We present an improved search for neutrinoless double-beta (0νββ) decay of 136 Xe in the KamLANDZen experiment. Owing to purification of the xenon-loaded liquid scintillator, we achieved a significant reduction of the 110m Ag contaminant identified in previous searches. Combining the results from the first and second phase, we obtain a lower limit for the 0νββ decay half-life of T 0ν 1=2 > 1.07 × 10 26 yr at 90% C.L., an almost sixfold improvement over previous limits. Using commonly adopted nuclear matrix element calculations, the corresponding upper limits on the effective Majorana neutrino mass are in the range 61-165 meV. For the most optimistic nuclear matrix elements, this limit reaches the bottom of the quasidegenerate neutrino mass region. DOI: 10.1103/PhysRevLett.117.082503 Neutrinoless double-beta (0νββ) decay is an exotic nuclear process predicted by extensions of the Standard Model of particle physics. Observation of this decay demonstrates the nonconservation of lepton number, and proves that neutrinos have a Majorana mass component. In the framework of light Majorana neutrino exchange, its decay rate is proportional to the square of the effective Majorana neutrino mass hm ββ i ≡ j P i U 2 ei m ν i j. ) provide upper limits on hm ββ i of ∼0.2-0.4 eV using available nuclear matrix element (NME) values from the literature. The sensitivities of these searches correspond to mass scales in the so-called quasidegenerate mass region.KamLAND-Zen is a double-beta decay experiment that exploits the existing detection infrastructure and radiopurity of KamLAND [5,6]. The KamLAND-Zen detector consists of 13 tons of Xe-loaded liquid scintillator (Xe-LS) contained in a 3.08-m-diameter spherical inner balloon (IB) located at the center of the KamLAND detector. The IB is constructed from 25-μm-thick transparent nylon film and is surrounded by 1 kton of liquid scintillator (LS) contained in a 13-m-diameter spherical outer balloon. The outer LS acts as an active shield. The scintillation photons are viewed by 1879 photomultiplier tubes (PMTs) mounted on the inner surface of the containment vessel. The Xe-LS consists of 80.7% decane and 19.3% pseudocumene (1,2,4-trimethylbenzene) by volume, 2.29 g=liter of the fluor PPO (2,5-diphenyloxazole), and ð2.91 AE 0.04Þ% by weight of isotopically enriched xenon gas. The isotopic abundances in the enriched xenon were measured by a residual gas analyzer to be ð90.77 AE 0.08Þ% 136 Xe, ð8.96AE 0.02Þ% 134 Xe. Other xenon isotopes have negligible presence. The two electrons emitted from 136 Xe ββ decay
Recurrence expressions are derived for various types of molecular integrals over Cartesian Gaussian functions by the use of the recurrence formula for three-center overlap integrals. A number of characteristics inherent in the recursive formalism allow an efficient scheme to be developed for molecular integral computations. With respect to electron repulsion integrals and their derivatives, the present scheme with a significant saving of computer time is found superior to other currently available methods. A long innermost loop incorporated in the present scheme facilitates a fast computation on a vector processing computer.
General recurrence formulas for various types of one- and two-electron molecular integrals over Cartesian Gaussian functions are derived by introducing basic integrals. These formulas are capable of dealing with (1) molecular integrals with any spatial operators in the nonrelativistic forms of the relativistic wave equations, (2) those with the kernel of the Fourier transform, (3) those with arbitrarily defined spatial operators so far as the integrals can be expressed in terms of the basic integrals, and (4) any order of their derivatives with respect to the function centers in the above integrals. Thus, the present formulation can cover a large class of molecular integrals necessary for theoretical studies of molecular systems by ab initio calculations, and furthermore provides us with an efficient scheme of computing them by virtue of its recursive nature.
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