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Semi-leptonic electroweak interactions in nuclei - such as \beta decay, \mucapture, charged- and neutral-current neutrino reactions, and electronscattering - are described by a set of multipole operators carrying definiteparity and angular momentum, obtained by projection from the underlying nuclearcharge and three-current operators. If these nuclear operators are approximatedby their one-body forms and expanded in the nucleon velocity through order|\vec{p}|/M, where \vec{p} and M are the nucleon momentum and mass, a set ofseven multipole operators is obtained. Nuclear structure calculations are oftenperformed in a basis of Slater determinants formed from harmonic oscillatororbitals, a choice that allows translational invariance to be preserved.Harmonic-oscillator single-particle matrix elements of the multipole operatorscan be evaluated analytically and expressed in terms of finite polynomials inq^2, where q is the magnitude of the three-momentum transfer. While results forsuch matrix elements are available in tabular form, with certain restriction onquantum numbers, the task of determining the analytic form of a responsefunction can still be quite tedious, requiring the folding of the tabulatedmatrix elements with the nuclear density matrix, and subsequent algebra toevaluate products of operators. Here we provide a Mathematica script forgenerating these matrix elements, which will allow users to carry out all suchcalculations by symbolic manipulation. This will eliminate the errors that mayaccompany hand calculations and speed the calculation of electroweak nuclearcross sections and rates. We illustrate the use of the new script bycalculating the cross sections for charged- and neutral-current neutrinoscattering in ^{12}C.

A Mathematica script for harmonic oscillator nuclear matrix elements arising in semileptonic electroweak interactions