**5. The Region of 78Ni**

78Ni has recently been established as a double-*jj* magic nucleus from the relatively high energy of 2.6 MeV for the 2<sup>+</sup> <sup>1</sup> state [35]. More detailed magic properties can be obtained from the *D*(*N*) and *D*(*Z*), derived from new experiments on the masses around 78Ni. The ESPE can be established from the masses together with the low-lying spectra of 77Ni, 79Ni, 77Co and 79Cu. A proton knockout experiment from 80Zn has recently been used to establish excitation energies of low-lying states in 79Cu [35] In particular, the ground state and two lowest-lying states are likely associated with the triplet of states shown in Figure 9. In comparison with the extrapolations of CI calculations, shown in [35], the order is likely to be 0 *f*5/2, 1*p*3/2 and 1*p*1/2. The single-particle nature of low-lying states around 78Ni will require one-nucleon transfer experiments.

The position of the proton 0*g*9/2 orbital above 78Ni is important for Gamow–Teller strength in the electron-capture rates for core-collapse supernovae similations [110,111]. The filling of the 0*g*9/2 orbital leads to 100Sn on the proton drip line. 100Sn has the largest calculated reduced Gamow-Teller transition probability, *B*(*GT*), value (see Table A1 in [112]) due to nearly filled 0*g*9/2 orbital decaying into the nearly empty 0*g*7/2 orbital. The understanding of 100Sn [113] and other nuclei near the proton drip line in this mass region will be improved by radioactive-beam experiments.

As shown in Figure 4b of [35], large-scale CI calculations predict a deformed band with *<sup>β</sup>* <sup>≈</sup> <sup>+</sup>0.3 at approximately 2.6 MeV. 56Ni is also spherical with a 2<sup>+</sup> <sup>1</sup> state observed at 2.7 MeV. For 56Ni, the deformed band is predicted to start at 5.0 MeV as shown in Figure 13. The relatively low-lying deformed band in 78Ni is predicted to lead to a "5th island-of-inversion" in 76Fe and other nuclei with *N* = 50 below *Z* = 28 [114].

#### **6. Conclusions**

I have discussed the new physics related to the properties of nuclei near the drip lines that will be studied by the next generation of rare-isotope beam experiments. In particular, I have focused on four "outposts" for the regions of 28O, 42Si, 60Ca and 78Ni, where new experiments will have the greatest impact on understanding the evolution of nuclear struture as one approaches the neutron drip line.

**Funding:** This research was funded by the National Science Foundation under Grant PHY-2110365.

**Acknowledgments:** I thank Ragnar Stroberg for providing the VS-IMSRG Hamiltonian for 42Si.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References**

	- *103*, 054610. [CrossRef]

**Jianguo Li 1, Yuanzhuo Ma 1, Nicolas Michel 2,3, Baishan Hu 1, Zhonghao Sun 1, Wei Zuo 2,3 and Furong Xu 1,\***


**Abstract:** The Gamow shell model (GSM) is a powerful method for the description of the exotic properties of drip line nuclei. Internucleon correlations are included via a configuration interaction framework. Continuum coupling is directly included at basis level by using the Berggren basis, in which, bound, resonance, and continuum single-particle states are treated on an equal footing in the complex momentum plane. Two different types of Gamow shell models have been developed: its first embodiment is that of the GSM defined with phenomenological nuclear interactions, whereas the GSM using realistic nuclear interactions, called the realistic Gamow shell model, was introduced later. The present review focuses on the recent applications of the GSM to drip line nuclei.

**Keywords:** Gamow shell model; realistic nuclear forces; phenomenological interactions; resonance; continuum; drip line nuclei
