Breakdown of vibrational motion in the isotopes ${}^{110\text{−}116}\mathrm{Cd}$

A systematic study is made of the Cd isotopes ${}^{110\text{−}116}\mathrm{Cd}$ by making use of available experimental data and interacting boson model calculations incorporating both normal vibrational levels and intruder excitations. At the two-phonon level, the calculations appear to reproduce the data reasonably well in ${}^{110\text{−}114}\mathrm{Cd}$, whereas they break down completely for the $0^{+}$ states in ${}^{116}\mathrm{Cd}$. At the three-phonon level, systematic deviations occur across the Cd isotopic chain, revealing the breakdown of vibrational motion in low-spin states. Combined with the failure to reproduce ${}^{116}\mathrm{Cd}$ at the two-phonon level, it is possible that the Cd isotopes may not represent vibrational systems and that the essential physics of their motion has been missing.

Figure 1

Levels and relative $B(E2)$ values expected for an harmonic quadrupole vibrator.

Figure 2

Results of IBM-2 calculations (described in the text) for levels below 1.8 MeV in ${}^{110}\mathrm{Cd}$, using the parameter values determined by Délèze et al. [16], compared with experimental results (left). The top panel displays the $(E0)$ transitions labeled by their ${10}^3{\rho }^2(E0)$ values (from Ref. [42]), in the middle panel the transitions are labeled by their $B(M1)$ values in units of ${10}^{-3}{\mu }_N^2$, and in the bottom by their $B(E2)$ values where greater than 1 W.u. (from Refs. [25, 43]).

Figure 3

Results of IBM-2 calculations (described in the text) for levels below 1.5 MeV in ${}^{112}\mathrm{Cd}$, using the parameter values determined by Délèze et al. [16], compared with experimental results (left). The top panel displays the $(E0)$ transitions labeled by their ${10}^3{\rho }^2(E0)$ values (from Ref. [42]), in the middle panel the transitions are labeled by their $B(M1)$ values in units of ${10}^{-3}{\mu }_N^2$, and in the bottom by their $B(E2)$ values where greater than 1 W.u. (from Refs. [9, 44]).

Figure 4

Results of IBM-2 calculations (described in the text) for levels below 1.5 MeV in ${}^{114}\mathrm{Cd}$, using the parameter values determined by Délèze et al. [16], compared with experimental results (left). The top panel displays the $(E0)$ transitions labeled by their ${10}^3{\rho }^2(E0)$ values (from Ref. [42]), in the middle panel the transitions are labeled by their $B(M1)$ values in units of ${10}^{-3}{\mu }_N^2$, and in the bottom by their $B(E2)$ values where greater than 1 W.u. (from Ref. [45]).

Figure 5

Results of IBM-2 calculations (described in the text) for levels below 1.5 MeV in ${}^{116}\mathrm{Cd}$, using the parameter values determined in the present work, compared with experimental results (left). The top panel displays the $(E0)$ transitions labeled by their ${10}^3{\rho }^2(E0)$ values (from Ref. [42]), in the middle panel the transitions are labeled by their $B(M1)$ values in units of ${10}^{-3}{\mu }_N^2$, and in the bottom by their $B(E2)$ values where greater than 1 W.u. (from Refs. [32, 46]).

Figure 6

Systematics of $0^{+},2^{+},3^{+},4^{+},6^{+}$, and $3^{-}$ levels across the Cd isotopes. Data have been taken from Refs. [9, 12, 13, 14, 25, 26, 31, 32, 34, 35, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56].

Figure 7

Spin $0^{+}$ states in the vicinity of the expected three-phonon levels for ${}^{110,112,114,116}\mathrm{Cd}$. Data are from Refs. [9, 15, 16, 17, 25, 26, 28, 31, 32, 33, 43, 44, 45, 46, 51].

Figure 8

Candidate $2^{+}$ states in the vicinity of the expected three-phonon levels for ${}^{110,112,114,116}\mathrm{Cd}$. Data are from Refs. [9, 15, 16, 17, 25, 26, 28, 31, 32, 33, 43, 44, 45, 46, 51, 52].

Figure 9

Candidate $3^{+}$ states in the vicinity of the expected three-phonon levels for ${}^{110,112,114,116}\mathrm{Cd}$. Data are from Refs. [9, 15, 16, 17, 25, 26, 28, 31, 32, 33, 43, 44, 45, 46, 51].

Figure 10

Candidate $4^{+}$ states in the vicinity of the expected three-phonon levels for ${}^{110,112,114,116}\mathrm{Cd}$. Data are from Refs. [9, 15, 16, 17, 25, 26, 28, 31, 32, 33, 43, 44, 45, 46, 51].

Figure 11

Candidate $6^{+}$ states in the vicinity of the expected three-phonon levels for ${}^{110,112,114,116}\mathrm{Cd}$. Data are from Refs. [9, 15, 16, 17, 25, 26, 28, 31, 32, 43, 44, 45, 46, 58].

Figure 12

Experimental $B(E4\downarrow )$ values for ${}^{110,112,114,116}\mathrm{Cd}$. Data are from Refs. [8, 19, 22].

Figure 13

Enhanced $B(M1)$ values observed for $4^{+}\to 4_1^{+}$ transitions in ${}^{110,112,114,116}\mathrm{Cd}$. Data are from Refs. [9, 25, 26, 28, 31, 32, 51].