Nuclear Instruments and Methods in Physics Research A 744 (2014) 21–29
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in
Physics Research A
journal homepage: www.elsevier.com/locate/nima
Observation and modeling of
222
Rn daughters in liquid nitrogen
N. Frodyma, K. Pelczar n, M. Wójcik
M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
art ic l e i nf o
a b s t r a c t
Article history:
Received 16 July 2013
Received in revised form
27 December 2013
Accepted 17 January 2014
Available online 29 January 2014
The results of alpha spectrometric measurements of the activity of 222Rn daughters dissolved in liquefied
nitrogen are presented. A direct detection method of ionized alpha-emitters from the 222Rn decay chain
(214Po and 218Po) in a cryogenic liquid in the presence of an external electric field is shown. Properties of
the radioactive ions are derived from a proposed model of ion production and transport in the cryogenic
liquid. Ionic life-time of the ions was found to be on the order of 10 s in liquid nitrogen (4.0 purity class).
The presence of positive and negative ions was observed.
& 2014 Elsevier B.V. All rights reserved.
Keywords:
222
Rn
Low-background
High purity
Ion mobility
Alpha spectrometry
Positive and negative ions
1. Introduction
Ultra-pure liquefied gases can serve as a passive shielding
material and a cooling medium for the low background experiments searching for rare events. Additionally, scintillation light
induced by internal radioactive decays or external radiation
sources may be used as a 4-π anti-coincidence, further reducing
the background. Although the liquid is highly purified it may still
contain traces of intrinsic radioactive contamination. The surrounding material of the supporting structures and the cryostat
container also present a source of internal background.
The natural presence of 226Ra in all construction materials is a
constant source of alpha emitters, belonging to the 222Rn decay
chain (214Po and 218Po) (Fig. 1). 222Rn is a noble gas able to diffuse
from the bulk to the surface of porous materials. It is also emitted
from surfaces contaminated with 226Ra. Consequently 222Rn dissolves in cryogenic liquids, entering the surrounding active
volume of a detector. Ions produced in the decays of 222Rn and
its daughters may reach vicinity of e.g. the germanium detectors
by means of convection flows or electrostatic drifting of the
radioactive ions. Such processes present a constant in time source
of radioactive background. Thus, 222Rn contamination results in a
severe background (caused by energetic alpha- and beta-decays
from the 222Rn decay chain) which is difficult to control. Inve
stigation of the behaviour of 222Rn and its progeny in cryogenic
liquids is thus of great importance for ultra-low background
experiments using liquefied gas as shielding, a target or a detecting medium (e.g. two phase Time Projection Chamber in the
n
Corresponding author.
0168-9002/$ - see front matter & 2014 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.nima.2014.01.039
DarkSide experiment [1], liquid argon as a passive shielding
material and a cooling medium for the germanium detectors in
the GERDA [2] experiment).
2. Detection of
214
Po and
218
Po in liquid nitrogen
2.1. Experimental setup
The experimental setup is presented in Fig. 2. A bare Si-PIN
diode (Hamamatsu model S1223-01 with removed glass window)
is immersed in liquid nitrogen under normal pressure, contained
in a 32 L dewar. The diode is wired using a standard 50 Ω coaxial
cable. The housing of the diode is grounded and connected to the
signal cable shield. The diode is operated under a nominal voltage
of þ28 V (relative to the ground), specified for the best energy
resolution for registering 5 MeV α-particles in air (5 mm distance).
The chosen diode type operates stably in the cryoliquid for long
periods of time, extending over two weeks. The diode is connected
to a standard spectrometry electronics chain – charge preamplifier
and the active filter amplifier. The readout system consists of a
multi channel analyzer, recording alpha-energy spectrum data in
fixed time windows (series of measurements). Changes in the
dewar gross weight (32 L of total volume) are registered on-line to
calculate losses of the cryoliquid due to evaporation (boil-off).
The dewar is electrically isolated from the ground. The metal
housing of the dewar is wired to a bipolar high voltage (HV) power
supply. Applying positive bias to the housing has the same effect
as biasing the diode with negative high voltage of the same
magnitude. In this biasing scheme the Si-PIN diode, having lower
potential than the dewar, attracts cations. Reversely, negative bias
22
N. Frodyma et al. / Nuclear Instruments and Methods in Physics Research A 744 (2014) 21–29
Fig. 3. Setup for dissolving gaseous 222Rn in the liquid nitrogen (not to scale).
Radon from the source, together with the gas carrier, is transported through a cold
trap to reduce humidity content. Some of the 222Rn atoms may freeze out on the
cold parts of the piping operated in the cryogenic liquid. Consequently, 222Rn
dissolves with less than 100% efficiency.
Fig. 1.
222
Rn decay chain.
ranges from roughly 10 to 15 kBq. The radon source consists of 0.1 L of
226
Ra solution (18.5 kBq of activity) enclosed in a tight silicon pipe and
placed in a 4.6 L metal vessel. More than 90 % of the 222Rn generated
in the solution diffuses through the pipe walls into the vessel volume.
The volume is then flushed with a carrier gas (nitrogen). The carrier
gas enriched in radon is transported through a cold trap (temperature
ranges from 65 to 70 1C) to remove traces of humidity. The thin
gas outlet is submerged in liquid nitrogen. Some fraction of radon
atoms may freeze out on the cold surfaces of the piping before
entering the volume of the liquid. Bubbles of the carrier gas ascend to
the surface partially dissolving in the cryogenic liquid. Radon activity
enclosed in the bubbles is then entirely transferred to the cryoliquid.
The exhaust gas is monitored for the residual radon activity using a
ZnS(Ag) scintillation chamber. The whole procedure lasts for about
30 min, and uses a carrier flow of about 0.5 L/min to fully flush the
radon source volume.
2.3.
Fig. 2. Sketch of the measurement setup (not to scale). The Si-PIN diode is operated
under a nominal voltage of þ 28 V relative to the ground. The dewar's metal
housing is usually biased to 7 2 kV. If the housing is biased to þ2 kV, then the
configuration is equivalent to approximately 2 kV applied to the diode housing
and dewar grounded.
on the dewar puts the diode at a higher potential. Positive ions are
then repelled from the diode.
2.2.
222
Rn doping procedure
An amount of radon activity on the order of 15 kBq from a radon
generator is dissolved in liquid nitrogen (purity class 4.0) at the
beginning of each measurement cycle (Fig. 3). The dissolved activity
214
Po and
218
Po alpha activity measurements
The first measurement is taken at least 3 h after the dissolving
procedure, to achieve decay (secular) equilibrium in the volume of
the cryoliquid between 222Rn and its daughters. The recorded signal
of 214Po and 218Po α-decays is corrected for 222Rn life-time and
liquid losses in off-line analysis. Background alpha-energy spectrum
recorded by the Si-PIN diode immersed in the liquid nitrogen (no
222
Rn dissolved) is shown in Fig. 4. For comparison, a typical spectrum
recorded in a 222Rn doped nitrogen is shown in Fig. 5. The dewar was
biased to þ 2 kV during these two measurements. Fig. 6 presents the
energy spectrum recorded with 2 kV bias applied to the dewar. The
shape of the α-peaks indicates that the drifted ions decay very close or
stick to the active surface of the diode (the distance is much shorter
than the range of alphas from 214Po and 218Po decays in liquid
nitrogen).
Each time, the α-energy spectrum was recorded in 900 s real time
windows, and stored as a multi-channel histograms. The 214Po energy
peak around Q¼7.69 MeV is selected from the spectrum (channels
5200–7000) and the gross count rate in the respective window is
corrected for 222Rn decay and liquid boil-off. The count rate is then
analyzed as a function of the time elapsed since the 222Rn doping and
changes of the bias voltages applied to the dewar. The sign of the
analyzed ions was selected by the bias voltage polarity. Distance
between the Si-PIN diode and the bottom of the tank may be changed
to limit the collection volume of the ions.
Analysis of the 218Po signal is rather difficult due to the
background generated by 214Po (cf. Fig. 5) in the energy range of
the 218Po alpha peak. The analysis is based on simultaneous fitting
N. Frodyma et al. / Nuclear Instruments and Methods in Physics Research A 744 (2014) 21–29
23
6.0
Counts
4.5
3.0
1.5
0.0
0
1000
2000
3000
4000
5000
6000
7000
8000
Channel number
Fig. 4. Background spectrum of the Si-PIN diode operated in liquid nitrogen which is not doped with 222Rn. The spectrum was recorded in 3600 s. The dewar was biased to þ 2 kV.
Counts
55
40
25
10
0
0
1000
2000
3000
4000
5000
6000
7000
8000
Channel number
Fig. 5. Energy spectrum recorded using Si-PIN diode immersed in liquid nitrogen doped with 222Rn. The 214Po activity generates background in the 218Po energy range.
Extraction of the 218Po signal is therefore based on fitting with peak shapes. Low energy part of the spectrum is due to β decays present in 222Rn decay chain. The dewar was
biased to þ2 kV.
10
Counts
8
6
4
2
0
0
1000
2000
3000
4000
5000
6000
7000
8000
Channel number
Fig. 6. Energy spectrum recorded by the Si-PIN diode in liquid nitrogen doped with 222Rn, obtained for the negative polarization of the dewar ( 2 kV). In this configuration
negative-like ions were drifted to the diode (cf. Fig. 5).
of the 214Po and 218Po alpha peak shapes to properly model the
background from 214Po under the 218Po alpha peak. The 214Po peak
shape f was modeled using the following equation [3]:
!
!
rffiffiffiffi
ðx x0 Þ2
π
2εi ðx x0 Þ þ s2
f ðxÞ ¼ A exp þ As
∑a exp
2 i i
2s2
2ε2i
erfc
εi ðx x0 Þ þ s2
pffiffiffi
2εi s
103
102
where A is the height of the full energy peak at channel x0, s is the
width of the peak (Gaussian), ai is the height of the i-th tail
function relative to A, εi is the decay constant of the i-th tailing
function, and erfc is the complementary error function. The 214Po
peak shape was best modeled using three tailing functions (i¼1, 2, 3).
The 218Po peak shape was modeled only by Gaussian function
(contribution of the tailing functions is negligible for low activities of
218
Po). Fig. 7 shows, as an example, results of simultaneous fitting of
the 214Po and 218Po peak shapes to the data.
Four series of measurements were performed in total using
described setup. Every 15 min alpha energy spectrum was stored for
later analysis. During each of the measurement series the dewar
electric bias was changed once. The aim was to model the electric field
drifting the ions such that different properties of ions can be studied.
During the first measurement the dewar bias was set to þ2 kV to
collect only positive ions on the Si-PIN diode's surface. After several
hours of ion collection (at least 3 h to reach secular equilibrium of the
222
Rn progenies on the diode) the dewar was grounded (bias turned
off, þ 2-0 kV). Effectively the flux of positive ions drifted by
the electric field was stopped. The observed decay of the 214Po nuclei
10
1
0
1000
2000
3000
4000
5000
6000
7000
8000
Fig. 7. Alpha energy spectrum fitted with 214Po and 218Po peak shapes. The fit for
MCA channels 3000–7000 is shown by the dashed gray line. The extracted 218Po peak
from the fit is shown in solid red line. The fit range is limited to channel 3000 due to
visible low energy background from beta decays. χ2/ndof of the fit is 114.3/107. (For
interpretation of the references to color in this figure caption, the reader is referred to
the web version of this article.)
allowed to estimate content of 222Rn daughters in the ionic flux.1 The
observed 214Po signal is presented in Fig. 8.
In the second series of measurements the dewar was first
grounded and then the þ2 kV of bias was applied (0- þ 2 kV).
This measurement (shown in Fig. 10) provided a way to check
1 214
Po is a short-lived daughter of 214Bi (T 1=2 ¼ 164 μs), and as such cannot
contribute significantly to the ionic flux. The observed 214Po activity is related to
214
Bi, 214Pb or 218Po deposited on the diode's surface only.
24
N. Frodyma et al. / Nuclear Instruments and Methods in Physics Research A 744 (2014) 21–29
whether changes of the ionic flux in time resemble the activity
build-up characteristic for the 222Rn progenies.
The third and fourth series of measurements were intended to
study the ionic life-time of positive and negative ions. During
these measurements the bias polarity was flipped ( þ 2- 2 kV to
study the drifting of negative ions and 2- þ 2 kV for the positive
ones). Figs. 11 and 12 show the 214Po count rates registered for the
two measurement series.
3. Results and discussion
3.1. Deposition of the ions on surface of the detector
7.5
Si−PIN diode
on −2 kV for
more than 3 h
Bias removed (0 V)
5.0
2.5
214
Po signal (in 15 min bins)
10.0
0.0
−0.1
0.0
0.1
0.2
0.3
Time since HV switch (days)
Fig. 8. A typical 214Po signal transition registered while the dewar bias was
changed from þ2 kV to 0 V. The horizontal scale is expressed in days. The 214Po
counts are corrected for 222Rn decay.
The Si-PIN diode registers only decays occurring up to 50 μm
away from the semiconductor surface due to the stopping of
alphas in the cryoliquid. After turning off the bias (grounding of
the container, Fig. 8) or reversing the bias polarity (Figs. 11 and 12),
the activity remaining on the surface (or in its direct closure) is
a source of exponentially decaying signal with a time constant
characteristic to the 222Rn chain. The measured alpha activity of
214
Po was fitted with a Bateman relation describing the observed
diode activation by the 222Rn decay chain isotopes (218Po - 214Pb 214
Bi). By fitting the Bateman equations we were able to determine
relative activities of specific isotopes deposited directly on the diode
surface. Table 1 summarizes fit results (relative amounts of 218Po,
214
Pb and 214Bi) of the Bateman equation for three investigated
types of bias change, causing isotope deposition (2-0 kV,
2-2 kV and 2- 2 kV). One could estimate the residual activities of the isotopes deposited. 214Bi was found to dominate in the
ionic flux, therefore it is assumed in the later analysis that the flux of
ions consists only of 214Bi ions. Decays of 218Po were also directly
registered, but the observed activity was on average two orders of
6
4
Bias not applied
Si−PIN diode on −2 kV
2
214
Po signal (in 15 min bins)
Fig. 9. Pictures showing a static situation when þ2 kV of bias voltage is applied to the dewar (a), and a situation right after reversing of the dewar bias (b). (a) Density of the
cations is higher close to the Si-PIN diode. The anions (impurities and electronegative compounds) are attracted towards the walls and (b) the anions are being attracted to
the Si-PIN diode. Increased density of the impurities results in lower ionic life-time of the 222Rn daughters. Similar situation is observed after bias reverse in both cases.
Signal registered by the Si-PIN diode comes from electronegative compounds.
0
0.0
0.4
0.8
Time since HV switch (days)
Fig. 10. A typical 214Po signal transition registered while the dewar bias was changed from 0 V to þ 2 kV (the moment indicated by a vertical dashed line). The horizontal
scale is expressed in days. The 214Po counts are corrected for 222Rn decay.
N. Frodyma et al. / Nuclear Instruments and Methods in Physics Research A 744 (2014) 21–29
25
2.0
1.5
Si−PIN diode
on −2 kV for
more than 3 h
1.0
Si−PIN diode
on +2 kV
0.5
214
Po signal (in 15 min bins)
2.5
0.0
0.0
0.4
0.8
Time since HV switch (days)
Fig. 11. A typical 214Po signal transition registered while the dewar bias was changed from þ 2 kV to 2 kV (the moment indicated by a vertical dashed line). The horizontal
scale is expressed in days. The 214Po counts are corrected for 222Rn decay.
2
Si−PIN diode
on +2 kV for
more than 3 h
Si−PIN diode
on −2 kV
1
214
Po signal (in 15 min bins)
3
0
0.0
0.4
0.8
Time since HV switch (days)
Fig. 12. A typical 214Po signal transition registered while the dewar bias was changed from 2 kV to þ 2 kV (the moment indicated by a vertical dashed line). The horizontal
scale is expressed in days. The 214Po counts are corrected for 222Rn decay.
Table 1
Amounts of isotopes deposited on the Si-PIN diode surface before changing of the
bias (90% C.L.). The numbers are given in arbitrary units. After reversing of the bias
polarity the flux of radioactive ions towards the diode changes. Fitting Bateman
equations reproduces the signal of the remaining activity right after the bias
polarity change, giving relative amounts of distinct isotopes deposited on the diode
surface (cf. Figs. 8, 11, 12). The activity of 218Po was additionally determined directly
from the alpha energy spectrum to be two orders of magnitude lower than the
registered 214Po signal (not shown in the table).
Isotope
2-0 kV
2-2 kV
2- 2 kV
218
o 5:1
o 9:4
9.4(0.3)
0.11(0.03)
o 0:90
o 1:0
0.21(0.08)
o 0:012
o 0:77
o 1:4
2.00(0.08)
o 0:0064
41:4
4 0:28
4 1:9
Po
Pb
Bi
Background
214
214
Ratio of
214
Bi to
214
Pb activity
magnitude lower (cf. Fig. 7). Furthermore, due to the long time
windows for alpha energy spectrum registration (15 min compared
to the 3.1 min nuclear half life-time of 218Po), one could not expect
to disentangle 218Po activity from Bateman equations.
The nonzero background, sometimes observed in measurements, is probably related to the diode bias voltage (þ28 V),
always present on the diode housing during the measurements.
The diode active surface is virtually at the ground potential
ensured by the charge amplifier input. Since the distance between
diode housing and the active surface is short, the field strength is
able to constantly collect positive ions over time.
3.2. Minimum detected activity
Under the assumption that 100 % of the transferred 222Rn activity
is dissolved in the cryoliquid, one can estimate the effective volume
of the cation collection Veff:
þ 2 kV
V eff
¼
V c A214
32 l 10 Bq
0:14 l
¼
18:5 kBq 50 %
ARn εG
where A214 is the highest measured 214Po signal for a positive dewar
bias (þ 2 kV), ARn is the dissolved radon activity, Vc is the cryostat
(liquid) volume, and εG is the geometric detection efficiency of the
diode. Here, we also assume that all nuclear decays result in the
þ 2 kV
production of positive ions giving the lower limit for V eff
.
The minimum detected activity (MDA) of the positive ions is
determined via the background measurement. In the energy
region of 214Po α-decay the background index B was found to be
5.3(71.2) 10 3 cps. The value was determined by a 1 h measurement in liquid nitrogen not doped with 222Rn (Fig. 4). The
detection limit (defined as signal to background ratio S=B ¼ 1) is
therefore:
MDA ¼
B
þ 2 kV
V eff
¼ 3:8 Bq=m3 ðliquidÞ
The MDA yields in gas phase 6.0 mBq/m3, compared to less
than 1 mBq/m3 for e.g. gas phase radon monitors [4]. One must
note that MDA depends significantly on the ion collection, and
might be greatly improved by the proper electric field shaping or
mixing of the liquid (influencing Veff).
3.3. Estimation of the ionic life-time
The ion of interest can retain charge long enough to be
transported by the electric forces with characteristic mobility μion.
Velocity of the ion is proportional to the applied electric field:
!!
!!
v ð r Þ ¼ μion E ð r Þ
ð1Þ
The range of the ion depends on the ionic life-time τ or nuclear lifetime, whichever is significantly shorter, and on external electric
field, i.e. strength E and shape. The cations (anions) drift along the
electric field lines, from higher to lower (lower to higher) potential
26
N. Frodyma et al. / Nuclear Instruments and Methods in Physics Research A 744 (2014) 21–29
areas:
! !!
!!
dr ¼ v ð r Þ dt ¼ μion E ð r Þ dt
ð2Þ
The ions may also form chemical compounds or complexes having
nonzero dipole moments, able to move in external nonuniform
electric field. Such movement is guided by the gradient of the E-field.
IThe drifting ends when the ion of interest decays in a new
ionization event or neutralizes by attaching a free electron or by the
electron exchange process. The cation may also stick to a surface in the
liquid environment (electrode, container wall, etc.). The ability of the
ion to adhere to the surface is determined by physical and chemical
properties of the ion and the surface. The possible mechanisms are
neutralization on the metallic surfaces, chemical binding (chemical
reactions with reactive surfaces), triboelectric or mechanical binding
(in pores or surface roughness, etc.).
In our setup the surface of the Si-PIN diode was usually placed
d¼ 65 mm away from the bottom of the dewar, facing downwards.
The mean field strength induced by 72 kV of the bias was thus
E¼ 30 V/mm. In the case of positive ions the life-time can be estimated
(cf. Eq. (1))
τþ ¼
d
65 mm
r 91 s
¼
Eμion 30 V=mm 0:024 mm2 =Vs
ð3Þ
comparable to the life-time found for 208Tl ions [5]. The inequality sign
in Eq. (3) was deduced from a dedicated measurement, in which the
distance between the Si-PIN diode and the dewar bottom was
reduced, but no significant change in 214Po activity was observed.
For the negative-like ions similar measurements gave τ Z 46 s, since
the negative-like ion mobility is usually two times higher than that of
cations. The lower limit was indicated by the lowering of 214Po
registered activity in correlation to the reduction of the distance
between the Si-PIN diode and the bottom of the dewar. The value of
the mobility μion in both cases was adapted from data obtained for
226
Th ions in liquid xenon [6], which has a comparable atomic weight.
n ultra-pure liquids the life-time of positive ions should be
much longer. Lower concentration of neutralizing agents should
also suppress formation of the negative-like compounds of 222Rnborn isotopes.
3.3.1. Signal shape during change of the bias polarity or magnitude
The 214Po signal shape during the bias polarization change
(preserving the HV magnitude or turning on of the bias) may be
described as a combination of two processes: (a) decay of the
diode surface residual activity, and (b) time varying flux ΦðtÞ of the
new ions attracted by the reversed bias
AðtÞ þ = ¼ Bðt; N Po ; N Pb ; N Bi Þ þ bþ ΦðtÞ
ð4Þ
214
where B is the Bateman expression for
Bi activity (observed via
214
Po) as a function of time and amounts of 218Po, 214Pb and 214Bi
deposited on the Si-PIN diode before the bias change – cf. Table 1
(residual activities are not necessarily in secular equilibrium),
b – background, and Φ – flux of the incoming ions.
The flux ΦðtÞ depends on geometry of the electric field, ion
production and transport mechanisms and ionic life-time. To a
first approximation, one can assume that the E-field close to the
diode has the spherical symmetry of a charged sphere (EðrÞ ¼ k=r 2 ,
radius assumed to be equal 10 mm.2)
The distance dr traveled by an ion in a time dτ is directly related
to the ion transport properties (cf. Eq. (2))
dr ¼ μion EðrÞ dτ ¼ μion
k
dτ
r2
ð5Þ
2
The constant k may be easily found by evaluating the applied voltage on a
distance between the diode (spherical surface) and the dewar bottom (d ¼ 65 mm):
R 10 þ 65
R 75
2000 V ¼ 10
EðrÞ dr ¼ 10 ðk=r 2 Þ dr.
Table 2
Parameters of the 214Po signal investigated during bias voltage transitions (cf.
Eqs. (6) and (7). τmax was found to equal 88 s as a consequence of geometrical
limits. The Tm value in boldface (transition þ 2 kV- 2 kV) was fixed because the
fitting gave results beyond the life-time of the 222Rn daughters (the value
corresponds to the mean life-time of 214Bi.).
Transition
0-2 kV
2- 2 kV
2-2 kV
εC (%)
T0 (s)
Tm (s)
r (d 1)
47.1(0.5)
5.9(0.1)
21.6(0.3)
4.4(0.2)
0.65(0.02)
0.4(0.1)
1188
11.80(1.0)
55.6(0.3)
0.098(0.008)
9.56(0.06)
10.4(0.2)
Ions
Positive
Negative-like
Positive
where time τ is the ion collection time, limited by geometry of the
dewar. The maximum value of τ for positive ions was roughly
estimated to be τ þ ¼ 1:5 min. Also, ion flux is limited by both
neutralization (ionic life-time varying with time) and nuclear lifetimes (which are constant), therefore dΦðtÞ e λion ðtÞτ e λτ . Since
dΦðtÞ r 2 dr ¼ r 2 ðμion k=r 2 Þ dτ ¼ μion k dτ:
Z τmax
ΦðtÞ ¼ μion kρεC e λion ðtÞτ e λτ dτ ð1 e λt Þ
Z 0τmax
0
e λ ðtÞτ dτ ð1 e λt Þ
¼ μion kρεC 0
0
1 e λ ðtÞτmax
ð1 e λt Þ
¼ μion kρεC λ0 ðtÞ
ð6Þ
where ρ is the density of dissolved 222Rn activity (18.5 kBq in 32 L
of cryogenic liquid), εC is the probability of cation survival during
the germinate neutralization (determined in fitting of the data),
and 1 e λt term represents the activity buildup (it is assumed,
based on the previously determined Bateman equation coefficients, that the flux Φ consists only of 214Bi ions). Using this
equation one can also find the εC for negative-like ions (anions),
assuming that they exhibit mobility two times higher than the
mobility of cations. We also assume for simplicity, that the εC is
constant over the ion drifting range (site of ion production). Fig. 9
depicts the considered model of dewar bias change.
The ion life-time (T ion ðtÞ ¼ lnð2Þ=λion ðtÞ) depends on the local
concentration of the electronegative impurities (close to the diode
surface), which may be changed by presence of the E-field,
diffusion or other transport processes. Both maximum and minimum (local) concentrations of the impurities are limited by
convectional mixing of the cryoliquid, and are bound by the total
concentration of the impurities present in the dewar. One can
also conclude that the ionic life-time changes with time from a
minimum to a maximum value. This behaviour may be modeled
using a limited growth function
T ion ðtÞ ¼
T 0 T m ert
T m þ T 0 ðert 1Þ
ð7Þ
where T0 is the minimum ionic life-time (related to the maximum
local concentration of the impurities), Tm is the maximum ionic
life-time (minimum local concentration of the impurities), and
r is a change rate. (This function is a solution to the differential
equation dx=dt ¼ rxð1 xÞ, where xðtÞ ¼ T ion ðtÞ=T m and requiring
T ion ð0Þ ¼ T 0 ). Fig. 12 shows the signal shape for bias changed from
2 kV to þ2 kV. Table 2 summarizes the fit parameters. The value of
εC probability is comparable with the value calculated in Section 4.2.1.
Metallic surfaces of the container may adsorb impurities,
diffusing from the bulk towards walls of the dewar. This process
may be responsible for the observed 214Po signal shape when the
value of bias voltage is changed. Impurities neutralizing the
radioactive ions within normal operation of the system diffuse to
N. Frodyma et al. / Nuclear Instruments and Methods in Physics Research A 744 (2014) 21–29
the surfaces of the dewar and the diode. Bias potential prevents
them from re-entering the volume close to the sensitive surface of
the diode once they stick to other surfaces. When the bias voltage
is changed, the system becomes disturbed and impurities may be
freed, and begin to diffuse towards the surfaces again. For the
typical dimension of the diode (10 mm) the time scale of the
diffusion is 3 h (cf. Section 4.3), corresponding to the observed rate
r of ionic life-time change.
4. Model of ions behaviour in cryoliquids
Radon daughters form positive ions after α and β decays. Electrostatic force is capable of attracting them to the polarized surfaces. A
similar mechanism of ion drifting may be a source of increased
background for other isotopes present in liquid gases, like 42K, a
daughter of 42Ar abundant in natural argon. We discuss here processes
responsible for formation of ions and electron–cation pairs after
α- and β-decay processes occurring in liquefied gases.
4.1. Ionization
Radioactive decays in liquefied gases produce electron–ion
pairs along the track of an alpha or beta particle. Loss of the
released kinetic energy is dominated by electronic interactions
and collisions in traversing matter [a- and e-star]. Radiative loses
may be neglected for typical energies deposited by radiation (e.g.
Q¼7.7 MeV for 214Po and Q¼3.3 MeV for 214Bi). The deposited
energy Q is therefore expended in the production of a number
of electron–ion pairs, Ni, excitation of atoms and sub-excitation
electrons, and directly in atomic motion Ek
Q ¼ E þEk
ð8Þ
where E is an average energy transferred to the electrons of the
medium. E is defined as
E ¼ Ni Ei þ Nex Eex þ Ni ε
ð9Þ
where Ni is the number of electron–cation pairs produced with an
average energy Ei, Nex is the number of medium excited atoms
with an average energy Eex, and ε is the average kinetic energy of
the sub-excitation electrons (unable to ionize or excite atoms,
considered as heat). The average energy required to produce one
electron–ion pair W is defined as
W ¼ E=N i
ð10Þ
E.g. the value of W for liquid argon is 23.670.3 eV, small compared to
the Q value.
Alpha decay recoil atoms also become charged after the decay.
Recoil energy of the ion (typically 100 keV per recoil atom in
α-decays) is dissipated in subsequent collisions with the surrounding matter, creating electron–ion pairs (with pair production
energy W). An initially negatively charged recoil atom (due to
emission of an alpha particle) easily strips off its valence electrons
in these interactions. In consequence the atom becomes positively
charged. If the cation is multiply charged, then the process of
recombination described later in this paper, leads to the singularly
charged cation state. Likewise in the case of β decay, in which the
recoil energy is much lower, the atom is already initially positively
charged and no electron stripping occurs.
4.2. Recombination
The cations (recoil ions and ions of the medium) eventually
recombine. There are three recognized types of recombination.
The initial recombination (also called germinate recombination) is
important for understanding the differences in the amount of
ionization induced by α and β-decays. The bulk recombination is
27
connected with the nonzero impurity content of the cryoliquid.
Columnar recombination is only relevant in the unlikely case that
the tracks of ionizing particles are parallel to the external electric
field, and thus will not be discussed.
4.2.1. Initial recombination
An electron freed from an atom in an ionization process may
neutralize the cation of its origin. High ionization density of
α-decays leads to more efficient initial recombination. Electron–
cation pairs produced in β-decays are less prone to initial recombination due to lower ionization density.
The response of a charged particle to the pull of an electric field
in dense medium depends on the size of the particle. The mobility
of free electrons μ is high (μ ¼ 1:5 102 cm2 V 1 s 1 [7]) in
comparison to the mobility of heavier ions (μion ¼ 2:4
10 4 cm2 V 1 s 1 for 226Th in liquid xenon [6]). Consequently,
an electric field rapidly separates the electrons from the almost
immobile ions. Effective charge dissociation depends upon the
field strength, and facilitates preservation of the cations during the
initial recombination.
The model proposed by Thomas and Imel [8] (and its extension
discussed by Thomas and Imel in further publications) describes
the probability of survival of the charge C0 (electron–cation pairs),
depending on the type of the energy deposition processes leading
to electron–ion pair formation (α- or β-decay) and on the external
electric field
C ¼ C0
lnð1 þ ξÞ
ξ
;
ξ¼
Ni α
4a2 μ E
ð11Þ
where Ni is, as previously, the number of electron–cation pairs
produced within a box of dimensions a, α the recombination
coefficient, μ is electron mobility, and E is the electric field
strength. The value of ξ is usually treated as a free parameter and
fitted to the data, e.g. the result of the fit provides ξβ E ¼ 840 V=cm
for 364 keV electrons, and ξα E ¼ 470 kV=cm for 5.64 MeV
α-decays [8]. The significant difference in the ξ values for α and
β particles originates from the different ionization densities
caused by α and β radiation (through Ni and a).
The probability of cation survival C=C 0 during the germinate
neutralization in the electric field E ¼30 V/mm, produced by a
β-particle is εC β ¼ 48%, whereas in the case of α radiation the
probability is εC α ¼ 0:47%, over 100 times lower. This result could
explain the big relative difference in observed 218Po and 214Po
count rates (cf. Table 1). 218Po is produced in alpha decays, thus
becomes ionized with much lower probability, compared to 214Bi
ions produced in beta decays.
4.2.2. Bulk recombination
The cations dispersing in the volume may be neutralized in
several ways. Cryoliquids contain electronegative impurities, such
as traces of oxygen, carbon dioxide and nitrous oxide. The
impurity atoms attach to free electrons, and then may neutralize
ions of interest in an electron exchange process. The reaction is
21x
Y þ þ Z -21x Y þ Z
21x
ð12Þ
222
218
214
where
Y denotes one of the
Rn daughter atoms ( Po,
Pb,
214
Bi), and Z is the impurity atom. The decrease of cation
concentration ½Y is given as
d½Y
¼ kYZ ½Y½Z
dt
ð13Þ
where ½Z is the concentration of impurities, and kYZ is the
attachment rate constant. The attachment rate constant depends
on the type of neutralized ion Y, and the type of electronegative
impurity Z. The temporal behaviour of the cation concentration ½Y
28
N. Frodyma et al. / Nuclear Instruments and Methods in Physics Research A 744 (2014) 21–29
Table 3
First and second ionization potentials of the chosen elements from 222Rn decay
chain and gap energies of select liquefied gases used in low background experiments. Gap energy is the energy required to free a bound electron in dense
environments (liquids and solids).
Atom
1st (eV)
2nd (eV)
Rn
Po
Pb
Bi
10.8
8.43
7.42
7.29
–
–
15.0
16.7
Gap energy (eV)
Ar
N2
Kr
Xe
15.8
14.5
14.0
12.1
–
–
–
–
ð14Þ
and the time
τ ¼ ðkYZ ½ZÞ 1
ð15Þ
is called the cation (ionic) life-time. Attenuation length of the
cations, i.e. the distance traveled in electric field E with mobility
μion, on which 1=e of the cations retain their charge, is therefore
λ ¼ μion Eτ
ð16Þ
If the cation undergoes a radioactive decay, then the nuclear lifetime comparable with τ or shorter should also be taken into
account when calculating the attenuation length.
The cations may also be directly neutralized by the free
electrons
21x
Y þ þ e -21x Y
ð17Þ
but the level of impurities is the ion life-time limiting factor. The
amount of impurities outnumbers electron–cation pairs produced
in α or β-decays (typical impurity content of 4.0 class liquid
nitrogen or argon is at the level of ppm3 or more).
The first ionizing potential (IP) is the energy required to remove
a bound shell electron from a neutral atom. The second ionizing
potential is a potential associated with the removal of a second
electron from a singly ionized atom. Ionizing potentials of 222Rn
daughters are given in Table 3, together with gap energies of
liquefied gases for comparison. Gap energy is the energy required
by a valence electron (bound on the outer shell) to become a
mobile charge carrier, able to move freely within the dense
material (liquefied gases).
Differences in the first IPs of recoil ions and gap energies of the
medium atoms exceeding 2 eV allow an electron exchange process
between the neutral recoil atom (possibly neutralized after the
decay) and an ion of the medium:
21x
Y þ A þ -21x Y þ þ A
ð18Þ
Therefore the recoil atom may be recharged in the certain circumstances, and may exhibit extended ionic life-time. High values of
the second IPs of the elements disallow multiple ionization
(21x Y þ þ , 21x Y þ þ þ , etc.) in the electron exchange process, favoring
singular ionization.
4.3. Diffusion of impurities
Neutralizing agents and the ions are also subject to diffusion processes in the cryoliquids. The diffusion is governed by
3
ppm – parts per million.
where D is the diffusion coefficient and t is the time of random
walk. An ion carrying a charge q, following Einsteins relation, has
the diffusion coefficient D expressed as
kT
D¼μ
q
is therefore
½YðtÞ ¼ Y 0 e kYZ ½Zt
3-dimensional Brownian motion. The average distance s traveled
by a particle is
pffiffiffiffiffiffiffiffi
s ¼ 6Dt
ð19Þ
ð20Þ
The same estimation may be valid for neutral atoms (like impurities), assuming that their diffusion coefficient is comparable
with the diffusion coefficient of the same charged atoms in the
cryoliquid. While the drift induced by an electric field is dominant
for charged atoms, the diffusion processes might be important for
neutral corpuscles.
A typical value of mobility of 226Th (NBP4) [6], μion ¼ 2:4
2
10
mm2 V 1 s 1 , yields the value of Dion ¼ 1:6 10 4 mm2 s 1 .
The average distance traveled by a neutral particle in 60 s is then
s ¼ 0:23 mm. The distance traveled in the same time by a charged
particle in a field E¼ 30 V/mm is r¼43 mm. In the case of lighter ions
[9], like impurities, the mobility μimp ¼ 2:5 10 1 mm2 V 1 s 1 ,
renders Dimp ¼ 1:66 10 3 mm2 s 1 . The average diffusion range is
then s ¼ 0:77 mm in 60 s.
Also, one should consider other causes of atomic motion
present in the liquids, like convection. Mixing of the liquid caused
by temperature gradients present in the experimental setup may
float the atoms of interest regardless of their charge, type, etc.,
altering the effective particle mobility in the macroscopic scale.
5. Conclusions and outlook
We have shown that it is possible to observe alpha-activity of
positive and negative 222Rn-born ions, enhanced by electrostatic
collection in cryogenic liquids. The maximum life-time of ions,
varying in long time-scales, was found to be on the order of 10 s.
We also conclude, that the changes in local properties of the liquid,
such as diffusion of electronegative impurities on long time-scales,
influence the measurement results. This effect should be further
investigated. We have also shown, that the Box model of germinate neutralization well describes observed differences in 214Po
(214Bi) and 218Po activities. The amount of negative-like ions
produced is below 1 %, and their life-time is mainly limited by
the nuclear life-time.
The main source of systematic errors, not covered in detail in
our data analysis, was the uncertainty originating in 222Rn dissolving procedure. We would like to pursue our activities further
investigating 218Po transport and production properties, and limiting sources of uncertainties. We also plan to employ electric field
calculations to improve understanding of the germinate neutralization process influence on ion production (in reality εC depends
on the ion production site as the E-field varies with distance [10]).
We would also like to perform detailed MC simulations of the
214
Po peak shape to determine the exact location of 214Bi ions in
the vicinity of the Si-PIN diode.
Various background reduction techniques essential to the
experiments are adopted, such as material selection, purification
and cleaning, signal analysis, crystal segmentation and cryogenics.
Submerging bare germanium crystals in a high purity cryogenic
liquid is one of the most promising developments in ultra low
background spectroscopy. The IGEX [11] and Heidelberg–Moscow
(HdM) [12] double-beta decay detectors were both shielded
4
NBP – normal boiling point (temperature of a liquefied gas under standard
pressure).
N. Frodyma et al. / Nuclear Instruments and Methods in Physics Research A 744 (2014) 21–29
against external background using muon veto and passive shielding
and were located in underground laboratories (IGEX in Canfranc
Underground Astroparticle Laboratory and HdM in Laboratori Nazionali del Gran Sasso). As shown by those experiments, the main source
of background in the detector after the removal of radon was the
radioactive contamination of the supporting structures of the germanium crystals held in ordinary vacuum cryostats and the shielding
materials.
The concept of bare HPGe detectors operated in liquid nitrogen
or argon was initially developed for experiments searching for
neutrinoless double-beta decays, such as GERDA, designed to both
achieve the lowest possible background levels and to maximize
experiment's sensitivity to registering rare events.
The electrostatic drifting of the radioactive ions present in
cryogenic liquids could be used as a new background reduction
technique in ultra-low background experiments employing the
knowledge gained in this research. The ion life-time, charge and
mobility have great importance in the design of new experiments. The long life-time allows to effectively shift the ions
distribution before the radioactive ions decay inside the active
volumes of experiments. The negative-like ions produced
should also be taken into account as they move in the electric
field opposite to the direction of the positive ones. Even the
small fraction of negative-like ions activity may build up in the
active volume due to the electric field posing as an unintended
background source.
29
Acknowledgments
The authors wish to thank G. Zuzel of M. Smoluchowski
Institute of Physics, Jagiellonian University Kraków, for valuable
discussions. We acknowledge support by the Foundation for Polish
Science – MPD program, co-financed by the European Union
within the European Regional Development Fund. This work was
also supported by a grant from the NCBiR in the frame of the ERANET ASPERA II Programme. We also acknowledge financial support
by Jagiellonian University (Institute of Physics, DSC 2012).
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