Cryogenic Micro-Calorimeters for studies of LE Implanted
RNBs
P. A. Voytas
Physics Department, Wittenberg University, Springfield, OH 45501-0720 USA
Abstract. Cryogenic micro-calorimeters can serve as sensitive and efficient high-resolution detectors for low-energy
phenomena–particularly those involving short-range products. Specific details of the use of these detectors will be discussed
in the context of recent measurements of the L/K capture ratio in 7Be [1]. Applications to other low-energy measurements
will also be explored.
INTRODUCTION
Absorber
Many discoveries in physics (as well as other fields) have
been the result (or at least the beneficiaries) of technological advancement. Such advancements improve our
ability to probe and to observe a great variety of phenomena. Over the last 15 years, the cryogenic microcalorimeter has emerged as a technology with unique capabilities. Combined with the capability for implantation
that comes with the availability of low energy (LE) radioactive nuclear beams (RNB), microcalorimeters have
been opening up new measurement possibilities, particularly for low-energy nuclear phenomena.
Thermometer
Weak Link
Heat Sink
FIGURE 1. Schematic of a cryogenic micro-calorimeter.
(NTD) thermistor. The sensitivity of calorimeters based
on these thermometers is governed by the random transfer of energy between the absorber/thermometer and the
heat sink. A simplistic statistical model of these fluctuations in energy results in an expression [2] for their amplitude:
∆E 2 kT02C (1)
CRYOGENIC MICRO-CALORIMETERS
As the name implies, cryogenic micro-calorimeters operate on the long-understood principles of calorimetry. A
given energy deposited in a given material results in a
temperature rise. The cryogenic micro-calorimeter consists of a sample or absorber (of heat capacity C) in
which the deposited energy causes the temperature rise,
some sort of thermometer to measure the temperature,
and a weak thermal link (of thermal conductivity G) connected to a heat sink. A schematic diagram of such a device is shown in Figure 1. There are two widespread implementations of the cryogenic micro-calorimeter, differing primarily in the type of thermometer employed.
Here, T0 is the temperature of the heat sink, C is the (temperature dependent) heat capacity of the absorber, and k
is the Boltzmann constant. These fluctuations represent
the background noise of the system above which any signal must be detected. From Equation 1 it is easy to see
that a low temperature is beneficial directly (through the
T02 term) and indirectly (through the temperature dependence of C). Indeed, for insulators and narrow-gap semiconductors, the heat capacity is dominated at low temperatures by the T3 dependence of the lattice contribution. This makes possible extremely low values of C rendering these materials particularly attractive for microcalorimeters. In contrast, the Fermi gas contribution from
Thermistor-Based Calorimeters
The first and most well-developed version of the
micro-calorimeter uses a neutron-transmutation-doped
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
56
ture is considerably more difficult than the NTD thermistor based ones.
A further advantage of using a TES sensor is that
the faster response time effectively allows larger heat
capacity absorbers to be used without sacrificing energy
resolution.
the conduction electrons in metals is problematic in some
calorimeter designs.
The choice of size and material for the absorber is
dependent on the desired resolution and on the thermal
properties of the absorber material. If the statistical fluctuations are not to dominate at, for example, the 1 eV
level, then an operating temperature of 50 mK would imply a heat capacity of 4 64 106 eV/K or 7 4 10 13
J/K. While small, these heat capacities are obtainable
in insulators and narrow-gap semiconductors. HgTe is a
zero-gap semiconductor and one of the best-studied absorber materials in the context of x-ray detection. Insulators suffer by comparison in that some of the deposited
energy can be trapped in non-thermal modes (for example electron-hole pairs) which can lead to pulse-height
defects.
A key advantage of the thermistor-based microcalorimeter is that it is able to take advantage of the
expertise in micro-machining and doping of silicon that
is available from the semiconductor industry.
The signal in such a calorimeter is characterized by
rapid rise in temperature followed by an exponential falloff that has a time constant equal to C/G. This time scale
may be on the order of 10 ms or more, depending on the
details of the design. This timescale limits the acceptable
count rate for thermistor based micro-calorimeters to 1
Hz or less to avoid significant pile-up problems.
Implantation
Implantation has great promise in the improvement
of the measurements discussed in the next section. The
uniform distribution and direct coupling between the radioactive atoms of interest and the absorber that is possible with implantation should greatly improve the reliability and resolution of the experiments. To date, implantation has not been very widely used with microcalorimeters. The complexity of the cryogenic microcalorimetric techniques has been difficult enough during
its development stage to make implantation seem an impracticable extra. With more RNB facilities on-line and
coming on-line and with a more mature calorimeter technology, combining the two techniques is more attractive
and feasible.
MICRO-CALORIMETER
APPLICATIONS
Transition-Edge-Sensor-Based
Micro-calorimeters
We turn now to past and present applications of these two
versions of these detectors.
The second variety of micro-calorimeter uses a superconducting film to determine the energy deposited. The
film is operated in the middle of the transition between
the normal and superconducting state. Since the transition can be quite sharp, this type of detector has a high
sensitivity. Furthermore, if it is operated under conditions of Extreme Electrothermal Feedback (ETF)[3] it
can have an effective time constant that is much shorter
than the C/G time scale mentioned above. In ETF, the superconducting film is voltage biased until the Joule heating exactly balances heat transfer to the heat sink. When
energy is deposited in the absorber, the temperature rises,
the resistance increases, and the Joule heating decreases.
By monitoring the current at a given bias voltage, the total reduction in energy supplied by Joule heating can be
measured. This energy is equal to the energy deposited in
the absorber. This method involves a faster response time
and is not limited to resolutions implied by Equation(1)
because the mechanism is not governed by lattice conduction to the reservoir. Count rates of 100-500 Hz have
been achieved with these Transition Edge Sensor (TES)
based calorimeters detecting x-rays, but their manufac-
Neutrino Masses
Neutrinos have long been assumed to be massless or
nearly massless. Great attention has been focused in the
last few decades on experimental determinations of their
mass. This attention has grown more intense with the
recent evidence for a nonzero mass difference between
at least two flavors of neutrinos[4]. The absolute scale of
any neutrino mass has yet to be determined, though direct
measurements have produced the bound mν e 3 eV/c2
[5]. Micro-calorimeters are one technology that has the
potential for pushing this bound below 1 eV.
Micro-calorimeters have been used in several ways to
look for massive neutrinos. All make use of the advantage these detectors have over the usual spectroscopic
techniques. In these applications, micro-calorimeters use
completely contained radioactive sources, allowing the
total decay energy (less the energy carried away by the
neutrino) to be measured. This is in contrast to most other
techniques in which involve separate source and detector.
In separate source/detector experiments, the energy of
57
the outgoing electron is affected by the final atomic state
the source atom or molecule happens to be left in. For
useful limits to be placed on eV scale neutrino masses,
these final state effects in the source must be determined
to at least the eV scale as well.
Searches for mν e
Q-value for the decay, and Ei is the excitation energy
released after the capture of the electron.
This technique is only sensitive if the neutrino mass
is close to the Q-value. 163 Ho has the lowest Q-value
electron capture at 2.5 keV. Experiments reported on
in 1998 [9] demonstrated proof-of-principle, but were
limited by an inhomogeneous sample. Implantation or
alloying would greatly improve uniformity and provide
a feasible mass measurement.
0 in β decay
The shape of the spectrum in β decay is different
if mν e 0 than if the neutrino is massless. Searching
for this shape difference has been a primary means of
investigating neutrino mass issues and has largely been
done using magnetic spectrometers of various types. An
early calorimetric measurement of mν e was made during
the search for the 17 keV neutrino. 107 Pd was enclosed in
an absorber and attached to a NTD thermistor [6]. This
was one of the first cryogenic measurements that did not
support the 0.8% branch of a 17 keV neutrino.
A 3 H experiment which uses TES based sensors has
had some preliminary data taken[7]. This experiment
used tritium implanted in copper foil. Unfortunately,
problems with the TES producing apparatus stalled
the work and the 187 Re eperiment below shows more
promise statistically due to the lower endpoint energy of
187 Re.
187 Re is the experiment that has produced the tightest
limits to date[8]on mν e . Due to the high natural abundance of 187 Re (62.6%) and its long lifetime (4 12
1010 yr)this experiment requires a sample of about 1.5 mg
and implantation would be of no benefit. This experiment
is poised to play a part in pushing the limits on mν e below
1 eV.
Searches for mνe
Other Observables
Besides mν e and mνe , the calorimetric methods are
well suited to measuring other beta decay observables
in low energy systems. Q-values determined calorimetrically for 163 Ho[9],187 Re[10], and 107 Pd[6] have all made
significant improvements (by factors of 5-30) over previous values. This is, again, due primarily to the lack of
atomic final state effects which usually complicate these
low energy measurements.
Another observation has been the first detection in
187 Re of a unique effect due to the presence of the surrounding crystal. This effect arises when the outgoing
electron interferes with its reflection from the surrounding crystal lattice. This changes the decay rate in a way
that is periodic with the outgoing electron’s momentum
[11].
Other Effects in Electron Capture
7 Be is the lightest nucleus that decays via electron cap-
ture, with a maximum energy release (excluding the energy of the emitted neutrino) of 112 eV. This is divided
between the nuclear recoil of the daughter nucleus and
the energy release, in the form of x-rays or Auger electrons, due to the rearrangement of the atomic shells. Due
to this very small energy release, the properties of the
decay have been very difficult to study and the L/K ratio
has never been accurately measured. Using a NTD based
cryogenic micro-calorimeter with an energy resolution of
8.5 eV FWHM and an threshold of about 20 eV, we have
been able to separate the different features of the decay
energy spectrum, leading to the first direct exploration of
the L/K ratio in 7 Be [1].
The 7 Be was produced with the TWINSOL [12] secondary radioactive beam facility at the University of
Notre Dame. A 100 particle-nA beam of 6 Li at 15 MeV
was incident on a 2.54 cm long gas cell filled with one
atmosphere of 3 He, producing 7 Be via the 3 He(6 Li,7 Be)d
reaction. Recoil 7 Be ions at a central energy of 8.5 MeV
were brought to a focus 5.5 m downstream of the 3 He
cell by two superconducting solenoids. A target holder
0 in electron-capture decays
While much emphasis has been placed on mν e
searches in β decays, the electron capture (EC) process
is sensitive to certain ranges of mνe . This sensitivity
comes about from the fact that the electron capture rate
depends on the energy released in the decay and that
energy depends (due to differences in atomic electron
binding energy) on which atomic shell the electron was
captured from. In general the capture rate from shell i is
λi
K βi2 Bi QEC Ei QEC Ei 2
m2ν (2)
where λi is the EC rate from atomic shell i, K contains
nuclear matrix elements and weak interaction strengths,
β is the value of the electron wavefunction at the nucleus,
Bi takes into account exchange effects and the imperfect
overlap of initial and final atomic states, QEC is the
58
electron capture of the parent atom residing in a lattice
have had great success in quantitatively describing the
change in lifetime of 7 Be when it is implanted in a host
lattice [15]. (A correct treatment of this effect is quite
important since it affects the determination of the nuclear matrix elements used in describing the fusion reactions in the sun and therefore the rate of neutrino production.) Subsequent calculations of this "in-medium" effect
on the L/K ratio [16] predicts a value of about 0.052 for
the L/K ratio of 7 Be implanted in HgTe, in much better
agreement with our measured value.
PROSPECTS AND CONCLUSIONS
These results are but a sampling of the work that is
being done with cryogenic micro-calorimeters to study
low-energy nuclear phenomena and represents only the
beginning of their possible applications. At the present
time they are limited more by a lack of widespread
awareness of their capabilities and lack of imaginative
use than by any technical hurdles.
FIGURE 2. Energy spectrum from 7 Be electron capture decay. The smooth curve is the combined fit with individual contributions to the fit shown below it. The peaks labeled K-Gnd
and L-Gnd correspond to captures from the K- or L-shell, respectively, to the ground state of the 7 Li nucleus. The regions
labeled K-Ex and L-Ex correspond to captures to the first excited state of the 7 Li nucleus.
ACKNOWLEDGMENTS
Supported in part by the National Science Foundation
and Wittenberg University.
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