Shape coexistence in nuclei appears to be unique in the realm of finite many-body quantum systems It differs from the various geometrical arrangements that sometimes occur in a molecule in that in a molecule the various arrangements are of the widely separated atomic nuclei In nuclei the various ''arrangements'' of nucleons involve (sets of) energy eigenstates with different electric quadrupole properties such as moments and transition rates, and different distributions of proton pairs and neutron pairs with respect to their Fermi energies Sometimes two such structures will ''invert'' as a function of the nucleon number, resulting in a sudden and dramatic change in ground-state properties in neighboring isotopes and isotones In the first part of this review the theoretical status of coexistence in nuclei is summarized Two approaches, namely, microscopic shell-model descriptions and mean-field descriptions, are emphasized The second part of this review presents systematic data, for both even- and odd-mass nuclei, selected to illustrate the various ways in which coexistence is observed in nuclei The last part of this review looks to future developments and the issue of the universality of coexistence in nuclei Surprises continue to be discovered With the major advances in reaching to extremes of proton-neutronmore » number, and the anticipated new ''rare isotope beam'' facilities, guidelines for search and discovery are discussed« less

Shape coexistence in atomic nuclei

Nuclear Data Sheets for A = 33

From RISING to the DESPEC fast-timing project within NUSTAR at FAIR: sub-nanosecond nuclear timing spectroscopy with LaBr3 scintillators.

The half-life of the 2305-keV, Iπ=4(−) intruder state in 34P has been measured as t1/2=2.0(1) ns using γ-ray coincidence, fast-timing techniques with the Bucharest HPGe and LaBr3:Ce detector array. Excited states in 34P were populated using the 18O(18O,pn)34P fusion-evaporation reaction at a beam energy of 36 MeV. Reduced transition probabilities have been calculated for different values of the M2/E3 mixing ratio, δE3/M2, and compared with shell-model estimates. For small values of the mixing ratio, the B(M2) value was found to be consistent with similar transitions associated with the occupation of neutron f7/2 configurations in this mass region.

/pdf/half-life-of-the-i-pi-4-intruder-state-in-p-34-m2-transition-42xcws661y.pdf

Half-life of the I-pi=4(-) intruder state in P-34: M2 transition strengths approaching the island of inversion

Level lifetimes in the $^{32}\mathrm{P}$ nucleus have been determined using the Doppler-shift attenuation method (DSAM). Conventional DSAM measurements employ a thin target on a thick, high-$Z$ backing. An extension of the technique to thick molecular targets is presented. The necessary modifications in the standard analysis procedures, pertaining to the incorporation of stopping power estimations for molecular media and evolution of residue cross section in a thick target, have been implemented. Further, x-ray powder diffraction (XRD) and scanning electron microscopy (SEM) have also been carried out to probe the structural composition of the target. The lifetime results have been validated with respect to the previous measurements and upper limits on lifetimes of seven levels have been determined for the first time. Large-basis shell model calculations have been carried out and compared with the experimental measurements.

/pdf/level-lifetimes-in-p-32-obtained-using-the-doppler-shift-476ueikqa1.pdf

Level lifetimes in P 32 obtained using the Doppler-shift attenuation method with thick molecular targets

We report the observation of high-spin states in nuclei in the vicinity of the ``island of inversion,'' populated via the $^{18}\mathrm{O}+^{18}\mathrm{O}$ fusion reaction at an incident beam energy of $34$ MeV. The fusion reaction mechanism circumvents the limitations of other reactions used so far to populate excited states in these nuclei. The level structures of $^{33,34}\mathrm{P}$ and $^{33}\mathrm{S}$ have been investigated and their level schemes were substantially extended. The intensities and branching ratios of the $\ensuremath{\gamma}$ transitions were measured. The observed $\ensuremath{\gamma}$ coincidence intensity anisotropy and polarization asymmetry were analyzed for a consistent assignment of the spins and parities of the nuclear levels. The $1876$-keV transition in $^{34}\mathrm{P}$ that had an ambiguous multipolarity assignment has been confirmed to be a mixed transition. Truncated (1p-1h) shell model calculations within the ``$\mathit{sdpf}$'' valence space were performed. These calculations reproduce the experimental excitation energies of $^{34}\mathrm{P}$ but fail to explain the observed mixing ratio for the $1876$-keV transition.

Experimental study of nuclei in the vicinity of the "island of inversion" through the fusion-evaporation reaction

We report the first observation of high-spin states in nuclei in the vicinity of the "island of inversion", populated via the 18O+18O fusion reaction at an incident beam energy of 34 MeV. The fusion reaction mechanism circumvents the limitations of non-equilibrated reactions used to populate these nuclei. Detailed spin-parity measurements in these difficult to populate nuclei have been possible from the observed coincidence anisotropy and the linear polarization measurements. The spectroscopy of 33,34P and 33S is presented in detail along with the results of calculations within the shell model framework.

Study of nuclei in the vicinity of the "Island of Inversion" through fusion-evaporation reaction

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Experimental study of nuclei in the vicinity of the "island of inversion" through the fusion-evaporation reaction

Study of nuclei in the vicinity of the "Island of Inversion" through fusion-evaporation reaction