Characterization of octupole-type structures in ${}^{221}\mathrm{Th}$

A detailed level scheme for ${}^{221}\mathrm{Th}$ has been established in an experiment using the ${}^{18}\mathrm{O}+{}^{207}\mathrm{Pb}$ reaction at 96 MeV. The evaporation residues from this fissile system were selected with the HERCULES detector array and residue-gated $\gamma$ rays were measured with Gammasphere. Three band structures of interlinked, alternating-parity levels are observed, two of which are non-yrast. In addition, several high-lying excitations are found. The yrast band is seen up to spin-parity $37/2^{-}$ and $39/2^{+}$, beyond which a high-spin feeding transition is observed. The non-yrast sequences are interpreted as parity-doublet structures, based on a configuration similar to that of the yrast band in ${}^{223}\mathrm{Th}$ $(K=5/2)$. The key properties of even-odd nuclei in this mass region $\left[B\right(E1)/B(E2)$ and $B\left(M1\right)/B\left(E2\right)$ ratios, spin alignments, parity splittings] are reviewed.

Figure 1

The level scheme for ${}^{221}\mathrm{Th}$ obtained in the ${}^{207}\mathrm{Pb}{(}^{18}\text{O},4n)$ reaction. The level spins and parities are given in the figure. The values given in parentheses are tentative. The widths of the filled and open parts of the arrows are proportional to the $\gamma$-ray and internal conversion intensities, respectively. The energy unit is keV. The labels associated with the various sequences are introduced for the ease of the discussion.

Figure 2

Representative ER-gated $\gamma$-ray coincidence spectra for ${}^{221}\mathrm{Th}$. The gating $\gamma$-ray transitions have the respective energies of (a) 251, (b) 237, and (c) 486 keV. The inset in panel (a) displays a fraction of the spectrum highlighting coincident transitions above 600 keV. The spectrum in panel (c) is contaminated by $\gamma$ rays from ${}^{218}\mathrm{Ra}$, labeled by “c”, and from ${}^{219}\mathrm{Ac}$, given in parentheses.

Figure 3

Similar to Fig. 2, but for gating transitions with the respective energies of (a) 275, (b) 239, and (c) 287 keV. Contaminant $\gamma$ rays are labeled by “c” and are from ${}^{218}\mathrm{Ra}$ in spectra (a) and (c), but from ${}^{222}\mathrm{Th}$ in spectrum (b).

Figure 4

Similar to Fig. 2, but for gating transitions with the respective energies of (a) 225, and both (b) and (c) 531 keV (see text). Contaminant $\gamma$ rays labeled by “c” are from ${}^{219}\mathrm{Ra}$.

Figure 5

Similar to Fig. 2, but for gating transitions with the respective energies of (a) 618, (b) 243, and (c) 714 keV. The spectrum in panel (b) is contaminated by $\gamma$ rays from ${}^{218}\mathrm{Ra}$, labeled by “c”.

Figure 6

Sample ER-gated and $E_{\gamma }\text{−}{E}_{\gamma }$ double-gated spectra. The combinations of the gating transitions are (a) 152–486 keV, (b) 222–243 keV, and (c) 251–735 keV and 251–251 keV for the spectra in the main panel and the inset, respectively. The 423-keV line in spectrum (b) is a ${}^{218}\mathrm{Ra}$ contaminant.

Figure 7

Similar to Fig. 2, but for gating transitions with the respective energies of (a) 695, (b) 246, and (c) 735 keV. The contaminants in spectrum (b), labeled by “c”, are attributed in part to ${}^{218}\mathrm{Ra}$. The inset in this panel highlights the coincident 695-keV transition.

Figure 8

Similar to Fig. 2, but for gating transitions with the respective energies of (a) 879 and (b) 849 keV.

Figure 9

Representative $\gamma$-ray angular distributions for yrast transitions in ${}^{221}\mathrm{Th}$. Panels (a)–(c) are for the 235-, 509-, and 287-keV transitions, respectively. Some of the error bars are within the size of the symbols. The $A_k$ $(k=2,4)$ coefficients, obtained from Legendre-polynomial fits and normalized to $A_0$, are given in Table 1.

Figure 10

Similar to Fig. 9, but for transitions in the sequences “b1” and “b2” (see text). The transitions have the respective energies of (a) 486, (b) 152, and (c) 618 keV.

Figure 11

Similar to Fig. 9, but for transitions in the sequences “c1” and “c2” (see text). The transitions have the respective energies of (a) 246, (b) 735, and (c) 743 keV.

Figure 12

Decay intensity versus spin for the states of the octupole-band structures in ${}^{221}\mathrm{Th}$. The yrast band, and the structures “b1”, “b2”, and “c1”, “c2” are represented by circles, diamonds, and squares, respectively. The states are further distinguished by open and filled symbols for positive and negative parity, respectively. Some of the error bars are within the size of the symbols. The inset provides the intensity of the yrast band at the highest spins.

Figure 13

(a) $B\left(E1\right)/B\left(E2\right)$ ratios versus initial spin for yrast transitions in ${}^{221}\mathrm{Th}$. The states are further distinguished by open and filled symbols for positive and negative parity, respectively. The horizontal bar represents the range of the error associated with the weighted average of all ratios. (b) Same, but for the non-yrast transitions. This data set represents essentially transitions in structure “b1”, “b2” (diamonds). (c) Combined plot for transitions in ${}^{219}\mathrm{Ra}$, based on Ref. [15], for comparisons used in the discussion.

Figure 14

$B\left(M1\right)/B\left(E2\right)$ ratios versus initial spin for transitions from the $19/2^{-}$ and $23/2^{-}$ states in ${}^{221}\mathrm{Th}$ (diamonds) and for certain levels in ${}^{223}\mathrm{Th}$ (circles) [12] and ${}^{219}\mathrm{Ra}$ (single dotted line) [15]. The bands joining the groups of ${}^{221}\mathrm{Th}$ and ${}^{223}\mathrm{Th}$ data points represent the weighted averages of these ratios and their errors. For ${}^{219}\mathrm{Ra}$, only an upper limit (abbreviated u.l.) is available. The spin range has been truncated at the upper end (cf. Table 4).

Figure 15

Relative energies $E_{\mathrm{rel}}=E(s=+i)-E(s=-i)$ for the odd-mass ${}^{219–225}\mathrm{Th}$ nuclei [(a)–(c)] and their respective ${}^{219,221}\mathrm{Ra}$ isotones [(d) and (e)]. The ${}^{221}\mathrm{Th}$ panel (b) shows $E_{\mathrm{rel}}$ vs spin for both the two non-yrast bands (triangles) and the corresponding set of non-yrast and yrast band (line). The ${}^{223}\mathrm{Th}$ panel (c) contains also the $E_{\mathrm{rel}}$ function for ${}^{225}\mathrm{Th}$, shown as a dotted line. Only the ground-state bands in ${}^{221}\mathrm{Th}$ and ${}^{219}\mathrm{Ra}$ are $K=1/2$ structures. Note that ${}^{217}\mathrm{Ra}$ has no multiple octupole-type structures, while the ${}^{223}\mathrm{Ra}$ level scheme is inconclusive in this respect.

Figure 16

Spin vs $\hslash \omega$ for the yrast sequences in ${}^{221}\mathrm{Th}$ and ${}^{219}\mathrm{Ra}$ [(a) and (b)] and some neighboring odd-mass isotopes, ${}^{223}\mathrm{Th}$ and ${}^{221}\mathrm{Ra}$ [(c) and (d)]. The positive- and negative-parity states of a simplex-partner band are represented by open and full symbols, respectively. The high-spin extension of the positive-parity states in ${}^{221}\mathrm{Th}$ is represented by a cross. The yrast structure of ${}^{223}\mathrm{Th}$ and ${}^{221}\mathrm{Ra}$ consists of two degenerate sequences with $s=-i$ and $s=+i$. The display of the latter is offset by $2\hslash$ for clarity. A sequence of the corresponding “reference” even-mass isotope (see text) is shown as a thick line in each case.

Figure 17

Spin vs $\hslash \omega$ for the yrast sequences in the neighboring ${}^{220,222,224}\mathrm{Th}$ (top) and ${}^{218,220,222}\mathrm{Ra}$ nuclei (bottom). The positive- and negative-parity states of a simplex-partner band are represented by open and full symbols, respectively. The data for ${}^{218}\mathrm{Ra}$ and ${}^{220}\mathrm{Ra}$ are truncated above spin 25.

Figure 18

Similar to Fig. 16, but for the non-yrast sequences in ${}^{221}\mathrm{Th}$ (a) and ${}^{219}\mathrm{Ra}$ (b) and the yrast ${\left(g_{9/2}\right)}^3$ sequence in ${}^{219}\mathrm{Th}$ (c). The two sequences in ${}^{221}\mathrm{Th}$ are presented separately in the main panel $(s=+i)$ and the inset $(s=-i)$ for clarity. The “reference” even-mass isotope is different from Fig. 16 (see text).

Figure 19

Parity splitting, $\delta E$, as a function of the spin for the yrast sequences in ${}^{220,222,224}\mathrm{Th}$ (top) and ${}^{218,220,222}\mathrm{Ra}$ (bottom).

Figure 20

Parity splitting as a function of the spin above the ground state, $(I-I_0)$, for ${}^{221}\mathrm{Th}$ (a), ${}^{219}\mathrm{Ra}$ (b), ${}^{223}\mathrm{Th}$ (c), and ${}^{221}\mathrm{Ra}$ (d). The yrast structures are labeled by “y”. The $\delta E$ function for ${}^{225}\mathrm{Th}$ is included in panel (c) and only the $s=-i$ structure is shown (dotted line) as it is representative of both simplex sequences of the yrast structure.