Constraints

In the code HFBTHO (v1.66p), the HFB energy (9) can be minimized under the constraint of a fixed quadrupole moment. This option should be used if one is interested in the potential energy surface of a nucleus along the quadrupole collective coordinate. The quadrupole constraint is assumed in the standard quadratic form [40]:

$${E}^{Q} = C_{Q} \left(\langle\hat Q\rangle - \bar Q\right)^2,$$ (78)

where $\langle\hat Q\rangle$ is the average value of the mass-quadrupole-moment operator,

$$\hat{Q}=2z^2-r^2,$$ (79)

$\bar Q$ is the constraint value of the quadrupole moment, and $C_{Q}$ is the stiffness constant.