Fragmentation binding energies and cross sections of isotopes near the proton dripline

An exponential correlation has been observed between the cross section $\sigma$ and the average binding energy $\langle B^{\prime }\rangle$ of proton-rich isotopes measured in the $650A\mathrm{MeV}{}^{58}\mathrm{Ni}+{}^9\mathrm{Be}$ projectile fragmentation reaction. Based on the correlation, both the cross section and the binding energy of the isotope, which is close to the proton-drip, can be predicted. The binding energy of $Z=21\text{–}28$ isotopes with $T_z$ from $-3$ to $-2$, have been determined from their measured cross sections. And the cross sections for isotopes without experimental results have been predicted by adopting the evaluated binding energy in AME16. The determined binding energies of isotopes in the $650A\mathrm{MeV}{}^{58}\mathrm{Ni}+{}^9\mathrm{Be}$ reaction have also been used to study the isotopes production in the $140A\mathrm{MeV}{}^{58}\mathrm{Ni}+{}^9\mathrm{Be}$ reaction. The determined binding energies of the isotopes are verified to obey a scaling phenomenon of mirror nuclei.

Figure 1

The correlation between $\sigma$ and $\langle B^{\prime }\rangle$ for the proton-rich $Z=21\text{–}28$ isotopes in the $650A\mathrm{MeV}{}^{58}\mathrm{Ni}+{}^9\mathrm{Be}$ reaction. The lines are the fitting results using Eq. (1). The full symbols denote the experimental $\sigma$ and $\langle B^{\prime }\rangle$. The half-full symbols denote the calculated $\langle B^{\prime }\rangle$ using the experimental $\sigma$, and the open symbols denote the calculated $\sigma$ using the theoretical $\langle B^{\prime }\rangle$.

Figure 2

The correlation between $M(N-|I|,Z)-M(N,Z-|I\left|\right)$ and ${\delta }_{\mathrm{coul}}$ for the mirror nuclei. The open symbols denote the same results in Ref. [27] obtained from the experimental binding energy in AME12 [28]. The solid symbols denote the $\left|I\right|=4$, 5, and 6 nuclei predicted in this work.

Figure 3

The predicted $\sigma$ for the proton-rich isotopes in the $140A\mathrm{MeV}{}^{58}\mathrm{Ni}+{}^9\mathrm{Be}$ reaction. The full symbols denote that both the $\sigma$ and $B$ are experimentally determined. The half-full ones denote that $\sigma$ are predicted by experimental $\langle B^{\prime }\rangle$ by using Eq. (1). The open ones denote that $\sigma$ are predicted by $\langle B^{\prime }\rangle$ determined in the $650A\mathrm{MeV}{}^{58}\mathrm{Ni}+{}^9\mathrm{Be}$ reaction as listed in Table 1. The lines denote the fitting by Eq. (1).

Figure 4

The predicted $\sigma$ for the proton-rich isotopes in the $140A\mathrm{MeV}{}^{58}\mathrm{Ni}+{}^9\mathrm{Be}$ and $650A\mathrm{MeV}{}^{58}\mathrm{Ni}+{}^9\mathrm{Be}$ reaction. The full and open symbols denote the ${}^{58}\mathrm{Ni}+{}^9\mathrm{Be}$ reaction at $650A$ and $140A\mathrm{MeV}$, respectively.