Nucleon separation energies in the valence correlation scheme

Abstract

In this paper we study the one-and two-nucleon separation energies (S n , S p , S 2n , and S 2p ) by using the Atomic-Mass-Evaluation-2011 Preview. We show the linear dependence of separation energies, previously investigated for S n and S p of even-even nuclei, in terms of αN p + βN n (N p and N n is the valence proton number and valence neutron number, respectively, with respect to the nearest magic closure), hold in a broader sense. It is applicable equally well to odd-mass and odd-odd nuclei. New odd-even staggerings are found for S n and S p , and are discussed by using the pairing interaction and the symmetry energy. Predictive power of these simple relations is discussed.

Odd-even staggering in the neutron-proton interaction and nuclear mass models

“…The empirical neutron-proton interaction between the last neutron and the last proton of nuclei, denoted as δV 1n−1p , exhibits a sizable odd-even staggering between even-A and odd-A nuclei [12,23], despite the fact that the pairing interaction of like nucleons is approximately canceled out in δV 1n−1p . This suggests an extra binding energy for even-A nuclei [24][25][26], and this extra energy leads to a subtle odd-even feature for one-nucleon separation energies [25,27]. The third-order derivative of nuclear mass gives an interesting odd-even phenomenon of the GKs [16,28,29], despite the fact that the pairing interaction of like nucleons and the extra binding of even-A nuclei are both approximately canceled out.…”

Pairing interactions and one-nucleon separation energies

“…In Ref. [15] the staggerings were attributed to pairing interaction between like nucleons and symmetry energy in the modified Bethe-Weizsäcker formula; in this paper they were further explained in terms of three types of pairing interactions, i.e., proton-proton, neutron-neutron, and protonneutron pairing interactions.…”

“…Second, there are two types of odd-even staggering reported in Ref. [15]. For convenience we exemplify them by using S p and S n of nuclei in the A ∼ 130 region in Fig.…”

“…In Ref. [15] Jiang et al showed that the relation in Eq. (1) holds not only for even-even but also for even-odd, odd-even, and odd-odd nuclei.…”

“…[13,15], in terms of pairing interaction and so-called nonpairing interactions. We suggest that the linear correlation in S p (S n ) is given by the smooth and slow change of these interactions, and that the odd-even staggering is originated from the paring interactions.…”