Influence of secondary decay on odd-even staggering of fragment cross sections

Odd-even staggering (OES) appears in many areas of nuclear physics and is generally associated with the pairing term in the nuclear binding energy. To explore this effect, we use the improved statistical multifragmentation model to populate an ensemble of hot primary fragments, which are then de-excited using the Weisskopf-Ewing statistical emission formalism. The yields are then compared to experimental data. Our results show that, before secondary decay, OES appears only in the yields of even mass fragments and not in the yields of odd mass fragments. De-excitation of the hot fragments must be taken into account to describe the data, suggesting that the OES in fragment yields is a useful criterion for validating or adjusting theoretical de-excitation models.

Figure 1

$Z$ distribution of fragments observed in the projectile fragmentation of several projectiles on a ${}^9$Be target. The data are taken from Ref. [8] whereas the calculations correspond to the grand-canonical version of the ISMM, using the improved liquid drop formula of Ref. [9], at breakup temperature $T=4.0$ MeV. For details, see the text.

Figure 2

Ratio between $Y_Z\left(Z\right)$ and ${\overline{Y}}_Z\left(Z\right)$ for the four projectiles in Ref. [8].

Figure 3

Comparison between staggering behavior in experimental binding energies (top panels) and primary yields from the ISMM (bottom panels). Fragments with odd neutron excess are shown on the left panels, while fragments with even neutron excess are shown on the right.

Figure 4

The results obtained using the ISMM with Weisskopf-Ewing de-excitation are displayed in the top panels, and the experimental results obtained with the projectile fragmentation data reported in Ref. [8] are shown in the bottom panels. Odd values of neutron excess are exhibited in the left panels, whereas even values are displayed in the right. For details, see the text.

Figure 5

Comparison of the ratios obtained with $N-Z=-1$ and $N-Z=1$ for the ${}^{58}$Ni projectile (lower panels) and with $N-Z=1$ and $N-Z=5$ in the case of the ${}^{64}$Ni projectile (upper panels). The experimental ratios are calculated using the yields of Ref. [8]. For details, see the text.