Enhanced mixing of intrinsic states in deformed Hf nuclei

Excited low-spin, nonyrast states in ${}^{170,172,174}\mathrm{Hf}$ were populated in ${\beta }^{+}/\epsilon$ decay and studied through off-beam γ-ray spectroscopy. New coincidence data allowed for a substantial revision of the level schemes of ${}^{170,172}\mathrm{Hf}$ and a confirmation of the level scheme of ${}^{174}\mathrm{Hf}$. The Hf isotopes represent a unique situation in which a crossing of collective intrinsic excitations occurs, enhancing significantly the effects of mixing. Using branching ratios from excited $2^{+}$ states, this mixing is followed and studied. The resulting mixing matrix elements are found to be $~30$ keV—an order of magnitude larger than estimated previously for nearby nuclei. In the case of ${}^{170}\mathrm{Hf}$, the $2_{\beta }^{+}$ and $2_{\gamma }^{+}$ level are shown to be completely mixed.

Figure 1

Energy systematics of the $2_{\gamma }^{+}$ and $2_{\beta }^{+}$ levels in the Hf isotopes. The parenthesis for the $2_{\beta }^{+}$ level in ${}^{166}\mathrm{Hf}$ indicates a tentative assignment. Band assignments taken from Refs. [14, 15, 16, 17, 18].

Figure 2

Complete level scheme for ${}^{170}\mathrm{Hf}$ populated in the ${\beta }^{+}/\epsilon$ decay of ${}^{170}\mathrm{Ta}$. Levels are marked with their energy in keV. γ-ray transitions are labeled by their energy in keV and relative intensities (in italics), normalized to the 221-keV, $4_1^{+}\to 2_1^{+}$ transition ($I_{221}\equiv 100$).

Figure 3

(a) Spectrum gated on the 101-keV, $2_1^{+}\to 0_1^{+}$ transition in ${}^{170}\mathrm{Hf}$ illustrating the unobserved coincidences with 887- and 1058-keV transitions. (b) Composite spectrum gated on 437- and 710-keV transitions feeding the level at 988 keV in ${}^{170}\mathrm{Hf}$, showing the 988-, 666-, and unobserved previously reported 887-keV branches from the 988-keV level.

Figure 4

Spectrum gated on the 221-keV, $4_1^{+}\to 2_1^{+}$ transition in ${}^{170}\mathrm{Hf}$ illustrating the observed coincidences with 837- and 906-keV transitions and the unobserved coincidence with a 898-keV transition.

Figure 5

Spectrum gated on the 321-keV, $6_1^{+}\to 4_1^{+}$ transition in ${}^{170}\mathrm{Hf}$ illustrating the observed coincidences with 516- and 585-keV transitions and the unobserved coincidence with a 577-keV transition.

Figure 6

Spectra providing evidence for the new placement of a 1120-keV transition in ${}^{170}\mathrm{Hf}$. (a) Spectrum gated on the 221-keV, $4_1^{+}\to 2_1^{+}$ transition. (b) Spectrum gated on the 1120-keV transition.

Figure 7

Level scheme for ${}^{172}\mathrm{Hf}$ populated in the ${\beta }^{+}/\epsilon$ decay of ${}^{172}\mathrm{Ta}$ for levels below 1500 keV. Levels are marked with their energy in keV. γ-ray transitions are labeled by their energy in keV and relative intensities (in italics), normalized to the 214-keV, $4_1^{+}\to 2_1^{+}$ transition ($I_{214}\equiv 100$).

Figure 8

Spectrum gated on the 319-keV, $6_1^{+}\to 4_1^{+}$ transition in ${}^{172}\mathrm{Hf}$, illustrating observed coincidences with 501-, 676-, and 766-keV transitions and the unobserved coincidence with a 402-keV transition.

Figure 9

Spectrum providing evidence for the new placement of a 722-keV transition in ${}^{172}\mathrm{Hf}$. Spectrum is obtained by gating on the 1187-keV transition in ${}^{172}\mathrm{Hf}$, illustrating strong coincidences with a 722-keV transition.

Figure 10

Spectrum gated on the 427- and 564-keV transitions that populate the level at 1075 keV in ${}^{172}\mathrm{Hf}$. Coincidences are observed with the previously reported depopulating transitions of 980 and 1076 keV, as well a newly observed 766-keV depopulating transition.

Figure 11

Spectra providing evidence for the placement of a newly observed 177-keV transition in ${}^{172}\mathrm{Hf}$. (a) Summed spectrum gated on the 289- and 366-keV transitions that populate the level at 1130 keV. (b) Spectra gated on the 857-keV, $2_2^{+}\to 2_1^{+}$ transition.

Figure 12

Level scheme for ${}^{174}\mathrm{Hf}$ populated in the ${\beta }^{+}/\epsilon$ decay of ${}^{174}\mathrm{Ta}$ for levels below ∼1500 keV. Levels are marked with their energy in keV. γ-ray transitions are labeled by their energy in keV and relative intensities (in italics), normalized to the 206-keV, $4_1^{+}\to 2_1^{+}$ transition ($I_{206}\equiv 1000$).

Figure 13

Spectra providing evidence for the placement of a newly observed 162-keV transition in ${}^{174}\mathrm{Hf}$. (a) Spectrum gated on the 809-keV, $2_2^{+}\to 2_1^{+}$ transition. (b) Spectrum gated on the 441-keV transition that populates the level at 1062 keV.

Figure 14

Spectrum gated on the 1176-keV transition that populates the level at 1227 keV in ${}^{174}\mathrm{Hf}$. Coincidences are observed with the previously reported 1136- and 1227-keV depopulating transitions as well as a newly observed 929-keV depopulating transition.

Figure 15

Branching ratio $B(E2;2_i^{+}\to 0_1^{+})/B(E2;2_i^{+}\to 4_1^{+})$ from excited $2^{+}$ states in the Hf nuclei. The points for $2_2^{+}$ in ${}^{166}\mathrm{Hf}$ and ${}^{168}\mathrm{Hf}$ are lower limits due to the nonobservation of the $2_2^{+}\to 4_1^{+}$ transition (reported with an upper limit on intensity).