Tsoulfanidis N. Measurement and detection of radiation

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448

MEASUREMENT

AND

DETECTION

RADIATION

Channel

Figure

13.16

The relationship between energy and pulse height (channel) for ions with different

masses

(from Ref.

33).

The

nuclear defect

is due to nuclear collisions. As a result of such collisions,

the moving ion imparts energy upon other nuclei. The recoiling nuclei lose

their energy partly in electronic ionizing collisions and partly in nuclear

nonionizing ones. The nuclear defect has been

~alculated~~ based on the

work of

~ohr' and of Lindhard et a1.39 (see also Chap. 4).

The

recombination defect

arises from incomplete collection of the charge

produced in the detector. A heavy ion is a strongly ionizing particle. It creates

a dense plasma of electron-hole pairs along its path, a plasma that reduces

the electric field established by the external bias applied to the detector. The

reduction of the electric field intensity hinders the drifting of the electrons

and holes and thus increases the probability of recombination. The calcula-

tion of this defect is not so easy as that of the nuclear one, but an

approximate calculation was performed by Wilkins et

a1.33

The

window defect

is due to energy loss in the dead layer (window) of the

front surface of the detector. It can be obtained from the thickness of the

window and the stopping power of the ion. The thickness of the window can

CHARGED-PARTICLE SPECTROSCOPY

449

be measured by determining the change in pulse height as a function of the

incident angle (see Problem 7.6).

The PHD for iodine and for argon ions has been measured by Moak et

a1.:'

using the

channeling effect

in silicon. Pulse-height distributions were measured

by first aligning the direction of incident ions with the

[I101

crystal axis of the

silicon surface-barrier detector and then by letting the ions impinge at an angle

with respect to the same axis. In the first case, the ions moved along the channel

between two planes (channeled ions); in the second, they did not (unchanneled

ions). The channeled ions showed an energy resolution about three times better

than that of unchanneled ones, and essentially no PHD (Fig. 13.17). This result

can be explained by assuming that the channeled ions traveling between atomic

planes lose all their energy in ionizing collisions, all the way to the end of their

track. Similar results have been obtained with

235~

fission and 252~f

fission fragmenk4'

The lack of nuclear collisions for channeled ions is not the only phe-

nomenon that affects the pulse height. It is known that the electron density is

much reduced along the channel. As a result, the electronic stopping power is

lower and, consequently, so is the charge density produced by the heavy ion.

Thus, not only the nuclear but also the recombination defect is reduced for the

channeled ions.

The PHD increases slowly with ion energy, as shown in Fig.

13.18.

800

I I

Extrapolated olparticle line

ions unchanneled

ions channeled

ions unchanneled

ions

channeled

Ion energy, MeV

Figure

13.17

Pulse-height response of a Si surface-barrier detector for "channeled" and "unchan-

neled" ions (from Ref.

40).

450

MEASUREMENT

AND

DETECTION

RADIATION

Figure

13.18

The dependence of the pulse

height defect on ion energy (from

Ref.

33).

10 10'

lo3

The numbers correspond, approximately, to

MeV

uranium ions.

13.5.2

Energy Calibration: The Schmitt Method

The relationship between the pulse height

and the kinetic energy

of a heavy

ion was determined by Schmitt et a1.42,43 to be of the form

where

is the mass of the ion and

and

are constants. The calibration

of the detector, i.e., the determination of the constants a,

and d, can be

achieved in two ways. The first is an absolute calibration, and the second is a

relative one.

Absolute energy calibration is performed with the help of an accelerator.

One measures the pulse heights of four monoenergetic beams of ions with

known mass. Substitution of the known energy, mass, and pulse height into Eq.

13.13

provides four equations with four unknowns that can be solved for the

constants a,

and

For fission-fragment measurements, a relative calibration is used. The

calibration constants of

Eq.

13.13

are determined in terms of two pulse heights

and

of a fission-fragment spectrum (Fig.

13.19),

where

and

represent

pulse height corresponding to the mid-point at three-quarters maximum of the

heavy or light fragment peak, respectively. The equations for the constants are

a=-

L-H

b=-

L-H

and the constants a,, a2, a,, a, for 252~f and

235~

fission fragments are given in

Table

13.1.

The constants a,, a,, a,, and a, do not dependton the detector. The quality

of the detector with respect to energy resolution is determined from a set of

criteria developed by Schmitt and

leas on ton^^

and shown in Table

13.2.

Figure

13.19

explains the symbols used (see also Ref.

45).

CHARGED-PARTICLE

SPECIROSCOPY

451

CF-252

Pulse height spectrum

Run

9/25/74

-36

1428

97.84

Detector

1 1-1 02A

1814

142.43

Total counts

98301

650

19.23

66.96

16.57

164.63

97.66

Channel

Figure

13.19

The 252~f fission-fragment spectrum used for the determination of the detector

calibration constants (from Ref.

44).

Table

13.1

Schmitt Calibration Constants for '''~f and

U5~

Fission

~ragrnents~~'~~

Constant

lr2

23s

452

MEASUREMENT

AND

DETECTION

RADIATION

Table

13.2

Acceptable Parameters for a 252~f Fission-Fragment Spectrum

Spectrum parameters Expected values Spectrum

Fig.

13.19

13.5.3 Calibration Sources

Monoenergetic heavy ions necessary for energy calibration can be provided only

by accelerators. Fission fragments, which are heavy ions, cover a wide spectrum

of energies (Fig. 13.19). The isotope 252~f is a very convenient source of fission

fragments produced by the spontaneous fission of that isotope. Uranium,

plutonium, or thorium fission fragments can only be produced after fission is

induced by neutrons; therefore, a reactor or some other intense neutron source

is needed.

13.5.4 Fission Foil Preparation

Fission foils are prepared by applying a coat of fissile material of the desired

thickness on a thin metal backing. Details of several methods of foil preparation

are given in Refs. 29-32.

technique used for the preparation of uranium foils

is described here.

Enriched uranium in the form of uranium nitrate hexahydrate crystals is

dissolved in ethanol until it forms a saturated solution.

small amount of

collodion is added to the solution to improve its spreading characteristics.

thin

metal foil-e.g., nickel-that serves as the backing material is dipped into the

solution and then heated in an oven in a controlled temperature environment.

The heating of the foil is necessary to remove organic contaminants and to

convert the uranium nitrate into uranium oxides (mostly

U,O,).

The tempera-

ture is critical because if it is too high, part of the uranium diffuses into the

backing material, causing fragment energy degradation. Dipping produces a

two-sided foil. If the material is applied with a paint brush, a one-sided foil is

formed.

The dipping (or brush-painting) and heating is repeated as many times as

necessary to achieve the desired foil thickness. The thickness of the foil is

determined by weighing it before and after the uranium deposition or, better

yet, by counting the alphas emitted by the uranium isotopes. Most of the alphas

come from

234~; therefore the fraction of this isotope in the uranium must be

known.

CHARGED-PARTICLE SPECTROSCOPY

453

13.6

THE TIME-OF-FLIGHT SPECTROMETER

The time-of-flight (TOF) method, which is also used for the measurement of

neutron energy (see Sec. 14.8), has been applied successfully for the determina-

tion of the mass of fission fragments and other heavy ions.

The principle of TOF is simple. A beam of ions is directed along a flight

path of length L (Fig. 13.20). The time t it takes the ions to travel the distance

L determines their speed

L/t. This information, combined with the mea-

surement of the energy of the particle, gives the mass (nonrelativistically):

The errors in determining the mass come from uncertainty in energy,

E, in

time, At, and in length of the flight path, AL. The mass resolution is then given

Usually, the system is designed in such a way that

L/L is negligible compared

to the other two terms of

Eq.

13.19.

Assuming that this is the case, consider the

sources of uncertainty in energy and time.

The uncertainty AE/E is the resolution of the detector measuring the

energy of the ion. The best energy resolution that can be achieved with silicon

surface-barrier detectors is about 1.5-2 percent. The resolution can be improved

with magnetic or electrostatic analyzers

(DiIorio and wehring4' achieved 0.3

percent energy resolution using an electrostatic analyzer).

The time

it takes the particle to travel the distance

is the difference

between a START and a STOP signal (Fig. 13.20). The STOP signal is generated

by the detector, which measures the energy of the ion. This detector is usually a

surface-barrier detector. The START signal is generated by a transmission

counter, also called the 6E detector. The ion loses a tiny fraction of its energy

going through the START detector.

Several types of

6E detectors have been used.48 Examples are totally

depleted surface-barrier

detector^,^^.'^

thin

kg/m2

100 pg/cm2)

plastic

scintilla tor^,^^

ionization

chamber^,'^

and secondary-electron emission

Ion

beam

detector

;,-L

START

signal

STOP

signal

Figure

13.20

The principle of time-of-flight for the determination of the mass of heavy ions.

454

MEASUREMENT

AND

DETECTION

RADIATION

dete~tors.~~,~~-~~ Secondary-electron emission detectors fall into two categories.

In the first, the ions traverse a thin foil (e.g., carbon foil

lop4

kg/m2

pg/cm2 thick) and generate secondary electrons that are accelerated and

focused to strike a scintillator coupled to a photomultiplier tube. In the second

category belong the

channel electron multipliers

(CEM) and the

microchannel

plates

(MCP).

CEM is essentially

thin glass tube

mm diameter) shaped into a

spiral, with its inside surface coated with a semiconducting material that is also a

good secondary electron emitter.

accelerating field is created in the tube by

applying a high voltage along its length. Electrons multiply as they proceed down

the tube. Figure 13.21 shows one possible arrangement for the use of a CEM.

MCP is a glass disk perforated with a large number of small-diameter

(10-100 pm) holes or channels. Each channel is a glass tube coated with a

resistive secondary electron-emitting material. If a voltage is applied, each

channel acts as an electron multiplier.

The state of the art of

detector systems is such that At

100 ps has

been achieved and the flight path

can become long enough that the time

100-300 ns. Thus, the time resolution of

TOF

measurements is

and the mass resolution (Eq. 13.19) is essentially limited by the energy .resolu-

tion. The mass measurement is actually the measurement of the mass number A

(A M/M

A/A). Since

is an integer, the lowest limit for mass resolution is

Assuming

0.7, Fig. 13.22 gives the ion energy necessary for such

resolution as a function of A and

L/A~.~~

For heavy ions, mass resolution as

low as AA

0.2 has been rep~rted.~'

If the mass of the ion is known, the

TOF

technique can be used to

determine the energy of the ion with a resolution much better than with any

detector in use today. Indeed, if AM

0, Eq. 13.19 gives

Ion

path

Figure

13.21

The

use

CEM

detector.

CHARGED-PARTICLE

SPECTROSCOPY

455

lmor-l'--T

Figure

13.22

Energy of ion at which adjacent isotopes

can be resolved, as a function of

for different values

L/At

(from Ref.

57).

13.7

DETECTOR TELESCOPES

dE/h

DETECTORS)

The

TOF

method discussed in the previous section measures the energy and the

mass of the ion. This section presents

method that identifies the atomic

number

and the mass number

of the parti~le.~'

Identification of

and

is possible by making use of a detector telescope

consisting of a very thin detector measuring

dE/&

and a thick detector that

stops the particle. The geometric arrangement is similar to that shown in Fig.

13.20. The particle traverses the thin detector after depositing there an energy

equal to (dE/dr)t (where

is the detector thickness), and stops in the

detector." The total energy of the particle is obtained from the sum of the two

detector signals. The product E dE/h can be written, using

Eq.

4.2 or 4.33, as

where

Zef

is the effective charge of the ion. Since the logarithmic term changes

very slowly with energy,

Eq.

13.20 gives a value for

MZ~.

Another method, giving better results, is based on the fact that the range of

heavy ions is given, over a limited energy range,

an equation of the form

where

is a constant. If a particle deposits energy

(dE/&)t in a detector

of thickness

and then deposits energy E in the second detector, one can say

that the range of the particle with energy

SE is

units longer than the

range of the same particle with energy E. Using

Eq.

13.21, one can write

Thus,

Eq.

13.22 provides the value of

MZ;

since t, E, and SE are known. The

constant

is also assumed to be known for the ion of interest.

456

MEASUREMENT

AND

DETECTION

RADIATION

Equations 13.20 to 13.22 were written in terms of the mass M of the

particle. For nonrelativistic particles, M has a nonintegral value very close to

the value of

which in turn, is given by an integer. This is fortunate because Z

also assumes integral values only, and the product

MZ'

assumes unique values

for many particles. For example, for protons, deuterons, tritons, and alphas, the

value of MZ2 is 1, 2,

and 16, respectively.

13.8

MAGNETIC SPECTROMETERS

Magnetic spectrometers (or analyzers) are instruments that exhibit high-energy

resolution. They are used mainly in experiments involving high-energy particles,

but they can be used with low-energy particles as well. Energy resolutions

achieved with this type of spectrometer are of the order of AE/E

lop4

for

high-energy electrons6' and AE/E

for heavy ions.61

Many types of magnetic spectrometers have been developed, differing

mainly in the shape of the magnetic field ~sed.~'-~' The basic principle common

to all of them is the action of the force from a magnetic field on a moving

charged particle. If a particle with charge Ze moves with velocity v in a magnetic

field of strength

the force

on the particle is given by

Zev

(13.23)

Since the magnetic force is always perpendicular to the direction of motion

of the particle, it does not change the energy but only the direction of motion of

the particle. If the velocity is perpendicular to the magnetic field, the particle

trajectory will form a circle of radius p given by the equation

M*U~

ZevB

which after rearrangement becomes

M*v

ZeBp (13.25)

where M*

p2, the total mass of the particle.

Equation 13.25 is the basis of magnetic spectroscopy. It expresses the fact

that the momentum of the particle is proportional to the quantity Bp, called the

magnetic

rigidity

of the particle. The relationship between kinetic energy and

rigidity is obtained from the equation linking energy and momentum (see Chap.

3). The relativistic equation for the kinetic energy

\I(MC')~

Mc2

The nonrelativistic equation is

CHARGED-PARTICLE

SPECIROSCOPY

457

To understand how a magnetic spectrometer works, consider two particles

with momenta

Mlul

and

M2u2

coming into a space with

constant magnetic

field

(Fig. 13.23). Assuming that the magnetic field is perpendicular to the

velocity and also perpendicular to the plane of the figure, the two particles will

move along circular paths of radii p, and p, given by

Eq.

13.25.

If the particles

are allowed to complete half a circle, they will hit the "focal" plane at points

and

Thus, if one determines

and

and the charge of the particles is

known, the momentum can be determined from

Eq.

13.25. If the mass of the

particle is also known, the energy can be determined from

Eq.

13.26 or 13.27.

Obviously, for a given rigidity Bp, the energy

depends on the factor

z2/M.

one determines the energy by other meansWe.g., by using a semiconductor

detector-the magnetic spectrometer may give the

Z2/M

value.

In practice, the value of B is accurately known; therefore, the real task is

the accurate determination of the radius

The radius

(or the distance

2p)

measured with the help of position-sensitive detectors placed at the focal plane.

Any uncertainty in the value of p, or in general in the value of Bp, introduces

an uncertainty in the value of energy.

all the particles move in parallel paths

when they enter the spectrometer, the energy resolution obtained from

Eq.

13.26 or

Eq.

13.27 is given by

Relativistic

Nonrelativistic

AT A(

Be)

The position can be determined with an accuracy of less than a millimeter. Since

a typical value of

0.80

m, the expected resolution is

Figure

13.23

Two particles with ve-

locities

and

follow trajectories

with radius

and

respectively,

and are separated spatially (points

and

B).