Excited states in 64 Ni, 66 Ni, and 68 Ni were populated in quasielastic and deep-inelastic reactions of a 430-MeV 64 Ni beam on a thick 238 U target. Level schemes including many nonyrast states were established up to respective excitation energies of 6.8, 8.2, and 7.8 MeV on the basis of γ -ray coincidence events measured with the Gammasphere array. Spin-parity assignments were deduced from an angular-correlation analysis and from observed γ -decay patterns, but information from earlier γ -spectroscopy and nuclear-reaction studies was used as well. The spin assignments for nonyrast states were supported further by their observed population pattern in quasielastic reactions selected through a cross-coincidence technique. Previously established isomeric-state decays in 66 Ni and 68 Ni were verified and delineated more extensively through a delayed-coincidence analysis. A number of new states located above these long-lived states were identified. Shell-model calculations were carried out in the p 3/2 f 5/2 p 1/2 g 9/2 model space with two effective interactions using a 56 Ni core. Satisfactory agreement between experimental and computed level energies was achieved, even though the calculations indicate that all the states are associated with rather complex configurations. This complexity is illustrated through the discussion of the structure of the negative-parity states and of the M1 decays between them. The best agreement between data and calculations was achieved for 68 Ni, the nucleus where the calculated states have the simplest structure. In this nucleus, the existence of two low-spin states reported recently was confirmed as well. Results of the present study do not indicate any involvement of collective degrees of freedom and confirm the validity of a shell-model description in terms of neutron excitations combined with a closed Z = 28 proton shell. Further improvements to the calculations are desirable.

þ states, pointing to the oblate, spherical, and prolate nature of the consecutive excitations. In addition, they account for the hindrance of the E2 decay from the prolate 0 þ 4 to the spherical 2 þ 1 state, although overestimating its value. This result makes 66 Ni a unique nuclear system, apart from 236;238 U, in which a retarded γ transition from a 0 þ deformed state to a spherical configuration is observed, resembling a shape-isomerlike behavior. DOI: 10.1103/PhysRevLett.118.162502 The concept of potential energy surface (PES) is central in many areas of physics. Usually, the PES displays the potential energy of the system as a function of its geometry. As an example, the PES of a molecule expressed in such coordinates as bond length, valence angles, etc., can be used for finding the minimum energy shape or calculating chemical reaction rates [1]. The idea of potential energy surface in deformation space has also been widely applied to the nucleus at a given spin. For an even-even nucleus at spin 0, the lowest PES minimum corresponds to the ground state (g.s.), while there may exist additional (secondary) minima in which excited 0 þ states can reside: they can be interpreted as ground states of different shapes [2][3][4][5][6]. When a secondary minimum is separated from the main minimum by a high barrier, in the extreme case a long-lived isomer, called shape isomer, can be formed [7]. Shape isomerism at spin zero, so far, has clearly been observed only in actinide nuclei -these isomers decay mainly by fission, and in two cases only, 236 U and 238 U, by very retarded γ-ray branches [8][9][10][11].The existence of shape isomers in lighter systems has been a matter of debate for a long time. Already in the 1980s, a study based on microscopic Hartree-Fock plus BCS calculations, in which a large number of nuclei was surveyed, identified ten isotopes in which a deformed 0 þ state is separated from a spherical structure by a significantly high barrier:66 Ni and 68 Ni, 190;192 Pt, 206;208;210 Os, and 194;196;214

When a heavy atomic nucleus splits (fission), the resulting fragments are observed to emerge spinning 1 ; this phenomenon has been a mystery in nuclear physics for over 40 years 2,3 . The internal generation of six or seven units of angular momentum in each fragment is particularly puzzling for systems that start with zero, or almost zero, spin. There are currently no experimental observations that enable decisive discrimination between the many competing theories for the mechanism that generates the angular momentum [4][5][6][7][8][9][10][11][12] . Nevertheless, the consensus is that excitation of collective vibrational modes generates the intrinsic spin before the nucleus splits (pre-scission). Here we show that there is no significant correlation between the spins of the fragment partners, which leads us to conclude that angular momentum in fission is actually generated after the nucleus splits (post-scission). We present comprehensive data showing that the average spin is strongly mass-dependent, varying in saw-tooth distributions. We observe no notable dependence of fragment spin on the mass or charge of the partner nucleus, confirming the uncorrelated post-scission nature of the spin mechanism. To explain these observations, we propose that the collective motion of nucleons in the ruptured neck of the fissioning system generates two independent torques, analogous to the snapping of an elastic band. A parameterization based on occupation of angular momentum states according to statistical theory describes the full range of experimental data well. This insight into the role of spin in nuclear fission is not only important for the fundamental understanding and theoretical description of fission, but also has consequences for the γ-ray heating problem in nuclear reactors 13,14 , for the study of the structure of neutron-rich isotopes 15,16 , and for the synthesis and stability of super-heavy elements 17,18 .

Abstract:Yrast and near-yrast levels up to spin values in excess of I = 30ħ have been delineated in the doubly-magic 208 Pb nucleus following deep-inelastic reactions involving 208 Pb targets and, mostly, 430-MeV 48 Ca and 1440-MeV 208 Pb beams. The level scheme was established up to an excitation energy of 16.4 MeV, based on multi-fold γ-ray coincidence relationships measured with the Gammasphere array. Below the well-known, 0.5-μs 10 + isomer, ten new transitions were added to earlier work. The delineation of the higher parts of the level sequence benefited from analyses involving a number of prompt-and delayed-coincidence conditions. Three new isomeric states were established along the yrast line with I π = 20 -(10342 keV), 23 + (11361 keV), and 28 -(13675 keV), and respective half-lives of 22(3), 12.7(2), and 60(6) ns. Gamma transitions were also identified preceding in time the 28 -isomer, however, only a few could be placed in the level scheme and no firm spin-parity quantum numbers could be proposed. In contrast, for most states below this 28 -isomer, firm spin-parity values were assigned, based on total electron-conversion coefficients, deduced for low-energy (<500 keV) transitions from γ-intensity balances, and on measured γ-ray angular distributions. The latter also enabled the quantitative determination of mixing ratios. The transition probabilities extracted for all isomeric transitions in 208 Pb have been reviewed and discussed in terms of the intrinsic structure of the initial and final levels involved. Particular emphasis was placed on the many observed E3 transitions as they often exhibit significant enhancements in strength (of the order of tens of W.u.) comparable to the one seen for the neutron j 15/2 →g 9/2 E3 transition in 209 Pb. In this context, the enhancement of the 725-keV E3 transition (56 W.u.) associated with the decay of the highest-lying 28 -isomer observed in this work remains particularly challenging to explain. Large-scale shell-model calculations were performed with two approaches, a first one where the 1, 2, and 3 particle-hole excitations do not mix with one another, and another more complex one, in which such mixing takes place. The calculated levels were compared with the data and a general agreement is observed for most of the 208 Pb level scheme. At the highest spins and energies, however, the 2 correspondence between theory and experiment is less satisfactory and the experimental yrast line appears to be more regular than the calculated one. This regularity is notable when the level energies are plotted versus the I(I+1) product and the observed, nearly linear, behavior was considered within a simple "rotational" interpretation. Within this approximate picture, the extracted moment of inertia suggests that only the 76 valence nucleons participate in the "rotation" and that the 132 Sn spherical core remains inert. --------------------------