PHYSICAL REVIEW C 109, L041604 (2024) Letter Longitudinal ternary fission G. Royer , * A. Aguilera, and V. Fasquel Subatech Laboratory, UMR: IN2P3/CNRS-Université-IMT, 44307 Nantes, France (Received 24 February 2024; accepted 28 March 2024; published 15 April 2024) The longitudinal ternary fission is studied using the generalized liquid drop model. The proximity energy and the charge and mass asymmetries are taken into account. Spherical parent and daughter nuclei are considered. The shape sequence selected to simulate the quasimolecular three-body shapes is built from different but connected elliptic half lemniscatoids. The potential barriers are much lower when the central fragment is the smallest one and particularly when it is an α particle. The 2α emission can be described as a particular prolate fission with emission of two particles at the tips of the deformed nucleus. The associated potential barriers are high and thin. DOI: 10.1103/PhysRevC.109.L041604 Ternary fission is a very rare nuclear decay mode but it has been observed in several experiments at low energy [1,2] or in heavy-ion reactions [3–5]. The third particle is mainly an α particle. In the reaction with 36 Ar beams on a 24 Mg target at high angular momentum, narrow correlations have been interpreted as a ternary fission from an elongated shape, the lighter mass in the neck region consisting of one, two, or even three α particles with very low momentum in the center-of-mass frame [6]. α particles emitted at rest in the breakup of 28 Si into the 12 C +α + 12 C moleculelike configura- tion have also been observed [7]. Another example is the true ternary fission of 252 Cf leading to 132 Sn + 48,50 Ca + 70,72 Ni in collinear geometry [8]. For general decays it has been shown that the formation of the lightest fragment at the center has the highest probability [9]. It has also been proved that the potential barriers of the oblate ternary fission are higher than the ones of the prolate ternary fission except perhaps for the superheavy nuclei [5,10]. Theoretically, the ternary fission has been investigated stat- ically and dynamically, assuming mainly specific shapes and the formation in the neck of a third light particle which stays almost at rest between the two other fragments which go away [11–20]. The next question is now to study the possibility for a nu- cleus to emit simultaneously two α particles. An experiment has been proposed at CERN to investigate the double-α decay from a nucleus. Theoretically, recently [21] a model for the description of the simultaneous emission of two α particles from the opposite sides of the nucleus has been discussed in detail for nuclei with Z < 95. It uses analytical nuclear and Coulomb potentials. Within a modified generalized liquid drop model [22] the 2α decay has been studied in the re- gion 93 < Z < 102 [23]. A microscopic theoretical approach based on relativistic energy density functionals has also been * royer@subatech.in2p3.fr used to compute axially symmetric deformation energy sur- faces as functions of quadrupole, octupole, and hexadecupole collective coordinates [24]. It is focused on 216−220 Rn and 220−224 Ra. The purpose of this work is to determine the potential barriers of the path leading a nucleus to emit one particle at each tip of the initial nucleus within the generalized liquid drop model [25] and selected shapes [26]. To study the fusion and binary fission through compact and creviced shapes, a shape sequence was defined [25] using two halves of different lemniscatoids joined by a same radius of the neck (see Fig. 1). In polar coordinates this shape is given by R(θ ) 2 =  a 2 sin 2 θ + c 1 2 cos 2 θ 0  θ  π/2, a 2 sin 2 θ + c 2 2 cos 2 θ π/2  θ  π, (1) where a is the transverse distance and the radius of the neck when there is a crevice, while c 1 and c 2 are the elongations along the axis of revolution. To simulate the longitudinal ternary fission with the small- est fragment in the middle [14], a symmetry plane was introduced cutting one fragment along its maximal orthogonal distance (see Fig. 2). The same shape sequence can be used when the central fragment is the biggest one, the two nuclei at the extremes being identical. In particular, this allows us to describe the simultaneous emission of two α particles at the two opposite tips of the fissioning parent nucleus (see Figs. 3 and 4). Such a true ternary fission is very different from the formation of a small nucleus in the neck between nascent fragments. Mathematically (Fig. 5), the two dimensionless parameters s 1 = a/c 1 and s 2 = a/c 2 completely define the shape, with a being the neck radius. The shape sequence evolves from a sphere when s 1 = s 2 = 1 to three aligned spherical fragments in contact when s 1 = s 2 = 0. For a given reaction with an emission of a central fragment of radius R 2 and of two other external identical fragments of radius R 1 , the parameters s 1 2469-9985/2024/109(4)/L041604(5) L041604-1 ©2024 American Physical Society