New Beyond-Mean-Field Theories: Examination of the Potential Shell Closures atN=32or 34

A beyond-mean-field theory of new generation has been developed and applied for the first time to discuss the controversial $N=32$ and/or $N=34$ shell closures and the puzzling behavior of the transition probabilities from the ground to the first $2^{+}$ state in the titanium isotopes. In the numerical applications, the finite range density dependent Gogny interaction has been used. As compared with the experimental data for several calcium, titanium, and chromium isotopes, we obtain a good agreement for the excitation energies and a reasonable one for the transition probabilities. Our calculations support a shell closure for $N=32$ but not for $N=34$.