Investigation of the ${}^{128}\mathrm{Ba}$ nucleus with the $(p,t)$ reaction

The low lying states in ${}^{128}\mathrm{Ba}$ have been investigated for the first time with the ${}^{130}\mathrm{Ba}(p,t){}^{128}\mathrm{Ba}$ reaction. The experiment was performed at the Munich Q3D magnetic spectrograph with a 25-MeV proton beam and a high-resolution, 1.5-m-long focal plane detector. As a result of this experiment 27 excited levels with energies below 3.7 MeV have been observed for the first time, significantly increasing (by $~50\%$) the number of levels observed in ${}^{128}\mathrm{Ba}$. Angular distributions of tritons were measured and their comparison with the distorted wave Born approximation calculation allowed in most cases spin and parity assignments for the nuclear levels. The experimental two-neutron transition strengths with transferred angular momentum $L=0$ and 2 are compared with the predictions of the IBA-1 model with a new set of parameters. The results indicate for the first time from a hadronic probe perspective a transitional structure close to the O(6) symmetry for the ${}^{128}\mathrm{Ba}$ nucleus, confirming previous conclusions of $\gamma$-ray spectroscopy studies.

Figure 1

Triton spectra from the ${}^{130}\mathrm{Ba}(p,t){}^{128}\mathrm{Ba}$ reaction in the first magnetic setting of the Q3D spectrograph, measured at a laboratory angle of $6^{°}$ (in the lower panel) and ${15}^{°}$ (in the upper panel). The energies of the strong $0^{+}$ and $2^{+}$ excited levels are marked on the figure and are determined following a calibration procedure described in the text. The horizontal arrow placed below the lower panel and labeled “Ov.” indicates the region overlapped with the second magnetic setting.

Figure 2

Illustration of the energy calibration procedure for the second magnetic setting (highest energy) of the Q3D spectrograph. The spectra drawn in panels (a) and (b) are obtained in the same setting of the spectrograph. The peaks from ${}^{142}\mathrm{Sm}$ (a) are well known and their energies (in keV) are taken from Ref. [8]. The procedure for transferring the calibration from ${}^{142}\mathrm{Sm}$ to ${}^{128}\mathrm{Ba}$ (b) revealed a constant shift of 24(1) keV (see text).

Figure 3

Experimental angular distributions (points) and DWBA calculations (curves) for the transferred angular momentum $L=0,2,3$, and 4, in the ${}^{130}\mathrm{Ba}(p,t){}^{128}\mathrm{Ba}$ reaction at 25 MeV. The shape for $L=0$ transfer is unambiguously identified in both magnetic settings. The angular distributions with only two angles, measured for the second magnetic setting ($E_x>2600$ keV) cannot discriminate among $L=2,3$, and 4 shapes. (The $L=2$ shapes are represented with full lines, $L=3$ with dashed lines, and $L=4$ with dash-dotted lines.) For these angular distributions the $L$ assignment is based on the $R_{\sigma }$ ratio used for $L$-transfer estimation (see text).

Figure 4

Experimental excitation energies and transition probabilities or relative intensities of the $\gamma$-ray transitions for the low-lying levels of ${}^{128}\mathrm{Ba}$ compared with the present IBA-1 model calculation. $B(E2)$ values are indicated for some transitions. The numbers within quotation marks are the relative values (branching ratios) for decays where the absolute values are not known. The parameters used for calculations are those from Table . The $\gamma$-ray experimental data are taken from Refs. [3, 4].

Figure 5

Comparison of the measured $L=0$ transfer intensities for the $0^{+}$ states in ${}^{128}\mathrm{Ba}$ with the IBA-1 predictions. Values are normalized to 100 corresponding to the $0_1^{+}({}^{130}\mathrm{Ba})\to 0_1^{+}({}^{128}\mathrm{Ba})$ transition. The vertical arrow indicates the pairing gap, calculated from the odd-even mass difference. The vertical dashed line indicates only the energy of the next excited $0^{+}$ state predicted by the IBA-1. It is located at 2307 keV and has a vanishingly small $(p,t)$ intensity.

Figure 6

Comparison of the experimental $2n$-transfer intensity for the $2^{+}$ states and IBA-1 predictions. The intensities are normalized to the $0_1^{+}({}^{130}\mathrm{Ba})\to 2_1^{+}({}^{128}\mathrm{Ba})$ transition. The vertical dashed line indicates the position of the next two excited $2^{+}$ states produced by the IBA-1 model. The FTNT code prohibits calculation of the $2n$-transfer matrix elements to more than four states.

Figure 7

The positioning of the ${}^{128}\mathrm{Ba}$ and ${}^{130}\mathrm{Ba}$ nuclei in the IBA symmetry triangle based on the values of the IBA-1 parameters (Table ) and the procedure from Ref. [19] (see text for details). Also included in the figure are the polar coordinates ρ and θ as defined in Ref. [19].