator was calculated

with a Monte Carlo program. It simulates the production

of recoil protons and their transport through the telescope,

including energy loss straggling and angle straggling. The

cross sections for

n-p scattering were based on experimen-

tal results published by Fink et al. [3] These data, which

were determined with total uncertainties of less than 2%,

are about 5% higher at 27 MeV and 10% higher at 39

MeV than those from a phase shift analysis for the scat-

tering angles which were observed with the PRT. The

phase shift was employed for interpolating the measured

data in energy and angle.

The tissue absorbed-dose determination depends upon

knowledge of the relative rate of charged-particle energy

production per unit mass for the tissue and tissue substitute

FIGURE 10.4 Schematic drawing of the PRT with radiator (R), “pillbox”-proportional counters ( and ), solid-angle deﬁning

aperture (

A), and semiconductor detectors ( and ). The PRT is irradiated from the right. The radiator assembly consists (from

right to left) of a graphite disc, a Ta backing, and a PE disc. The assembly was turned by 180 degrees for the background measurement.

(From Reference [2]. With permission.)

Ch-10.fm Page 427 Friday, November 10, 2000 12:04 PM

428 Radiation Dosimetry: Instrumentation and Methods

material, i.e., the kerma or kerma factor ratio. As the kerma

ratio is a function of the neutron energy, information about

the neutron energy spectrum is needed. Hence, neutron

dose determinations using tissue-substitute materials

require accurate kerma factor values for all constituent

materials for both the tissue and tissue substitute over the

entire neutron energy range. [4] Recommended hydrogen

kerma factors for neutron energies from 10 to 70 MeV

calculated from cross sections obtained from the “VL 40”

phase shift analysis are given in Table 10.1. Figure 10.5

shows the information known for both measured calculated

neutron kerma factors for carbon as a function of incident

neutron energy. Figure 10.6 shows a summary of measured

and calculated neutron kerma factors for oxygen as a

function of incident neutron energy. The experimental

database for oxygen is limited.

Modern neutron radiotherapy employs energies extend-

ing to 70 MeV, while industrial applications such as trans-

mutation and tritium breeding may generate neutrons

exceeding energies of 100 MeV. Secondary neutrons pro-

duced by advanced proton therapy facilities can have ener-

gies as high as 250 MeV. Evaluated nuclear data were

presented for C, N, and O by Chadwick et al. [5].

An important consequence of these microscopic

cross-section calculations is the determination of integral

radiation dosimetry quantities—kerma factors. Figure

10.7 shows total and ejected particle partial kerma factors

for C and O. Such detailed information is a direct result

of the inclusive modeling technique. Note that the proton

kerma increases rapidly with energy and exceeds that for

alpha particles at 50 MeV(C) and 42 MeV(O). Another

striking consequence is the contribution of deuterons,

which exceeds that for alpha particles at higher neutron

energies, reaching 25%(C) and 20%(O) of the total kerma

at 100 MeV. This rapid increase in proton and deuteron

kerma at higher energies due to pre-equilibrium mecha-

nisms was not recognized in the earlier extension to 32 MeV

of ENDF/B-VI.

Kerma factors of carbon and A-150 tissue-equivalent

plastic have been measured by Schrewe et al. [6] in nearly

monoenergetic neutron beams at energies between 45 and

66 MeV. The kerma was measured with low-pressure pro-

portional counters (PC), with the walls consisting either

of graphite or A-150 plastic material, and the neutron

beam ﬂuence was measured with a proton recoil tele-

scope. The kerma factor corrections were determined from

TABLE 10.1

Recommended Neutron Kerma Factor

for Hydrogen.

(MeV) K

(fGy.m

)

10.00 45.69

12.38 46.59

15.62 46.93

20.46 46.50

31.42 44.21

46.19 41.11

59.79 38.92

70.00 37.80

The table is designed for linear-linear interpolation. The uncertainty

(1 standard deviation) is l% at all energies.

From Reference [4]. With permission.

FIGURE 10.5 Measured and calculated neutron kerma factors for carbon as a function of incident neutron energy from 0 to 70 MeV.

(From Reference [4]. With permission.)

Ch-10.fm Page 428 Friday, November 10, 2000 12:04 PM

Neutron Dosimetry 429

time-of-ﬂight measurements with NE213 scintillation detec-

tors and PCs. At neutron energies of (44.5  2.6) MeV and

(66.0  3.0) MeV, the kerma factors were (40.9  4.1) pGy

and (49.5  8.7) pGy cm

for carbon and (80.4  6.3)

pGy cm

and (80.1  8.2) pGy cm

for A-150 plastic.

The kerma K produced by monoenergetic neutrons of

energy E and ﬂuence  may be expressed as K(E) 

, where is the kerma factor. Kerma factors may

be calculated from the cross sections as the sum

of the interactions of type j which produce charged parti-

cles of an average energy , multiplied by the number

of target atoms per unit mass n:

(10.10)

Above 20 MeV, however, calculations are much more

complex, since the number of reaction channels rises dras-

tically with increasing neutron energy, there is a lack of

precise cross-section data and the reaction kinematics are

scarcely known, particularly for the multi-particle breakup

reactions. Since kerma and absorbed dose are numerically

almost equal if the charged secondary particle achieves

equilibrium, the kerma was determined by measuring the

absorbed dose with a cavity chamber.

The total kerma obtained from the PC measure-

ment can be written as the sum of three portions: the

desired kerma of the nominal energy , which refers to

the neutron energy range to , and two background

contributions and . and are made accessible

by the two TOF measurements; is produced by neu-

trons of energy , and by .

The correction factor , deﬁned as the ratio ,

can be expressed as:

(10.11)

where is directly obtained from the PC-TOP mea-

surements and is calculated from the spectral neu-

tron ﬂuences and kerma factors extrapolated from recent

measurements and theoretical predictions. Although the

kerma fraction of low-energy neutrons, , was

quite substantial, was determined with a relatively low

uncertainty (see Table 10.2).

The ICRU has introduced the quantity Personal Dose

Equivalent, (see Chapter 1), as an estimator for the

effective dose, E, as the primary limiting quantity for all

conditions of penetrating radiation, i.e., radiation-type energy

and angle of incidence. It is deﬁned as the dose equivalent

in 10 mm depth of an individual. The deﬁnition of Personal

Dose Equivalent, , does not lead to a unique value

because it depends on both the individual and the site chosen

in which to obtain . [7] For the purposes of devel-

opment, type testing, and calibration of individual dosime-

ters, the quantity was extended by the ISO to the TE slab

phantom. In this case has a unique value for a given

radiation ﬁeld. It serves as some kind of “estimator for the

estimator” and shall be sufﬁciently conservative compared

with the effective dose, at least for an irradiation incidence

which is restricted to the frontal half-space. Monte Carlo

calculations were performed by Leuthold et al. [7] using the

MCNP code version 4A. This code is capable of transport-

ing neutrons and photons as well as electrons.

FIGURE 10.6 Measured and calculated neutron kerma factors for oxygen as a function of incident neutron energy from 0 to 70 MeV.

(From Reference [4]. With permission.)

k

E() k



E()

K nE

E()



E()





tot

max

0 E

 K



K

tot

K

tot

1 K

K

tot

()1 K

K

()

K

tot

K

1 k

()

10()

Ch-10.fm Page 429 Friday, November 10, 2000 12:04 PM