COLLECTIVE MODES IN NEUTRON-RICH NUCLEI

Correlations due to pairing, core polarization, and clustering are crucial in exotic nuclei. In neutron drip-line systems, skin excitations (soft modes, pygmy resonances) represent new collective modes characteristic of weakly bound nuclei. Since the energy of the pigmy resonance in neutron-rich nuclei is close to the neutron separation energy, the presence of soft vibrational modes is also important in the context of the astrophysical r-process [19].

Figure 4 demonstrates, however, that one does not need to go all the way to the neutron drip line to see surprising deviations from well-established trends. The diagram shows the systematics of experimental data for 2⁺₁ states around ¹³²Sn. Interestingly, both excitation energies and B(E2) values exhibit an unusual pattern as one crosses N=82. Namely, there is a striking asymmetry in the position of 2⁺₁levels in N=80 and 82 isotopes of Sn and Te, and the $B(E2;0^+ \rightarrow 2^+_1)$rate in ¹³⁶Te stays unexpectedly low [20], defying common wisdom that the decrease in E_2⁺1 in open-shell nuclei must imply the increase in $B(E2;0^+ \rightarrow 2^+_1)$.

  

Figure 4: Left: experimental 2⁺₁ levels in N=80,82,84 Sn and Te isotopes and measured values of $B(E2;0^+ \rightarrow 2^+_1)$ for even-even Sn, Te, Xe, Ba, and Ce isotopes around neutron number N=82. Filled symbols indicate the recent RNB measurements at the HRIBF facility at ORNL (from Ref. [20]). Right: energy and B(E2) of the 2⁺₁state in ¹³⁶Te as a function of the neutron pairing gap. The values of $\Delta_n$in ^132,136Te are marked by arrows (from Ref. [21]).

In order to explain this unusual pattern, we performed calculations using the Quasi-particle Random Phase Approximation (QRPA) with the separable quadrupole-plus-pairing Hamiltonian [21]. Whenever possible, s.p. energies were taken from experiment [22] (the remaining levels were calculated). For the two-body residual interaction used in QRPA, we took the quadrupole-quadrupole forces (with both isoscalar and isovector components) and the quadrupole pairing force [23]. The monopole pairing gaps were taken from experiment [12] except for magic nuclei (Z=50 and/or N=82) where we have used $\Delta$=0.4 MeV. Since in QRPA we employed a large configuration space, the B(E2) rates were calculated using bare charges.

Our calculations reproduce well the experimental pattern displayed in Fig. 4 [21]. The observed abnormal behavior in ¹³⁶Te and ¹³⁴Sn has been explained in terms of the reduction in the neutron pairing gap when going from N=80 to N=84 (resulting from the lowered density of the neutron s.p. states above N=82). As seen in Fig. 4, for larger values of $\Delta_n>0.7$ MeV, one obtains the familiar pattern (E_2⁺1 increases while B(E2) decreases), while at intermediate values of pairing both excitation energy and transition rate increase with $\Delta_n$. The idea of reduced neutron pairing in N=84 Sn and Te isotones is consistent with the experimental odd-even mass differences and results of mixed-pairing calculations shown in Fig. 2, and also explains the unusual lowering of the energies of 2⁺₁ states in ¹³⁶Te and ¹³⁴Sn (which are primarily two-quasineutron in character).