Abstract. Actinide nuclei are found to be good candidates for the formation of high angular momentum, broken-pair excitations in the second minimum of the potential-energy surface. Configuration-constrained calculations of the energy surfaces, including reflection asymmetry, give predictions of the properties of high-K states in the second well. In addition to excitation energies, spins and parities, the calculations indicate increased barriers towards fission, consistent with the extended half-lives observed experimentally.PACS. 2 1.10. 23.20.Lv Broken-pair excitations can lead to metastable states with an excitation of the quantum degree of freedom, K, that is the angular-momentum projection onto the symmetry axis of a deformed nucleus. A high-K excitation can result in highly forbidden decays to low-K states, due to the K selection rule [1], leading to the formation of longlived high-K isomers, which exist widely in the nuclear chart [2]. From the excitation energies and configurations of the isomers, insight can be gained into the shell structure of nucleon orbits, since quasiparticle excitations are closely related to the orbital fillings of the unpaired nucleons and their intrinsic angular momenta.In atomic nuclei there is another kind of metastable state that owes its existence to a second well of the potentialenergy surface (PES) of the nucleus with a highly elongated shape (where the first well generates the ground state). In the Z > 90 actinide region, the shape-trapping state decays mostly by spontaneous fission (SF), and hence is usually called a 'fission isomer'. The emergence of the second energy minimum is due to the special shell structure of nucleon orbits where clear shell gaps exist at large deformation. Because of very different shapes and a significant barrier between the first and second minima, the decay from the fission isomer to the ground state is inhibited. Indeed, actinide nuclei are well known for fission isomers [3,4] with highly elongated ('superdeformed') shapes, having major-to-minor axis ratios of about 2:1.It is natural to consider the possibility of high-K isomerism in the second well. The superdeformed axiallysymmetric shape is an excellent condition for the conserSend offprint requests to:vation of the K quantum number. In addition, a high-K configuration at the fission shape could increase the stability of an isomer against fission, in a similar manner to the fission inhibition in the first well [5]. This is in accord with experimental observations of longer-lived fission isomers, excited within the second well [3]. We call the state associated with the double isomerism of high K and shape a 'high-K fission isomer'.As early as the 1970s, Limkilde and Sletten explained the observed T 1/2 = 5 ns state in 238 Pu as a K isomer [6], contrasting with the 0.5 ns 0 + fission isomer. The experimental energy relative to the 0 + fission isomer was consistent with twice the pairing gap, as expected for a broken-pair excitation. Recently, high-K fission isomers were investigated the...