Mass differences and neutron pairing in Ca, Sn and Pb isotopes

Abstract

Various estimates of the even-odd effect of the mass shell of atomic nuclei are considered. Based on the experimental mass values of the Ca, Sn, and Pb isotopes, the dependence of the energy gap on the neutron number is traced and the relationship of this characteristic to the properties of external neutron subshells is shown. In nuclei with closed proton shells, effects directly related to neutron pairing and effects of nucleon shells are discussed.Key words nucleon interaction, models of atomic nuclei, nucleon pairing in atomic nuclei

Empirical pairing gaps and neutron-proton correlations

“…Diagrams of various indicators of np-correlations in nuclei. The coefficients are given for the values of binding energies in the ratios for a) ∆np -indicator (2), b) 2∆ In our previous work [19] the interrelation of dif-…”

“…∆ p = ∆ (5) p (N, Z), even Z (18) and δ np (19) are shown in Fig. 1i and f. From the diagrams, the relationship between δ np and previously introduced indicators ∆ np , ∆ (6,n) np and ∆ (6,p) np is clear: in fact, as in the case of identical nucleons, the relations from [61] are a further averaging of the np-interaction energy ∆ np over the mass surface.…”

“…4 shows a scheme that allows one to estimate the values of π and d on the basis of S n (N ) in isotones. The mass difference relations for identical nucleons were considered in our previous paper [19] in detail. The interaction of n neutrons in j 1 state and p protons in j 2 state can be written as the sum of two terms [64]:…”

“…The contribution of I is mapped, by analogy with like nucleon pairing, by indicators ∆ (6, (19)). Comparison of the diagrams for indicators ∆ np and ∆ (6,p) np (see fig.…”

“…For example, it is well known that pairing of identical nucleons leads to stratification of the mass surface and can be quantified from the odd-even staggering (OES) value [11][12][13]. Various versions of the estimation of the pairing energy of identical nucleons in even-even isotopes based on the masses of neighbouring nuclei have been studied in detail, but despite the long history of the study of the problem, the question of which relation corresponds to the pair interaction most closely, is still under discussion [14][15][16][17][18][19].…”