Set of Nuclear-Mass Relations and a Resultant Mass Table

Abstract

Two new independent mass relations are derived and are shown to be consistent with several existing nuclear models. The most general functional dependence on proton number, neutron number, and mass number (or isospin value) of masses which satisfy these relations exactly is discussed, and a procedure for determining the values of these functions which give a best least-squares fit to the body of known masses is developed. The functions which give the best over-all fit are listed together with the resulting theoretical mass table which shows the discrepancies to known masses and the theoretical values for proton, neutron, and alpha-particle decay energies.

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].…”

Improved radial basis function approach with odd-even corrections

“…By analyzing the systematic trends in the mass surface and its derivatives, masses of nuclei near the region of known masses can be estimated with the Audi-Wasptra extrapolation method [3][4][5][6]. The local mass relations, such as the Garvey-Kelson (GK) relations [7][8][9][10][11], the systematics of proton-neutron interactions [12,13] and the Coulombenergy displacement [14,15], and systematics of α-decay energies [16,17] can also be applied to predict the masses of nuclei near the known region, although the intrinsic errors grow rapidly when these local mass relations are used for predictions in an iterative way.…”

Decay energies of gaseous fission products and their daughters for A=88 to 93

“…aj.. (4). This mass relation is based on the single-particle model of the nucleus and utilizes symmetries implicit in isospin formalism.…”