Basdevant J.-L., Rich J., Spiro M. Fundamentals in Nuclear Physics: From Nuclear Structure to Cosmology

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272 5. Radioactivity and all that

Table 5.8. Typical annual eﬀective doses [57].

source dose

(mSv)

cosmic radiation

sea level 0.26

2000m 0.40

air travel (per 1600 km) 0.01

ground γ−rays 0.46

air (radon) 2.0

Weapons test fallout 0.01

Dwelling (stone/brick/concrete) γ−rays 0.07

Food and drink 0.3

Television 0.01

medical x-rays 0.40

total 3.6

Table 5.9. The whole-body eﬀective dose (radiotoxicity) due to selected radionu-

clides if taken internally [59]. Note the similar doses of the three ﬁssion products

Sr,

131

I and

137

Cs in spite of their very diﬀerent lifetimes, indicating that their

values of τ

eﬀ

are similar, due to short biological retention times.

Isotope t

1/2

E dose principal organs

(MeV) (µSv kBq

−1

)aﬀected

Sr 28.79 yr 1.3(β

−

) 30 (28) bone marrow, lungs

131

I8.02 day 0.5(β

−

) 11 ( 22) thyroid

137

Cs 30.07 yr 0.8(β

−

, γ) 6.7 (13) whole body

The eﬀective mass of the organism, m

eﬀ

, is the body mass if one calculates

the full-body dose or the mass of the organ in which the radioactive material

is attached if one wishes to calculate the dose received by that organ.

The radiotoxicity is mostly discussed in the context of nuclear accidents

and nuclear-waste storage. The evaluation of the expected dose from with a

given nuclide must also take into account the relative risk that the element can

be introduced into the food chain. One can also protect oneself from certain

nuclides by saturating the body with non-radioactive isotopes. This is how

one protects the thyroid from radioactive iodine after a nuclear incident.

The medical risks associated with radiation can be divided into short-term

and long-term risks. The lethal dose deﬁned as a 50 % risk of death within

30 days is 3 Sv if it is absorbed in a short time over the whole body. The

spinal chord is the most critically aﬀected. The long-term risks of cancer are

5.5 Applications of radiation 273

estimated to be about 0.02 Sv

−1

meaning that 2% of people exposed to 1 Sv

will develop a cancer due to this exposure before dying of unrelated causes.

This very broad estimate can be reﬁned to take into account the source of

radiation and the parts of the body that are exposed or contaminated. Note

however that in the approximation that cancer rates are proportional to the

dose and independent of the organ exposed, the total cancer rate does not

depend on these considerations. It should also be mentioned that there is an

active and unresolved debate about whether or not these estimates apply to

very low levels of radiation.

The recommendation for workers or medical patients exposed to radioac-

tivity in a regular manner is that the equivalent dose absorbed by someone

should be less than 20 mSv per year averaged over a period of 5 years, with a

maximum of 50 mSv in a single year. For the public, the absorbed dose must

be smaller than 5 mSv per year in addition to the natural dose and possible

medical doses.

5.5 Applications of radioactivity

5.5.1 Medical applications

The disrupting eﬀect on cells of ionizing radiation can be used to human

advantage by killing unwanted, e.g. cancerous cells. The use of radiation from

external radioactive sources or accelerated particle beams in cancer therapy

has a long history.

It is interesting to examine the cases of protons or heavy ions. Figure

5.15 shows the energy deposition in the medium in terms of the penetration

distance. We see that practically all the energy is deposited in a very localized

region near the stopping point. This comes from the 1/β

factor in equation

(5.30). Also shown in the ﬁgure is a comparison between the eﬀect of ion

beams and of photons. One can see the great advantage, from the medical

point of view, of heavy ion beams which attack and destroy tumors in a very

accurate and localized manner, as opposed to γ-rays which produce damage

all around the point of interest.

It is also useful to sometimes inject, intravenously or orally, radioactive

substances into the body in a chemical form that accumulates preferentially

in particular organs or cancerous tissue. The subsequent decays can then

irradiate the tumor or betray its position by emitting externally detectable

γ-rays. Pure β

−

emitters are preferred for tumor irradiation since all energy is

deposited within a few millimeters of the decay. Positron emitters (see below)

are preferred for position measurements.

Much progress has been made in the production of radioactive tracers

that give a physical manifestation of certain biological functions in human

bodies. One can make tracers with given chemical or biological properties, so

that they become ﬁxed in deﬁnite organs or biological functions. For example,

274 5. Radioactivity and all that

penetration distance (mm water)

dose (Gray)

cell survival fraction

0.1

0.2

0.5

1.0

150

100

15010050

Fig. 5.15. Energy loss of ions (left) and survival rate of cells (right) as a function

of the penetration depth. Because of the v

−2

factor in the Bethe–Bloch formula

(5.30), most of the energy is deposited near the stopping point. The dashed curve

corresponds to the same quantities for photons. We can see the considerable medical

advantage to use heavy ion beams.

glucose accumulates in tumors that have a high metabolic rate. Iron is used

to study the various phases of hemoglobin, Iodine is used for the thyroid

gland, rare gases (xenon and krypton) in pneumology; phosphorus for the

metabolism, etc.

For position measurements, of special interest are β

-emitters which yield

pairs of 511 keV photons when the positrons annihilate. The emission of two

particles allows one to more easily constrain the origin of the emission. The

principle of this “positron emission tomography” (PET) is illustrated in Fig.

5.16. A commonly used positron emitter is

F that is produced and decays

via

O → n

F .

F →

1/2

= 109.8m . (5.44)

Protons of energy ∼ 15 MeV are used and the 109.8 m half-life of

F al-

lows one to chemically separate and prepare a ﬂuorine containing compound.

For instance,

F-containing glucose can be prepared and then ingested suf-

ﬁciently rapidly for it to accumulate in high-metabolic tumors.

5.5.2 Nuclear dating

One of the most intellectually interesting applications of radioactivity has

been to provide accurate estimates of ancient objects, ranging from archae-

ological artifacts to stars. Important examples are the use of

C to date

archaeological organic material and

Rb to give an accurate age of the solar

system.

5.5 Applications of radiation 275

annihilation

Fig. 5.16. The principle of positron-emission tomography. A β

-emitter is injected

into a body in a chemical form such that it accumulates in the organ or tissue

that one wishes to study. Positrons from β

-decay stop in the material and then

annihilate, e

−

→ γγ. The detection of the two “back-to-back” photons constrains

the position of the decay to lie along the line connecting the two detector elements.

Accumulation of many events allows one to reconstruct the geometry of the decay

region.

To understand the principle of nuclear dating, we consider a closed system

containing initially N

nuclei A and N

nuclei B.Byclosed,wemeanthat

there are no exchanges of A and B nuclei with the exterior. If A decays to

B, then their numbers at some time t are

(t)=N

−t/τ

(5.45)

(t)=N

(1 − e

−t/τ

)+N

= N

(t)e

t/τ

(1 − e

−t/τ

)+N

, (5.46)

where τ is the (known) mean lifetime of A.If,attimet, N

and/or N

are

measured and if N

and/or N

are known, we may be able to deduce the

age t by solving one or both of the equations. We note the following cases:

1. N

is measured. We must then know N

to deduce t from (5.45).

2. N

is measured. We must know both N

and N

to deduce t from

(5.46).

3. N

and N

are measured. We need only N

or N

Generally neither N

nor N

are known but are rather deduced from

the measured amount of another species A



or B



for which the ratio N



or N



is known. Usually, A



) is another isotope of A (B). In many

applications, A



and B



arestablesothatN



and N



are time-independent.

In this case we write (5.45) and (5.46) as

276 5. Radioactivity and all that

(t)



−t/τ

(5.47)

(t)



(1 − e

−t/τ



(t)



t/τ

(1 − e

−t/τ



, (5.48)

C dating uses (5.47) with A =

CandA



= natural carbon (

Cand

C). Radioactive

C is produced continuously in the atmosphere, mostly

via the exothermic (n,p) reaction induced by cosmic-ray neutrons

N → p

C Q=0.63 MeV (5.49)

The produced

Cismixedintheatmosphereandthenﬁxedincarbon-

breathing plants. This leads to an isotopic abundance of

C in organic ma-

terial of

C+

=1.2 × 10

−12

, (5.50)

corresponding to a speciﬁc activity of 250 Bq kg

−1

. There are good reasons

to believe that the cosmic-ray ﬂux has been constant over many

C lifetimes

so that this ratio has remained constant in time, at least until atmospheric

nuclear weapon testing between 1955 and 1963. The neutron ﬂux during

these tests resulted in a doubling of the

C content of objects living at that

time. Since the end of the tests, the

C content has returned to within a

few percent of the pretest value, and may even have decreased due to the

increased burning of

C-free fossil fuels.

When a living organism dies, it stops ﬁxing carbon so the

C contained

in the organism decays with t

1/2

= 5730 yr. The amount of

C relative to

natural carbon measured in an object allows one to date the object through

(5.47). The amount of

C is generally determined by measuring the β-activity

of carbon chemically extracted from the sample, though recently mass spec-

trometer techniques have been become suﬃciently precise to directly measure

the small amounts of

Figure 5.17 shows some early data that was used to verify the technique.

The test uses objects whose age can be determined by independent means.

The activity of the samples decrease with the known age of

C. This indicates

that the production rate of

C has, indeed, been roughly constant over the

last few millenniums.

This method is usefully applied to objects with ages between, say, 500

and 50000 years. Older objects have very little of the original

C, making

measurements diﬃcult.

The ages of minerals can sometimes be dated using potassium-argon dat-

ing

− 40

K →

Ar ν

1/2

=1.28 × 10

yr . (5.51)

5.5 Applications of radiation 277

Percentage of modern radiocarbon acticity

100

Historical Age (years)

0 2000

4000 6000

Tree ring 1072 A.D.

Zoser 2700

Tree ring 575 A.D.

Tree ring 580 A.D.

Ptolemy 200

Redwood 979

52 B.C.

Tayinat 675

50 B.C.

Dead Sea Scrolls 100

100 B.C.

Sesostris 1800 B.C.

75 B.C.

Sneferu 2625

200 B.C.

Hemaka 2950

150 B.C.

Fig. 5.17. Calibration of the

C dating method with objects of known age [58].

In this method, (5.46) can be used directly assuming that the initial abun-

dance of the noble gas argon was very small in the mineral. The age is then

deduced from the measured

Kand

Ar abundances. It should be noted

that the measured age refers generally to the last solidiﬁcation of the mineral

since melting would generally lead to loss of the argon.

In a similar technique, uranium ores can be dated by measuring the quan-

tities of the descendants

206

Pb (from

238

U) or

207

Pb (from

235

U). In this case,

it is not reasonable to assume that the initial abundances of the lead isotopes

vanished. It is therefore necessary to use (5.48) with B



204

Pb which has

no radiogenic source.

The ages of meteorites have been most accurately measured using the

decay

Rb →

Sr e

−

. (5.52)

278 5. Radioactivity and all that

In this case, (5.48) is used with A =

Rb, B =

Sr and B



Sr:









t/τ

(1 − e

−t/τ





t=0

, (5.53)

While the chemical composition, i.e. the Rb/Sr ratio, depends on the precise

conditions of the formation of an individual meteorite, the isotopic ratio

Sr/

Sr should be uniform at the formation in a well-mixed pre-solar cloud.

In this case, (5.48) predicts that if all meteorites have the same age, a plot of

the measured value of

Sr/

Sr vs. the measured value of

Rb/

Sr should

be a straight line with the slope of exp(t/τ)(1 − exp(−t/τ) ∼ t/τ . Figure

5.18 [60] indicates that this is the case and that the meteorites have a common

age of ∼ 4.5 × 10

yr.

0.7

0.8

0.9

1.0

2.0 3.0

4.0

5.0

Sr /

Fig. 5.18. The abundance ratio

Sr/

Sr vs. the ratio

Rb/

Sr for a collection

of meteorites [60]. The fact that the points lie on a straight line indicate that the

meteorites have a common age of ∼ 4.53 × 10

yr. At the epoch of formation, the

meteorites had a common isotopic ratio

Sr/

Sr = 0.7003.

The mean time since the formation of terrestrial heavy elements can be

estimated from the abundances of two isotopes of uranium, observed to be

235

238

U=0.00714 ± 0.00008. One uses (5.47) with A =

235

UandA



238

U but modiﬁed to take into account the ﬁnite lifetime of

238

5.5 Applications of radiation 279



235

238





235

238



t=0

−t/τ

235

t/τ

238

, (5.54)

with t

1/2

(235) = 7.07 ×10

yr and t

1/2

(238) = 4.5 × 10

yr. The two isotopes

are believed to have been formed in nearly equal amounts (Sect. 8.3), so (5.54)

implies t ∼ 6 ×10

yr. The age of the Earth or of meteorites is noticeably less

(4.5 × 10

yr) so most the the uranium on Earth had spent a considerable

amount of time in interstellar space before condensing on the Earth.

The ages of very old stars have been measured by comparing their atmo-

spheric abundances of uranium and thorium. One uses









t=0

−t/τ

238

t/τ

232

(5.55)

where the half-life of

232

Th is 1.405 × 10

yr and for very old stars one can

assume that all the uranium is

238

U. The oldest stars [61] so far found have

a uranium–thorium ratio of about 0.2 implying ages of about 1.2 × 10

(assuming equal initial abundances). This is of the order of the estimated age

of the Universe, 1.3 × 10

yr, indicating that stars formed within the ﬁrst

∼ 10

yr after the big bang (Chap. 9).

Finally, while (5.47) and (5.48) are generally used to derive the ages of

samples using a known lifetime, they can also be used to measure the life-

time of a nuclide using a sample of known age. While this may seem like a

strange way to measure a nuclear lifetime, a comparison with the laboratory-

measured lifetime amounts to a comparison of the present-day lifetime with

the lifetime in the past. If the two lifetimes are consistent, this veriﬁes the

hypothesis that laws and constants governing the decays have not varied.

Very restrictive bounds on such variations have been found using the

decay

187

Re →

187

Os e

−

1/2

=4.35 ×10

yr (laboratory) .(5.56)

The age has also been measured [62] using meteorites whose age was de-

termined by U-Pb or Rb-Sr dating. The

187

Re half-life can then be de-

termined by using

186

Os as the standard in (5.48). The derived value is

1/2

=(4.16 ± 0.04) × 10

yr is in reasonable agreement with the labora-

tory measurement. This indicates that the

187

Re half-life has changed little

over the past 4 × 10

yr.

The particular interest of using

187

Re →

187

Os is that the tiny energy

release, Q

=2.64 keV, makes the decay rate extremely sensitive the the

fundamental constants. For example, the value of Q

is sensitive to the value

of the fundamental charge through its eﬀect on the Coulomb energy in the

Bethe–Weis¨acker formula (2.13), (0.7103Z

1/3

) MeV. The contribution of

this term to the binding energy of

187

Re is 698 MeV while that for

187

Os is

717 MeV for a diﬀerence of 19 MeV. A relative change in the square of the

fundamental charge of only 10

−4

would be suﬃcient to make

187

Os lighter

than

187

Re so that the former is stable rather than the latter. Smaller changes

280 5. Radioactivity and all that

totheelectricchargewouldchangethelifetimeof

187

Re through the Q

dependence of β-decay rates calculated in Chap. 4 (4.98). It is therefore simple

to transform the limit on the change in the

187

Re lifetime into a limit on the

time variation of the electric charge, or equivalently on the time variation

of the ﬁne-structure constant, proportional to the square of the fundamental

charge. Following Dyson [63] a limit |∆α/α| < 2 × 10

−6

for the variation of

α over the last

187

Re lifetime was recently derived [64].

5.5.3 Other uses of radioactivity

We mention here a few of the other uses of radiation and radioactivity.

• Sterilization of foodstuﬀs

This consists of exposing foodstuﬀs to ionizing radiations in order to de-

stroy insects or micro-organisms and delay the deterioration without al-

tering the edibility. Sources of

Co emitting ∼ 1 MeV photons are most

commonly used. This technique generates a loss of the germinal potential.

Vegetables are treated this way, such as potatoes, fruits, onions etc. The

treatment is simple and produces less alteration of the nutritious prop-

erties and taste, compared to classical treatments such as sterilization or

chemical treatments. This method has other advantages: it is eﬃcient, non-

toxic and has a low cost. It is believed to be “danger-free” and it is under

considerable development.

• Creation of genetically modiﬁed plants

The irradiation by γ rays of genes of certain plants (wheat, barley, rice,

sugar cane, cotton, ...) gives them new properties which can be selected to

give better resistance to diseases, to heat, to winter conditions, to unfavor-

able soils. It also allows one to control the ripening, be it sooner or later,

and to improve yields. Radioactive mutation techniques have been known

since the 1960’s. They have been used in Europe and in the former USSR

for the culture of wheat, in the United States for the culture of barley, of

beans and of grapefruits, in Pakistan for the culture of rice, in India for

cotton and cane sugar, etc. This can be viewed as a primitive form of the

more systematic genetic modiﬁcation now practiced by biologists.

• Sterilization of insects

The same method consists in exposing male insects born in a laboratory

to suﬃcient doses of radiation in order to sterilize them. They are then

released in large numbers in infected zones. Female insects who mate with

these insects have no descendants and the population of harmful insects

decreases progressively. This method has the big advantage that it does not

bring chemical pollution, unlike pesticides. It has been successfully used in

Japan against the melon ﬂy, in Mexico, in Peru, and in Egypt against the

fruit ﬂy, and in Africa against the tsetse ﬂy.

• Gammagraphy

X rays which are used in radiography of the body or materials of low den-

5.6 Bibliography 281

sity, are not penetrating enough to be used for dense or thick materials. In

that case, one can use γ rays. The principle is the same: the γ rays irradiate

a sample of material and the outgoing rays are recorded on a photographic

plate. this reveals possible defects coming from the manufacturing or wear-

ing eﬀects.

• Radioactive tracers

If a radio-element is introduced into a body, it is possible to follow its

trajectory through the body. By measuring the emitted radiation, tracers

allow for instance to follow the displacements of products in circuits of

chemical factories, the detection of leaks in dams or in buried pipes. This

technique is used in particular to monitor oil pipelines.

• Fire detectors

A radioactive source (

241

Am) ionizes the air permanently. The ionization is

modiﬁed if smoke particles are present. This modiﬁcation triggers a warn-

ing signal. Such detectors are sensitive to very small amounts of smoke.

They are widely used in stores, in factories and in oﬃces.

• Nuclear batteries

Radioactive sources such as

238

Pu,

Co and

Sr are used to construct

batteries of several hundred Watts. The heat produced by radioactivity is

converted into electricity. Such batteries are used in satellites and in distant

meteorological stations. They can function for several years without any

maintenance. For example, the Voyager spacecraft was powered by three

238

Pu generators. It was launched in 1977, reached Neptune in august 1989,

and is now beyond the solar system. Nuclear Batteries are also used in heart

pacemakers.

• Conservation of the artistic objects

The exposition of works of art and of archaeological documents to radia-

tions can destroy insects, microorganisms and mold that they contain and

ensures an excellent sterility. This technique has been used in particular to

treat the mummy of Ramses II.

The impregnation of wooden or stone objects by a polymer under gamma

irradiation is the principle of the “Nucleart ” process. It allows one to treat

and to recover pieces of buried water-logged wood.

5.6 Bibliography

1. James E. Turner, Atoms, Radiation, and Radiation protection, John Wi-

ley, New York, 1995.

2. J.E. Coggle, Biological eﬀects of radiation

, 1983.

3. Edward Pochin, Nuclear radiation : risks and beneﬁts

, Oxford Science

Publication, 1983.

4. R. E. Taylor, Radiocarbon Dating: An Archaeological Perspective

,Aca-

demic Press, Orlando, 1987.