By employing the angular momentum projection technique, we propose a method to reliably calculate the quantum spectrum of nuclear collective rotation. The method utilizes several cranked mean-field states with different rotational frequencies, which are superposed in the sense of configuration mixing or the generator coordinate method after performing the projection; the idea was originally suggested by Peierls–Thouless in 1962 [Nucl. Phys. 38, 154 (1962)]. It is found that the spectrum as a result of the configuration mixing does not essentially depend on chosen sets of cranking frequencies if the number of mean-field states utilized in the mixing is larger than a certain small value. We apply this method to three examples employing the Gogny D1S effective interaction and show that it is useful to study high-spin rotational bands by means of the angular momentum projection method.
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