Overview on neutrinos and the Daya Bay experiment

Abstract

Neutrinos are elementary particles in the Standard Model. Neutrino oscillation is a quantum mechanical phenomenon beyond the Standard Model. Neutrino oscillation can be described by two independent mass-squared differences \mathrm{\Delta }{m}_{21}^2, \mathrm{\Delta }{m}_{31}^2 (or \mathrm{\Delta }{m}_{32}^2) and a 3\times 3 unitary matrix, containing three mixing angles {\theta }_{12}, {\theta }_{23}, {\theta }_{13}, and one charge-parity (CP) phase. {\theta }_{12} is about {34}^{\circ } and determined by solar neutrino experiments and the reactor neutrino experiment KamLAND. {\theta }_{23} is about {45}^{\circ } and determined by atmospheric neutrino experiments and accelerator neutrino experiments. {\theta }_{13} can be measured by either accelerator or reactor neutrino experiments. On Mar. 8, 2012, the Daya Bay Reactor Neutrino Experiment reported the first observation of non-zero {\theta }_{13} with 5.2 standard deviations. In June, with 2.5\times previous data, Daya Bay improved the measurement of {\sin }^{2}2{\theta }_{13}=0.089\pm 0.010(\mathrm{stat})\pm 0.005(\mathrm{syst}).

Graphical abstract

Keywords

neutrino oscillation / neutrino mixing / Daya Bay

1 Introduction to neutrino and neutrino oscillation

Neutrinos are elementary particles in the Standard Model. There are three flavors of neutrinos, known as {\nu }_e, {\nu }_{\mu } and {\nu }_{\tau }. Neutrinos exist everywhere: the nuclear fusion in the sun, β-decays of radioactivities inside the Earth, the Big Bang remnant, the supernova explosion, or interactions between cosmic rays and the atmosphere of the Earth. Besides the natural sources, neutrinos can be also produced artificially in reactors and accelerators. The neutrino flavor states are superpositions of three mass eigenstates ({\nu }_1, {\nu }_2 and {\nu }_3), which undergo quantum interference during the traveling, causing neutrino flavor changes. This phenomenon is known as neutrino oscillation. The amplitude of oscillation is connected to the mixing angles {\theta }_{12}, {\theta }_{23} and {\theta }_{13}. The oscillation frequencies are determined by the difference of squared neutrino masses, \mathrm{\Delta }{m}_{ij}^2=m_i^2-m_j^2.

As of one year ago, all of the mixing parameters had been measured except for {\theta }_{13}. Solar neutrino experiments measured {\theta }_{12} and \mathrm{\Delta }{m}_{21}^2. Atmospheric neutrino experiments measured {\theta }_{23} and \left|\mathrm{\Delta }{m}_{32}^2\right|. The CHOOZ experiment set a limit of at 90% CL [1, 2] by the measurements of antineutrinos emitted from nuclear reactors. In 2011, two accelerator experiments T2K [3] and MINOS [4], and one reactor experiment Double Chooz [5], showed indication of none-zero {\theta }_{13} at the level of 1 to 2.5 standard deviations.

In Mar. 2012, the Daya Bay Reactor Neutrino Experiment reported the first observation of non-zero {\theta }_{13} with 5.2 standard deviations [6]. About one month later, the RENO experiment gave a consistent result with 4.9 standard deviations [7]. In June, with 2.5\times previous data, Daya Bay has improved the measurement of {\theta }_{13} [8].

2 {\theta }_{12} and solar neutrino experiments

In the late 1960s, the Homestake [9] experiment observed a deficit in the flux of solar neutrinos with respect to the prediction from the Standard Solar Model. This experiment had been running for nearly 30 years, and the deficit persists [10], which is known as the solar neutrino problem. In 2001, the SNO [11] experiment detected neutrinos via both charge-current and neutral-current interactions, confirming that solar electron neutrinos do not disappear, but oscillate into the muon and tau flavors. The oscillation takes place inside the Sun through a matter-induced resonance known as MSW effect [12, 13]. Further measurements of the solar neutrino flux, as well as measurements of reactor neutrino flux by the KamLAND experiment, determined \mathrm{\Delta }{m}_{21}^2 and {\theta }_{12}. The latest experiment values of these two oscillation parameters are \mathrm{\Delta }{m}_{21}^2={7.50}_{-0.20}^{+0.19}\times {10}^{-5}{\mathrm{eV}}^2, {\tan }^2{\theta }_{12}={0.452}_{-0.033}^{+0.035} [14].

Recent results from Borexino [15–17], Super Kamiokande (Super-K) [18] and SNO [19] focused on low energy solar neutrinos between 1 MeV to 5 MeV. In this region, the solar neutrino disappearance is dominated by vacuum oscillation, compared to matter-enhanced oscillation in high energy range (> 5 MeV). These measurements not only improved the precision of oscillation parameters, but also confirmed the MSW effect and the Standard Solar Model.

3 {\theta }_{23} and atmospheric neutrino experiments

The interaction of cosmic rays with the atmosphere of the Earth produces secondary particles, including hadrons and their decay products. In particular, pions produce neutrinos through the decay chain: \pi \to \mu +{\nu }_{\mu }, \mu \to e+{\nu }_e+{\nu }_{\mu }. Neutrinos from these interactions with energies from 100 MeV to about 100 GeV are called atmospheric neutrinos. The ratio of {\nu }_{\mu } to {\nu }_e should be 2 at low energy range (< 1 GeV). Since 1980s, a few experiments measured this ratio and found it’s smaller than the expectation [20], which is known as the atmospheric neutrino problem. In 1998, the Super-K experiment provided a very precise measurement of atmospheric {\nu }_{\mu } and {\nu }_e flux, and found a deficit of {\nu }_{\mu } in the energy range of hundreds of MeV to a few GeV, at a distance of the diameter of the earth, which can be explained by a {\nu }_{\mu }\to {\nu }_{\tau } oscillation. {\theta }_{23} and \left|\mathrm{\Delta }{m}_{\mathrm{atm}}^2\right| (which is an approximation of \left|\mathrm{\Delta }{m}_{32}^2\right|) were determined accordingly [21].

Muon neutrinos can also be produced in accelerators with a high intensity, which give a good opportunity for neutrino oscillation study. Recently, the MINOS experiment, using the neutrino beam in the Fermilab, updated the result of {\theta }_{23} and \left|\mathrm{\Delta }{m}_{\mathrm{atm}}^2\right|, by measuring the disappearance of {\nu }_{\mu } or {\overline{\nu }}_{\mu } at a distance of 735 km. \left|\mathrm{\Delta }{m}_{\mathrm{atm}}^2\right|={2.39}_{-0.27}^{+0.22}\times {10}^{-3}{\mathrm{eV}}^2, {\sin }^{2}2{\theta }_{23}={0.96}_{-0.04}^{+0.04} in the neutrino mode, and \left|\mathrm{\Delta }{m}_{\mathrm{atm}}^2\right|={2.48}_{-0.27}^{+0.22}\times {10}^{-3}{\mathrm{eV}}^2, {\sin }^2(2{\theta }_{23})={0.97}_{-0.08}^{+0.03} in the antineutrino mode [22]. So the muon antineutrino disappearance is in good agreement with the neutrino result, which gives no indication of charge-parity-time reversal (CPT) violation.

4 {\theta }_{13} in accelerator experiments

Besides determining {\theta }_{23} and \left|\mathrm{\Delta }{m}_{\mathrm{atm}}^2\right|, neutrinos from accelerators can also be used to measure {\theta }_{13}, as well as studies of CP violation and the mass ordering of {\nu }_2 and {\nu }_3. The probability of muon neutrinos translating to electron neutrinos can be described as

\begin{array}{}\text{(1)}& \begin{array}{cc}P({\nu }_{\mu }\to {\nu }_e)=\hfill & {\sin }^2(2{\theta }_{13}){\sin }^2{\theta }_{23}{\sin }^2(1.27\mathrm{\Delta }{m}_{31}^{2}L/E)\hfill \\ \hfill & +(\mathrm{solar}\mathrm{term})\hfill \\ \hfill & +(\mathrm{CP}\mathrm{violation}\mathrm{term})\hfill \\ \hfill & +(\mathrm{CP}\mathrm{conservation}\mathrm{term})\hfill \\ \hfill & +(\mathrm{matter}\mathrm{effect}\mathrm{term})\hfill \end{array}\end{array}

where \mathrm{\Delta }{m}_{31}^2 can be approximated by \mathrm{\Delta }{m}_{\mathrm{atm}}^2, E is the neutrino energy in GeV and L is the distance in km between the neutrino source and the detector (baseline). The matter effect term can be enhanced with longer baseline, which gives the information of the mass ordering (mass hierarchy) of {\nu }_2 and {\nu }_3.

The T2K experiment uses the Super-K detector to detect neutrinos from J-PARC facility in Tokai, which is 295 km away from the detector. In Jun. 2011, T2K announced the observation of six electron neutrinos compared to an expected background of 1.5, which gives an indication of none-zero {\theta }_{13} with a significance of 2.5 standard deviations [3]. Soon thereafter, the MINOS experiment reported their first result of {\theta }_{13}, which also favors none-zero {\theta }_{13}, and the significance is 1.7 standard deviations [4]. Both of T2K and MINOS gave an updated measurement of {\theta }_{13} in Jun. 2012 with more statistics, and improved the significance to 3.2 [23] and 2.0 [24] standard deviations, respectively.

5 {\theta }_{13} in reactor experiments

For reactor-based experiments, {\theta }_{13} can be extracted from the survival probability of the electron antineutrino at a distance of 1–2 km from the reactors

\begin{array}{}\text{(2)}& P({\overline{\nu }}_e\to {\overline{\nu }}_e)\approx {\sin }^2(2{\theta }_{13}){\sin }^2(1.27\mathrm{\Delta }{m}_{31}^{2}L/E)\end{array}

where E is the {\overline{\nu }}_eenergy in MeV and L is the distance in meters between the {\overline{\nu }}_e source and the detector (baseline).

The past reactor experiments, such as Palo Verde [25] and CHOOZ [1], measured the neutrino flux with a single detector, and compared it with predictions from the reactor neutrino flux model, to get the oscillation probability. The sensitivity of such an absolute measurement is low due to large uncertainties from reactors and detectors. A relative measurement by detectors at two distances was proposed [26] to improve the sensitivity to oscillation due to {\theta }_{13}. There are three ongoing reactor experiments using the method of multiple detectors: Daya Bay, Double Chooz, and RENO. The baselines of their far detectors are 1.65 km, 1.05 km, 1.44 km, respectively. Table 1 shows the comparison of their reactor power, detector(Det.) target mass in near/far(N/F) site, overburden and estimated sensitivity of {\theta }_{13} measurement after 3 years of data taking.

In Nov. 2011, Double Chooz reported their first result of {\theta }_{13} based on the measured neutrino rate in the far detector. It excludes vanishing {\theta }_{13} at 1.7 standard deviations [5]. A shape analysis of the neutrino energy spectrum was applied later to reduce systematic uncertainties. In Jun. 2012, the updated result improved the significance to 2.9 standard deviations [28] with more data. The result of RENO was reported in Apr. 2012 with a measurement of antineutrinos in both near and far detectors. Details of Daya Bay experiment will be introduced in the next section.

6 The Daya Bay experiment

The Daya Bay experiment was designed to provide the most precise measurement of {\theta }_{13} among existing and near future experiments, with a sensitivity to at the 90% C.L. [29].

6.1 Experiment site

The experiment is located near Daya Bay, Ling Ao and Ling Ao-II nuclear power plants in southern China, 45 km from Shenzhen city. As shown in Fig. 1, there are six functionally identical reactor cores, grouped into three pairs. The last core started commercial operation by the middle of 2011. Three underground experimental halls (EHs) are connected with horizontal tunnels. Before Aug. 2012, six functionally identical antineutrino detectors (ADs) were installed. Two of them were located in EH1, one in EH2, and three near the oscillation maximum in EH3 (the far hall). The distances from the six ADs to the six cores were surveyed with the Global Positioning System (GPS) and with modern theodolites, resulting in a precision of 18 mm.

6.2 Detectors

The {\overline{\nu }}_e interacts with proton via the inverse β-decay (IBD) reaction in gadolinium-doped liquid scintillator (Gd-LS), and releases a e^{+} and a neutron. The e^{+} deposits its energy quickly, providing a prompt signal. The energy of e^{+} carries most of the kinetic energy of the neutrino. The neutron is captured by Gd after an average time of \sim30 μs, then releases several gammas with a total energy of \sim8 MeV, providing a delayed signal. The coincidence of prompt-delayed signals provides a distinctive {\overline{\nu }}_e signature.

Each experimental hall is equipped with ADs and muon veto system. Figure 2 shows a typical detector configuration taking EH1 as an example. Each AD is made of three nested cylindrical volumes separated by concentric acrylic vessels. The inner volume is filled with 20 t of Gd-LS with 0.1% Gd by weight and serves as the antineutrino target. The middle volume holds 20 t un-doped liquid scintillator (LS), for detecting gammas that escape from the target. The outer volume contains 37 t of mineral oil (MO) to protect Gd-LS and LS from radioactivities. There are 192 8-inch photo-multiplier tubes (PMTs) installed inside the mineral oil, to detect the optical photons from the neutrino interaction in the detector.

The muon veto system consists of a water shield and a resistive plate chamber (RPC). The water pool is divided into two parts, and equipped with PMTs in each part, forming inner (IWS)and outer (OWS) cherenkov detectors. The resistive plate chamber contains 9\times 6(9\times 9) modules in the near(far) site. Each module has four layers with alternating orientated readout strips providing a spatial resolution of \sim8 cm.

6.3 Data analysis

The number of detected antineutrinos N_{det} is given by

\begin{array}{}\text{(3)}& N_{det}={\displaystyle \frac{N_p}{4\pi L^2}}{\displaystyle \int ϵ\sigma P_{sur}(E,L,{\theta }_{13})S\text{d}E}\end{array}

where N_p is the number of free protons in the target, L is the distance of the detector from the reactor, ε is the efficiency of detecting an antineutrino, σ is the total cross-section of the IBD process, P_{sur} is the {\overline{\nu }}_e\to {\overline{\nu }}_e survival probability that depends on the value of {\sin }^{2}2{\theta }_{13}, and S is the differential energy distribution of the antineutrino.

For a single reactor core and single near and far detectors, the ratio of the number of antineutrino events with energy E detected at distance L_f (far detector) from the reactor core to that at a distance L_n (near detector) is given by

\begin{array}{}\text{(4)}& {\displaystyle \frac{N_f}{N_n}}=\left({\displaystyle \frac{N_{p,f}}{N_{p,n}}}\right){\left({\displaystyle \frac{L_n}{L_f}}\right)}^2\left({\displaystyle \frac{{ϵ}_f}{{ϵ}_n}}\right)\left[{\displaystyle \frac{P_{sur}(E,L_f,{\theta }_{13})}{P_{sur}(E,L_n,{\theta }_{13})}}\right]\end{array}

where N_{p,f} and N_{p,n} refer to the number of target protons at the far and near sites, respectively. The reactor neutrino flux and IBD cross-section are totally canceled, and the relative detector efficiency ({ϵ}_f/{ϵ}_n) can be determined more precisely than the absolute efficiency.

The IBD process is identified as a prompt-delayed pair, by requiring 0.7 12 MeV, 6 12 MeV, and 1 200 μs, where E_p is the energy of prompt signal, E_d is the energy of delayed signal, \mathrm{\Delta }t is the time interval between two signals. To remove backgrounds introduced by cosmic ray muons, the IBD candidate is removed if it follows a muon tagged by water shield or AD. A multiplicity cut requires no other > 0.7 MeV event 200 μs before the prompt signal or 200 μs after the delayed signal. Using 127 days data taken from Dec. 24, 2011 to May 11, 2012, a total number of 234 217 antineutrino candidates were measured by the six detectors.

The total residual backgrounds is 1.9% at the near halls and 4.7% at the far hall. The dominate background is accidentals, coming from two uncorrelated background radiation interactions that randomly satisfy the energy and time correlation for inverse β-decay antineutrino selection. It can be calculated by measuring the rate of both prompt- and delayed-type signals, and then estimating the probability of their accidental coincidences. The dominate uncertainty of background is from two sources of correlated signals. One is cosmogenic β-n isotope ⁹Li/⁸He, which can be measured by the time interval to previous muons. The other is from Am-C neutron calibration sources, which is estimated by Monte Carlo simulations, and constrained by the measurement of single event rate from Am-C sources. Other backgrounds such as fast neutrons produced by cosmic ray muons and ¹³C{(\alpha ,n)}^{16}O nuclear interactions are negligible in comparison. The total uncertainty of backgrounds is 0.2% at the near halls and 0.35% at the far hall.

The expected antineutrino rate in each AD can be obtained from the reactor neutrino flux, the neutrino interaction in the target and the detection efficiency. The reactor neutrino flux is calculated from the simulated fission rate and the antineutrino spectrum per fission of four main isotopes. The thermal power data were provided by the power plant. The target mass is measured during filling of GD-LS and the liquid level is monitored during the detector running. The uncorrelated uncertainty among ADs is 0.03%. The absolute efficiency is mainly given by the Monte Carlo study, and the uncertainty is 1.9%. In a relative measurement, only the uncorrelated uncertainty is considered, which is 0.2% determined with a side-by-side comparison of ADs [30].

A blind analysis strategy is adopted for the prediction of the antineutrino rate. The true value of reactor power, baseline and target mass is blinded till the analysis algorithms and parameters are fixed, to avoid unintended biasing of a result in a particular direction.

6.4 Experiment result

Antineutrino rates in the near detectors were used to predict the rates in the far detectors assuming no oscillation. The far detectors found 0.944\pm 0.007(\mathrm{stat})\pm 0.003(\mathrm{syst}) of the expected flux relative to the near sites. An analysis of the relative antineutrino rates of the six detectors in a standard three-flavor oscillation model found {\sin }^2(2{\theta }_{13})=0.089\pm 0.010(\mathrm{stat})\pm 0.005(\mathrm{syst}), as shown in Fig. 3.

A comparison of {\sin }^2(2{\theta }_{13}) measurements from different experiments is shown in Fig. 4. Using different neutrino sources such as solar neutrinos, accelerator neutrinos and reactor neutrinos, all of the experiments give consistent results.

7 Other neutrino experiments

Besides the three-flavor neutrino oscillation study, there are many other interesting topics and progresses related to neutrino experiments. An unexpected neutrino oscillation mode was reported in both accelerator and reactor experiments, known as the LSND anomaly [32] and reactor anomaly [33]. This phenomenon requires a new type of neutrinos called sterile neutrinos, which becomes a hot topic in neutrino physics. Geo-neutrinos produced in the Earth are good tools to study how the earth’s interior works. In 2010, Borexino [34] and KamLAND [35] improved the significance of geo-neutrino measurements to better than 4 standard deviations, which is revealing more information about the Earth’s heat production. The absolute mass of neutrinos can be measured by the end point of the electron energy spectrum in β-decays. The KATRIN [36] experiment aims for 0.93 eV energy resolution at the end point of 18.6 keV, corresponding to a sensitivity of 200 meV to the effective electron neutrino mass. On the other hand, an effective Majorana mass of neutrinos can be obtained from the measurement of the half-life of the neutrino-less double-β decay. This measurement may also answer the nature of massive neutrinos. In 2012, the EXO experiment [37] and the KamLAND-Zen experiment [38] obtained a lower limit for the neutrino-less double-β decay half-life as 16\times {10}^{24} yr. and 5.7\times {10}^{24} yr. at 90% CL, corresponding to a upper limit of 140–380 meV and 300–600 meV for the Majorana mass, respectively.

8 Summary and prospective

There was significant progress in the understanding of the neutrino in the past years. After the Daya Bay experiment measured {\theta }_{13}, all three mixing angles which determine the amplitudes of neutrino oscillations are known. Large {\theta }_{13} makes it easier for the next generation neutrino experiments to determine neutrino mass hierarchy and search for CP violation in neutrino oscillations. The latter may answer the question that why there is more matter than antimatter in the Universe.

References

[1] M. Apollonio, et al. [CHOOZ Collaboration], Phys. Lett. B, 1999, 466(2–4): 415

[2] M. Apollonio, et al. [CHOOZ Collaboration], Eur. Phys. J. C, 2003, 27: 331

[3] K. Abe, et al. [T2K Collaboration], Phys. Rev. Lett., 2011, 107(4): 041801

[4] P. Adamson, et al. [MINOS Collaboration], Phys. Rev. Lett., 2011, 107(18): 181802

[5] Y. Abe, et al. [Double Chooz Collaboration], Phys. Rev. Lett., 2012, 108(13): 131801

[6] F. P. An, et al. [Daya Bay Collaboration], Phys. Rev. Lett., 2012, 108(17): 171803

[7] J. K. Ahn, et al. [RENO Collaboration], Phys. Rev. Lett., 2012, 108(19): 191802

[8] F. P. An, et al. [Daya Bay Collaboration], Chin. Phys. C, 2013, 37: 011001, arXiv: 1210.6327

[9] R. Davis, D. S. Harmer, and K. C. Hoffman, Phys. Rev. Lett., 1968, 20(21): 1205

[10] B. T. Cleveland, T. Daily, R. Jr Davis, J. R. Distel, K. Lande, C. K. Lee, P. S. Wildenhain, and J. Ullman, Astrophys. J., 1998, 496(1): 505

[11] Q. R. Ahmad, et al. [SNO Collaboration], Phys. Rev. Lett., 2001, 87(7): 071301

[12] L. Wolfenstein, Phys. Rev. D, 1978, 17(9): 2369

[13] S. P. Mikheev and A. Yu.  Smirnov, Sov. J. Nucl. Phys., 1985, 42: 913

[14] A. Gando, et al. [The KamLAND Collaboration], Phys. Rev. D, 2011, 83(5): 052002

[15] G. Bellini, et al. [Borexino Collaboration], Phys. Rev. D, 2010, 82(3): 033006

[16] G. Bellini, et al. [Borexino Collaboration], Phys. Rev. Lett., 2011, 107(14): 141302

[17] G. Bellini, et al. [Borexino Collaboration], Phys. Rev. Lett., 2012, 108(5): 051302

[18] K. Abe, et al. [Super-Kamiokande Collaboration], Phys. Rev. D, 2011, 83(5): 052010

[19] B. Aharmim, et al. [SNO Collaboration], arXiv: 1109.0763, 2011

[20] W. Anthony Mann, arXiv: hep-ex/9912007v2, 1999

[21] Y. Fukuda, et al. [Super-Kamiokande Collaboration], Phys. Rev. Lett., 1998, 81(8): 1562

[22] P. Adamson, et al. [The MINOS Collaboration], Phys. Rev. Lett., 2012, 108(19): 191801

[23] T. Nakaya, Plenary talk at the XXV International Conference on Neutrino Physics and Astrophysics, Kyoto, Jun. 2012

[24] R. Nichol, Plenary talk at the XXV International Conference on Neutrino Physics and Astrophysics, Kyoto, Jun. 2012

[25] F. Boehm, J. Busenitz, B. Cook, G. Gratta, H. Henrikson, J. Kornis, D. Lawrence, K. B. Lee, K. McKinny, L. Miller, V. Novikov, A. Piepke, B. Ritchie, D. Tracy, P. Vogel, Y. F. Wang, and J. Wolf, Phys. Rev. Lett., 2000, 84(17): 3764

[26] L. A. Mikaelyan and V. V.  Sinev, Phys. Atom. Nucl., 2000, 63: 1002, arxiv: hep-ex/9908047

[27] J. Cao, Plenary talk at the 36th International Conference on High Energy Physics, Melbourne, Jul. 2012.

[28] Y. Abe, et al. [Double Chooz Collaboration], arXiv: 1207.6632, 2012

[29] DayaBay Collaboration, arxiv: hep-ex/0701029, 2007

[30] F. P. An, et al. [Daya Bay Collaboration], Nucl. Inst. And Meth. A, 2012, 685: 78

[31] S. Jetter, Plenary talk at the First International Conference on new Frontiers in Physics, Crete, Jun. 2012

[32] A. Aguilar, et al. [LSND Collaboration], Phys. Rev. D, 2001, 64(11): 112007

[33] G. Mention, M. Fechner, T. Lasserre, T. Mueller, D. Lhuillier, M. Cribier, and A. Letourneau, Phys. Rev. D, 2011, 83(7): 073006

[34] G. Bellini, J. Benziger, S. Bonetti, M. B. Avanzini, et al., Phys. Lett. B, 2010, 687(4–5): 299

[35] A. Gando, Y. Gando, K. Ichimura, H. Ikeda, et al., Nat. Geosci., 2011, 4(9): 64

[36] F. M. Fraenkle, arXiv: 1110.0087, 2011

[37] M. Auger, et al. [EXO Collaboration], Phys. Rev. Lett., 2012, 109(3): 032505

[38] A. Gando, et al. [KamLAND-Zen Collaboration], Phys. Rev. C, 2012, 85(4): 045504

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