Abstract
A new technique for calculating the resonating-group-method (RGM) kernels is proposed by use of frequency transformations in order to treat cluster systems involving unequal oscillator frequencies. The present technique is useful for both analytical and numerical deviations of matrix elements of the RGM kernels. The eigenvalue problem of the norm kernel of the RGM is solved for a wide range of systems consisting of an α-particle and a closed-shell nucleus ( 16O, 40Ca, 48Ca, 56Ni, 80Zr, 90Zr, 120Sn, 140Yb or 208Pb) with realistic oscillator frequencies. These eigenvalues and eigenfunctions are shown to have characteristic features. With these eigenvalues, α-particle reducedwidth amplitudes and spectroscopic factors of the ground states of 20Ne, 44Ti, 94Mo, 124Te and 212Po are calculated by employing simple configurations of the harmonic-oscillator shell model. In heavy nuclei the results with realistic oscillator frequencies are shown to be very different from those with a common oscillator frequency. The effect of the spurious c.m. motion in the generator coordinate method is discussed.
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