Kerman-Onishi conditions in self-consistent tilted-axis-cranking mean-field calculations

Abstract

Background: For cranked mean-field calculations with arbitrarily oriented rotational frequency vector $\ensuremath{\omega}$ in the intrinsic frame, one has to employ constraints on average values of the quadrupole-moment tensor, so as to keep the nucleus in the principal-axis reference frame. Kerman and Onishi [Nucl. Phys. A 361, 179 (1981)] have shown that the Lagrange multipliers that correspond to the required constraints are proportional to $\ensuremath{\omega}\ifmmode\times\else\texttimes\fi{}\mathbf{J}$, where $\mathbf{J}$ is the average angular momentum vector.Purpose: We study the validity and consequences of the Kerman-Onishi conditions in the context of self-consistent tilted-axis-cranking (TAC) mean-field calculations.Methods: We perform self-consistent two-dimensional-cranking calculations (with and without pairing) utilizing the symmetry-unrestricted solver hfodd. At each tilting angle, we compare the calculated values of quadrupole-moment-tensor Lagrange multipliers and $\ensuremath{\omega}\ifmmode\times\else\texttimes\fi{}\mathbf{J}$.Results: We show that in self-consistent calculations, the Kerman-Onishi conditions are obeyed with high precision. Small deviations seen in the calculations with pairing can be attributed to the truncation of the quasiparticle spectrum. We also provide results of systematic TAC calculations for triaxial strongly deformed bands in ${}^{160}$Yb.Conclusions: For nonstationary TAC solutions, Kerman-Onishi conditions link the nonzero values of the angle between rotational-frequency and angular-momentum vectors to the constraints on off-diagonal components of the quadrupole-moment tensor. To stabilize the convergence of self-consistent iterations, such constraints have to be taken into account. Only then one can determine the Routhian surfaces as functions of the tilting angles.