Leroy C., Rancoita P.-G. Principles Of Radiation Interaction In Matter And Detection

Подождите немного. Документ загружается.

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

720 Principles of Radiation Interaction in Matter and Detection

9.11.5 The Muon Component of Extensive Air Showers

The muon component of the air shower results from the decay of secondary pi-

ons and kaons produced by the interaction of nucleons in the atmosphere. The

muon cascade grows towards a maximum and then slowly decays due to the

(µ

−

) → e

−

) ¯ν

(ν

) ν

( ¯ν

) decays and its small cross section for radiation

and pair pro duction. The behavior of the muon component diﬀers from that of the

electromagnetic component, which rapidly increases with the atmospheric depth tra-

versed and gets rapidly absorbed after the maximum. In fact, the electron–photon

component is about one or two order of magnitude larger than the muon component,

in the initial stage of the cascade development. This smaller (muon) component

grows to a maximum and remains almost constant because of the long interaction

length of muons, while the electromagnetic cascade, which initially represents the

highest number of particles in the shower, has a relatively small range compared

to the thickness of the atmosphere. Therefore, the electron–photon component of

the shower becomes completely absorbed, after having reached a maximum, leaving

muons as the dominant population in the shower as sea level is reached. The lateral

distribution of muons, as a function of the perpendicular distance from the shower

axis, is given in units of muons/m

by [Greisen (1960)]:

(r) =

Γ(2.5)

2π Γ(1.5) Γ(1.5) (R/meter)

−0.75

1 +

−2.5

, (9.108)

where N

is the number of muons and R is a few hundred meters (455 m and

320 m in [Aglietta et al. (1997); Greisen (1960)], respectively). The diﬀerent behavior

displayed by the muon and electromagnetic components oﬀers the possibility of

studying the shower development by a measurement of the ratio of the numb er

of muons to electrons. The relation between the number of muons, N

, and the

numb er of electrons, N

, is:

= KN

(9.109)

with n = 0.75 [Aglietta et al. (1997)] and K a normalization factor.

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

Chapter 10

Superheated Droplet (Bubble) Detectors

and CDM Search

A superheated droplet (Bubble) detector consists of a suspension of liquiﬁed gas

droplets (active medium) dispersed in a polymerized gel [Ing, Noulty and McLean

(1997)]. Presently, these droplet detectors consist of an emulsion of metastable

superheated freon-like C

(like CF

Br, CCl

, C

) droplets of 5 to

100 µm diameter, dispersed in an aqueous solution. An appropriate concentration

of heavy salt (e.g., CsCl) is added to the solution in order to obtain the same den-

sity as the droplets [(1.3–1.6) g/cm

], thus preventing the downward migration of

the droplets. The solution is then polymerized to prevent the upward migration of

the bubbles (in the sensitive mode) created, when enough energy is deposited in

a droplet by an incoming particle. By applying an adequate pressure, the boiling

temperature can be raised, allowing the emulsion to be kept in a liquid state. Under

this external pressure, the detectors are insensitive to radiation. By removing the

external pressure, the liquid becomes superheated and sensitive to radiation. The

interactions, between the incoming radiation and the nuclei of the active medium,

can lead to suﬃcient energy deposition to trigger a liquid-to-vapor phase transi-

tion. Another technique exists to prepare droplet detectors. This technique, devel-

oped by Apfel (1979), consists in disp ersing droplets of a liquiﬁed gas in a viscous

gel. The droplet size (typical diameter of 100 µm) is uniform and the droplets are

maintained in suspension by viscosity. When they burst, the resulting bubbles mi-

grate to the surface of the gel. Based on our own experience, this chapter will only

treat detectors prepared according the BTI technique [Ing, Noulty and McLean

(1997)].

The need to achieve a minimal energy deposition to induce the phase transition

features droplet detectors as threshold detectors. Their sensitivity to various types

of radiation strongly depends on the temperature and pressure of operation. The

liquid-to-vapor transition is explosive in nature and accompanied by an acoustic

shock wave, which can be detected by piezoelectric sensors. These detectors are

re-usable by re-compressing the bubbles back to droplets.

Droplet detectors of small volume, typically 10 ml [representing (0.1–0.2) g of

active material], are currently used in several applications such as portable neutron

dosimeters for personal dosimetry or for measuring the radiation ﬁelds in irradi-

721

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

722 Principles of Radiation Interaction in Matter and Detection

Fig. 10.1 A 1.5 l detector module equipped with piezoelectric sensors [Barnab´e-Heider et al.

(2002)].

ation zones near particle accelerators or reactors. These detectors can also serve

for detection of radon or be used for the measurement of the transit neutron dose

received in-ﬂight by aviation crews, an important component of the total radiation

exposure. More details and a description of other applications can be found in [Ing,

Noulty and McLean (1997)]. For such small volumes (low gas loading), the counting

of bubbles accumulated for a period of time can be visually performed.

More recently, the PICASSO group [Barnab´e-Heider et al. (2002)] has developed

large volume detectors of the type shown in Fig. 10.1 with the aim to perform a

direct measurement of neutralinos, predicted by minimal supersymmetric models

as Cold Dark Matter (CDM) particles. The very low interaction cross section bet-

ween CDM and the detector active medium nuclei requires the use of very massive

detectors to achieve a sensitivity level, allowing the detection of CDM particles in

the galactic environment [Boukhira et al. (2000)]. Detectors of large volumes (1.5

and 3 litres) are shown in Fig. 10.1 in containers capable to hold pressures up to 10

bars. Piezo-sensors are glued on the container surface for signal detection. Typical

gas loading presently achieved for this type of detector is in the (5–10) g/litre

range.

Droplet detectors have high eﬃciency for detecting neutrons while being insensi-

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

Superheated Droplet (Bubble) Detectors and CDM Search 723

tive to minimum ionizing particles (mips) and to nearly all sources of background,

when operated at proper temperature and pressure. One can observe, from ki-

nematical considerations [see Eq. (10.5), below], that nuclear recoil thresholds in

droplet detectors can be obtained in the same range for neutrons of low energy (e.g.,

from 10 keV up to a few MeV) and massive neutralinos (mass of 60 GeV/c

up to

1 TeV) with no sensitivity to mips and γ-radiation. Therefore, for CDM searches, the

droplet detector response to neutrons has to be fully investigated. The heavy salt,

present in the gel at production stage, contains α-emitters (U/Th and daugthers),

which are the ultimate background at normal temperature of operation. Other back-

grounds only contribute to the detector signal for higher temperatures [Boukhira

et al. (2000)]. Puriﬁcation techniques are applied to remove these α-emitters [Di

Marco (2004)]. Presently, contamination levels of 10

−11

g/g for U and 10

−10

g/g for

Th are obtained, toward a ﬁnal goal around 10

−14

g/g. Regardless of the level of

the purity achieved, the response of droplet detectors to α-particles has to be fully

understoo d. Recently

∗

, the PICASSO collaboration observed for the ﬁrst time a

signiﬁcant diﬀerence between acoustic signals induced by neutrons and α-particles

in a detector based on superheated liquids. This observation brings the possibility of

improved background suppression in CDM searches based on superheated liquids.

Sections in this chapter are devoted to neutron and α-particle response mea-

surements. These data provide an understanding of the physics mechanisms at the

base of droplet detector operation. Finally, a section is dedicated to the search for

CDM particles and, in particular, to the spin dependent part of their cross section.

10.1 The Superheated Droplet Detectors and their Operation

The response of a droplet detector to incoming particles or radiation is determined

by the thermodynamics properties of the active gas, such as operating temperature

and pressure. The detector operation can be understood in the framework of Seitz’s

theory [Seitz (1958)], in which bubble formation is triggered by a heat spike in the

superheated medium produced, when a particle deposits energy within a droplet.

The droplet should normally make a transition from the liquid phase (high po-

tential energy) to the gaseous phase (lower potential energy). However, undisturbed,

the droplet is in a metastable state, since it must overcome a potential barrier to

make the transition from the liquid to the gas phase. This transition can be achieved

if the droplet receives an extra amount of energy, such as the heat due to the energy

deposited by incoming particles. The potential barrier is given by Gibbs equation:

16π

σ(T )

− p

)

, (10.1)

where the externally applied pressure, p

, and the vapor pressure in the bubble,

, are functions of the temperature T . The diﬀerence between these two pressures

∗

See Aubin, F. et al. (2008), Discrimination of nuclear recoils from alpha particles with super-

heated liquids, arXiv:0807.1536v1 [physics.ins-det].

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

724 Principles of Radiation Interaction in Matter and Detection

Fig. 10.2 Detector response to 200 keV neutrons as a function of temperature at various pres-

sures. The 8 ml detector is loaded with a 100% C

gas. The 200 keV neutrons used for these

measurements were obtained from

Li(p,n)

Be reactions at the tandem facility of the Universit´e

de Montr´eal [Barnab´e-Heider et al. (2002)].

Fig. 10.3 Detector response to 400 keV neutrons as a function of temperature at various pres-

sures. The 8 ml detector is loaded with a 100% C

gas. The 400 keV neutrons used for these

measurements were obtained from

Li(p,n)

Be reactions at the tandem facility of the Universit´e

de Montr´eal [Barnab´e-Heider et al. (2002)].

determines the degree of superheat. The surface tension of the liquid-vapor interface

at a temperature T is given by

σ(T ) =

− T )

− T

)

where T

is the critical temperature of the gas (deﬁned as the temperature at which

the surface tension is zero), σ

is the surface tension at a reference temperature T

(usually the boiling temp erature T

). For a combination of two gases, T

and T

can

be adjusted by choosing the mixture ratio. For instance T

= −19.2

◦

C, T

= 92.6

◦

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

Superheated Droplet (Bubble) Detectors and CDM Search 725

E+00

E+01

E+02

E+03

E+04

E+05

E+06

E+07

5.0

30.0

35.0

temperature (˚C)

eutrons minimal energy (keV

)

1 bar operating pressure

33 bar operating pressure

66 bar operating pressure

Fig. 10.4 Minimal neutron-energy (E

R,th

) as a function of temperature for various pressures of

operation [Barnab´e-Heider et al. (2002)].

for a detector loaded with a gas mixture; T

= 1.7

◦

C, T

= 113.0

◦

C for a detector

loaded with 100% C

gas [Boukhira (2002)]. Various types of droplet detectors

responses, corresponding to diﬀerent gas mixtures, can be uniﬁed via their amount

of so-called reduced superheat, s, introduced in [d’Errico (1999)] and deﬁned as

s =

T − T

− T

. (10.2)

Bubble formation will occur, when a minimum energy E

R,th

deposited, for exam-

ple, by the nuclear recoils induced by neutrons, exceeds the threshold value, E

within a distance l

= aR

, where the critical radius R

is given by:

2σ(T )

− p

)

. (10.3)

A value a ≈ 2 is suggested from Apfel, Roy and Lo (1985). However, larger values

of a (up to 13) can be found in literature [Bell, Oberle, Rohsenow, Todreas and Tso

(1973)] and from recent simulation studies [Barnab´e-Heider et al. (2004)], as will be

seen below. If dE/dx is the eﬀective energy deposition per unit distance, the energy

deposited along l

dep

= dE/dx × l

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

726 Principles of Radiation Interaction in Matter and Detection

Fig. 10.5 Response of a droplet detector (loaded with a gas mixture) to beams of monoenergetic neutrons for diﬀerent temperatures. Using the

known tabulated neutron cross section on

C and

F, the ﬁt to the data for diﬀerent temperatures gives an exponential temperature dependence

for E

(T ), and the eﬃciency ²

, T ) is obtained with α = 1.0 ± 0.1 [Genest (2004)]. In ordinate, the count rate is in arbitrary units.

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

Superheated Droplet (Bubble) Detectors and CDM Search 727

Note that dE/dx is a function of the energy of the nuclei recoiling after their collision

with the incident particle. The condition to trigger a liquid-to-vapor transition is

dep

≥ E

R,th

. Since it is not the total energy deposited that will trigger a liquid-to-

vapor transition, but the fraction of this energy transformed into heat, the actual

minimum or threshold energy E

R,th

for recoil detection is related to E

by an

eﬃciency factor

η =

R,th

(2 < η < 6%) [Apfel (1979); Harper and Rich (1993)]. Since the threshold energy

value depends on the temperature and pressure of operation, the detector can be set

into a regime where it mainly responds to nuclear recoils, allowing discrimination

against background radiations such as mip’s and γ-rays.

10.1.1 Neutron Response Measurement

As an example, we will consider the case of nuclear recoils induced by neutrons of low

energy (E

≤ 500 keV). It is possible to determine precisely the threshold energy as

a function of temperature and pressure by exposing the detector to monoenergetic

neutrons at various temperatures and pressures of operation. The detector responses

(count rates) to monoenergetic neutrons of 200 and 400 keV, measured as a function

of temperature for various pressures of operation, are shown in Figs. 10.2 and 10.3,

respectively, for a 8 ml detector.

From such curves (e.g., Figs. 10.2 and 10.3), one can extract the threshold

temperature T

for a given neutron energy by extrapolating the curves to their

lowest point (a few degrees below the measured lowest point). Then, it is possible

to represent the neutron threshold energy as a function of temperature for various

pressures (Fig. 10.4).

As can be seen from Fig. 10.4, for a practical range of temperature of operation,

R,th

follows a temperature dependence expressed as:

R,th

= E

−K(T −T

)

, (10.4)

where K is a constant to be determined experimentally and E

is the threshold

energy at the boiling temperature T

To understand the response of this type of detector to neutrons, one has to

study the interaction of neutrons with the nuclei (e.g.,

F and

C) of the active

material. The interactions of neutrons with the freon-like droplets (C

) lead to

recoils of

F and

C nuclei, inducing the phase transition. Inelastic collisions are

possible if the center-of-mass kinetic energy of the neutron–nucleus system is higher

than the ﬁrst excitation level of the nucleus (1.5 and 4.3 MeV for

F and

respectively). Absorption of a neutron by the nucleus followed by an ion, proton

or alpha-particle emission requires a neutron threshold energy of 2.05 MeV. The

absorption of a neutron by the nucleus may also lead to the emission of γ, but the

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

728 Principles of Radiation Interaction in Matter and Detection

Fig. 10.6 Minimal neutron-energy as a function of the reduced superheat parameter s [Barnab´e-

Heider et al. (2002)].

droplet detectors are only sensitive to γ at high temperature of operation. In our

example, the neutron energy is lower than 500 keV. Therefore, it mainly interacts

through elastic scattering on ﬂuor and carbon nuclei. Assuming neutron elastic

scattering on nucleus, the recoil energy E

of the nucleus i is given by:

(1 − cos θ)

+ m

)

, (10.5)

where E

is the incident neutron energy and θ is the neutron scattering angle in the

center-of-mass system; m

and m

are the masses of the neutron and the nucleus

i, resp ectively. The nucleus recoil energy is zero if the nucleus i recoils along the

neutron incident direction. The recoil energy of the nucleus i is maximum if θ =

180

◦

R,max

+ m

)

= f

. (10.6)

The f

factor is the maximal fraction of the energy of the incident neutron that

can be transmitted to the nucleus i: f

= 0.19 and 0.28 for

F and

C, respecti-

vely. The ranges for

F and

C depend on the value of E

R,max

[Eq. (10.6)] and

on their speciﬁc energy-losses dE/dx, which can be calculated using TRIM, a code

calculating the transport of ions in matter [Ziegler and Biersack (2000)].

At a given neutron energy E

, the recoiling nuclei i (i =

C) are emitted

with an angular distribution: every angle is associated with a speciﬁc recoil energy,

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

Superheated Droplet (Bubble) Detectors and CDM Search 729

Fig. 10.7 The response of two detectors one called BD100 (loaded with a gas mixture) and the

other called BD1000 (loaded with 100% C

) to neutrons from an AcBe source as a function

of reduced superheat s. The use of the reduced superheat parameter allows the uniﬁcation of the

response of the two detectors. With parameter s, the response for diﬀerent gases is computed with

c,eﬀ

= 0.9 T

[Barnab´e-Heider et al. (2002)].

ranging between 0 keV up to a maximum energy E

R,max

. Therefore, the nucleus re-

coil energy distribution, dn

/dE

, is determined by the

F and

C recoil angular

distributions. Not all recoil energy depositions are detectable, since there exists a

threshold recoil energy, E

R,th

, below which no phase transition is triggered. E

R,th

depends on the temperature and pressure of operation and is related to the neutron

energy threshold, E

, by the relation E

R,th

= f

. The threshold energy has

an exponential dependence on temperature [Eq. (10.4) and Fig. 10.4]. The proba-

bility, P(E

R,th

(T )), that a recoiling nucleus i at an energy near threshold will

generate an explosive droplet-to-bubble transition is zero for E

< E

R,th

and will

increase gradually up to 1 for E

> E

R,th

. This probability can be expressed as:

P (E

, E

R,th

(T )) = 1 − exp

−α

− E

R,th

(T )

R,th

(T )

, (10.7)

where α is a parameter to be determined experimentally. Therefore, the eﬃciency

, T ), that a i -type recoil nucleus triggers a droplet-to-bubble phase transition

at a temperature T after being hit by a neutron of energy E

, is given by comparing

the integrated recoil spectrum with and without threshold:

, T )=

R,max

R,min

P (E

, E

R,th

(T )) dE

R,max

. (10.8)

For neutrons of energy lower than 500 keV, collisions with

F and

C are elastic