Low-lying $E1,M1$, and $E2$ strength distributions in ${}^{124,126,128,129,130,131,132,134,136}\mathrm{Xe}$: Systematic photon scattering experiments in the mass region of a nuclear shape or phase transition

Systematic nuclear resonance fluorescence (NRF) experiments on all nine stable (seven even-even and two odd-mass) Xe isotopes have been performed at the bremsstrahlung facility of the 4.3-MV Stuttgart Dynamitron accelerator. For the first time thin-walled, high-pressure gas targets (about 70 bar) with highly enriched target material were used in NRF experiments. Precise excitation energies, transition strengths, spins, and decay branching ratios were obtained for numerous states, most of them previously unknown. The systematics of the observed $E1$ two-phonon excitations ($2^{+}\otimes 3^{-}$) and $M1$ excitations to $1^{+}$ mixed-symmetry states in the even-even isotopes are discussed with respect to the new critical point symmetry E(5). The fragmentation of these fundamental dipole excitation modes in the odd-mass isotopes ${}^{129,131}\mathrm{Xe}$ is shown and discussed. In the even-even nuclei several low-lying $E2$ excitations were observed.

Figure 1

Ratio $R$ of the excitation energies $E(4_1^{+})$ and $E(2_1^{+})$ of the first excited $4^{+}$ and $2^{+}$ states in the even-even Xe, Ba, Nd, and Sm isotopes as a function of the neutron number $N$. The data points of the investigated stable Xe isotopes are emphasized by full symbols.

Figure 2

Systematics of ($\gamma ,{\gamma }^{\text{'}}$) spectra observed for all stable even-even ${}^{124-136}\mathrm{Xe}$ isotopes investigated in Stuttgart NRF experiments using a bremsstrahlung end-point energy of 4.1 MeV. Shown is the energy region where the $E1$ two-phonon excitations and $1^{+}$ mixed-symmetry states are expected. Peaks attributed to these excitations are marked by $1^{-}$ and $1^{+}$. Peaks labeled by ${}^{27}\mathrm{Al}$, ${}^{48}\mathrm{Ti}$, or Bg belong to transitions in the aluminum photon flux calibration standard or in the titanium target container material or are background lines from the environmental radioactivity, respectively. In the energy range 3200–4000 keV the ordinate scale is enlarged by a factor of 10.

Figure 3

Results of the angular distribution measurements in the reaction ${}^{124}\mathrm{Xe}$ ($\gamma ,{\gamma }^{\text{'}}$). Plotted are the intensity ratios $W({90}^{°})/W({127}^{°})$ for the observed ground-state transitions. The dotted and dashed lines show the expected values for dipole and quadrupole transitions (spin sequences 0–1–0 and 0–2–0, respectively). The open diamonds show the ratios for the nearly isotropic transitions in ${}^{27}\mathrm{Al}$, normalized to unity for the 2982-keV transition in ${}^{27}\mathrm{Al}$.

Figure 4

Systematics of dipole strength distributions in all stable even-even Xe isotopes ${}^{124-136}\mathrm{Xe}$ observed in the present NRF experiments. Plotted are the reduced ground-state transition widths ${\Gamma }_0^{\mathrm{red}}$ as a function of the excitation energy. Candidates for the $E1$ two-phonon excitations are marked by open diamonds and those for $M1$ excitations to the $1^{+}$ mixed-symmetry states by full circles. For further explanations see text.

Figure 5

($\gamma ,{\gamma }^{\text{'}}$) spectra observed for stable odd-mass isotopes ${}^{129,131}\mathrm{Xe}$ in comparison with those of their even-even neighbor isotopes. For further explanations see caption of Fig. 2.

Figure 6

Systematics of dipole strength distributions in the odd-mass isotopes ${}^{129,131}\mathrm{Xe}$ in comparison with those in their even-even neighbor isotopes. For further explanations see caption of Fig. 4.

Figure 7

Systematics of $E1$ two-phonon excitations in the even-even Xe isotopes. Upper part: Energies of the $2_1^{+}$ (open triangles) and $3_1^{-}$ (open squares) one-phonon excitations and of the observed $1^{-}$ two-phonon excitations (full circles) in ${}^{124-136}\mathrm{Xe}$ compared to the expected sum energies $\Sigma =E_{2^{+}}+E_{3^{-}}$ (open diamonds). Lower part: Experimental $B(E1)\uparrow$ values for the two-phonon excitations (full symbols). Error bars are smaller than the symbol sizes if not explicitly depicted.

Figure 8

Reduced transition probabilities $B(E1,1^{-}\to 0^{+})=\frac{1}{3}B(E1,0^{+}\to 1^{-})$ for $E1$ ground-state transitions of the two-phonon $1^{-}$ states in spherical nuclei near the $N=82$ shell closure, marked by the bold line. Data are from the recent compilation of Ref. 28, supplemented by the present new Xe data (shown on the gray line).

Figure 9

Systematics of the candidates for $M1$ excitations to mixed-symmetry $1^{+}$ states in the even-even Xe isotopes as a function of the mass number $A$. Upper part: Excitation energies. Lower part: $B(M1)\uparrow$ excitation strengths. The dotted line gives the strengths predicted by IBM-2 in the O(6) limit. The gray areas in the bars for ${}^{124,126}\mathrm{Xe}$ represent the summed strengths of the fragments of the $M1$ excitations. For further explanations see text.

Figure 10

Decay branchings of the candidates for mixed-symmetry $1^{+}$ states in the even-even Xe isotopes as a function of the mass number $A$ (see text). Upper part: Decay branching $R_{\exp .,1}$ for the decay to the first excited $2^{+}$ state. Lower part: Decay branching $R_{\exp .,2}$ for the decay to the second excited $2^{+}$ state. The full and dotted lines give the values as predicted by IBM-2 in the O(6) limit. The error bars of the data are smaller than the symbol sizes.

Figure 11

Summed $B(M1)\uparrow$ strengths observed in the even-even Xe isotopes as a function of the squared deformation parameter ${\beta }_2$. The dashed line represents a fit of a linear function to the data and serves to guide the eyes.

Figure 12

Upper part: Summed $B(M1)\uparrow$ strengths observed in the even-even Xe isotopes as a function of the mass number $A$. The full line represents a fit of a step function to the data (see text). The dotted line shows the values predicted by the IBM-2 model in the O(6) limit. Lower part: The first derivatives of both curves.