New Nuclidic Mass Relationship

Abstract

Arguments are presented which show that the transverse and longitudinal nuclidic mass relationships of Garvey and Kelson (GK-T and GK-L) contain small but systematic errors. If masses far off the line of fl-stability are calculated, these errors accumulate in the repeated application of the relationships, and the diverging predictions from GK-T and GK-L seem to represent estimates of upper and lower limits only. A new generalized nuclidic mass relationship is introduced.Nuclidic mass relationships constitute an important tool for estimating the masses of unknown nuclei close to and far away from the region of known nuclei. Garvey and Kelson 1 derived the relationship M(A, T~+ 2)-M(A, Tz)+ M(A-1, T~+ 89 -M(A-1, T~+~)+M(A+I, T~+ 891, T~+~)~0(1) assuming an independent-particle model with fourfold degenerate singleparticle orbits. In a later article Garvey et aI. 2 showed that Eq. (1) can also be derived by requiring that the sum over a subset of masses leads to a first-order cancellation of all single-particle energies and of the interactions between nucleons. These requirements also lead to another mass relationship 2, namely M(A+4, T~)-M(A, T~)+M(A+ I, T~+ 89 -M(A+3, T,+ 89Tz-89 T~-89Eqs.(1) and (2) will be referred to as the transverse and the longitudinal Garvey-Kelson nuclidic mass relationships GK-T and GK-L, respectively. The relationship GK-T has been widely used in the past to estimate * On sabbatical leave from The University of Michigan, Ann Arbor, Michigan.

Nuclear mass predictions for the crustal composition of neutron stars: A Bayesian neural network approach

“…Falling within this category are the Garvey-Kelson relations (GKRs), which are based on two local mass relations each involving six neighboring nuclei [17,18]. As such, the GKRs may be used to predict the mass of an unknown nuclide in terms of its known neighbors.…”

“…Given that successive derivatives of any smooth function are progressively smaller, the GKRs are well satisfied by the large and smooth contribution of the underlying mass function. Moreover, the GKRs were constructed in such a way that all residual two-body interactions that enter into mass relations are exactly cancelled to first order [17,18,23]. Although not rooted in firm fundamental physical principles, the GKRs predictions rival some of the most successful mass formulae available in the literature [20,21].…”

N=Znuclei: a laboratory for neutron–proton collective mode

“…This is also related to the fact that, as mentioned in Ref. [49], the average np interactions for even-even and odd-odd nuclei as extracted from the binding energies predicted by the Garvey-Kelson mass relations [53] satisfy…”

High-accuracy mass determination of unstable cesium and barium isotopes

“…7 the di erence is given between experimental and calculated masses for the model of Janecke and Masson [36]. This mass formula belongs to a class of models based on the so-called Garvey-Kelson relations [37]. Due to its very strong connection with experimental values in an extreme single particle picture this model reproduces most successfully the experimental masses but it has a very limited predictive p o w er for nuclei far from stability [38].…”