Coulomb-energy radii from isobaric mass parabolas

Abstract

The mass difference for mirror nuclides is expressed in terms of the curvature 2C2 of the corresponding isobaric mass parabola and the (fractional) 'atomic number' Z* corresponding to its minimum. With the Coulomb energy of a nucleus taken as gamma AZ(Z-1)/A1/3, it is shown that C2(A-2Z*)= beta + gamma A(A2/3-A-1/3) where beta represents the hydrogen-neutron mass difference. The relationship is valid for both odd and even values of A. The availability of empirical values of C2 and Z* permits the evaluation of gamma A and thence the 'Coulomb- energy radius' Rc=rAA1/3 where rA identical to 3/5e/2 gamma A. Consideration of a 'quantal' formula for the Coulomb energy of a nucleus shows that the 'quantal' values of rA are slightly smaller than the 'classical' values but the difference becomes negligible for large values of A. Although there are significant variations in rA, the general trend is to smaller values of rA as A gets larger, e.g. rA=1.47 fm for 16<or=A<or=74 whereas rA=1.30 fm for 120<or=A<or=198. Values of rA corresponding to almost all values of A from 16 to 249 are given graphically and estimates of the error are included.