Jastrow functions in double-beta decay J. Engel Dept. of Physics and Astronomy, University of North Carolina, Chapel Hill, NC, 27516-3255, USA J. Carlson Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA R.B. Wiringa Physics Division, Argonne National Laboratory, Argonne, IL 60439 We use simple analytic considerations and a Monte Carlo calculation of nucleons in a box to argue that the use of Jastrow functions as short-range correlators in the commonly employed two- body-cluster approximation causes significant errors in the matrix elements for double-beta decay. 1 The Jastrow approach appears to agree with others, however, if many-body clusters are included. 1 A careful treatment of the charge-changing analog of the nuclear pair density shows, in addition, 0 that differences between Unitary Correlator Operator Method and Bruecknermethods for treating 2 short-range correlations in double-betaare less significant than suggested by previouswork. n a J I. INTRODUCTION overlap preservation and a range of successful applica- 3 tions [7]. Refs. [8] and [9] computed the effects of short- range correlations within well-defined Brueckner-based New experiments to measure the rate of neutrinoless ] approximation schemes. All these papers found smaller h double-beta(0νββ)decaywillprovideinformationabout effects on matrix elements than the phenomenological t neutrinomassesifneutrinosareMajoranaparticles. Un- - Jastrow function yields. Because they all limited their l fortunately, one must know the value of the nuclear ma- c analysis to two-body correlations,however, their predic- trixelementgoverningthedecaytoextractthatinforma- u tions for the size of short-rangeeffects do not come with n tion from an observed rate (or rate limit) [1]. For that an iron clad guarantee. [ reason,attempts to better calculate the matrix elements appear regularly in the literature. Infact,allthesemethodsimplytheexistenceofmany- 1 body effects that are always neglected in applications The matrix elements involve products of one-body de- v to double-beta decay. In Jastrow-based treatments, our 4 cay operators and a sum over intermediate states, but subject here, the full correlated wave function is written 5 the closureapproximationallowsthem tobe represented 5 to high accuracy [2] by the ground-state-to-ground-state schematically as 0 transition matrix element of a two-body operator . 1 10 M0ν ≡ Mab. (1) |Ψi= a

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