CUORE: a Cryogenic Underground Observatory for Rare Events

ABSTRACT

We suggest the construction of an array of one thousand cryogenic thermal detectors as an observatory for rare events to be located in the Gran Sasso underground laboratory. CUORE (Cryogenic Underground Observatory for Rare Events) is a large extension of our array of twenty TeO₂ crystals. We discuss, in this design study, detectors with 750 g TeO₂ absorbing crystals, but other materials like Germanium and Lead Tungstate can also be considered. The potentialities and the flexibility of CUORE are discussed in view of experiments on double beta decay, direct detection of Weakly Interacting Massive Particles, solar axions and possibly also interactions of antineutrinos from artificial sources.

Some practical considerations and the conditions to make the construction of CUORE a realistic project are tentatively reported.

1. INTRODUCTION

Most of the interest in underground physics is presently devoted to the search for rare events. Typical examples are radioactive processes like single and double beta decay [1], decays in alpha particles or other complex nuclei [2] and interactions of solar neutrinos [3], axions [4] and Weakly Interacting Massive Particles (WIMPS) [5]. Underground experiments with "artificial" neutrinos have been carried out with ⁵¹Cr sources to test the performance of solar neutrino detectors [6], but measurements of neutrino interactions, especially with the aim to search for a non zero neutrino magnetic moment have also been considered [7]. At higher energy, long baseline underground experiments with neutrinos from accelerators are also planned [8].

In all these experiments the overburden of rock in an underground laboratory ensures against the background due to cosmic rays. In the search for low energy events it is also essential to suppress the radioactive environmental background and to investigate and reduce the intrinsic radioactive contamination of the detector. Other requirements are a good energy resolution, low threshold and in some cases, like in the search for WIMPS, a specific good detection efficiency for particles like nuclear recoils. The use of large cryogenic thermal detectors in searches for rare events like double beta decay has been suggested since 1984 [9] and a series of experiments with large TeO₂ bolometers has been carried out in the last 8 years by the Milano group in the Gran Sasso underground Laboratory. The same group has recently constructed and is going to operate an array of twenty of these crystals with a total mass of almost seven kilograms [10]. Three other calorimetric experiments specifically devoted to the search for WIMPS are presently in the running stage [11-13], others are planned [14].

The principle of operation of these bolometers [15] is as follows. A dielectric and diamagnetic crystal is kept at low temperatures (tens of millikelvin) in a dilution refrigerator. In such conditions the heat capacity is very low, being proportional to the cube of the ratio between the operating and Debye temperatures. As a consequence even the tiny energy released in the crystal by a nuclear event can be revealed and measured by the increase in temperature recorded by a sensor in thermal contact with the absorber. We would like to note that the energy resolution of these bolometers is theoretically much superior than that of conventional detectors, since the "elementary energy deposition steps" produced by the particle are phonons with energies of 10^-4 to 10^-5 eV. As an example a bolometer made by one kilogram of germanium operated at 10 mK would yield a FWHM resolution of 10 eV even at energies around one MeV. In practice however effects like microphonism , sensor and spurious electronic noise , position effects , instability of the temperature and therefore of the gain etc. prevent from reaching these exceptional goals. At present, however, microbolometers with an absorber mass of a milligram or less reach energy resolutions superior by an order of magnitude with respect to Si(Li) semiconductors in the keV region , while in the MeV region macrobolometers with masses of a few hundred grams are competitive with Germanium diodes.

The twenty TeO₂ crystals array of our group is going to be used to search for double beta decay of ¹³⁰Te, for direct interactions of WIMPS and for the recently proposed search for solar axions [16,17]. As a further decisive step we propose an international collaboration to construct CUORE (Cryogenic Underground Observatory for Rare Events) a cryogenic set-up made by a thousand crystals [18] each of a mass similar to the present ones, and a total mass near to one ton. In our opinion this set-up will allow to achieve important results in fields like double beta decay, direct interactions of WIMPS, solar axions and neutrino interactions from an artificial source. We would like however to stress that the possibilities offered by the device proposed here should be by no means limited to these subjects. A peculiar property of cryogenic detectors, unlike conventional ones, is that they offer a very broad choice of nuclei in the detecting materials and an the possibility to exchange them or, at least in principle, to run the set-up contemporarily with different nuclear targets. This will make CUORE an essential facility for the development of future underground physics.

The study of solar neutrinos and particularly the solar neutrino spectroscopy with cryogenic detectors is of obvious interest and we have already considered a possible experiment with NaBr crystals [19]. CUORE has a mass obviously inadequate to these aims, but could represent the first and decisive step towards this ambitious goal.

We present here a scheme of the detector and a brief outline of some experiments to be performed with it. Some practical considerations and a very rough evaluation of the time needed for its construction will be also reported.

2. SCHEME OF CUORE

The scheme proposed here is to be considered as a preliminary one and it is obviously based on the experience collected so far by us in the construction of our array of twenty crystals of TeO₂ of 340 g each, whose main aim is the search for double beta decay. The size of the crystals proposed here is different and the mass larger by a factor of two: this should be checked and tested previously in collaboration with our furnisher: the Shanghai Quinghua Nonmetal Material Corporation, the largest producer of crystals of this material. We would like to stress however that by no means we should consider only this material and therefore only this furnisher. The advantage in CUORE of the unique flexibility of cryogenic detectors in the choice of the detecting materials should not be forgotten . While essential for double beta decay of ¹³⁰Te and also promising for searches of WIMPS, TeO₂ is not one of the best candidates for a thermal detector, also because its Debye temperature is of 265 K only. Other materials have been tested as absorbers for bolometers, in particular CaF₂, LiF, NaBr, CdWO₄, Ge by us and Al₂O₃, Si,Ge and LiF by other groups [15,18]. As a possible alternative to TeO₂ we are going to discuss, especially for searches on WIMPS, other materials of high atomic number. In particular we will consider, and are going to test in the immediate future, large crystals of PbWO₄ made in collaboration with the Preciosa factory in the Czech Republic with Roman lead pre-measured and provided by us (see later).

We will discuss now a few preliminary experimental and technical details.

2.1. THE CRYSTALS

Our tentative plan is based on an array of one thousand cubic crystals of TeO₂ of 5 cm side with a mass of 750 grams each, about twice the mass of the presently operating ones. We expect that they should operate successfully , but a final decision on the sizes will be taken only after tests in collaboration with Shanghai Quinghua Nonmetal Material Co, or eventually with other factories. The array will be made by a cube with ten crystals on each side with a determined orientation (e.g. <100> ) for a possible search on axions (see later). Taking into account also the copper frame necessary to hold the crystals and allowing for thermal and electronic connections, we foresee a cube of 70 cm side and a total mass around one ton. Stabilization of the crystal response is essential to cure thermal instabilities and consequent fluctuations in the gain. We plan to adopt the same procedure that we have already tested and that will be adopted in the the twenty crystal array: a periodic injection in the absorber of Joule power through an heavily doped meander on a Si chip glued on it [20].

2.2. THE THERMAL SENSORS

In the present array we adopt Neutron Transmutation Doped (NTD) germanium thermistors, provided us by prof. E. Haller, as thermal sensors glued on the crystals. They are very reproducible and easy to handle , which is obviously essential in an array with a large number of bolometers. Our collegues of the CDMS dark matter experiment, who also adopt germanium NTD thermistors as sensors, but in eutectic contact with Germanium absorbers [11], claim a large background at low energy due to contamination of tritium which is normally produced in the thermistors as a consequence of the neutron irradiation. In our case this background seems not to be a serious problem, since the thermal signals in the thermistor can be easily distinguished from those in the absorber by pulse shape discrimination. In the CDMS experiment [11] some pulses seem to come indeed from the absorber where some tritium has possibly diffused through the eutectic germanium-gold-germanium contact. The problem needs obviously to be studied further.

An alternative option for thermal sensors is adopted by the CRESST dark matter collaboration [12] with tungsten superconducting phase transition thermometers, read out by commercial DC-SQUIDS. These and other [15] thermal sensors could also be considered , but we believe at present that the NTD option is preferable in a large array like ours, being simpler , less critical to changes in the temperature of each absorber and definitely less expensive. Crystals operated contemporarily with NTD thermistors and with superconducting edge thermometers, to investigate the high and low energy regions of the spectrum , respectively, could also be considered if this solution should prove to be technically and financially viable.

2.3. LOCATION AND CRYOGENICS

The best location for CUORE is the future Hall D to be constructed in the Gran Sasso Underground Laboratory (LNGS) and to be devoted to cryogenic experiments. In the case this Hall should not be constructed in time, other locations in the same laboratory are possible even if much less preferable. The overburden of rock in LNGS reduces the muon and neutron background by six and three orders of magnitude, respectively [21].

The construction of a dilution refrigerator capable to cool the array down to 10 mk should be done in collaboration with a highly specialized factory. Much care will be devoted , like in the past, to the choice of materials with very low radioactive contamination to be employed in the construction. As a first hint we are considering a structure made by vertical copper bars to which the bolometers are fastened in order to allow a reasonably easy access to all of them. This would enable each crystal to "see" almost completely all the surrounding ones and allow the use of the coincidence-anticoincidence method which we consider essential for the background reduction. We expect the total volume of the cryogenic set-up to be of 70 x 70 x70 cm³. Taking into account the thermal shields, a reasonable final structure of CUORE would be a cube of 90 cm side. The total mass of the copper frame could be about 200 kilograms.

Severe technological problems should come from the internal shield of Roman lead directly connected to the mixing chamber and from the large number of wires entering the array. We foresee 2000 wires connected to the sensors and 200 wires for the heaters which allow response stabilization [20] (groups of 10 heaters would be linked in parallel). In addition 50 wires will be needed to connect 25 thermometers in various positions inside the array. Alternative electric connections can be envisaged, and are presently being studied.

2.4. SHIELDING

The shielding against local radioactivity could be an improved version of the one presently adopted for the twenty crystal array. An internal shield could be made by a layer of 4 cm minimum thickness of Roman lead which has been found [22] to be totally free from radioactivity due to ²¹⁰Pb (see later). To avoid any perturbation on the cryogenic system (excessive cooling time etc) most or all the lead could be placed immediately outside the cryostat. Even in this case the amount of Roman lead needed (about 2.5 tons for a thickness of 4 cm) would be available in the Gran Sasso Laboratory together with the expertise to produce an efficient shielding. The external shield should be made by two layers of lead with low and medium content of ²¹⁰Pb, respectively, and with a minimum thickness of 10 cm each. The masses would be of about 10 and 12 tons , respectively.

The entire set-up should be inside a Faraday cage to avoid electromagnetic interferences.

2.5.BACKGROUND

At present our cryogenic experiments have not been optimized for the background: the external shielding (10 cm of normal lead) is insufficient and there is no internal or external shielding with Roman lead , which would have strongly suppressed the bremsstrahlung due to ²¹⁰Pb [23,24]. Moreover the material of the crystal holder, in immediate contact with the crystal, is not our final choice for very low radioactive contamination. We have however reached a background of spurious counting rate only one order of magnitude higher than in the Heidelberg-Moscow or IGEX experiments [25,26] in the region of neutrinoless bb decay. We think that, using carefully chosen materials and with an appropriate shield, we should reach the same results as these experiments. Further improvements could come from the obvious shielding effect of the external layers of crystals and from the application of the anticoincidence method, already tested in our detector array [27-29], thus achieving a very efficient Compton suppression. We are going to evaluate it with a detailed Monte Carlo calculation.

2.6 FRONT END ELECTRONICS AND DATA ACQUISITION

As detector crystals will have large mass, a large rise and decay thermal time constant are expected, and the signal energy spectrum will be confined in a frequency band extending from DC to a few tens of Hz. Under such circumstances we do not expect excessive integration of the signal in the parasitic capacitance of the detector-preamplifier link. Low noise JFET preamplifers located outside the cryostat could be used avoiding inside power dissipation. Considering the large number of channels, this will translate into a non-negligible saving of liquid helium consumption. With room temperature electronics two noise sources must be kept under control: parallel noise due to FET leakage current and microphonics and coherent noise picked-up by a long link. The JFET leakage current is reduced by cooling the input FET to ~-30^o C, while pick-up noise is largely reduced by adopting a symmetrical detector bias and a differential preamplifier configuration. This readout approach has been already tested with our previous detector set-ups [30] and will be applied to the 20 crystals array. It was verified with all our large mass detectors that microphonic noise of thermal origin ( not suppressed by the differential readout) limits the energy resolution at a level higher than that determined by series noise of our preamplifiers, which , for a reasonable gain of 300 mvolt/MeV is about a few hundred eV FWHM.

One aspect that deserves due attention is the stabilization of the overall system gain, which is determined by measuring the height of a known energy pulse and the detector bias voltage. On the detector side, as said in a previous paragraph, it will be done by injecting a small thermal power in the absorber. On the preamp side, as it is DC coupled, its drift must be kept at the lowest level. A special circuit has already been designed to fulfill this requirement [30].

As an alternative solution, we do also consider biasing the detector with AC current to shift the signal energy to a narrow band centered around ~ 130 Hz . In that case a simple AC coupled preamplifier would amplify the modulated AC carrier while signal would be recovered by using lock-in techniques. This should result in still better DC drift and lower 1/f noise.

Bolometer characteristics are not uniform and their working conditions may differ considerably. The setting of all necessary parameters for each detector must be done remotely. The very front end of the readout chain consists of the detector bias network, the preamplifier followed by an amplifier, and an antialiasing filter: the value of the load resistors, the amplitude of the bias voltage, the amplifier gain and the bandwidth of the antialiasing filter is set remotely by a computer. Zeroing the baseline is possible simply by the setting of a single flag for a small interval of time. This last possibility allows also the automatic characterization of each detector in a very simple way [31]. The front-end electronics is completed by an analog optical coupler [10], which breaks the ground loops reducing mains related disturbances and a further antialiasing filter and a 16 bits ADC.

Since the pulse shape of large bolometers contains very useful information on the event, the data acquisition has to be specifically studied to collect the entire signal pulse. In the Milano experiment we use a low sampling rate ADC (400 ksamples/sec maximum) multiplexed on our twenty channels. A sample per millisecond is normally acquired. In addition, for a measurement with large dynamic range (from a few keV to around 10 MeV) and the good resolution expected an ADC with at least 16 bits is needed.

We presently use a threshold trigger which allows the acquisition of the signal with a voltage amplitude above a pre-defined level. An interrupt would be generated and the triggered channel acquired. Since for an experiment like CUORE it is very important to reach an energy threshold as low as possible, we plan to adopt a trigger approach based on neural network analysis. It would then be possible, at least in principle, to recognize the presence of the signal by its shape and not by the crossing above a certain voltage level. The actual realization of this type of trigger requires further analysis. It will be possible with an hardware approach, but it will not be simple, in this case, to instruct the neural network. On the contrary a software approach would require a powerful computer, capable to recognize the signals in real time.

The off line analysis of the acquired pulses adopted by the Milano group is based on the optimum filter approach [32]. This analysis allows to maximize the signal to noise ratio especially for slow detectors, like bolometers, where the contribution of a non-white noise is very important. In practice a mean signal and a power spectrum of the noise are acquired and from these data a weight of the power spectrum of the acquired signal over the noise is obtained. An optimization of the algorithm implies a dynamical evaluation of the noise during all the measurement to keep its power spectrum updated. Previous experience has in fact shown that noise is not necessarily stationery. Evaluation of different mean signal samples for different energy regions is also considered. Better optimization of the signal to noise ratio will be, at least in principle, possible with this optimization.

3. THE ROLE OF CUORE IN UNDERGROUND PHYSICS

The field and subjects of underground physics are evolving very rapidly, and searches on new phenomena especially in astroparticle physics are continuously proposed in addition to the "classical' ones (e.g. double beta decay, WIMPS interactions etc.). A peculiar advantage of a cryogenic detector like CUORE is the a extensive choice of possible detecting nuclei . In addition to a search on neutrinoless double beta decay , which is the main aim to which this proposal is addressed, we will discuss here a few subjects which in our opinion could be efficiently studied with CUORE. We do not believe however that the impact of this detector in the future underground physics will be limited to them.

3.1. DOUBLE BETA DECAY

This rare process was the first proposed to be searched for with low temperature calorimeters [9]. The most popular decay channels are:

(A,Z) à (A,Z+2) + 2 e^- + 2 n_e (1)

(A,Z) à (A,Z+2) + 2 e^- + c (2)

(A,Z) à (A,Z+2) + 2 e^- (3)

The first of these channels (two neutrino double beta decay) is allowed by the Standard Weak Interaction Theory and has been detected or at least indicated in ten nuclei (⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ⁹⁶Zr, ¹⁰⁰Mo, ¹¹⁶Cd, ¹²⁸Te, ¹³⁰Te and ¹⁵⁰Nd [1,33]). The second , where a massless Majoron c is emitted, will not be considered here. The third , the so called neutrinoless double beta decay, would prove violation of the total lepton number and indicate that neutrino is a Majorana particle with an effective non zero mass. Its rate would be strongly enhanced with respect to process (1), thus providing a very powerful test of the lepton number conservation. From its rate one can derive a value for an average neutrino mass <m_n> which is however subject to the large uncertainty of the nuclear matrix element calculations [33]. From the experimental point of view, neutrinoless double beta decay would be revealed by the presence of a peak corresponding to the transition energy in the spectrum of the sum of the two electron energies. We would like to stress that this requires a very good energy resolution of the detector. With a poor resolution even a strong reduction of the background could not help: the peak could be hidden in the end tail of the sum energy spectrum of the two neutrino double beta decay.

Due to the uncertainty in nuclear matrix calculations, searches for neutrinoless double beta decay should be extended to as many favorable nuclear candidates as possible. Particularly effective to search for this channel is the source=detector approach [34], where the detecting material contains the candidate nucleus for double beta decay. This is a peculiar advantage of thermal detectors [9,14,15], due to their ample choice of detecting materials.

The limitations in experiments on neutrinoless double beta decay stay on background, energy resolution and effective mass of the candidate isotope. In most of the present experiments this last requirement was achieved by using the large stocks of enriched materials available in the former Soviet Union. A substantial increase in the mass of isotopically enriched materials seems at present financially impossible, unless new enrichment methods will be discovered. Taking this in mind we will consider here a few candidates:

3.1.1 ¹³⁰Te ( 33.8% isotopic abundance , 2528 keV transition energy)

The best results on this nucleus have been obtained by our group with bolometers made of crystals of TeO₂. We would like to stress that Tellurium is the candidate with one of the largest natural atomic abundances, thus allowing a massive double beta decay experiment even with natural Tellurium. In addition, TeO₂ is a cheap material relatively free from radioactive impurities, apart the rapidly decaying ²¹⁰Po. We present here a version of CUORE made of crystals of tellurium oxide, which we consider the best ones to search for neutrinoless double beta decay, but also very promising for experiments on WIMPS , solar axions and possibly also underground low energy neutrino interactions.

Let us consider an array made by 10x10x10 TeO₂ cubic crystals of paratellurite with 5 cm side. The mass of each crystal would be of 750 g, about twice the mass of the crystals in the present twenty bolometer array. The total mass of Tellurium would be almost 600 kilograms, corresponding to about 10²⁷ nuclei of ¹³⁰Te. The sensitivity to neutrinoless double beta decay depends obviously on the background. In a year of effective running time with a 5 keV resolution and the present background of the Heidelberg-Moscow or IGEX experiments the sensitivity to neutrinoless double beta decay should be of a few 10²⁵ years. We do not like to extract from this number a limit on the average neutrino mass, since it is strongly dependent on nuclear matrix elements [33], but only indicate a value around a tenth of electronvolt or less .

3.1.2 ⁷⁶Ge ( 7.4 % isotopic abundance, 2038 keV transition energy)

Experiments on double beta decay of this nucleus using germanium semiconductors are running since 30 years [35], and are presently yielding impressive limits on neutrinoless double beta decay [25,26]. Germanium crystals can and have already been [11,13,15] operated as thermal detectors with an energy resolution which could in principle be competitive with that of germanium diodes (the Debye temperature is around 370 kelvin). In addition, the standard crystals to be used in a bolometer need only to be free from radioactive contamination: they should therefore be much cheaper than crystals to be used as semiconductor detectors. Let us consider a version of CUORE made by one thousand bolometers with 5x5x5 cm³ crystals of natural germanium as absorbers . The total mass would be 665 kilograms corresponding to about 50 kilograms of ⁷⁶Ge, only about three times the total active mass in the presently running experiments with enriched germanium diodes. Since the background would be much larger due to larger mass, we do not consider this version of CUORE to be much competitive for double beta decay compared with present experiments on ⁷⁶Ge double beta decay. On the contrary, as discussed later, this detector can be competitive for searches on WIMPS, axions or possibly neutrino interactions. A detector like CUORE filled with germanium enriched in ⁷⁶Ge could be competitive with the recently proposed GENIUS experiment [36] , but we consider its cost to be prohibitive, at least for us.

3.1.3 Other double beta decay candidates

Other nuclei , like ⁴⁸Ca, ¹⁰⁰Mo, ¹¹⁶Cd, ¹²⁴Sn and ¹⁵⁰Nd have been suggested for searches on double beta decay with thermal detectors [18] , and bolometers with CdWO₄ and CaF₂ as absorbers have been operated [37,38] (the latter in coincidence with scintillation). The isotopic abundance of the candidate nucleus in all these elements is rather low and prevents, at least at present, an experiment with natural material. An additional difficulty in the case of CdWO₄ comes from the pile-up due to the natural occurring single beta decay of ¹¹³Cd.

3.2 SEARCHES ON DIRECT INTERACTIONS OF WIMPS

A great variety of experiments is being carried out underground on direct interactions of WIMPS as a component of dark matter [5]. In addition to those performed with conventional detectors four recent ones [11-13,27] are based on thermal detection. A relevant parameter in these searches is the so called Quenching Factor, namely the ratio between the pulses produced by a nuclear recoil due to the WIMP interaction and by an electron of the same energy. While in conventional detectors this factor is normally below 30% , in bolometers it has been proved to be around one for slow recoiling nuclei independently on energy [29]. While conventional detectors allow a model dependent suppression of the background by pulse shape discrimination [5], a similar suppression can be achieved in bolometers by recording simultaneously ionization and heat [11,13] or scintillation and heat [38]. Even in case of favorable materials , like Germanium, Lead tungstate (see later) or CaF₂ we consider this approach too complicate for CUORE.

Experiments performed so far on direct detection of WIMP's consist with few exceptions [5,39-41] of measurements of the background counting rate in the low energy region of the recorded pulse spectrum. The exclusion plots which are extracted from them depend therefore on the background counting rate per unit mass. With the configuration proposed for CUORE we expect a very low background in the central part of the array since these detectors can be placed in anticoincidence with all the surrounding ones. This will provide a very strong Compton suppression , and therefore will minimize the continuum background at low energy where the counts due to direct interactions of WIMPS could be hidden. An unambiguous evidence for WIMPS can come from detection of an effect typical of the interactions of these particles, like the seasonal variation of the counting rate due to the revolution of the Earth around the Sun. This requires a large detector mass and this is the case with CUORE.

We consider here different options of materials to be used in CUORE:

3.2.1: The TeO₂ option

The background of CUORE in the low energy region should be reduced to the level of the present Heidelberg-Moscow or IGEX experiments [25,26]. In fact the former of these collaborations claims that half of this background is due to the presence of a tiny contamination of ²¹⁰Pb in their Johnson and Mathey lead, which will be totally absent in our shielding of Roman lead.

In our detectors we plan to reach a thermal and therefore effective threshold of 5 keV, which would be equivalent to 1 keV in a germanium diode due to the corresponding Quenching Factor. Our background in the energy region of interest for coherent interactions of WIMPS in a mass region equivalent with the mass of Tellurium nuclei can be estimated to be one event kg^-1 d¹. From the absence of a 5% seasonal effect we would exclude in a model independent mode a WIMP interaction rate of more than .07 interaction kg^-1 d^-1.

3.2.2 The Germanium option

The Germanium option in CUORE seems at present roughly equivalent to the TeO₂ one. Due to the larger Debye temperature, the thermal performance, and therefore the energy resolution and the threshold, should be better. On the contrary the larger atomic number of Tellurium represent a considerable advantage when searching for coherent interactions of WIMPS of large mass. The already mentioned possibility to run all the Germanium crystals in the ionization+heat mode is obviously very attractive, but complicate in a such a large array.

3.2.3 The PbWO₄ option

Our group has successfully operated bolometers with large crystals of CdWO₄ made with non enriched materials as absorbers [37]. Their use for searches on WIMPS was obviously prevented by the presence of the naturally occurring single beta decay of ¹¹³Cd. We are presently investigating the possibility to use crystals of PbWO₄ on the basis of a series of measurements carried out on the intrinsic radioactive contamination of Lead. No presence of ⁴⁰K , and of the nuclei of the ²³²Th and ²³⁸U chains (when in secular equilibrium) was found in clean samples of this metal [24]. This is not the case for ²¹⁰Pb which obviously breaks secular equilibrium and whose activity in materials used in normal shields was found to be up to 200 Bequerel kg^-1. We have determined with a cryogenic experiment that even the best (and very expensive) Lead with low ²¹⁰Pb content available commercially has an activity of 250 mBq kg^-1 [42] This result is confirmed, for a similar sample, by the Heidelberg-Moscow experiment [25]. We have however extracted [23] from the wreck of a Roman ship sunk near Sardinia a considerable amount of Roman lead which is totally free from ²¹⁰Pb (22.3 years lifetime) contamination. In fact an upper limit of 4 mBq kg^-1 has been measured cryogenically by us [42]. As a consequence we are constructing , in collaboration with the PRECIOSA factory in Czech Republic , crystals of PbWO₄ made with Roman Lead. We are going to test them in the Gran Sasso Laboratory to determine their thermal properties , which we expect however to be very promising , since the Debye temperature of this material should be near 400 Kelvin. In this case the PbWO₄ option should be a very promising competitor for searches on Dark Matter.

3.2.4 Other candidates for Dark Matter Search

Many other materials are of obvious interest for searches of Dark Matter with CUORE. Examples of good "thermal" candidates are Al₂O₃ , CaF₂, LiF etc. which present, especially in the first case , a large Debye temperature. We have also operated crystals of these materials , but we prefer to consider for this preliminary version of CUORE only materials with high Z nuclei. They are complementary to those already adopted in the presently running and planned experiments. In addition the N² enhancement factor for vector interactions seems to us very promising in searches for WIMPS in the high mass region.

4. SEARCHES FOR AXIONS FROM THE SUN

The possibility to search for direct interaction of axions by coherent Primakoff conversion in germanium detectors has been recently proposed by R.J.Creswick et al [16]. Detection rates in a deeply located germanium diode would be enhanced if axions from the Sun coherently convert into photons when their incident angle with a given crystalline germanium plane fulfills the Bragg condition. This modulation of the rates would be correlated to the relative position of the lattice planes of the detector with respect to the Sun , and would lead to a sub-diurnal rate variation. An experiment has been already carried out by analyzing the temporal behavior of the rates recorded by a germanium detector operated underground [17]. Even if only one of the axis of the lattice cell was known, the experiment yielded an upper limit of 2.7 x 10^-9 GeV^-1 on the axion-photon coupling. A similar experiment will be performed by our group in the Gran Sasso laboratory with the presently installed array of twenty TeO₂ crystal, whose lattice planes are oriented.

CUORE seems to us an ideal detector to search for coherent interactions of axions coming from the Sun and from other cosmic sources. The TeO₂ crystals which we are presently using have a tetragonal structure and (100)(010)(001) orientation. In the crystal cell the (100) side is equal to the (010) one and different from (001). The crystal is normally grown along the (100) side. As a consequence different coherent interactions would take place in correlation with the position of the (100)(010) and (100)(001) planes relative to the Sun.

Different orientations for the direction of growing with respect to those of the crystal cell can be considered and will be discussed with the Shanghai Qinghua Nonmetal Co. Growing along the (001) axis would lead to identical (001) (100) and (001) (010) orthogonal orientation planes, and therefore to a signal modulation repeated twice.

The sensitivity of the CUORE observatory to coherent interactions of axions would be many orders of magnitude superior than in the presently running germanium experiments for the following reasons:

1. large mass

2. an axion cross section proportional to the square of the atomic number

3. perfect orientation of the lattice planes.

5. STUDY OF THE INTERACTIONS OF ANTINEUTRINOS FROM AN ARTIFICIAL SOURCE

Up to few years ago the study deep underground of interactions of neutrinos from artificial sources was considered impossible, the only experiments being those conducted at a moderate depth with reactors. Recently however intense sources of neutrinos from electron capture of ⁵¹Cr have been obtained to test solar neutrino experiments [6]. In particular a source of ⁵¹Cr , made by neutron activation of a 40 kg sample of Chromium enriched in ⁵⁰Cr yielded almost 7 x 10¹⁶ neutrinos per second corresponding to about 5 x 10¹¹ neutrinos s^-1 cm^-2 at one meter from its center. This is less by only two orders of magnitude with respect to the flux of antineutrinos at 10 meters from the center of a powerful nuclear reactor. Artificial sources of antineutrinos from beta decay leading to larger fluxes have been recently proposed and could be funded by the Institution for Peaceful Application of Nuclear Energy in Russia [43,44]. As an example let us consider the 5 Megacurie source of ¹⁴⁷Pm recently suggested by V.N. Kornoukhov [43]. This nucleus decays with a lifetime of 2.62 years and a transition energy of 264 keV. The source should be placed near the detector inside a 30 cm Tungsten shield. Its thermal insulation and especially the suppression of background due to gamma rays requires obviously a detailed study and appropriated simulations. Of particular interest is the study of the electromagnetic interaction induced by a neutrino with non-zero magnetic moment, whose cross section increases with energy more slowly than the cross section for weak interactions. As a consequence, a large contribution of the electromagnetic interactions to the total rate of events is expected for sources with relatively low transition energy like ¹⁴⁷Pm . On the other side the low energy threshold and the large electron density (1.8 x 10²⁴ electrons cm^-3) could make CUORE a possible detector to study neutrino interactions and particularly their electromagnetic interactions. If the source with its tungsten shield would be placed in contact with the lead shield of the detector, the total rate for neutrino-electron scattering would be about ten per day with an energy threshold of 1 keV. A further contribution to the rate , of the order of 20%, could come from electromagnetic interactions for a neutrino magnetic moment of 10^-11 m_B. For a 5 keV threshold the rate would be reduced to 8 events per day and the ratio to 15%, respectively. For a significant detection of these antineutrino interactions one should reduce the background to definitely less than 0.1 counts keV^-1 d^-1 in the low energy region, a difficult, but perhaps not impossible task. The study of antineutrino interactions in CUORE seems therefore at present less promising than searches for neutrinoless double beta decay or interactions of WIMPS or solar axions. We would like to note however that the use underground of artificial antineutrino sources with relatively long half lifetimes like ¹⁴⁷Pm are being considered for other experiments in Gran Sasso , as for instance the search for a non zero neutrino magnetic moment suggested by the DAMA collaboration [45]. The possibility to expose also CUORE to them should be kept in mind.

A proposal for an intense source of tritium produced in a reactor has been presented by V.N. Trofimov [44]. Due to the low transition energy (18.6 keV) the ratio between the signal due to electromagnetic and weak interactions would be in this case much larger and would allow a much better sensitivity in the search for a non-zero neutrino magnetic moment. The construction of this source is probably more difficult , but the requirements in shielding and refrigeration much easier to achieve. We believe however that the energy resolution , and therefore the threshold of CUORE will be insufficient for this experiment.

6. SOME PRACTICAL CONSIDERATIONS AND A TENTATIVE SCHEDULE OF THE EXPERIMENT

We would like to stress that the present document is only a design study and not yet a proposal for an experiment. For a firm proposal the following conditions , which we are going to investigate in the next months, should be fulfilled:

1. the feasibility and the cost of a single dilution refrigerator capable to cool to 7 mK the entire copper structure on which the bolometers will be framed

2. further understanding of the present background for its reduction

3. the possibility , the time needed and the cost to produce one thousand cubic crystals of TeO₂ of 5 cm side and of the same excellent thermal quality as the present ones (3x3x6 cm³). The possibility of a similar array of 2000 crystals with half this mass like the presently operating ones could also be acceptable.

4. an international participation to CUORE , since our group, presently

made by 12 physicists, is admittedly insufficient to carry on the project,not only from the technical, but also from the financial point of view. We would much welcome the participation of the Gran Sasso Underground Laboratory and of other national laboratories in Italy and of groups involved in cryogenic experiments.

Evaluation of the cost of the project is difficult at present since two very relevant items, namely the dilution refrigerator and the production of the TeO₂ crystals have still to be negotiated. We believe however it would be one to two orders of magnitude lower than the cost of a similar experiment carried with enriched germanium diodes [36].

The time schedule for the construction of CUORE depends strongly on the availability of funds , and on the participation of other groups with experience in cryogenics and in large cryogenic detectors. A tentative schedule would be the following:

1. design of the cryogenic "holder" of the crystals, and test on the possibility to reach a temperature below 7 mK in any position of a "dummy" holder fastened to an existing dilution refrigerator in 1998

2. construction of a first "reproducible" module of the final bolometers with a baseline rms resolution around one keV before the end of 1999

3. preliminary measurements with 100 crystals in the final dilution refrigerator during 2000

4. the final experiment starting from 2001

Ettore Fiorini

(on behalf of the Milano group)

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