Ground-state phase transition in odd-Aand odd-odd nuclei nearN=90

Abstract

Ground-state phase transitions in odd nuclei are examined. Especially, the phase transitions in odd-odd nuclei are revealed. It is found that odd-even effects may reach their maximal or minimal values around the critical point at N = 90; the signals of phase transition in odd nuclei are greatly enhanced relative to those in the adjacent even-even species. Moreover, a pairing model analysis of the phase transition in Sm isotopes indicates that the critical behaviors related to pairing may be driven by the decrease in the pair strength G with a sudden flattening in G around the critical point.

Ground state phase transition in the Nilsson mean-field plus standard pairing model

“…The odd-even differences of α-decay energy D(Q α ) and double β − -decay energy D(Q 2β − ) in Sm and Eu isotopic chains were investigated previously [25], and the results suggested show that D(Q α ) and D(Q 2β − ) all reach their maximal values around N ≈ 90 based on experimental data but without theoretical model calculations. The odd-even differences of α-decay energy D(Q α ) and double β − -decay energy D(Q 2β − ) for Sm, Gd, and Nd are also calculated in the present model according to (16) and (17).…”

“…Furthermore, these quantities only depend on the number of nucleons with abundant experimental data available [2,[4][5][6]. However, through the analysis of these quantities and their odd-even differences [25], it is observed that nearly all the odd-even differences reach their extreme values (maximum or minimum) around the critical point, which, therefore, are more sensitive and suitable to be used as effective order parameters to manifest the shape phase transition. Hence, in the following, besides the odd-even mass differences P(Z, N), the odd-even differences of two-neutron separation energy, α-decay energy and double β − -decay energy will be calculated, where the odd-even difference of the two-neutron separation energy is given by…”

“…The neutron pairing strengths G determined for 144−155 Nd, 146−159 Sm, and 148−161 Gd are shown in Table I. In recent work [25], it is observed that the odd-even mass difference may serve as one of the effective order parameters to identify the ground state phase transition. The odd-even mass difference P(Z, N) of the three chains of isotopes are calculated according to Eq.…”

“…Very recently, the ground state phase transition in some eveneven, odd-A, and odd-odd nuclei in the A ∼ 150 mass region with the analysis of some experimental observables (the effective order parameters) has been investigated [25]. The experimental evidence reveals that the odd-even mass difference may reach the maximal or minimal value around the critical point at the neutron number N = 90.…”

“…The experimental evidence reveals that the odd-even mass difference may reach the maximal or minimal value around the critical point at the neutron number N = 90. The analysis of Sm isotopes based on the Nilsson mean-field plus the extended pairing model also indicates possible existence of critical phenomena which may microscopically be related to pairing interactions [25]. However, the nature of the critical behavior, including the role of pairing interaction, is still far from being clear.…”