Chiral bands in ${}^{135}\mathrm{Nd}$: The interacting boson-fermion model approach

The chiral interpretation of negative-parity twin bands in the odd-$A$ ${}^{135}\mathrm{Nd}$ nucleus was investigated in the interacting boson-fermion model. The IBFM calculation shows that the dominant role in the formation of the chiral pattern has the exchange interaction, i.e., the antisymmetrization of odd fermions with the fermion structure of the bosons. The structure of the twin bands in ${}^{137}\mathrm{Nd}$ has also been investigated, concluding that it is determined by shape fluctuations and prolate-oblate coexistence rather than by chirality.

Figure 1

(a) Experimental and (b) calculated negative-parity structure in ${}^{135}\mathrm{Nd}$. The $\nu h_{11/2}$ ground-state band is denoted as band G. The pair of twin bands based on $\nu h_{11/2}(\pi h_{11/2}){}^2$ configuration are denoted as band A and band B.

Figure 2

Experimental (EXP) and calculated (THE) $B(E2)$ and $B(M1)$ values for transitions in the yrast band A and side band B in ${}^{135}\mathrm{Nd}$. (a) $B(E2)$ values. (b) $B(M1)$ values for $\Delta I=1$ transitions.

Figure 3

Calculated distributions (a) $\zeta \hspace{0.5em}(J_{\pi }\hspace{0.5em}{j}_{\nu })$, (d) $\psi \hspace{0.5em}(J_{\pi }\hspace{0.5em}R)$, and (g) $\xi \hspace{0.5em}(j_{\nu }\hspace{0.5em}R)$ of the angles between ${\mathbf{J}}_{\mathbf{\pi }}$, ${\mathbf{j}}_{\mathbf{\nu }}$, and $\mathbf{R}$, and (j) the σ distribution for the $39/2_1$ state of the yrast band A in ${}^{135}\mathrm{Nd}$. Panels (b), (e), (h), and (k) present the corresponding distributions for the yrast $\pi h_{11/2}\hspace{0.5em}\nu h_{11/2}$ ${15}_1$ state in ${}^{134}\mathrm{Pr}$. Panels (c), (f), (i), and (l) show the corresponding distributions for the $39/2_1$ state of the yrast band A in ${}^{137}\mathrm{Nd}$.

Figure 4

Calculated distributions (a) $\zeta \hspace{0.5em}(J_{\pi }\hspace{0.5em}{j}_{\nu })$, (d) $\psi \hspace{0.5em}(J_{\pi }\hspace{0.5em}R)$, and (g) $\xi \hspace{0.5em}(j_{\nu }\hspace{0.5em}R)$ of the angles between ${\mathbf{J}}_{\mathbf{\pi }}$, ${\mathbf{j}}_{\mathbf{\nu }}$, and $\mathbf{R}$, and (j) the σ distribution for the $39/2_2$ state of the yrare band B in ${}^{135}\mathrm{Nd}$. Panels (b), (e), (h), and (k) present the corresponding distributions for the yrare $\pi h_{11/2}\hspace{0.5em}\nu h_{11/2}$ ${15}_2$ state in ${}^{134}\mathrm{Pr}$. Panels (c), (f), (i), and (l) show the corresponding distributions for the $39/2_2$ state of the yrare band B in ${}^{137}\mathrm{Nd}$.

Figure 5

IBFM $\beta$ and $\gamma$ distributions in ${}^{135}\mathrm{Nd}$, defined as in Ref. [13], for the (a) $31/2_1$ and (b) $31/2_2$ states; the (c) $37/2_1$ and (d) $37/2_2$ states; and the (e) $43/2_1$ and (f) $43/2_2$ states. The axes in the $\beta \text{−}\gamma$ plane have $\gamma =0^{°}$ and $\gamma ={60}^{°}$, while the middle line in the $\beta \text{−}\gamma$ plane marks $\gamma ={30}^{°}$.

Figure 6

Experimental (EXP) and calculated (THE) $B(E2)$ and $B(M1)$ values in ${}^{135}\mathrm{Nd}$ for intraband transitions in the yrast band A and side band B, and for the interband transitions deexciting states in band B. (a) $B(E2)$ values. (b) $B(M1)$ values for $\Delta I=1$ transitions. The $B(E2)$ values are calculated with $e^{\mathrm{vib}}=1.7$. For the $B(M1)$ values, the fermion gyromagnetic ratios are $g_l^{\pi }=1.1$, $g_s^{\pi }=\hspace{0.5em}{g}_s^{\pi ,\mathrm{free}}=5.586$, $g_l^{\nu }=-0.1$, and $g_s^{\nu }=g_s^{\nu ,\mathrm{free}}=-3.826$. The remaining charges and gyromagnetic ratios are the same as in the parametrization adopted in Fig. 2.

Figure 7

Experimental and IBFM signature $S(I)=[E(I)-E(I-1)]/2I$ vs spin plots for different strengths ${\Lambda }_0^{\nu }$ (in MeV) for the (a) yrast band A and (b) yrare band B in ${}^{135}\mathrm{Nd}$.

Figure 8

Experimental and IBFM signature $S(I)=[E(I)-E(I-1)]/2I$ vs spin plots for the (a) yrast band A and (b) yrare band B in ${}^{137}\mathrm{Nd}$.

Figure 9

IBFM $\beta$ and $\gamma$ distributions in ${}^{137}\mathrm{Nd}$, defined as in Ref. [13], for the (a) $31/2_1$ and (b) $31/2_2$ states; the (c) $37/2_1$ and (d) $37/2_2$ states; and the (e) $43/2_1$ and (f) $43/2_2$ states. The axes in the $\beta \text{−}\gamma$ plane have $\gamma =0^{°}$ and $\gamma ={60}^{°}$, while the middle line in the $\beta \text{−}\gamma$ plane marks $\gamma ={30}^{°}$.

Figure 10

Calculated (THE) $B(E2)$ and $B(M1)$ values for transitions in the yrast band A and side band B in ${}^{137}\mathrm{Nd}$. (a) $B(E2)$ values. (b) $B(M1)$ values for $\Delta I=1$ transitions. For comparison, the experimental (EXP) values in ${}^{139}\mathrm{Sm}$ are also shown.