Helical modes generate antimagnetic rotational spectra in nuclei

A systematic analysis of the antimagnetic rotation band using $r$-helicity formalism is carried out for the first time. The observed octupole correlation in a nucleus is likely to play a role in establishing the antimagnetic spectrum. Such octupole correlations are explained within the helical orbits. In a rotating field, two identical fermions (generally protons) with paired spins generate these helical orbits in such a way that its positive (i.e., up) spin along the axis of quantization refers to one helicity (right-handedness) while negative (down) spin along the same quantization-axis decides another helicity (left-handedness). Since the helicity remains invariant under rotation, therefore, the quantum state of a fermion is represented by definite angular momentum and helicity. These helicity represented states support a pear-shaped structure of a rotating system having $z$ axis as the symmetry axis. A combined operation of parity, time-reversal, and signature symmetries ensures an absence of one of the signature partner band from the observed antimagnetic spectrum. This formalism has also been tested for the recently observed negative parity $\mathrm{\Delta }I=2$ antimagnetic spectrum in odd-$A$ ${}^{101}\mathrm{Pd}$ nucleus and explains nicely its energy spectrum as well as the $B\left(E2\right)$ values. Further, this formalism is found to be fully consistent with twin-shears mechanism popularly known for such type of rotational bands. It also provides significant clue for extending these experiments in various mass regions spread over the nuclear chart.

Figure 1

The fixed frame of reference $X$, $Y$, $Z$ and the helicity frame $X^{\prime }$, $Y^{\prime }$, $Z^{\prime }$.

Figure 2

Pictorial representation of total angular momentum generated by diprotons in which axis of quantization is chosen along particle 1 together with a frame of reference of particle 2 having Euler angles (${\varphi }_2=0$, ${\theta }_2=2\theta {\psi }_2=0)$.

Figure 3

The calculated rotational energy vs. angular momentum is shown as full line. Also, the solid circles connected with solid line show the observed spectrum of the negative-parity AMR band in the ${}^{101}\mathrm{Pd}$ nucleus.

Figure 4

Variation of shears angle $\theta$ vs. the angular momentum.

Figure 5

The experimental and calculated angular momentum $I$ vs. the rotational frequency $\hslash \omega$ for the ${}^{105,107.109}\mathrm{Cd}$ isotopes.

Figure 6

The experimental and calculated $B\left(E2\right)$ values vs. $\hslash \omega$ for the ${}^{105,109}\mathrm{Cd}$ isotopes.

Figure 7

Left panel shows the observed dynamic moment of inertia ${\Im }^2$ vs. the angular momentum $I$, whereas the right panel shows the variation of angular momentum $I$ vs. the $\gamma$-ray energy $E_{\gamma }$.