Concluding Remarks

In this work, we have solved the generalized self-consistent Skyrme EDF equations including the arbitrary mixing between protons and neutrons in the p-h channel. The values of the total isospin and its $T_x$ and $T_z$ components of the system were controlled by the isocranking method, which is analogous to the tilted-axis cranking calculation for high-spin states. We have performed isocranking calculations for even-$T$ $A$=40 IASs and odd-$T$ $A$=54 IASs demonstrating that the single-reference EDF approach including p-n mixing is capable of quantitatively describing the IASs both in the even-even as well as in the odd-odd nuclei.

Here, we have used the isocranking method to control the isospin, which is a simple linear constraint method. In the code HFODD, we have also implemented a more sophisticated method for optimizing the constraint [4], known as the augmented Lagrange method, and we applied it to calculate the excitation energies of the $T \simeq 0,2,4,6,$, and $8$ states in $^{48}$Cr.

Recently, by extending an axially-symmetric Skyrme HFB code HFBTHO [3], another Skyrme EDF code with the p-n mixing has been developed in Ref. [5]. We performed benchmark tests by comparing the results of the isocranking calculations obtained with the codes HFBTHO and HFODD, and we obtained an excellent agreement.

As discussed in Ref. [11], there is spurious isospin mixing inherent to the mean-field approach. In order to remove this spurious mixing, one needs to perform the isospin projection and the subsequent Coulomb rediagonalization. The implementation of the isospin projection into our p-n EDF code is now in progress.