2. Recent HRIBF Research - Deviations from U(5) Symmetry in 116Cd
[J. C. Batchelder (UNIRIB), spokesperson]
The cadmium isotopes near their mid-neutron shell, i.e., N=66, exhibit one of the well-known examples of shape coexistence . In addition to the spherical quadrupole vibrational levels (hereafter referred to as normal phonon states), which are described within the Interacting Boson Model (IBM) by the U(5) limit, they possess intruding proton particle-hole configurations that give rise to additional states in the low-lying spectrum of levels .
These intruding excitations may mix with the normal states, perturbing their properties. However, once this mixing is accounted for , the underlying normal phonon states have been claimed to be very close to the U(5) limit, and, in fact, are often cited as the best examples of U(5) nuclei  and are often used in textbooks to illustrate quadrupole vibrational spectra in nuclear systems [5,6]. These nuclei span the "bottom of the parabola" that is characteristic  of intruding particle-hole configurations that underlie shape coexistence. The low-lying levels of 112,114Cd have been explained  as mixtures of vibrational and intruder configurations. Experimental studies of 110Cd [7,8,9], 112Cd [10,11,12,13], 114Cd  and116Cd [15,16] have supported this description. An intruder band structure has also been well established [7,15,17] in 110-116Cd, with enhanced intraband B(E2) values observed.
In the cases of 110,112,114Cd, it is the lowest excited 0+ states that have large B(E2) values for decay to the one-phonon 2+ states (and also the 2+ intruder states decay to them with enhanced B(E2) values), whereas the second excited 0+ states have much smaller B(E2) values for their decay [10,12,14]. This pattern can be explained well within the strong mixing approach as outlined in , and shown in [17,18], although the weak mixing approach can also explain the B(E2) pattern in 114Cd . In 116Cd, it is the second excited 0+ state, rather than the first, which has the enhanced B(E2) value for decay to the one-phonon 2+ level , and it is also this level that is fed by the strong B(E2) value from the 2+intruder level , a pattern that remains unexplained [18,20].
In order to better understand the behavior of 116Cd and all of the Cd isotopes, we reinvestigated the decay of levels in 116Cd populated via the beta-decay of 116Ag. Silver-116 was produced via the proton-induced fission of 238U at the Holifield Radioactive Ion Beam Facility (HRIBF). The proton induced fission products were then mass-separated by the OLTF and deposited on a moving tape collector (MTC). The collected samples were subsequently moved to the counting position located at the center of the CARDS array (Clover Array for Radioactive Decay Spectroscopy), which consisted of three segmented-clover Ge detectors, plastic scintillators, and a high-resolution (FWHM 1.5 keV at 44 keV) Si conversion-electron spectrometer . The BESCA detector had an efficiency for conversion electrons of ~2%, while the clovers had a summed efficiency of ~5% for 344-keV 152Eu gamma rays.
Figure 2-1: A comparison of experimental and IBM-2 B(E2) calculations for the 3+1 and 6+1 levels in 116Cd. All level lifetimes and mixing ratios are taken from  and transition strengths are quoted in W.u.
Figure 2-2: Experimental versus IBM-2 calculations for the 4+1 levels in 116Cd.
The results of our experimental observations confirm the existence and placement in the decay scheme of the five levels (1869.8, 1916.0, 1928.6, 1951.4, and 2026.7 keV) assigned in  to be the complete three-phonon state quintuplet. However, while the experimental B(E2) values for decay of the 3+, 4+ and 6+ levels (see Figs. 2-1 and 2-2) compare well with the calculations, the decay of the 0+ and 2+ levels is not consistent with this picture.
The experimental B(E2) values for the decay of the 2+4 state are completely different than those predicted by the IBM2 for a vibrational phonon state. As mentioned above, the decay pattern is different with the IBM2 predicting decays to the 2+2, 4+1, 0+2, 0+3, and 2+3 states. Of these states, only the decay to the 0+2 state is observed, along with decays to the 2+1 and 0+1 states. For the one transition that is observed (2+4 → 0+2), the experimental B(E2) value is 61 W.u. compared to the calculated value of 4.2 W.u. For comparison, the experimental and calculated B(E2) for decay of this level are shown in Fig. 2-3. The decay pattern of this level is not consistent with a three-phonon interpretation and the 1951.4-keV, 2+ level is more consistent with an isolated weakly-deformed band structure in view of the strength of the connecting 668.8-keV transition.
For the case of the 0+4 state in 116Cd, the experimental decay of this state is completely different than what is predicted by the IBM-2 calculations. The experimental relative B(E2)'s versus the predicted values are shown in Fig. 2-4 (the lifetime of the 0+4 state has not been measured, so the experimental B(E2) is unknown). From the IBM-2 calculations one would expect that the state should decay strongly to the 2+2 state (B(E2) = 43.5 W.u.) and very weakly to the 2+1 state. In fact the opposite is true, as we only observe a single transition de-exciting this state to the 513.5-keV 2+ state and an upper limit for the relative B(E2) to the 2+2 of 14%.
Figure 2-3: A comparison of experimental and IBM-2 B(E2) calculations for the 2+4 levels in 116Cd.
Figure 2-4: A comparison of experimental and IBM-2 B(E2) calculations for the 0+0 level in 116Cd.
The deviations in the experimental B(E2) values from IBM-2 calculations that are observed in 116Cd for the phonon-states cannot be explained through considered mixings with the intruder excitations or mixed-symmetry states. Along with the inability to explain the decays of the 0+2 and 0+3 levels, the present results for the proposed three-phonon levels show that the description of 116Cd as a vibrational nucleus with well understood mixing between normal and intruder states is inadequate.
A careful analysis of the other known even-even Cd isotopes (110-120) reveals that the discrepancy in the decay of the three-phonon 0+ and 2+ states with the U(5) description is a consistent feature in all these nuclei. Fig. 2-5 shows the decays of the 0+ and 2+ members of the three-phonon quintuplet for110Cd ,112Cd [24,25], 114Cd ,116Cd [this work], 118Cd , and 120Cd . In the U(5) description of the normal states, the 2+ three-phonon state would be expected to strongly decay to all three of the two-phonon states (0+, 2+, 4+). The decay of this state in 112,114,116Cd is to the 2+ two-phonon and 2+ one-phonon states, while in 110,118,120Cd, this state is only known to decay to the 2+ one-phonon state. (In Ref. , the 1915.8-keV state was labeled as a three-phonon state decaying to the 2+ two-phonon state, while Ref.  labels this state as an intruder state based on energy systematics). The three-phonon 0+ states in 110,112,114,116,118Cd decay only to either intruder states or the 2+ one-phonon state.
In all the neutron-rich even-even Cd nuclei from 110-120, none of the observed 0+ and 2+ states previously assigned as three-phonon states decay in a manner consistent with a three-phonon state. This discrepancy is unaccounted for to date in calculations that incorporate mixing between normal and intruder states. Further, the consistent decay pattern across the Cd isotopes, regardless of level spacings that would cause significant differences in energy denominators for mixing amplitudes, is suggestive that the deviations from the expected harmonic vibrator or U(5) selection rules are not due to mixing.
Figure 2-5: Comparison of the decays of the 0+ and 2+ members of the three-phonon levels in 110,112,114,116,118,120Cd. Relative B(E2)s are shown. Intruder states are circled to distinguish them from N-phonon states.
To continue this investigation, we have recently taken data with high statistics (1.4X108 events in the 2+1 → 0+1 gamma transition) on the beta-decay of 120Ag. This data is currently being analyzed.
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