DOI 10.1140/epja/i2002-10100-3 Eur. Phys. J. A 16, 353–358 (2003) T HE EUROPEAN P HYSICAL JOURNAL A Perturbative analysis of the 2νββ decays of 100 Mo and 116 Cd O. Civitarese 1, a , J. Suhonen 2 , and H. Ejiri 3,4 1 Department of Physics, University of La Plata, C.C. 67, 1900 La Plata, Argentina 2 Department of Physics, University of Jyv¨askyl¨a, P.O. Box 35, FIN-40351, Jyv¨askyl¨a, Finland 3 RCNP, University of Osaka, Suita Campus, 10-1. Mihogaoka, Ibaruki, Osaka, Japan 4 NPL. Department of Physics, University of Washington, Seattle, WA 98195, USA Received: 12 August 2002 / Revised version: 21 October 2002 / Published online: 18 February 2003 – c  Societ` a Italiana di Fisica / Springer-Verlag 2003 Communicated by V.V. Anisovich Abstract. We have performed a theoretical analysis of the ground-state–to–ground-state transitions in 100 Mo and 116 Cd, based on the quasiparticle random-phase approximation and on a straightforward per- turbative scheme. The results show that the single-state dominance found in the realistic calculations of the nuclear matrix elements, which is consistent with data, can be viewed as a result of the interference between few two-quasiparticle configurations. PACS. 23.40.Bw Weak-interaction and lepton (including neutrino) aspects – 23.40.Hc Relation with nuclear matrix elements and nuclear structure – 21.60.Jz Hartree-Fock and random-phase approximations – 27.60.+j 90 ≤ A ≤ 149 1 Introduction Nuclear double-beta-decay transitions have been inten- sively studied theoretically as well as experimentally, as given in recent reviews and references therein [1–7]. The half-lives of the already observed two-neutrino mode of double-beta decay (2νββ) are the longest ones ever mea- sured. In addition, very stringent half-life limits for the neutrinoless mode have been obtained [3–12]. Generally speaking, the complete theoretical understanding of these transitions is still a challenging question with obvious con- sequences upon the test of both electroweak interactions and nuclear structure. Due to the perturbative nature of the problem, in the weak-interaction sector of the theory, the calculation of nuclear matrix elements of two-neutrino double-beta-decay transitions involves a summation over the 1 + states of the intermediate nucleus participant in the decay chain connecting the initial and final even-even mass nuclei [1–5]. Thus two single-beta-decay transitions are involved, connecting the initial and final ground states to the ground and excited states of the participant inter- mediate odd-odd nucleus. These virtual transitions can be investigated experimentally by charge-exchange reactions on the initial and final nuclei [4] or by induced electron- capture and β-decays from the double-odd-mass nucleus. Considering these possibilities, it has been sug- gested [13] that, for those 2νββ transitions where the a e-mail: civitarese@fisica.unlp.edu.ar ground state of the intermediate nucleus is a J π =1 + state, the transition matrix element could be governed by two virtual transitions, the first one going from the initial ground state to the 1 + ground state of the intermediate nucleus and the second one going from this 1 + state to the final ground state. This assumption is known as the Single- State-Dominance (SSD) and its validity has been studied experimentally and theoretically in [14–17]. Data on the SSD have been reported by Garc´ ıa et al. [15], by Akimune et al. [16] and by Bhattacharya et al. [17]. The dominance of low-lying single particle-hole states in intermediate nu- clei have been shown experimentally for 2νββ decays in medium-mass nuclei and it was analyzed in terms of the couplings to GT giant resonances by Ejiri and Toki in [14]. A recent theoretical discussion of the SSD was presented in [18]. The SSD has been tested in EC measurements at Notre Dame [17] and in ( 3 He,t) experiments by the Osaka group [16]. The influence of the high-lying energy states, as the GT giant resonance, on the matrix elements of the 2νββ decay channels has been studied by M. Ericson, T. Ericson and P. Vogel [19]. In their paper the authors have ad- vanced qualitatively the notion that low-lying 1 + states dominate the decay. This finding was confirmed by the results of realistic calculations, although the connection between them and the schematic analysis of [19] has not been studied in detail. In this article we show the results of calculations of the two-neutrino double-beta decays of 100 Mo and