The Validity of the Strutinsky Method for the Determination of Nuclear Masses

Abstract

In theoretical estimates of nuclear masses of experimentally unknown isotopes, one has used two different kinds of methods. The first consists in deducing these masses from some known neighbouring ones with the help of a convenient extrapolation formula. This has been extensively discussed for instance in Ref.[1]. One of the problems of such an approach is that one cannot predict any sudden change (e.g. in deformation) in the unknown region if it has not shown up for any known nuclei in the vicinity. The other methods, on which we will concentrate here, are based on a detailed description of total binding energies within a given model. In the last two or three years, one has been able to parametrize phenomenological effective interactions and to give a very satisfactory systematic reproduction of nuclear masses on the whole chart of nuclides, using both the Hartree-Fock approximation[2–3] and the Hartree-Fock-Bogolyubov approximation [4]. But the oldest and still rather successful approach to nuclear masses is the liquid drop model[5]. For the description of fine details connected to the existence of magic nuclei one has been obliged to introduce some shell corrections as done in Ref.[6]. Strutinsky has given a consistent description of the nuclear binding energy in terms of a sum of a liquid drop energy plus first and higher order shell corrections[7]. Such an expansion relying on the validity of the Hartree-Fock description of the nuclear ground state is referred to as the Strutinsky energy theorem [8]. The energy averaging method widely used to extract the shell correction has been shown to be equivalent to many other possible prescriptions (such as the so-called temperature method or various semi-classical expansions) [9]. A consistent fit of the parameters of both the liquid drop model and the single particle potential needed in the Strutinsky method has been done by Seeger and co-workers (see e.g. Ref. [10] ) for nuclei with A ≥ 40. Such approaches to nuclear masses are met with two kinds of difficulties: i) how reliable is the extrapolation of single particle potential parameters? ii) What is the accuracy of the Strutinsky method itself?