Status and new data of the geochemical determination pp-neutrino ﬂux by LOREX

content LOREX, the acronym of LORandite EXperiment, is the only long-time solar neutrino experiment still actively pursued. It addresses the long-time detection of the solar neutrino ﬂux with the thallium-bearing mineral lorandite, TlAsS2 from the mine of Allchar, FYR Mazedonia, via the neutrino-capture reaction 205Tl + ν (e) → 205Pb + e(-). The ﬁnal step of LOREX would be the extraction of lorandite samples and the quantitative determination of the ratio of 205Pb / 205Tl atoms, thus providing the product of solar neutrino ﬂux and neutrino-capture cross section, integrated over the age of lorandite 4.31 • 10ˆ6 yr. The detector oﬀers the low threshold of only 52 keV for solar pp-neutrinos, to be compared with the next lowest 232 keV in the GALLEX and SAGE experiments. Moreover, LOREX would be unique in view of providing the mean luminosity of the sun over the last 4.3 million years. This paper presents new data on accurate geological age of the minerals at Allchar, and in particular the erosion rate in two with thallium enriched locations: ore body Crven Dol 33 – 35 m/10ˆ6 y and Central Part of 66 - 67 m/10ˆ6 y. This determination based on Accelerator Mass Spectrometry (AMS) of three independent investigation of 10Be, 26Al and 53Mn and GMI i.e. Geo-morphologic investigation. Reliable erosion rate is indispensable for proper determination of the background of 205Pb induced by cosmic radiation.


Introduction
The determination of the long-time average of the solar neutrino flux Φ ν with the thalliumbearing mineral lorandite, TlAsS 2 , from the mine of Allchar, Macedonia, is based on the neutrino capture reaction proposed by Freedman et al., 1976 1 : 205 Tl ν e −→ 205 Pb e − 1.1 The average flux Φ ν over the exposure time a age of lorandite since its mineralization follows from the common activation equation: where N is the total number of 205 Tl atoms, T the total number of 205 Pb atoms, B the number of 205 Pb atoms induced by background reactions mainly 205 Tl μ p, n 205 Pb , σ the solar neutrino capture cross-section of 205 Tl, ε the overall detection efficiency, λ the decay constant of 205 Pb and a the geological age of lorandite i.e., the age of mineralization .
The neutrino capture reaction: 205s Tl ν e E νe ≥ 50 keV −→ 205 Pb * e 1.3 exploits the by far lowest threshold of E νe ≥ 50 keV for solar neutrinos.The last step and the central problem of LOREX is the quantitative determination of 205 Pb atoms in lorandite.This renders finally the mean solar neutrino flux, that is, the mean luminosity of the sun during the last 4.31 million years, which is the geological age a of lorandite from Allchar, as given by Neubauer et al. 2 .Before entering the final phase of the experiment, four problems must be reliably addressed; however, 1 the age a of lorandite has to be known precisely: age of lorandite, 2 the background of 205 Pb atoms produced by cosmic radiation mainly μ p, nreactions and by natural radioactivity must be determined quantitatively.In this context the knowledge of the erosion rate of the overburden rocks during the existence of lorandite is of utmost importance: background and erosion, 3 the ratio 205 Pb/ 205 Tl provides only the product of solar neutrino flux and neutrino capture probability into different nuclear states of 205 Pb.However, the capture of neutrinos should populate predominantly the first excited state at E * 2.3 keV.Hence, to get the neutrino flux itself, one has to determine the capture probability into this low-lying state of 205 Pb: neutrino capture probability into the 2.3 keV state of 205 Pb,

Age of Lorandite
The age of the Tl mineralization is an essential parameter of the experiment, as it equals the integration time of mineral lorandite as the geochemical pp-solar neutrino detector.As it turned out, another important prerequisite for the realization of LOREX is that the ore deposit has to provide for more than two lorandite-rich ore bodies, located at significantly different depths.
Geological research demonstrated that lorandite in sufficient quantities occurs in the Allchar Sb-As-Tl-Au deposit located in FYR Macedonia at the north-western margins of the Kožuf Mountains, close to the border between FYR Macedonia and Greece.The mine contains the world's largest known concentrations of thallium-bearing minerals and, in particular, the mineral lorandite.The polychronous and polygenetic Sb-As-Tl-Au Allchar deposit was formed by complex physicochemical processes occurring in a heterogeneous geological environment.The deposit originated through polyphase interactions of hydrothermal fluids and the surrounding magmatic, sedimentary, and metamorphic rocks.The genesis of ore mineralization is genetically related to the products of Pliocene magmatic activity.The spatial location of the mineralization was controlled by magmatic, structural, and lithological factors as suggested by Janković and Jelenković 4 .The Allchar deposit comprises several ore bodies of various shapes, textural and structural characteristics, and associations of elements.
Thallium mineralization has been proved in two locations, that is, two ore bodies: Crven Dol and Centralni Deo ore bodies, situated in the northern and central part of the Allchar deposit, respectively, Figure 1 .
Troesch and Frantz determined the geological age of Tl mineralization in Crven Dol Figure 1 a as 4.22 ± 0.07 Ma, using sanidine from adit number 21 5 .This determination was obtained by isochrone 40 Ar/ 39 Ar five-degree measurement of argon content with the derivation 2σ of the first phase and 1σ of other four phases.
During the final stages of volcanic activity in the Allchar area occurred hydrothermal alteration of the wall rocks, and this can be considered as the period of initial deposition of ore minerals in this area.The age of K-feldspars alkali feldspar has a general formula: K, Na AlSi 3 O 8 , but varies in crystal structure depending on the temperature it formed at; the formula actually is a blend ranging from pure sodium albite to pure potassium end-member orthoclase, microcline, or sanidine in an altered zone at the Rudina locality is 4.31 ± 0.02 Ma according to Neubauer et al. 2 , which documents the beginning of intensive alteration and deposition of thallium mineralization.The close spatial association of mineralization and hydrothermally altered rocks is found by a drill-core B-2 Figure 1 b of the Rio Tinto company in 1999 at the Rudina locality, which is geologically connected with the ore body Centralni Deo.These drill cores revealed the presence of As-, Sb-, and S-mineralization and strongly altered rocks at depth intervals 30-60 m and 160-280 m, respectively, from Rio Tinto Co. 3 .

Background Reactions and Cosmic Ray Contribution
In the case of LOREX more than 30 processes have been identified and analyzed which potentially contribute to the "background" of 205 Pb.After careful evaluation only four processes turned out to potentially have nonnegligible contributions: 1 the 205 Tl μp, n 205 Pb reaction: contribution of fast muons,    in lorandite and surrounding rocks by Pavićević 6 , and the method by Heisinger and coworkers 7 as a function of the paleodepth d p of the deposit.
To determine the erosion rate in Allchar we applied terrestrial in situ cosmogenic nuclides including both radioactive 10 Be and 26 Al and stable 3 He and 21 Ne nuclides in different minerals and compared the obtained data with the results of geomorphologic analysis. 26Al concentrations of 16 samples have 1σ uncertainties of 26-58% and yield maximum erosion rates from ∼70 m/Ma to ∼600 m/Ma at different locations.The noble gas analyses included measurements of 3 He in one diopside sample and 21 Ne in quartz from five different locations and in one sanidine sample, revealing erosion rates between ∼20 m/Ma and ∼70 m/Ma, with asymmetric 1σ uncertainties between 10 and 200%.The 10 Be measurements revealed unrealistically high values and had to be omitted from interpretation.Both the combined 21 Ne- 26 Al data and the geological information indicate that a simple steady-state erosion history is not applicable to the Allchar area.Rather, long periods of burial ∼500 ka-3 Ma by volcaniclastic material and, possibly, glacier ice have interrupted the times of exposure and erosion.Nevertheless, it is remarkable that 85% of all erosion rate values determined from different cosmogenic nuclides 3 He, 21 Ne, 26 Al in various monitor minerals at various locations, as well as the results of geomorphologic analysis, yield consistent results in the range from ∼20 to ∼90 m/Ma.We argue that the 26 Al concentrations most likely reflect the erosion rate during the last, postburial period ∼100 ka .For the two most important Allchar locations with lorandite ore bodies Crven Dol and Centralni Deo we propose the erosion rates of ∼70 m/Ma and ∼130 m/Ma, respectively, according to Pavićević et al. 8 .The paleodepths for the four confirmed ore-bodies with significant quantity of lorandite are found from their present-day depths and the estimated thickness of eroded layers at corresponding locations Figure 1 and Table 1 .
Table 1 also lists the final estimates of concentrations of 205 Pb atoms per 10 kg lorandite at different depths; the concentration due to the cosmic-ray fast muons, the concentration due to pp-neutrino captures, and the total concentration.For the shallowest location d 1 the neutrino contribution amounts to ∼20%, while for the deepest one d 4 it amounts to ∼63%.
As seen in Figure 2, concentrations of 205 Pb in samples from different depths reflectdue to the muon contribution which is depth dependent-both the present-day depth of the sample as well as the erosion history of the overburden layers.Curves that correspond to different average erosion rates form a family of exponentials Aničin et al. 10 and experimental determination of 205 Pb concentrations in samples from a number of different depths allow for the simultaneous determination of both the muon contribution and the erosion history of the deposit.The contribution due to the 205 Pb mobilized from the surrounding rock at the time of lorandite mineralization, marked by "n", and that due to natural radioactivity in lorandite and in the surrounding rocks, marked by "r", contribute together by less than 4% to the total concentration U and Th concentrations are low: marble, dolomite, and quartz latite have contents of U in the range of 0.054-0.45ppm and Th of 0.061-0.66ppm, while the mean concentrations in lorandite amount to 0.12 ppm for U and 0.022 ppm for Th, respectively, as given by Pavićević 6 .
Estimate of contribution of "n," that is, mobilised 205 Pb from surrounding rocks at the time of the formation of the Tl-mineralization age of lorandite and the natural radioactivity contribution "r," as consequence trace concentrations of U and Th amount to less than 4% see Figure 2 .The low contribution of "n" is consequence of the very low concentration of U and Th in rocks: marble, dolomite, and Qz-rhyolite, which have the content of U 0.054-0.45ppm and Th 0.061-0.66ppm Pavićević 6 .The contribution of natural radioactivity "r" that is predominantly caused by U and Th in lorandite is low due to low concentrations of these elements in lorandite: U 0.12 ppm and Th 0.022 ppm Pavićević 6 .All background components not specific to lorandite not originating from thallium were estimated to amounts of between 3 and 15 SNU

Determination of the Neutrino Capture Probability into the 2.3 keV State of 205 Pb
From the relative abundance of 205 Pb with respect to 205 Tl, even corrected for all background effects, one can extract only the time-integrated product of solar neutrino flux and the neutrinocapture probability, leading from the nuclear ground state of 205 205 Pb is not known.There is one-and only one-possibility Kienle 18 to determine experimentally this unknown nuclear matrix element, namely, by measuring the bound-state beta decay β b decay of bare or hydrogenlike 205 Tl 81 into hydrogen-like helium-like 205   23 , where the signals of the stored and electron-cooled parent-and daughter ions, induced on pick-up plates, are steadily recorded, yielding their revolution frequencies which are unambiguously correlated to their corresponding mass-to-charge ratios.From these "Schottky lines," the numbers of both parent and daughter ions are recorded as a function of time, yielding the β b decay probability and, thus, the nuclear matrix element log ft value searched for.However, the revolution frequencies of parent and daughter ions could not be resolved in these experiments due to the very small Q values involved.Therefore, a special technique was applied, namely, the removal of the single bound electron of the daughter ions by means of an internal gas jet acting for a short time.

Figure 3:
The neutral 205 Tl 0 atom is stable with respect to β − decay into the continuum since the Q value for this decay is negative, Q β− −Q EC −50.5 keV.However, for bare 205 Tl 81 or hydrogen-like 205 Tl ions bound-state β decay becomes allowed, where the created electron remains bound in the K-shell of the daughter ion 205 Pb 81 .Due to the "saved" K-shell binding energy, the Q value for this decay Q βb K gets positive.Both, the capture of solar pp-neutrinos and the bound-state beta decay populate predominantly the first exited state 1/2 − of the 205 Pb nucleus at 2.3 keV and share the same nuclear matrix element for this transition.Therefore, the measurement of the bound-state β − decay probability of bare or hydrogen-like 205 Tl ions provides the unknown capture probability of the solar pp-neutrinos by the 205 Tl atoms.Based on the log ft values of comparable β − decays, the bound-beta half-life T 1/2 β b of bare 205 Tl ions was estimated by Takahashi and Yokoi 19 to about 120 d.Since this extrapolated value has to be regarded as uncertain within at least a factor of three, only the measurement of the bound-beta half-life can provide a safe number with a reliable error margin for the capture probability of solar pp-neutrinos by 205 Tl.
For the corresponding experiment concerning the β b decay of bare 205 Tl see Figure 3 with a comparable small Q value, exactly the same detection technique as in the two successful experiments mentioned above has been proposed.However, there were-and still are-serious and too expensive safety restrictions for the use of Tl in an ion source due to its toxicity, which prevented the realisation of this experiment over the last 18 years.Nonetheless, since this proposal remained all the time on the list of high-priority experiments, we were encouraged to search for another way of its realisation.We proposed as the "new technique" getting bare 205 Tl ions their indirect production by in-flight fragmentation of a primary 206 Pb beam in the fragment separator FRS together with their subsequent injection into the experimental storage ring ESR .The decisive point is that at least 10 6 bare 205 Tl ions have to be provided and stored, in order to obtain a minimum number of a few 100 β b decays within storage times of a couple of hours the β b half-life of bare 205 Tl is estimated to 120 days Takahashi and Yokoi 19 .By two major achievements of the last years this indispensable number of at least 10 6 stored bare 205 Tl ions can now be reached at high confidence see   206 Pb ions, accelerated in the synchrotron SIS to an energy of some 100 A MeV, hits the production target Be of the fragment separator FRS, where a plenty of highly-charged ions will be generated by nuclear reactions.With the aid of an appropriate setting of the FRS magnets and by exploiting the Z-dependent stopping power in a degrader placed in the symmetry point of the FRS black triangle , only bare 205 Tl 81 ions can pass through small slits at the end of the FRS.Those ions will be stored in the experimental storage ring ESR and accumulated by repeated injections until a number of at least 10 6 ions will be reached.After the application of electron cooling, the 205 Tl 81 ions are circulating in the ring for a couple of hours, where a few of them will decay to hydrogen-like 205 Pb by bound-state β decay.
2 By the combination of stochastic cooling and the storage of the injected ions at inner orbits several subsequent injections 10 • • • 30 can be applied without any losses of the already stored ions rf stacking of fragments .This technique has been successfully applied in several experiments within the last years.
Due to these important steps the reach of 10 6 stored and cooled bare 205 Tl ions is feasible.Therefore, this new procedure for the determination of the β b decay probability of bare 205 Tl-and, therewith, of the solar neutrino capture cross-section by 205 Tl-has been approved in June 2010 by the international experimental board of GSI ESR-proposal 100 .Six days of beam time and the highest priority "A" were assigned.A copy of this decision is attached in the supplement of this proposal.The experiment is now in the procedure of scheduling.Its realisation within the next 18 months is reliable, taking into account the "waiting list" for high-priority experiments at the FRS-ESR facility.

Extraction and Detection of Ultra-Low Amounts of 205 Pb in Lorandite
One of the key requirements of the geophysical LOREX project is the ultra-sensitive, quantitative detection of the neutrino-induced trace amounts of 205 Pb present in lorandite.For 10 kg lorandite TlAsS 2 one estimates about 3.5-11.6× 10 5 atoms of 205 Pb depending on the depth at Allchar at which the respective lorandite sample is mined.This implies a necessary separation factor of about 10 20 between 205 Pb and 205 Tl 70% isotopic abundance .Separation factors of this extreme magnitude are perhaps directly achievable for very shortlived radioisotopes through the measurement of their decay radiation Low Level Counting, LCC .For 205 Pb, with a half-life of about 17 million years and in view of the difficulty to detect electron capture decay, this is impossible.
For the LOREX, therefore, the direct detection and counting of the 205 Pb atoms was proposed, either with mass-spectrometric methods or with measurements of characteristic atomic transition radiation.The intrinsic limitation of these methods to small sample sizes is substantially helped with an initial chemical Pb-Tl separation, which has been established to provide a separation factor of 10 13 Pavićević and Bruechle 24 .For Allchar lorandite the Pb content has been found to be about 1.5 ppm Pavićević 6 .Thus, after the initial chemical Pb-Tl separation, a 20 mg Pb sample with a 205 Pb/Pb-ratio of ∼ 10 −15 will be obtained.The sample will also contain a residual amount of ∼10 12 Tl atoms.
The methods that appear suitable, in principle, for the detection of 205 Pb at trace amount levels under consideration here are low-energy mass spectrometry specifically ICP-MS, i.e., inductively coupled plasma mass spectrometry , high-energy mass spectrometry i.e., AMS, accelerator mass spectrometry , and laser-induced atomic spectroscopy.The latter includes in particular resonance ionization mass spectrometry RIMS and the recently developed atom trap trace analysis ATTA .Quality criteria in each case are the separation factors for Pb/Tl and 205 Pb/Pb and the overall detection efficiency.The latter is critical for a relevant statistical accuracy of the measured 205 Pb concentration.In summary, the unambiguous detection of the 205 Pb atoms with statistical uncertainty of less than 10%, requires a method that provides fully resolved separation of 205 Pb from 205 Tl at the 10 −7 level, and 205 Pb from other lead isotopes at the 10 −15 level, and detection efficiency for 205 Pb atoms of preferably 10 −2 but at a minimum of 10 −3 .High-energy AMS relies on the acceleration of ions to energies where molecules are fully destroyed through breakup in stripper foils, the differential energy loss provides chemical element identification of the remaining ions, and powerful ion-beam detectors could be taken from heavy-ion nuclear physics research.Trace concentrations have been reliably measured for low-mass radioisotopes A < 40 down to values of 10 −16 .However, for heavier nuclei the nuclear-charge separation is less pronounced at the typical heavy-ion accelerator because of increased energy-loss straggling and decreasing relative nuclear charge resolution.Earlier experiments of 205 Pb/ 205 Tl separation at about 6 MeV per nucleon beam energy Ernst et al. 25 ; Henning and Schuell 26 have produced separation factors of 10 2 to 10 3 between 205 Pb and 205 Tl, by far not sufficient for the 10 7 factor described above.In addition, the overall efficiency in these studies was found to be less than 10 −6 , and in the most optimistic extrapolations it was difficult to see how this could be brought to values better than 10 −4 .
A novel variant of AMS was then proposed, based on the recent developments of Schottky mass spectroscopy in a high-energy ion storage ring, following the acceleration of ions to several hundreds of GeV per nucleon energies and full stripping Radon et al. 27 .The heavy-ion storage-cooler ring ESR at the GSI Helmholtz Zentrum in Darmstadt, Germany, is uniquely suited for providing a clear-cut solution of the "isobar problem" being such a serious obstacle for tandems.After acceleration in a high-energy synchrotron all atomic species can be fully ionized, and transferred to the ESR where they will be electroncooled, affecting a common sharp velocity for all stored ions.In this case, the revolution frequency in the ESR depends only on the mass-to-charge m/q ratio of the ions which is-for fully stripped atoms-equal to m/Z.Therefore, isobars of different nuclear charge Z appear at widely separated revolution frequencies and are easily resolved.One also gets rid of any isobaric molecular contamination, which often represents the most serious obstacle for tandem-based AMS.
Moreover, the ESR provides the ultimate detection limit for heavy Z > 45 , highly charged ions: even one single stored and electron-cooled ion can be unambiguously detected see Figure 5 .The high resolving power and ultimate detection sensitivity of the ESR enabled "Schottky mass spectrometry SMS " that delivered new and precise atomic masses for more than 180 nuclides Litvinov et al. 23 .Related studies on other heavy-mass radioisotopes have demonstrated the needed separation factor, but the overall efficiency cannot be brought above 10 −4 for a heavy ion around mass 200 due to ion source efficiencies, the need for multiple stripping, and the general transmission losses experienced in the chain of accelerators to reach the required high energies.A variant we shall consider now is to  inject a lower charge state into the synchrotron accelerator and then to strip at the injection into the storage ring with very high efficiency.This eliminates, in effect, one stripping stage with a resulting broad charge state distribution and thus increases efficiency.Estimated to be around 10 −4 or better, the exact value needs to be experimentally determined.So there has been considerable progress in this "storage ring variant" of AMS, but the overall detection efficiency that can be finally reached finally is still unknown.Over the past decades, several methods of trace analysis based on laser spectroscopic techniques were proposed and very successfully developed.The high degree of selectivity obtained by these methods is a result of resonant laser-atom interaction.Atoms of different elements interact resonantly with light at significantly different frequencies owing to differences in their atomic structure.Atoms of different isotopes of the same element exhibit isotope shifts, a small change in their resonance frequencies caused by the variation in the nuclear mass and charge radius.By tuning the laser frequencies precisely onto the resonance frequencies of a particular isotope, one can selectively excite, ionize, or manipulate the atoms of this isotope while having a much smaller effect on the other isotopes and elements.
At the moment the recently developed method of trace analysis with an atom trap appears, with some caveats, a very promising approach.Atom trap trace analysis ATTA is a laser-based atom counting method originally developed at Argonne National Laboratory Chen et al. 28 .Its apparatus consists of lasers and vacuum systems of tabletop size.At its center is a magnetooptical trap, a MOT Raab et al. 29 .The MOT captures atoms of the desired isotope by using laser beams.When the laser frequency is tuned to within a few natural line widths on the low-frequency side of the resonance of the targeted isotope, only atoms of this particular isotope are trapped.Atoms of other isotopes are either deflected before reaching the trap or allowed to pass through the trap without being captured.The detection method e.g., a sensitive CCD camera takes full advantage of the high selectivity of photon burst spectroscopy.A single atom can be trapped and observed for 100 ms or longer, during which 10 6 fluorescence photons can be induced and as many as 10 4 photons can be detected.These advantages allow single atoms to be counted with a high signal-to-noise ratio, and, since the selectivity depends exponentially on the number of photons detected in a burst, they also ensure a superb selectivity.Indeed ATTA is immune to contamination from other isotopes, elements, or molecules.
For the present proposal we suggest to focus on the Schottky scan developments at the GSI-Darmstadt ESR heavy-ion storage ring.The crucial question that has to be answered in test and pilot experiments is whether or not an overall detection efficiency including all steps from the ion source to the storage ring of 10 −3 or better see the reasoning above for the 205 Pb ions can be achieved.In parallel we will carefully observe the progress and the developments in ATTA technology with regard to trace analysis of lead isotopes.The sensitivity improvements are key to sample size.The present proposal to obtain the order of 10 kg lorandite from the Allchahar mine is close to the needed sample size that current trace technologies require.But it is not quite there yet.Any further improvements in the detection techniques, which we believe will occur, have the potential of adding the necessary safety margins.However, this requires serious development and study.Any progress made though might not only benefit the present 205 Pb proposal but radioisotope trace analysis in general.

Summary
It has been shown that the first two of the four major problems of LOREX, as addressed at the beginning of this work, namely, the age of lorandite and the background-induced amount of 205 Pb, have been meanwhile successfully addressed and are near to a final conclusion.In particular, the determination of the erosion rate by cosmogenic nuclides was decisive for getting a first but reliable estimate for paleo-depth and, therefore for the amount of background.Furthermore, it has been demonstrated how the measurement of the boundbeta decay probability of bare 205 Tl can provide the unknown neutrino capture probability into the first excited state of 205 Pb.The corresponding experiment has been accepted for being performed at the GSI Helmholtzentrum.Finally it has been shown how the small amount of 205 Pb atoms to be expected could be determined by the Schottky noise technique at the ion storage ring of GSI which provides single-ion detection sensitivity.Taking into account the present-day state-of-the-art of all the techniques needed to solve the four problems of LOREX, we conclude that it is realistic to expect the first result for the solar pp neutrino flux averaged over the last 4.2 million years in a foreseeable future.This number will have most probably still a large error margin in the order of 50% or even more, at the 68% CL.We expect, however, that this accuracy could be improved with time, and that it might approach a level of ≤30% as discussed by Pavićević et al. 30 .

Figure 1 :
Figure 1: Geological cross-section of the ore body Crven Dol a and Centralni Deo b of the Allchar ore deposit together with the presumably eroded layer.

Figure 2
Figure 2 shows present estimates of different contributions to the production of 205 Pb in lorandite on the basis of the erosion rate 70 m/Ma and 130 m/Ma, traces of U and Th

Figure 2 :
Figure 2: Estimate of the present amount of 205 Pb in lorandite due to solar neutrinos and to background reactions in the last 4.31 • 10 6 years as a function of the paleodepth d p of lorandite.The values are calculated by Pejović by adopting the value of 0.55 μb for the neutrino capture cross-section for 205 Tl from Hartman et al. 9 , the contents of U and Th in lorandite and surrounding rocks are from Pavićević 6 and the method of Heisinger et al. 7 .n: contributions due to lead mobilized from the rock walls.r: contributions from natural radioactivity.N Pb 205 fast muons : contribution due to reactions induced by fast cosmic muons.N Pb 205 ν : number of Pb 205 due to solar neutrino capture, for a capture rate of 146 SNU 1 SNU 10 −36 captures/ target atoms • sec , obtained after correcting the original 260 SNU value for neutrino flavour-oscillations. N Pb 205 total : the sum of the neutrino contribution and of all background contributions.
Pb 81 , according to 205 Tl 81 −→ 205 Pb 81 * E * 2.3 keV e − b ν e bar , 2.5 where a neutron of the 205 Tl atomic nucleus transmutes to a proton, and where a monochromatic electron-antineutrino ν e bar is being created together with an electron that remains bound e − b in an inner shell mainly K or L-shell of the daughter ion 205 Pb 81 .The Q value of this decay amounts to only 52 keV.Since the nuclear parts of neutrino capture and of β b decay are identical, a measurement of the bound state beta-decay probability of bare or hydrogen-like 205 Tl provides the unknown nuclear matrix element log ft value for the transition to the first excited state of 205 Pb at E * 2.3 keV.Bound-state beta decay probabilities with comparable small Q values have been measured at the Experimental Storage Ring ESR of GSI in two pioneering experiments, for the examples of bare 163 Dy → hydrogen-like 163 Ho Jung et al. 20 , and of bare 187 Re → hydrogen-like 187 Os Bosch et al.21 , and of bare 207 Tl → hydrogen-like 207 Pb Ohtsubo et al. 22 .The well-developed technique of detecting β b decay, as exploited in these experiments, is "Schottky lifetime spectrometry" Litvinov et al.

Figure 4 . 1
By a significant improvement of the output of the lead ion source and the reduction of beam losses, a number of 2 • 10 9 206 Pb ions could be delivered safely to the FRS already in two experiments.Based on the known cross-section for in-flight fragmentation and the known distribution of atomic charge states, this would yield a number of about 10 5 bare 205 Tl ions per injection into the ESR.

FFigure 4 :
Figure 4: Part of the accelerator facility of GSI, relevant for the proposed measurement of the bound-beta half-life of bare 205 Tl 81 ions.A beam of206  Pb ions, accelerated in the synchrotron SIS to an energy of some 100 A MeV, hits the production target Be of the fragment separator FRS, where a plenty of highly-charged ions will be generated by nuclear reactions.With the aid of an appropriate setting of the FRS magnets and by exploiting the Z-dependent stopping power in a degrader placed in the symmetry point of the FRS black triangle , only bare 205 Tl 81 ions can pass through small slits at the end of the FRS.Those ions will be stored in the experimental storage ring ESR and accumulated by repeated injections until a number of at least 10 6 ions will be reached.After the application of electron cooling, the 205 Tl 81 ions are circulating in the ring for a couple of hours, where a few of them will decay to hydrogen-like205  Pb by bound-state β decay.

Figure 5 :
Figure5: Schottky spectra versus the down-scaled revolution frequencies of stored and cooled nuclei, circulating in the experimental storage ring.Each of the lines shows a different nuclear species.Since for cooled ions a one-to-one correspondence exists between their revolution frequency and their massto-charge ratio, those spectra provide a highly precise mass spectroscopy.The inset shows the Schottky signals of two Sm 62 ions, one of them in the nuclear ground state at the higher frequency , the other one in a metastable state at an excitation energy of 754 keV.This demonstrates convincingly the capability of the ESR to detect-with ultimate sensitivity-one single stored and cooled highly-charged ion together with its accurate mass determination Figure by courtesy ofLitvinov et al. 23 .

Table 1 :
Cosmic-ray contributed N μ − and total number N t of 205 Pb atoms per 10 kg of lorandite from different depths, known to contain significant quantities of lorandite.
Neumaier et al. 11 and can experimentally be determined by measuring the 205 Pb contents in monitoring minerals realgar As 2 S 2 and orpiment As 2 S 3 .From the data for N Pb 205 ν and N Pb 205 fast muons shown in Table 1 we estimated by a Monte Carlo simulation the mean neutrino flux Φ ν 1.2 during the geological age a of lorandite as Whereas the geological age a of lorandite and the decay constant λ of 205 Pb are by now satisfactorily well known, the solar neutrino capture cross-section σ of 205 Tl is experimentally unknown.The value assumed in 2.3 is not more than the best educated guess, based on previous estimates of Bahcall and other theorists Bahcall 12 , Wapstra and Audi 13 , Braun and Talmi 14 , Freedman and Nolte 15 , ana Ogawa and Arita 16 .How the nuclear matrix element for the dominant neutrino capture channel into the first excited state of 205 Pb E * 2.3 keV can be experimentally determined will be outlined in the next Section 2.3.Likewise, the total detection efficiency ε assumed in 2.3 is only a optimistic guess.It is obvious that one of the most demanding problems of LOREX is the measurement of the extremely low concentrations of This number corresponds to 10 kg of lorandite, collected at a sufficiently deep location, for the background B to be acceptable, namely, at a paleo-depth of d p 980 m, where the calculated background B of205Pb atoms amounts to about 46%, see third row of Table 1 σ 4.3 • 10 −45 2.15 • 10 −46 cm 2 , a 1.26 • 10 14 1.26 • 10 12 s,λ 1.48 • 10 −15 7.4 • 10 −17 s −1 , ε 1 • 10 −3 1 • 10 −4 .205Pb in potentially available samples of a generally very scarce material.Methods that might be suited to this difficult task are discussed in Section 2.4.
Tl I π 1/2 to individual excited nuclear states of 205 Pb * , according to 205 Tl g.s.ν e E νe ≥ 52 keV −→ 205 Pb * e − 2.4 with an energy threshold at E νe 52 keV, much lower than the corresponding thresholds of all other radio-or geochemical experiments which are either already performed e.g., GALLEX or proposed.The solar pp-neutrinos with a maximum energy of 422 keV can be captured only into the ground state I π 5/2 − , the first E * 2.3 keV, I π 1/2 − , and the second excited state E * 263 keV, I π 3/2 − of 205 Pb.It is obvious from the wellknown systematic of beta decay that the capture probability into the 2.3 keV state ΔI 0, parity change should be by far larger than the capture into the ground state ΔI 2 as well as into the second excited state with ΔI 1 Behrens and Jaenecke 17 .The nuclear matrix element for the transition to the 2.3 keV state in