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First result of the experimental search for the 9.4 keV solar axion reactions with Kr-83 in the copper proportional counter

The experimental search for solar hadronic axions is started at the Baksan Neutrino Observatory of the Institute for Nuclear Researches Russian Academy of Science. It is assumed that axions are created in the Sun during M1-transition between the first thermally excited level at 9.4 keV and the ground state in Kr-83. The experiment is based on axion detection via resonant absorption process by the same nucleus in the detector. The big copper proportional counter filled with krypton is used to detect signals from axions. The experimental setup is situated in the deep underground low background laboratory. No evidence of axion detection were found after the 26.5 days data collection. Resulting new upper limit on axion mass is m_{A}<130 eV at 95% C.L.


Introduction
A solution of the strong CP problem based on the global chiral symmetry U(1) was proposed by Peccei and Quinn (PQ) [1]. The existence of the axions was predicted by Weinberg [2] and Wilczek [3] as result of spontaneous breaking of the PQ-symmetry at the energy f A . The axion mass (m A ) and the strengths of an axion's coupling to an electron (g Ae ), a photon (g Aγ ) and nucleons (g AN ) are proportional to the inverse of f A . At the moment there are two classes of models for the axion: the hadronic axion (KSVZ-model) [4] and GUT axion (DFSZ-model) [5]. The axion mass in both models is defined as: where f π ≃ 93 MeV -pion decay constant, z = m u /m d ≃ 0.56 and w = m u /m s ≃ 0.029 -quark-mass ratios. It gives m A [eV] ≃ 6.0 × 10 6 /f A [GeV].
The main difference between models is that in contrast to the DFSZ-model in KSVZ-model axions have no coupling to leptons and ordinary quarks at the tree level. As result the interaction of the KSVZ axion with electrons through radiatively induced coupling is strongly suppressed [6].
If axions do exist, then the Sun and other stars should be an intense source of these particles. In 1991 Haxton and Lee calculated the energy loss of stars along the red-giant and horizontal branches due to the axion emission in nuclear magnetic transitions in 57 Fe, 55 Mn, and 23 Na nuclei [7]. In 1995 Moriyama proposed experimental scheme to search for 14.4 keV monochromatic solar axions that would be produced when thermally excited 57 Fe nuclei in the Sun relax to its ground state and could be detected via resonant excitation of the same nuclide in a laboratory [8]. Searches for resonant absorption of solar axions emitted in the nuclear magnetic transitions were performed with 57 Fe [9,10,11,12,13,14], 7 Li [15,16,17] and 83 Kr [18] nuclei.
In this paper we present the results of the search for solar axions using the the resonant absorption by 83 Kr nuclei. The energy of the first excited 7/2 + nuclear level is equal to 9.405 keV, lifetime τ = 2.23 × 10 −7 s, internal conversion coefficient α = 17.0 and the mixing ratio of M1 and E2 transitions is δ = 0.013 [19].
In accordance with indirect estimates the abundance of the krypton in the Sun (Kr/H) = 1.78 × 10 −9 atom/atom [20] that corresponds to N = 9.08 × 10 13 of 83 Kr atom per 1 g material in the Sun.
To estimate axion flux from the Sun, the calculation can be performed as in the Ref. [7]. The axion flux from a unit mass is equal where N -number of 83 Kr atoms in 1 g of material in the Sun, β T = E γ /kT , τ γ -lifetime of the nuclear level, ω A /ω γ -represents the branching ratio of axions to photons emission. The ratio ω A /ω γ was calculated in [7,21,22] as where µ 0 and µ 3 -isoscalar and isovector magnetic moments, g 0 and g 3 -isoscalar and isovector parts of the axion-nucleon coupling constant g AN and β and η -nuclear structure dependent terms.
In case of the 83 Kr nucleus, which has the odd number of nucleons and an unpaired neutron, in the one-particle approximation the values of β and η can be estimated as β ≈-1.0 and η ≈0.5.
In the hadronic axion models, the g 0 and g 3 constants can be represented in the form [6]: where D and F denote the reduced matrix elements for the SU(3) octet axial vector currents and S characterizes the flavor singlet coupling [6]. The parameter S characterizing the flavor singlet coupling still remains a poorly constrained one [14]. The most stringent boundaries (0.37 ≤ S ≤ 0.53) and (0.15 ≤ S ≤ 0.5) were found in [23] and [24], accordingly. The axion flux was calculated for the standard solar model BS05 [25] characterized by a highmetallicity [26]. The differential flux at the maximum of the distribution (6) is The width of the resulting distribution, which is described well by a Gaussian curve, is σ = 1.2 eV. This value exceeds substantially the recoil-nucleus energy and the intrinsic and Doppler widths of the level of 83 Kr target nuclei. The cross section for resonance axion absorption is given by an expression similar to the expression for the photon-absorption cross section, the correction for the ratio ω A /ω γ being taken into account.
where σ 0γ = 1.22 × 10 −18 cm 2 is the maximum cross section of the γ -ray resonant absorption and Γ = 1/τ . The total cross section for axion absorption can be obtained by integrating σ(E A ) over the axion spectrum. The expected rate of resonance axion absorption by the 83 Kr nucleus as a function of the probability for axion emission ω A /ω γ ; the parameter (g 3 − g 0 ), which describes axion-nucleon interaction; and the axion mass in the KSVZ model can be represented in the form (S = 0.5, z = 0.56): The number of detected photons following axion absorption is determined by the target mass, measurement time, and detector efficiency. At the same time, the probability of observing a peak at 9.4 keV is dependent on the background level in the experimental facility used.

Experimental setup
The experimental technic is based on registration of the γ-quantum and conversion electrons appearing after deexcitation of the 83 Kr nuclei. To register this process a large proportional counter (LPC) with a casing of copper is used. The gas mixture Kr(99.55%)+Xe(0.45%) is used as working media of the LPC. The isotopic composition of the krypton is: 78 Kr(0.002%) + 80 Kr(0.411%) + 82 Kr(41.355%) + 83 Kr(58.229%) + 84 Kr(0.003%). The LPC is a cylinder with inner and outer diameters of 137 and 150 mm, respectively. A gold-plated tungsten wire of 10 µm in diameter is stretched along the LPC axis and is used as an anode. To reduce the influence of the counter edges on the operating characteristics of the counter, the end segments of the wire are passed through the copper tubes (3 mm in diameter and 38.5 mm in length) electrically connected to the anode. These segments operate as an ionization chamber with no gas amplification. Taking into account teflon insulators dimensions, the distance from operation region to the flange is 70 mm. The fiducial length of the LPC is 595 mm, and the corresponding volume is 8.77 L. Gas pressure is 5.6 bar, and corresponding mass of the 83 Kr-isotope in fiducial volume of the LPC is 101 g. The LPC is surrounded by passive shield made of copper (∼20 cm), lead (∼20 cm) and polyethylene (8 cm). The setup is located in the Deep Underground Low-Background Laboratory at BNO INR RAS [27], at the depth of 4700 m w.e., where the cosmic ray flux is reduced by ∼ 10 7 times in comparison to that above ground, and evaluated as (3.0 ± 0.1) × 10 −9 cm −2 s −1 [28].
The detector signals are passed from one end of the anode wire to the chargesensitive preamplifier. A total shape of pulses (waveforms) are recorded by the digitizer after amplification in an auxiliary amplifier. A digital oscilloscope LAn-n20-12USB integrated with a computer via USB-port is used. Sampling frequency is 12.5 MHz and record window is 2048 bins (164 µs). Sample of the recorded waveform is presented in Fig.1a. There is a feature in the waveforms, namely the presence of secondary pulse after the primary pulse. Those secondary pulses are result of photoemission from the cathode. Photons appear near anode wire in time of the development of an electron avalanche from the primary ionization electrons. The relative height of the secondary pulse depends on the position of the events along anode wire due to the changing of a cathode view solid angle. The lowest value of the angle is reached at the ends of the anode wire and the smallest secondary pulses are appeared as a result. Recorded waveforms are processed to define parameters of the events. First of all, the response function of the LPC for single electron of the primary ionization is used to define the electron density profile for the given event (electron current). The shape of the responce function is defined as: where T = 460 µs, B = 2.4 · 10 −3 µs and τ = 240 µs. The cumulative sum (integral) of the electronic current is an corrected waveform as in the Refs. [29]. Samples of the recorded electronic current and the corrected waveform are presented in Fig.1a. Schematic description of the used parameters are presented in Fig.1b. The amplitude of the secondary pulse is used to define the relative position of the events along the anod wire by ratio: where A1 -amplitude of the secondary pulse, A0 -amplitude of the primary pulse (see Fig.1b).

Results
The background spectra collected during 26.5 days and fit result curve are presented in Fig.2. Fitting function is taken as The peak of 13.5 keV from K-capture of 81 Kr is well seen. 81 Kr is a cosmogenic isotope. It present as a trace admixture in the used samples of krypton. This isotope is produced in atmosphere mainly in reactions 82 Kr(n, 2n) 81 Kr and 80 Kr(n, γ) 81 Kr, the half-life time is T 1/2 = 2.1 · 10 5 y. There are two more peaks: ∼ 12 and ∼ 8 keV. The peak near 12 keV is produced by events, where the K-capture of 81 Kr happens near the end of the counter (out of the fiducial volume) and the characteristic  photon of daughter nuclide 81 Br is registered in the fiducial volume (K α1 =11.923 keV (57.1%), K α2 =11.877 keV (29.1%), K β1 =13.290 keV (12.7%), K β2 =13.465 keV (1.0 %) [30]). The peak near 8 keV is produced by characteristic photons from the copper (K α1 =8.047 keV (58.4 %), K α2 =8.027 keV (29.8%), K β1 =8.904 keV (11.7%) [30]). The distributions of the events versus pulse rise time and parameter λ are presented in Fig.3 and Fig.4 respectively. The events with pulse rise time ≃ 55 bins (4.4 µs) mostly are the single site events from the inner surface of the cathode (well seen in the distribution for the events with E > 15.0 keV). The pulses with londer pulse rise time are mostly the multi site events. The events with λ < 115 are mostly close to the edge of the fiducial volume (events in the peak of ≃ 12 keV) or out of it (high energy events at the ends of the counter, where no gas amplification).
Thus, as we are looking for single site events in the inner volume of the detector, the events with pulse rise time longer then 47 bins (3.8 µs) and λ lower then 115 are rejected. The resulting spectrum in comparison with original one is presented in Fig.5. There is no visible peak around 9.4 keV from axions. Region of interest is 8.2 ÷ 9.4 keV, where should be 47.5% of axion events. Detection efficiencies after applying energy cut, pulse rise time cut and λ cut are ε E = 0.475, ε τ = 0.94, ε λ = 0.91 respectively. The number of events in the region of interest after cuts applying equal to 703 cts. As there is no "signal" from axions, the upper limit on excitation rate of 83 Kr by solar hadronic axions in the detector is defined as: where: B -background in the region of interest, m Kr -the mass of the 83 Kr (gram), t meas -measurement time (day). The relation (14) obtained in the experiment limits the region of possible values of the coupling constants g 0 , g 3 and axion mass m A . In accordance with Eqs. (8)(9)(10), and on condition that (p A /p γ ) ∼ = 1 provided for m A < 3 keV one can obtain: m A ≤ 130 eV at 95% C.L.
The limit (16) is stronger then the constrain obtained with 14.4 keV 57 Fe solar axions -(m A ≤ 145 eV [14]) and is significantly stronger then previous result obtained in 83 Kr experiment [18].

Conclusion.
A search for resonant absorption of the solar axion by 83 Kr nuclei was performed using the proportional counter installed inside the low-background setup at the Baksan Neutrino Observatory. The intensity of the 9.4 keV peak measured for 26.5 days turned out to be ≤ 7.0 events/day. The obtained model independent upper limit on axion-nucleon couplings allowed us to set the new upper limit on the hadronic axion mass of m A ≤ 130 eV (95% C.L.) with the generally accepted values S=0.5 and z=0.56. The obtained limit on axion mass strongly depends on the exact values of the parameters S and z.
The work is supported by Russian Foundation of Basic Research (Grants No. 14-02-00258A, 13-02-01199A and 13-02-12140-ofi-m). V.V.Kobychev is supported in part by the Space Research Program of NAS Ukraine.