**9.** *A <sup>∼</sup>* **56 and** *N <sup>∼</sup>* **28: New Regions of Shape Coexistence at Closed Shells**

The observation of a deformed band in the double-closed shell nucleus 56Ni [232] suggested that an extension of shape coexistence from the 40Ca region to the *<sup>A</sup>* ∼ 56 region seemed promising. This has not yet materialized. A leading factor is lack of stable targets for multi-nucleon transfer reactions. However, an initiative is underway, with a highresolution internal-pair spectrometer, the *Super-e*, at the ANU to explore the occurrence of *E*0 transitions in this mass region [128,129,233–236]. However, there is evidence that shape coexistence is present in the *N* = 28 isotones 54Fe and 52Cr from transfer reactions: this is placed in a broad framework in Figure 60. Consistent with the transfer data, the ANU group observes *E*0 transitions in these *N* = 28 isotones.

The program of *E*0 decay studies at ANU has some surprises: while one expects a pattern of shape coexistence adjacent to 56Ni, associated with excited 0<sup>+</sup> states, similar to that observed in nuclei adjacent to 40Ca, this is not apparent in the studies done so far. Evidence of *E*0 transitions other than for *Z* = 28 isotopes and *N* = 28 isotones is limited. However, note that the use of *E*0 transition strength as a spectroscopic fingerprint for shape coexistence depends on a combination of two factors: coexistence of two configurations with very different mean-square charge radii and strong mixing of these configurations [40].

**Figure 60.** Systematics of the lowest positive-parity states in the *N* = 28 isotones. Candidate *ν* 2p-2h states are depicted in red. Electric monopole transitions from these states, where observed, are depicted as bold (orange) downwards-pointing arrows, the strengths are indicated where known. The 4282 keV 0<sup>+</sup> state in 48Ca, a *π* 2p - 2h state is also depicted in red. These assignments are based on two-neutron transfer reaction data [145,237–240]. The 58Ni(p,t)56Ni reaction does not strongly populate 0<sup>+</sup> states below 6.5 MeV [241]. Data for 46Ar are taken from [45,59,242]. The *B*(*E*2; 2<sup>+</sup> <sup>1</sup> <sup>→</sup> <sup>0</sup><sup>+</sup> <sup>1</sup> ) data are taken from [199]. Other data are taken from ENSDF [22], except the *B*(*E*2) value for the decay of the first 4<sup>+</sup> state in 52Cr, as quoted in ENSDF is in error; the value presented here is calculated from the half life quoted in ENSDF.

With reference to Figure 60, a search for deformed bands built on 0<sup>+</sup> and 2<sup>+</sup> states in 52Cr and 54Fe would be of great interest. Based on the energies of the first excited 2<sup>+</sup> states, deformation appears to dominate the ground-state structure of 40Mg and 42Si (lifetime data would help to support this suggestion). Strengths of *E*2 transitions are shown for the transitions depopulating the 2<sup>+</sup> <sup>1</sup> , 4<sup>+</sup> <sup>1</sup> , and 6<sup>+</sup> <sup>1</sup> states where lifetime data are available. In 52Cr, two 4<sup>+</sup> states are observed: the lowest is dominated by a seniority *v* = 4 *π*1 *f* <sup>4</sup> 7/2 configuration and the upper is dominated by a seniority *v* = 2 *π*1 *f* <sup>4</sup> 7/2 configuration. The weak *B*<sup>42</sup> value in 44S has been interpreted as due to *K* isomerism, but band structure is not observed [243]; a seniority isomer resulting from a *π*1*d*5/2 broken pair is equally plausible.

The evidence for shape coexistence in nuclei with *N* ∼ 28 and *Z* < 20 is highlighted in Figure 61, which summarizes the connection between intruder states in odd-mass nuclei and low-energy excited 0<sup>+</sup> states in neighbouring even-even nuclei. The accumulation of the necessary data to establish shape coexistence in such neutron-rich nuclei is very demanding with respect to technique and accelerator running times.


**Figure 61.** Selected pairs of nuclei showing a possible relationship between lp-2h intruder states (marked with solid triangles) and low lying excited 0<sup>+</sup> states. The data are from [244–249] and ENSDF [22]. The figure is adapted from [41].
