Investigation of excited 0 + states in 160 Er populated via the ( p , t ) two-neutron transfer reaction

Many efforts have been made in nuclear structure physics to interpret the nature of low-lying excited 0 states in well-deformed rare-earth nuclei. However, one of the difficulties in resolving the nature of these states is that there is a paucity of data. In this work, excited 0 states in the N = 92 nucleus 160Er were studied via the 162Er(p, t)160Er two-neutron transfer reaction, which is ideal for probing 0 → 0 transitions, at the Maier-Leibnitz-Laboratorium in Garching, Germany. Reaction products were momentum-analyzed with a Quadrupole-3-Dipole magnetic spectrograph. The 0+2 state was observed to be strongly populated with 18% of the ground state strength.

Two-neutron transfer reactions are excellent probes to study excited 0 + states as they are sensitive to pairing correlations in nuclei [14][15][16][17]. This is demonstrated by the strongly-populated 0 + 2 states which emerged in both (p, t) and (t, p) reactions in the N = 90 region [7]. In particular, the cross sections of the first excited L = 0 excitations were comparable to that of their ground states in N = 88 − 90 nuclei, indicating a rapid onset of deformation [7,13].
Evidence of collectivity in the N = 90 region is also demonstrated by the simultaneous increase of the B(E2; 0 + 1 → 2 + 1 ) value and the E 4 + 1 /E 2 + 1 energy ratio, plotted in Figure 1, indicating that a rapid transition between the vibrational and rotational limits occurs near N = 90. * e-mail: cburbadg@uoguelph.ca  Figure 1. B(E2; 0 + 1 → 2 + 1 ) value and E 4 + 1 /E 2 + 1 ratio systematics in the N = 90 region plotted as a function of neutron number. The dramatic increase in both quantities suggests that these isotopes lie in a transitional region of rapid shape change. The Er isotopic chain also possesses similar characteristics. Van de Graaff accelerator. The proton beam impinged on a highly-enriched 162 Er target. Reaction products were momentum-analyzed with a Quadrupole-3-Dipole (Q3D) magnetic spectrograph. In the focal plane of the Q3D, two proportional counters produce two energy-loss signals, ∆E and ∆E 1 . A thick plastic scintillator located behind the proportional counters stop the particles to determine their energy, E. An example of a ∆E-E histogram used to identify and gate on reaction ejectiles is shown in Figure 2. An elastic scattering angular distribution was collected from 15 • to 115 • to determine the target thickness and select an appropriate global optical model potential (OMP) [18][19][20][21][22] to be used in the Distorted Wave Born Approximation (DWBA) calculation. The target thickness was determined to be 61(3) µg/cm 2 by normalizing the cross section at 15 • to the Becchetti and Greenlees OMP [18], which best reproduced the distribution minima. In this work, the DWBA calculations were performed using FRESCO, a coupled-channel reactions code [26]. The isotopic purity of 99% is remarkable given the 0.14(1)% natural abundance [24] of 162 Er.

Results and Conclusions
Evaluated data for levels in 160 Er [23] were used to calibrate the triton spectrum, plotted in Figure 3. Members up to J π = 4 + were assigned by comparison of angular distributions to DWBA calculations. It is worth noting that some of the members of the higher-lying K π = 0 + and K π = 2 + bands are speculative, motivated by the similarity of the 160 Er band structures to those of 162 Er and 152 Sm, but are in agreement with those observed in unevaluated works [10,25].
To report the strength of the excited 0 + states relative to the ground state, the relative cross section strength, S, is defined by where the differential cross sections are stated in the centre-of-mass frame. Normalizing both the excited and ground states to the DWBA calculation applies a Q-value correction to account for the dependence of the reaction cross section on excitation energy. Figure 4 shows the agreement between the 0 + 1 and 0 + 2 state cross sections and their DWBA calculations.
The relative cross section strength of excited 0 + states in this work are listed in Table 1. The low-lying K π = 0 + band head is strongly populated with 18% of the ground state strength, while higher excited 0 + states have a relative strength of less than 2%. The strong population of the 0 + 2 in (p, t) reactions in the N = 92 region, reminiscent of the strong (p, t) strength in the N = 90 region [7], may suggest that the same mechanism is responsible for the strength of 0 + states in both N = 90 and N = 92 nuclei.