Evidence for a pairing anti-halo effect in the odd-even staggering in reaction cross sections of weakly bound nuclei

We investigate the spatial extension of weakly bound Ne and C isotopes by taking into account the pairing correlation with the Hartree-Fock-Bogoliubov (HFB) method and a three-body model, respectively. We show that the odd-even staggering in the reaction cross sections of ${}^{30,31,32}$Ne and ${}^{14,15,16}$C are successfully reproduced, and thus the staggering can be attributed to the pairing anti-halo effect. A correlation between a one-neutron separation energy and the anti-halo effect is demonstrated for $s$ and $p$ waves using the HFB wave functions.

Figure 1

Root-mean-square radii and the average pairing gap as a function of the single-particle energy ${\varepsilon }_{\mathit{WS}}$ in a Woods-Saxon mean-field potential. Top: shows the mean-square radius of the $2s_{1/2}$ wave function with and without the pairing correlation, denoted by HFB and Woods-Saxon, respectively. Middle: rms radii for ${}^{22}$O, ${}^{23}$O, and ${}^{24}$O, obtained with the Hartree-Fock (${}^{22}$O and ${}^{23}$O) and the Hartree-Fock-Bogoliubov (${}^{24}$O) calculations. Bottom: results of the HFB calculations for the average pairing gap of ${}^{24}$O.

Figure 2

Same as Fig. 1, but for the 2$p_{3/2}$ state and for ${}^{30,31,32}$Ne isotopes.

Figure 3

Reaction cross sections of Ne isotopes on a ${}^{12}$C target at $E_{\mathit{lab}}$=240 MeV/$A$. The cross sections are calculated with the Glauber theory with HF and HFB densities. The solid line with squares shows the results of $S_n$(${}^{31}$Ne) $=$$\left|\varepsilon \right(2p_{3/2}\left)\right|$=0.32 MeV, while the dashed line with triangles is obtained for $S_n$(${}^{31}$Ne) $=$$\left|\varepsilon \right(2p_{3/2}\left)\right|$=1.49 MeV. The experimental data are taken from Ref. [8].

Figure 4

Reaction cross sections of C isotopes on a ${}^{12}$C target at $E_{\mathit{lab}}$ = 83 MeV/$A$. The cross sections are calculated with the Glauber theory with three-body model densities. The experimental data are taken from Ref. [32].