LST function for HFB+THO calculations

The starting point of our new and improved HFB+THO procedure is, thus, to carry out a standard HFB+HO calculation for the nucleus of interest, thereby generating its local density and its local $\ell$=0 density $\bar{\rho}(r)$ (23), and then to use the method outlined in the previous subsection to correct that density at large distances (see Eq. (25)), by calculating $\tilde{\rho}(r)$. The next step is to define the LST [19] so that it transforms the HFB+HO $\ell$=0 density (23) into the corrected density of Eq. (25). This requirement leads to the following first-order differential equation,

$$\tilde{\rho}(r)=\frac{f^{2}({\cal R})}{{\cal R}^{2}}\frac{\p... ...l R}}\bar{\rho}\left( \frac{r}{{\cal R}}f( {\cal R})\right) ~,$$ (26)

which for the initial condition $f(0)=0$ can always be solved for $f({\cal R})$.

Once the LST function has been so obtained, we need simply diagonalize the HFB matrices in the corresponding THO basis. Most importantly, no information is required to build the THO basis beyond the results of a standard HFB+HO calculation. Since no further parameters enter, there is no need to minimize the HFB+THO total energy. As a consequence, with this new methodology we are able to systematically treat large sets of nuclei within a single calculation.

Despite the fact that the new HFB+THO method is simpler to implement than the earlier version, there are no discernible differences between the results obtained with the two distinct treatments of the LST function. Most importantly, the current formulation leads to the same excellent reproduction of coordinate-space results as did the previous one [19,18].