Complete results for five years of GNO solar neutrino observations

We report the complete GNO solar neutrino results for the measuring periods GNO III, GNO II, and GNO I. The result for GNO III (last 15 solar runs) is [54.3 + 9.9 - 9.3 (stat.)+- 2.3 (syst.)] SNU (1 sigma) or [54.3 + 10.2 - 9.6 (incl. syst.)] SNU (1 sigma) with errors combined. The GNO experiment is now terminated after altogether 58 solar exposure runs that were performed between May 20, 1998 and April 9, 2003. The combined result for GNO (I+II+III) is [62.9 + 5.5 - 5.3 (stat.) +- 2.5 (syst.)] SNU (1 sigma) or [62.9 + 6.0 - 5.9] SNU (1 sigma) with errors combined in quadrature. Overall, gallium based solar observations at LNGS (first in GALLEX, later in GNO) lasted from May 14, 1991 through April 9, 2003. The joint result from 123 runs in GNO and GALLEX is [69.3 +- 5.5 (incl. syst.)] SNU (1 sigma). The distribution of the individual run results is consistent with the hypothesis of a neutrino flux that is constant in time. Implications from the data in particle- and astrophysics are reiterated.


Introduction
The Gallium Neutrino Observatory (GNO) experiment at the Laboratori Nazionali del Gran Sasso (LNGS) has recorded solar neutrinos with energies above 233 keV via the inverse EC reaction 71 Ga (ν e , e -) 71 Ge in a 100-ton gallium chloride target (containing 30.3 tons of gallium) between May 1998 and April 2003 [1][2][3]. The data taking has now been terminated for external non-scientific reasons.
The GALLEX recordings (till 1997) established both the presence of pp-neutrinos [4] and a significant deficit (≈ 40 %) in the sub-MeV neutrino induced rate [5][6][7]. At that time, this was the strongest indication for neutrino transformations on the way between the solar core and the Earth, implying nonzero neutrino mass and non-standard physics [8][9][10][11]. The subsequent GNO observations have improved the quality of the data, added important restrictions on the presence of possible time variations, and substantially reduced the total error on the charged current reaction rate for pp-neutrinos as measured by the inverse EC reaction on gallium. Without radiochemical gallium detectors, the majority (93 %) of all solar neutrinos would still remain unobserved.
Gallium experiments at LNGS have now provided a long time record of low energy solar neutrinos and determined the bulk production rate with an accuracy of ± 5.5 SNU. This is based on 123 solar runs ("SR"), 65 from GALLEX and 58 from GNO. Results for the first 19 GNO runs (GNO I) were published in [1], here we report the full data for SR20 -SR43 (GNO II) and for SR44 -SR58 (GNO III).
The result and its precision will remain without competition from eventually upcoming low-threshold real-time experiments for many years to come. Recorded is a fundamental astrophysical quantity, the neutrino luminosity of the Sun. Lack of these basic data would have a very negative impact on the interpretation of the results from forthcoming second generation (real-time and low threshold) solar neutrino experiments such as BOREXINO (aiming for 7 Be neutrino detection). In the astrophysical context, the gallium results shed light also on the individual contributions of the PPI, PPII and CNO cycles to the solar luminosity and on the agreement of the energy production derived from the photonand from the neutrino luminosity respectively.
The plan of this article is as follows: In sect. 2 we describe some new experimental aspects and summarize the run characteristics. Data evaluation as well as the complete results and their errors are presented in sect. 3. In sect. 4 we discuss the internal consistency of all GNO and GALLEX data and the analysis for possible time variations of the neutrino signal. Sect. 5 is devoted to the interpretation of the results in the context of particle physics (5.1) and of astrophysics (5.2).

Experimental
The basic procedures in performing GNO extraction runs have been described before [1,[3][4][5][6][7]12]. Table 1 summarizes the GNO run characteristics. The operating periods defined as GNO II and GNO III comprised 24 and 15 solar runs respectively. Consecutive to the earlier 19 GNO I runs (results given in [1]), the new runs are labeled SR20-SR43 (GNO II) and SR44-SR58 (GNO III). The standard exposure time for solar runs was 4 weeks, with minor deviations due to practical reasons ( Table 1, 5 th column).

Ge extraction yields
Ge extraction yields were monitored with added Ge carriers ( ≈ 1 mg per run). The stable isotopes 70 Ge, 72 Ge, 74 Ge, and 76 Ge were used alternately (Table 1, 6 th column). The Ge recovery yields are listed in column 7 of Table 1. The yield refers to the percentage of initially added germanium that actually ended up in the counter. The complement of 100 % is the sum of the Ge that escaped extraction from the target and of the unavoidable losses that occur during the conversion of GeCl 4 into the counting gas component GeH 4 (germane) and in the counter filling procedure. Yields range from 91.2 % to 98.7 %, with a mean value of 95.7 %.
Compared to the standard Ge desorption conditions of GALLEX, desorption time and desorption gas volumes for GNO have been reduced from 12 to 9 hours and from 2500 to 1700 m 3 (at 20°C and 0.9 bar). This simplified the operating schedule at the expense of a slightly less efficient Ge desorption. The un-desorbed Ge-isotope carrier fraction remaining in the tank is expected to increase from about 0.2 % to values between 1 and 2 %. The fact that a homogeneously distributed Ge hold-back carrier level  76 Ge, respectively. c Integral tank-to-counter yield of Ge-carriers. The combined error assigned to the uncertainties of the yields and of the target mass is 2.2 %. d Counters have either iron (Fe) or silicon (Si) cathode. SC = silicon counter with shaped cathode, FC = iron counter with shaped cathode. e Efficiency > 0.5 keV. For distinction between "used" and "old", see text. * counter that is not absolutely calibrated (see sect. 2.2). never drops below ≈10 -13 mol per liter helps to exclude hypothetical 71 Ge loss scenarios that would involve the carrying-in of non measurable ultra-low trace impurities below that level.
The unavoidable Ge carrier residue that remains un-desorbed in a run is desorbed during the next run.
Its quantity can be determined by mass spectrometric analysis of the Ge recovered from the GeH 4 after counting. This is possible since we use in alternating sequence four different enriched stable Ge isotopes ( 70 Ge, 72 Ge, 74 Ge and 76 Ge) as mentioned above. The measurements are done with a multi-collector inductively coupled plasma mass spectrometer (MC-ICP-MS; NU Instruments, Wrexham, UK). Until now, about one third of the GNO runs have been analyzed in this way.
Based on textbook principles of isotope dilution analysis, the measured mass spectra allow splitting the composition of the analyzed Ge into the three potential contributions: principal carrier, carryover from the foregoing run, and Ge with natural isotopic composition (chemical contamination at trace level). The results shown in Table 2 are required for the precise determination of the chemical a Ge with natural isotopic composition, if not indicated otherwise. b does not include samples marked * due to known irregularities in the counting gas preservation and recovery or in the Ge preparation procedure for mass spectrometric analysis. 71 Ge recovery yields in the extraction runs. A first estimate from the samples analyzed so far is (1.4 ± 0.3) % for the residual Ge from the foregoing run. This average value has so far been applied in the data evaluation of all GNO runs. A more detailed evaluation of the isotopic data is going on and samples from the other GNO runs will be measured in order to establish a comprehensive picture.
Final corrections for each individual run will be possible when all MS data become available and the consistency of all GNO-measurements in this respect is ensured (within about one year from now). This is for scientific completeness. The maximum possible effective changes due to these refinements will under all circumstances be minor ( < 1 % ) with respect to the present overall result (the SNU-rate).

69 Ge counter calibration
The major contribution to the systematic errors of the GALLEX and GNO results so far (≈ 4 %) came from the insufficient knowledge of counter efficiencies (3.5 %). This is due to the fact that efficiencies for counters used in solar runs have not been measured directly because of contamination risk. Instead, they have indirectly been evaluated from measurements on other counters combined with a scaling procedure based on Monte Carlo simulations. However, some of the inputs needed in these MC simulations (counter volume, gas amplification curve) are not known with the accuracy that one can ambitiously desire.
In order to decrease this systematic error substantially, the GNO collaboration has developed a method that allows direct counter efficiency calibrations without introducing a major contamination risk [13]. 69 Ge-(and some 71 Ge-) activity is produced in the CN 7 MeV proton accelerator at the Legnaro INFN Laboratory (Italy) by the 69,71 Ga (p,n) 69,71 Ge reaction. 69 Ge (τ = 56.3 h) decays by β + and EC. In the latter case, the signal produced in the counter is indistinguishable from the one of 71 Ge decay, however coincident γ-rays are also emitted.
The irradiated Ga 2 O 3 is transported to Heidelberg. Then, the radioactive Ge is converted to GeH 4 and filled into the counters to be calibrated (usually 2 or 3 counters in one calibration run). The absolute efficiency is determined by measuring the count rate in the proportional counter in coincidence with the 1106 keV γ ray emitted in the EC decay of 69 Ge, detected by a 9"×9" well-type NaI detector. Data have been recorded with a conventional MCA system. From April 2002 onwards a VME system operating in list mode was used in addition. The advantage of the latter is the fact that the full information about each event is recorded. This allows optimizing the γ-ray coincidence conditions off-line, instead of having them fixed at the time of measurement.
Six (p,n) irradiations and subsequent 69 Ge calibration runs have been performed and a total of 12 GNO counters have been calibrated in these runs. While the statistical errors of the deduced efficiencies are always small (< 1 %), the limiting factor of the total error is due to systematic effects (corrections for β + contributions, the NaI background and instabilities of the electronics). The resulting total errors came out between 0.8 and 1.4 % (average 1.1 %). This constitutes a substantial reduction, as anticipated (compare columns 9 and 10 in Table 1). For 51 out of 58 GNO runs we have used counters that have been calibrated absolutely as described. Since the new efficiency determinations include also counters used in GNO I, slight changes of the data published in [1] result. This is one of the reasons why we have re-listed the GNO I results in Table 1. The absolute counter calibration program is going on, we plan to calibrate all counters (still alive) that have been used in relevant runs.
The efficiencies of the GNO counters depend only weakly on the gas filling (Xe/GeH 4 composition and pressure). Since the absolute efficiency measurements in Heidelberg have been performed with counter fillings close to the standard fillings in GNO runs, the efficiency values derived in Heidelberg are directly applicable to GNO solar runs.

Radon recognition and reduction
An elaborate radon test was performed with a modified counter containing a Ra source. The aim was to Using these data, we re-evaluated the inefficiency of the radon cut. The result is consistent with zero and the (2σ) upper value is 7.3 %. This replaces (for GNO) 1 the formerly determined value used in GALLEX, (9 ± 5) %.
Systematic tests on the synthesis line concerning GeCl 4 handling and the filling of GeH 4 into the counters have shown that the main sources of Rn contamination have been the mercury diffusion pump with its liquid nitrogen cold trap and the Xe storage vessel (Xe is admixed to GeH 4 to manufacture the counting gas).
The pump system was replaced by a turbo molecular pump in combination with a cold trap at -50 C°.
The compression ratio for Rn is now increased by a factor of ≈10 6 compared to the former case in which the diffusion pump was used. Furthermore, the storage vessel for Xe made of  Jenaer Glass was replaced by a Kovar glass vessel which has a five times smaller concentration of 226 Ra by weight.
The mean level of identified 222 Rn atoms per run during the GALLEX experiment was 4.5. Eleven runs were performed after the changes described above. Two runs with unusual technical problems yielded 3 atoms and 4 atoms of 222 Rn, respectively. In the other runs we found 3 times one and 6 times zero 222 Rn atoms. If the runs with technical problems are omitted, the mean value is now reduced to 0.33 222 Rn atoms per run.

Electronics and noise reduction
Analog and digital electronics, power supplies and data acquisition system have been completely renewed and reorganized after the accomplishment of GALLEX data taking. The analog bandwidth of the system has been increased to 300 MHz, the typical RMS noise is 2.8 mV. Due to these improvements and to a thorough screening of counters used in solar runs, the background in GNO is 0.06 counts per day in the relevant windows, corresponding to a 40 % background reduction compared to GALLEX.
In addition, a novel signal acquisition technique recently developed by us is the simultaneous recording of both, anode and cathode current from proportional counters [14]. The signal/noise ratio is increased by about 40 %. This is beneficial in particular for small signals. Furthermore, with this technique signals from inside the counters can be separated from signals picked up from the environment. For practical application, the counter boxes require mechanical modifications. So far, a prototype has been successfully applied in a blank run and in a solar run.

GNO blank runs
In addition to solar runs, one-day-exposure blank runs were also performed regularly in order to verify the absence of any artifact or systematics related to the target. During the period of operation of GNO, 12 blank runs ("BL") were successfully performed. The results are summarized in Table 3.
The absence of spurious effects or unknown background is confirmed by the fact that the small excess of 71 Ge counts in the blanks is consistent with the neutrino-induced production rate during the short exposure and the carry-over from the previous solar run.

Data evaluation and counting results
A random sampling of counter types was applied for the measurements (see Table 1, 8 th column). For the selection of the 71 Ge events we have subjected the counting data to our new neural network pulse shape analysis (NNPSA) [15] and to a subsequent maximum likelihood analysis [16]. Pulses are first selected according to their amplitude (L or K peak), following the procedure described in [1]. Those passing the energy cut are then subject to a pulse shape selection. This procedure is logically  [15].
We have verified that the NNPSA provides a better noise rejection than the previously used rise time selection method, especially in the L energy window, at similar 71 Ge acceptance efficiency (≥ 93 %). In particular, NNPSA is able to recognize some of the fast-rising background pulses that otherwise would have been accepted on the basis of their rise time alone, and to treat the double-ionization events in the K window in the proper way. All the results obtained with both methods are consistent, but with lower background levels for NNPSA. Moreover, since other discriminating parameters are taken into account in addition to rise time, the NN-based approach is more robust and effective than the previous one. This may be compared with the time independent counter background in the acceptance windows. Sum of fast K + L : 0.065 cpd ; Sum of NNPSA-selected K + L : 0.059 cpd For the K-and L energy windows, the quoted rates apply to the fast-rising or NNPSA-selected background pulses that can mimic 71 Ge pulses. The integral rate includes all the pulses in the whole energy range 0.5 keV ≤ E ≤ 15 keV.  Table 4 gives a summary of the measured backgrounds for the counters used in GNO, both with the rise time and the NNPSA selection. It is on average as low as ≈ 0.06 counts per day (Table 4). For a comprehensive documentation of our counter backgrounds, which is also of general interest concerning the frontiers of 'Low-Level' counting, see [17].
The individual run results for the net solar production rates of 71 Ge (based on the counts in the K and L energy-and neural network acceptance region) are plotted in Figure 1 and listed in Table 5, after subtraction of 4.55 SNU for side reactions as quoted in [1] and the correction for the annual modulation. Also listed in Table 5 are the combined results for the operating periods GNO III, GNO II and GNO I, respectively.  Table 1). Plotted is the net solar neutrino production rate in SNU after subtraction of side reaction contributions (see text). Error bars are ±1σ, statistical only.
The systematic errors are specified in Table 6. The total systematic 1σ error is 2.5 SNU. It is still dominated by the error of the counting efficiencies, however it is substantially lower than in GALLEX (4.5 SNU). Ge) is shown in Figure 2. It clearly identifies the 71 Ge electron capture spectrum with its peaks at 1 keV (relaxation of L-shell vacancy) and 10 keV (K-shell). The combined net result for all GNO runs (after subtraction of 4.55 SNU for side reactions) is 62.9 ± 6.0 5.9 SNU (1σ, incl. syst.) (see sect.4, especially Table 7).

Joint analysis of GNO and GALLEX and an examination of a possible time variation of the neutrino signal
In Table 7 we compile the basic results for GNO, GALLEX, and for a combined analysis of GNO and GALLEX together. The joined GNO + GALLEX result after 123 solar runs is 69.3 ± 4.1 (stat.) ± 3.6 (syst.) SNU (1σ) or 69.3 ± 5.5 SNU (1σ) with errors added in quadrature [19]. Our present joint result is now much more accurate, yet it retrospectively confirms the earlier GALLEX results which made the case to claim strong evidence for non-standard neutrino properties because the production rate predictions from the various standard solar models have always been much higher (120-140 SNU) than the measured rates [9]. The updated result of the SAGE experiment, 66.9 ± 5.3 5.0 SNU (1σ) [20], agrees well with our result. The results of all 123 individual GNO and GALLEX measurements of the neutrino capture rate are shown in Figure 4. Like in all of our previous papers, we estimate the gallium-solar neutrino interaction rate under the assumption of a neutrino flux constant in time. This assumption must be justified even though there are presently no attractive models that predict a time variable neutrino emission from the Sun. Observation of such a variation on a short (that is, non-secular) time scale would signal new and unexpected solar or neutrino physics. This cannot be excluded 'a priori'. Consequently, we analyze our (GNO+GALLEX) data for possible time variations during the ≈12-year period of data taking.  To test the null hypothesis of a capture rate constant in time we have used two different approaches: • Application of the maximum likelihood ratio test (see [5] for details). The resulting goodness of fit confidence levels are 25.1 % for GNO, 24.2 % for GALLEX, and 5.6 % for GALLEX+GNO.
• Fits of the results of the seven periods GNO III, II, I and GALLEX IV, III, II, I with (arbitrary) time-varying functions, e.g. f = a + bt , and compare the results with the null hypothesis. The resulting confidence levels for these options do not differ significantly (see Fig. 6).
We conclude that the results are consistent with a flat behaviour; however a weak time dependency (of unknown origin) is not excluded.  The finding that the solar data are consistent with a production rate constant in time does not invalidate other hypotheses that might give similar or even better (short) time dependent fits [21,22]. Respective searches for such time modulations in the GNO and GALLEX data [23] yield no statistically significant periodicity within the Lomb-Scargle [24,25] and maximum likelihood algorithms.

Particle physics context
Concerning both particle physics as well as astrophysics, low-energy solar neutrino experiments will be of high importance also in the years to come (e.g., [26]). Global fits of all solar and reactor neutrino data have established that the deficits observed in the signals of all experiments are caused by neutrino oscillations with parameters in the Large Mixing Angle (LMA) region (see e.g. [27] (SNO), [40] (Kamland), [26] (analysis)). If the LMA(MSW) oscillation solution is correct, the basic oscillation mechanism changes at a neutrino energy of about 2 MeV from the MSW matter mechanism (above 2 MeV) to the vacuum oscillation mechanism (below 2 MeV). This transition has not yet been checked experimentally in a model-independent way.
The gallium result fits well in the oscillation scenario. If one subtracts the 8 B neutrino contribution as measured by SNO [27] from the gallium signal and calculates the suppression factor P with respect to the BP04 SSM [28] for sub-MeV neutrinos (pp and 7 Be), the result is P = 0.556 ± 0.071. Assuming vacuum oscillations, P is given by: P = 1 -0.5 sin 2 (2 θ ). This yields θ = 35.2 +9. 8 -5.4 degrees. Although such an estimate is quite approximate, it is in good agreement with the latest determination (32.0 ± 1.6 degrees [26]), which essentially comes from 8 B neutrinos (i.e. matter effects dominate).
The GNO result is fully consistent both with the GALLEX result and with all other solar neutrino data if judged in the frame of the Standard Solar Model and the MSW scenario, where a gallium rate within a range of 70 ± 2 SNU is predicted.
In addition to the dominant LMA(MSW) conversion mechanism, the possible existence of sterile neutrinos and/or of flavor-changing neutrino matter interactions other than the MSW effect [29][30][31] can be investigated with low-energy solar neutrinos.
About 91 % of the total solar neutrino flux is expected to originate from low-energy pp-neutrinos. This fundamental prediction of the standard solar model has still to be tested experimentally by separate determinations of the solar neutrino fluxes of the pp, 7 Be, and CNO reactions.
Considerable effort was devoted to the improvement of GNO sensitivity and to the reduction of the statistical as well as the systematic errors, e. g. the installation of new electronics, the introduction of neural network data analysis and developments towards cryogenic detectors for an improved 71 Ge counting efficiency [3]. It will be for the next generation of large solar neutrino detectors to reach a sensitivity which not only will be sufficient for the determination of the individual solar neutrino fluxes but which will also enable investigations in other astrophysical fields via neutrino astronomy. Future low-energy neutrino detectors may very well allow studying physics beyond solar astronomy, for example supernovae and geophysics.

Comparison of gallium experimental results with solar models
Recent new experimental data on input parameters for solar model calculations led to improved predictions for neutrino fluxes and capture rates. In particular this refers to: • new measurements of the solar surface composition [32]. The new determination of the C,N,O surface abundances changes the metal to hydrogen ratio Z/X from 0.0229 previously to 0.0176 now.
The immediate consequences for the predicted neutrino fluxes (BP04 + vs. BP04 in Ref. [28]) are reductions for 8 B (9 %), 13 N (30 %) and 15 O (30 %) contributions (see Table 8). The updated model BP04 + foresees a depth of the convective zone R CZ /R 0 = 0.726. This is clearly in conflict with the very accurately measured helioseismological value of 0.713 ± 0.001. The change happns because once the surface heavy element composition is decreased, the radiative opacity and the central temperature will also decrease and the base of the convective zone is moving outward.
Due to this conflict, we prefer for the time being the partially updated model BP04 [28]. This model obeys neither the new value for Z/X nor the new value for S 0 [ 14 N(p,γ) 15 O] = 1.77 ± 0.2 keVbarn which practically is one-half of the previous best estimate for this cross section. This would cut almost in half the 13 N and 15 O neutrino fluxes (see Table 8, column for Franec04 + ).
In absolute terms, CNO nuclear reactions contribute 1.6 % to the solar luminosity in BP04 [28], however only 0.8 % in Franec04 + [36]. We included Franec04 + in Table 8 to illustrate the robustness of the neutrino capture rate predictions even under heavy modifications of the model calculations. Given the accuracy of both the gallium 2 and the chlorine experimental results it is impossible to distinguish between BP04 and Franec04 + , one can just notice that both the gallium and mainly the chlorine results are on the lower side of the predictions.  This assumes that nuclear fusion reactions are the only energy production mechanism inside the Sun.

Limits on the CNO cycle contributions to the solar luminosity
Apart from this basic assumption, the luminosity constraint does not depend on the solar model.
The fractional CNO luminosity is defined by: It can be calculated from the measured gallium rate where σ i (E) is the neutrino capture cross section on Ga, ϕ i (E) is the differential flux of solar neutrinos of species i, and P(E) is the electron neutrino survival probability. For this calculation we make the following assumptions: • the 8 B electron neutrino flux, and the electron neutrino survival probabilities are measured with a precision of the order of 12 % by SNO [27].
• the 7 Be neutrino flux is as deduced in BP04 SSM [28], with an uncertainty of 12 %. It is not directly measured up to now.
• the neutrino flux ratios pep/pp and 13 N/ 15 O are fixed from nuclear physics and kinematics with negligible uncertainties (see [26]).
• the neutrino capture cross section (and its uncertainty) on 71 Ga is theoretically calculated as in [38].
(4) Figure 9: Plot of the solar luminosity fraction due to CNO-cycle reactions versus the gallium neutrino capture rate. The underlying assumptions are discussed in the text. Contours are shown for the 1σ, 2σ, and 3σ limits that are allowed by the GALLEX/GNO experimental result on the gallium rate. The straight line is given by the luminosity constraint (see text).
The result is represented graphically in Figure 9 in the plane L CNO /L Sun vs. Ga rate. Plotted are the regions that are allowed at the 1σ, 2σ and 3σ sigma levels. The result is in good agreement with the predictions of the solar models, L CNO = 1.6 ± 0.6 %. This is a unique self-consistency test of the observed solar luminosity, the predicted neutrino fluxes, and the oscillation scenario.
We stress again that in order to obtain the above results we have assumed that the 7 Be neutrino flux is as predicted from the SSM, with an uncertainty of 12 %. Hopefully, this flux will soon be directly measured by BOREXINO [39] and/or KAMLAND [40]. When this will be done, the gallium rate will become a completely model independent test of the solar neutrino luminosity. An upper limit on the CNO luminosity from all currently available solar neutrino and reactor anti-neutrino experimental data is discussed in [26].