Origin of odd-even staggering in fragment yields: Impact of nuclear pairing and shell structure on the particle-emission threshold energy

Strong odd-even staggering (OES) of the yields of fragments, produced by fragmenting ${}^{78}\mathrm{Kr}$ projectiles, has been measured by employing the combination of an in-flight fragment separator and a storage ring. It is shown that the OES of fragment yields of $T_z=-1/2$ and $T_z=1/2$ mirror nuclei critically depends on both pairing and shell structure, especially at the closed shells $Z=20$ and 28. A comparison of the relative OES of yields and of particle-emission threshold energies reveals unambiguously that the origin of the OES of fragment yields is mainly determined by the OES of the particle-emission threshold energies, which contain both pairing and shell effects.

Figure 1

Part of the measured revolution time spectrum of $T_z=-1/2$ nuclides produced in ${}^{78}\mathrm{Kr}$ fragmentation reactions on a Be target. Mass and atomic numbers are indicated.

Figure 2

(a) Fragment yields of $T_z=-1/2$ and $T_z=1/2$ nuclei measured in this experiment. The error of about 10% is dominated by the systematic uncertainty of the estimations of transmission efficiencies [52, 53]. (b) The magnitude of the OES-FY for $T_z=-1/2$ and $T_z=1/2$ nuclei measured in this experiment, and the data from other experiments [15, 55], calculated according to Eq. (1). The inset shows the predicted OES-FY for nuclei produced in our experiment by the Abrasion-Ablation model [10], where the parameters are similar to those used in Ref. [53].

Figure 3

(a) Particle-emission threshold energy for $T_z=-1/2$ and $T_z=1/2$ nuclei, which equals the lowest value from the neutron- or the proton-separation energy of one particular isotope, except for ${}^{53}\mathrm{Co}$, where an isomeric state at an excitation energy of $E^{*}=3.174$ MeV was observed as the final particle stable state and this excitation energy is the PETE value. For the PETE, the error bars are less than 1% [13], except for ${}^{61}\mathrm{Ga}$. (b) Magnitude of the OES in PETE for $T_z=-1/2$ and $T_z=1/2$ nuclei, calculated with Eq. (1) and by substituting the yields $Y$ with PETE.

Figure 4

Difference between the relative OES in PETE, $\Delta D_{\mathrm{PETE}}$($A$) $=$ $D_{\mathrm{PETE}}$($A$, $T_z=-1/2$) $-$ $D_{\mathrm{PETE}}$($A$, $T_z=1/2$), and the relative OES-FY $\Delta D_{\mathrm{yield}}$($A$) $=$ $D_{\mathrm{yield}}$($A$, $T_z=-1/2$) $-$ $D_{\mathrm{yield}}$($A$, $T_z=1/2$) for mirror nuclei measured in our experiment, and the data from other experiments [55].