Partial-wave decomposition of the finite-range effective tensor interaction

Abstract

We perform a detailed analysis of the properties of the finite-range tensor term associated with the Gogny and M3Y effective interactions. In particular, by using a partial wave decomposition of the equation of state of symmetric nuclear matter, we show how we can extract their tensor parameters directly from microscopic results based on bare nucleon-nucleon interactions. Furthermore, we show that the zero-range limit of both finite-range interactions has the form of the N3LO Skyrme pseudopotential, which thus constitutes a reliable approximation in the density range relevant for finite nuclei. Finally, we use Brueckner-Hartree-Fock results to fix the tensor parameters for the three effective interactions. One of the key ingredients of the bare nucleon-nucleon (NN) interaction is the tensor part, which represents the most distinct manifestation on meson exchange process. Among the most important properties related to the tensor interaction, one can mention the quadrupole moment of the deuteron, the properties of excited states [1][2][3][4], the contribution to the spin-orbit splitting [5], and the shell evolution along isotopic chains [6]. Within the context of phenomenological interactions, one should in particular keep in mind that the strong competition between spin-orbit and tensor on the shell structure properties of atomic nuclei [2, 7-9], prevents to freely explore the parameter space, since a variation in the tensor can lead to a substantial change in the shell structure with the appearance of new magic numbers. A detailed discussion and list of references about these issues is given in the recent review article of Sagawa and Coló [10].Despite their importance, only a few exploratory attempts have been made in the past [11,12] to include explicit tensor terms within non-relativistic self-consistent mean-field or density functional nuclear models. More recently, such terms have been added to existing zero-or finite-range effective interactions, as the popular families of Skyrme [13], Gogny [14] or M3Y [15]. The parameters are usually fixed to reproduce some selected spinorbit splittings, with either a partial or a complete fit of parameters. However, the parametrizations can lead to the appearance of unphysical instabilities of the Fermi surface both in the zero-and long-range regimes [16][17][18]. To avoid them we have proposed [19,20] to incorporate into the fitting procedure the constraints obtained from linear response theory. Furthermore, we have also suggested [19,21,22] some new constraints from microscopic calculations based on the bare NN interaction: specifically, a partial wave decomposition on the so-called N3LO Skyrme pseudo-potential of the symmetric nuclear matter (SNM) equation of state (EoS) allows one to clearly identify the contribution of each term of the effective interaction, even for the tensor part. This decomposition can be used for an initial guess of the interaction parameters. The N3LO pseudo-potential represents the most general non-local zero-range pseudo-potential that incl...

Linear Response Theory with finite-range interactions

“…The apparent discrepancy between the AV18 tensor and the Gogny one was also discussed in Ref. [130] by comparing the partial wave decomposition of the EoS with the one obtained using ab-initio methods. For a more detail comparison between the two types of tensor, one can also inspect the corresponding Landau parameters as illustrated in Tab.…”

“…As discussed in Ref. [130], it is thus not clear whether the constraints on the tensor coming from finite nuclei are compatible with the ones coming from ab initio calculations. However it is neither clear if such a difference is relevant and has any impact on calculations of properties of finite nuclei.…”

Partial Wave Decomposition of Neutron Matter Equation of State

“…Partial wave decomposition A. Pastore we can take ad − hoc combinations of partial waves to cancel out the contribution of the central term and thus isolate the tensor and spin-orbit components (a similar procedure has already been discussed in Ref. [7]). By inspecting the equations, we find that the relevant combinations are…”

“…The Skyrme N3LO pseudo-potential [1,2] is an extension of the standard Skyrme interaction [3], obtained by including all possible combinations of momentum operators up to 6th order. In a recent series of articles [4,5,6,7,8], we have studied the properties of the Skyrme N3LO gauge-invariant interaction (see [1,2]) in infinite nuclear matter. Our main result is that the inclusion of higher order gradients gives an excellent flexibility, allowing us to give a fair description of the main physical results obtained with more involved calculations such as Brueckner-Hartree-Fock (BHF) [9,10] based on the Argonne AV14 two-body force plus the Urbana VII three-body force.…”

Infinite matter properties and zero-range limit of non-relativistic finite-range interactions

“…Thanks to the analytical properties of the infinite nuclear medium, we will show that the parameters of such an extended Skyrme interaction can be related in a simple way to the ones of Gogny or M3Y. By performing a systematic study of the partial wave decomposition, we will also discuss how the main contributions to the 2 EoS come from the partial waves S , P, D, F [34] which are naturally included into the N3LO pseudo-potential. The article is organized as follows: after recalling for completeness in Sect.…”