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Published January 21, 2011 | Published
Journal Article Open

Relation between the 0νββ and 2νββ nuclear matrix elements reexamined

Abstract

We show that the dominant Gamow-Teller part, M^(0ν)_(GT), of the nuclear matrix element governing the neutrinoless ββ decay is related to the matrix element M^(2ν)_(cl) governing the allowed two-neutrino ββ decay. That relation is revealed when these matrix elements are expressed as functions of the relative distance r between the pair of neutrons that are transformed into a pair of protons in the ββ decay. Analyzing this relation allows us to understand the contrasting behavior of these matrix elements when A and Z is changed; while M^(0ν)_(GT) changes slowly and smoothly, M^(2ν) has pronounced shell effects. We also discuss the possibility of phenomenological determination of the M^(2ν)_(cl) and from them of the M^(0ν)_(GT)values from the experimental study of the β^± strength functions.

Additional Information

© 2011 American Physical Society. Received 3 December 2010; published 21 January 2011. Useful discussions with Kazuo Muto are appreciated. The work of P.V. was partially supported by the US Department of Energy under Contract No. DE-FG02-88ER40397. A.F.,R.H., and F.S. acknowledge the support in part by the DFG project 436 SLK 17/298, the Transregio Project TR27 "Neutrinos and Beyond," and by the VEGA Grant agency under Contract No. 1/0249/03.

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September 18, 2023
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