Evolution of deformation in neutron-rich Ba isotopes up to $A=150$

The occurrence of octupolar shapes in the Ba isotopic chain was recently established experimentally up to $N=90$. To further extend the systematics, the evolution of shapes in the most neutron-rich members of the $Z=56$ isotopic chain accessible at present, ${}^{148,150}\mathrm{Ba}$, has been studied via $\beta$ decay at the ISOLDE Decay Station. This paper reports on the first measurement of the positive- and negative-parity low-spin excited states of ${}^{150}\mathrm{Ba}$ and presents an extension of the $\beta$-decay scheme of ${}^{148}\mathrm{Cs}$. Employing the fast timing technique, half-lives for the $2_1^{+}$ level in both nuclei have been determined, resulting in $T_{1/2}=1.51\left(1\right)$ ns for ${}^{148}\mathrm{Ba}$ and $T_{1/2}=3.4\left(2\right)$ ns for ${}^{150}\mathrm{Ba}$. The systematics of low-spin states, together with the experimental determination of the $B(E2:2^{+}\to 0^{+})$ transition probabilities, indicate an increasing collectivity in ${}^{148\text{–}150}\mathrm{Ba}$, towards prolate deformed shapes. The experimental data are compared to symmetry conserving configuration mixing (SCCM) calculations, confirming an evolution of increasingly quadrupole deformed shapes with a definite octupolar character.

Figure 1

${}^{148}\mathrm{Cs}\to {}^{148}\mathrm{Ba}\beta$-gated $\gamma$ spectrum recorded in the first 500 ms relative to a proton pulse. The main transitions populated through $\beta$ decay in ${}^{148}\mathrm{Ba}$ are labeled. Newly found transitions are indicated in bold. Contributions by the $\beta \text{−}n$ channel and granddaughter decay are indicated.

Figure 2

Time distribution relative to the proton pulse of the 109.8-and 141.6-keV transitions from ${}^{147}\mathrm{Ba}$ and ${}^{148}\mathrm{Ba}$, respectively. After renormalizing the 141.6-keV time distribution (factor 0.0286), the overlap of the two distributions is in very good agreement with the assumption that levels in ${}^{147}\mathrm{Ba}$ are only fed through the $\beta \text{−}n$ decay of ${}^{148}\mathrm{Cs}$ ($T_{1/2}=152\left(1\right)$ ms) rather than the $\beta$ decay of ${}^{147}\mathrm{Cs}$ ($T_{1/2}=230\left(1\right)\mathrm{ms}$).

Figure 3

Spectra extracted from $\gamma \text{−}\gamma$ matrices in coincidence with the 141.6-, 281.3-, and 633.1-keV $\gamma$ rays from ${}^{148}\mathrm{Ba}$ populated in the $\beta$ decay of ${}^{148}\mathrm{Cs}$ (top to bottom). Coincident transitions are indicated by their energy.

Figure 4

Extended level scheme for the decay ${}^{148}\mathrm{Cs}\to {}^{148}\mathrm{Ba}$ extracted from $\gamma \gamma$ coincidences. The $I_{\beta }$ and $\log ft$ are calculated from intensity balance as discussed in the text. For absolute intensity per 100 $\beta$ decays, multiply the $\gamma$ intensities by 0.30(4).

Figure 5

(a) ${}^{150}\mathrm{Cs}$ decay spectrum acquired within 200 ms from the proton pulse impinging on the UCx target. Long-lived activity (b) has been subtracted. Lines belonging to daughter decay are marked by their energy, while asterisks indicate lines coming from the $\beta$-delayed neutron emission channel (i.e. ${}^{149}\mathrm{Ba}$) and its subsequent decay (marked by the dollar symbol). Panels (c), (d), (e) and (f) show spectra in coincidence with transitions at 101.1, 217.1, 597.4 and 380.2 keV, respectively. The presence of peaks arising from Compton scattering of the 511-keV $\gamma$ rays is indicated by “&” symbol.

Figure 6

Proposed scheme for the decay ${}^{150}\mathrm{Cs}\to {}^{150}\mathrm{Ba}$ extracted from $\beta \gamma \gamma$ coincidences. The $Q_{\beta }$ value is taken from systematics [24], while the $I_{\beta }$ and $\log ft$ are calculated from intensity balance as discussed in the text. For absolute intensity per 100 $\beta$ decays, multiply the $\gamma$ intensities by 0.12(4). The indicated $P_n$ value is taken from [27].

Figure 7

Comparison between observed low-lying states and corresponding decaying transitions in ${}^{146,148,150}\mathrm{Ba}$. Transitions reported in this work for the first time and newly proposed $J^{\pi }$ assignments are highlighted in red italics. Levels and transitions of ${}^{146}\mathrm{Ba}$ are taken from Ref. [14].

Figure 8

(a) Two-dimensional projection on the energy plane of a $\gamma \gamma \mathrm{TAC}$ coincidence matrix built for ${}^{148}\mathrm{Ba}$. The black circular regions indicate the location of the bidimensional gates applied to extract the spectrum in panel (c) and the dotted shapes represent the background region which was subtracted. The time response obtained for the $2^{+}\to 0^{+}$ transition in ${}^{148}\mathrm{Ba}$ is shown, together with the convolution fit in panel (c). Panel (b) shows the $\beta$-TAC spectrum constructed for ${}^{150}\mathrm{Ba}$, while its projection is shown in panel (d). More details are presented in the text.

Figure 9

(a)–(e) Potential energy surfaces in the $({\beta }_2,{\beta }_3)$ plane for the Ba isotopic chain for $N=86\text{–}94$. Deformed minima, both prolate and oblate, are seen in all the isotopes, evolving towards larger deformations in the heaviest members of the chain. The energy is symmetric about the ${\beta }_3$ axis. See text for details. (f)–(j) Calculated collective wave functions of the ground states ($0^{+}$) are represented for ${\beta }_3\ge 0$. To better visualize the shape of the isotopes, the surface that joins the points with constant spatial density is also shown for each isotope. These densities are computed with the HFB wave functions that correspond to the maximum of each collective wave function (see the arrows). Pear shapes are clearly seen, together with an evolution towards more elongated quadrupole deformations for ${}^{148\text{–}150}\mathrm{Ba}$.

Figure 10

Systematic comparison of experimental (filled symbols) and theoretical (open symbols) energy spectra in the Ba isotopic chain. Positive-parity states are grouped in panel (a) while the negative-parity ones are grouped in panel (b). Levels in ${}^{142\text{–}148}\mathrm{Ba}$ are taken from the literature [9].

Figure 11

Filled symbols show $B(E2:2^{+}\to 0^{+}$) in Ba isotopic chain. They are extracted from the measured lifetimes in the case of ${}^{148\text{–}150}\mathrm{Ba}$ and from Ref. [12, 13, 29] in the lighter isotopes. The experimental data points are compared to results obtained from the calculations, shown with open symbols.