Figure 1

Behavior of $\widehat{\varphi }(r)=\varphi (r)/\sqrt{\beta }$ for $\beta =20$, 0.5, 0.2, and 0.05 at $\alpha =0.6$, for case III. These profiles are seen to increase with decreasing $\beta$, while they are independent of $\beta$ in the semiclassical approximation.Reuse & Permissions

Figure 2

The fluctuation integral $\mathcal{F}(r)$ for the Hartree backreaction (case III) as a function of $r$ for $\alpha =0.6$. The curves display the change with $\beta$; the parameter $\beta$ takes the values 10 (lowest intercept at $r=0$), 0.1, and 0.05 (highest intercept at $r=0$).Reuse & Permissions

Figure 3

Ratio $S_{\mathrm{eff}}/S_{\mathrm{semicl}}$ as a function of $\beta$ for $\alpha =0.05$. For this and the next two figures, the dotted line with full squares represents case I, empty squares represent case II, the long-dashed line with full circles represents case III, and empty circles are for case IV.Reuse & Permissions

Figure 4

Ratio of $S_{\mathrm{eff}}$ and $S_{\mathrm{semicl}}$ as a function of $\beta$ for $\alpha =0.2$ (for notation see Fig. 3).Reuse & Permissions

Figure 5

Ratio of $S_{\mathrm{eff}}$ and $S_{\mathrm{semicl}}$ as a function of $\beta$ for $\alpha =0.6$ (for notation see Fig. 3).Reuse & Permissions

Figure 6

Logarithm of the ratio $\Gamma /{\Gamma }_{\mathrm{semicl}}$ as a function of $\beta$ for $\alpha =0.05$. The notation here and in the next two figures is as follows: the line with full squares is for case I, empty squares represent case II, full circles represent case III, and empty circles are for case IV.Reuse & Permissions

Figure 7

Logarithm of the ratio $\Gamma /{\Gamma }_{\mathrm{semicl}}$ as a function of $\beta$ for $\alpha =0.2$ (for notation see Fig. 6).Reuse & Permissions

Figure 8

Logarithm of the ratio $\Gamma /{\Gamma }_{\mathrm{semicl}}$ as a function of $\beta$ for $\alpha =0.6$ (for notation see Fig. 6).Reuse & Permissions