Self-consistent orthonormalization and the BCS treatment of the charge-independent pairing correlation

A derivation of the pairing theory for nuclei is given based on a self-consistent orthonormalization procedure within the context of the equation of motion method. The procedure to minimize the fluctuation effects due to nonconservation of the nucleon number is given. The method is extended for treating the charge independent ($T=1\mathrm{}$) pairing correlations. A new method to deal with the fluctuations due to nucleon number and to isospin simultaneously, is outlined. Numerical computations are performed for the case of $N=Z$ nuclei.

NUCLEAR STRUCTURE ${}_{}{}^{58,60,62,64,66}{}_{}{}^{}\mathrm{Ni}$, calculated ground-state energies, single-particle levels occupation probabilities, pairing interaction. ${}_{}{}^{60,62,64}{}_{}{}^{}\mathrm{A}\mathrm{}(N+Z)\mathrm{}$, calculated $E_0\left(T_{max}\right)$; ${}_{}{}^{60}{}_{}{}^{}\mathrm{A}$ calculated $\Delta E=E_0\mathrm{}(T=2\mathrm{})-E_0\mathrm{}(T=0\mathrm{})\mathrm{}$; charge-independent $T=1\mathrm{}$ pairing interaction. Improved BCS approximation.