REVISTA MEXICANA DE FíSICA 47 SUPLEMENTO 2, 52-58 An algebraic rnodel for three-c1uster giant rnolecules P.O. Hess and R. Bijker Instituto de Ciencias Nucleares. Universidad Nacional Aut6noma de México Circuito exterior, Ciudad universitaria, Apartado postal 70.543, 04510 México, D.F., Mexico ~. M i~ieu Na/fonal bistfrute/or Nuclear Physics, Buchares! P. O. Box MG6, Romania lnstitut für Theoretische Physik, J. WV.-Goethe Universitiit Rober/-Mayer-Slr. 8-10, 60325 Frankfurl am Main, Germany Recibido el 3 de enero de 2001; aceptado el 23 de mayo de 2001 DICIEMBRE 2001 After an introduction lo the algebraic U(7) mooeJ for threc bodics. we presenl a rclalion of a geometrical description ofthree-cluster molecules lo the algebraic U(7) model. Stiffness paramClers of oscitlations bclwccn cach of two c1usters are calculatcd and translatcd to the model parameler values of the algebraic model. The model is applied to the trinuclear syslem 132Sn+o+116Pd which occurs in Ihe lemary cold tlssion of 252Cf. Keywords: Nuclear c1usters;algebraic model Después de una introducción del modelo algebraico de V(7) para tres cuerpos, presentamos la descripción de un modelo geométrico de una molécula nuclear de tres cúmulos con el modelo V(7). Se calculan los parámetros de rigidez enlre pares de cúmulos y se les traduce a los valores del modelo algebraico. El modelo es aplicado al sistema 132Sn+ o + 116Pd. Descriptores: Cúmulos nucleares; modelo algebraico PAes, 21.60.Gx; 21.60.Ev; 33.25.+k 1. Introduction The recent announced discovery of lOSe accompanied cold fission in Ihe sponlaneous fission Of 252 Cf [1 J is leading to Ihe astonishing result that long living trinuclear molecules may exist. The experiment was triggered to the electromagnetic transition 2t --+ ot of lOSe. The transitions of the accompa- nying clusters where measured in coinciden ce w ith the one of lOSe and the level spectrum was reconstructed, leading to an identification of the system 96Sr +10 De+ 146 Sa. As a surprise, no Doppler broadening of the Hnes was observed as one expeeted when Ihe nuclei deeay in flighI. This finding can be explained, assuming that the system emits the f rays at rest. Taking into account the Iife tim e of the 2t level in Be, which is 0.125 ps, the syslem has to live at leaS! as long as this. Independenlly, if this experimeni is eonfirmed, Ihere are sorne arguments that nuclear molecules of this type might exist: a) The cold fission Of 252 Cf into Ihree elusters is observed w ilh an a-particle as Ihe Iightesl nueleus [2]. b) If an o particle can be emitted, there is no reason to believe that larger clusters cannot be emitted too. As an example serves the observation of heavy cluster radioactivity [3]. though larger clusters are produced w ith a much smaller probability. e) lOSe consists of a core of two o-particles w ith two loosely bound neutrons [4] (and referenees therein), the laner being ideal to provide binding. el) In theoretical calculations of molecular potentials. minima are reproduced [5] (and references therein) for the system observed. Most of these arguments are, however, circumstantial and cannot prove the existence of these types of molecules. More experiments have to be done on these lines. In a series of anicles [5] a geometrical model for three- cluster molecules w.aspublished. It is based 00 an earlier mo- del for two-cluster molecules [6]. In arder to obtain an ana- lylical solution, several strong assumptions had to be made i) The system is in a linear configuration. ji) The inclination angles of the nuclear symmetry axis to the axis which defines the linear orientation should be very small. ¡ii) The Iight cluster has to be sandwiehed between Ihe two heavy ones. The intention of this contribution is to present an alge- braic model, inspired by previous work on baryon struc- ture [7], which might overcome these restrictions. The ad- vantage of this model is the easiness in how olle can describe complicated systems, which would require complex proce- dures in the geometrical modelo Also it permits to discuss possible dynamical symmetry Iim its. allowing for an analy- tical description of the spectrum. This laner pan w ill not be discussed here. The main idea of the algebraic model was al- ready presented in [8]. However, the problem remained, how lo obtain the model parumeters starting from known stiffness parameters, describing the pairwise interaction between the