Summary

The investigation of magnetic rotation and of chiral bands, both predicted by Tilted Axis Cranking (TAC) model calculations, are presently two of the most relevant subjects of nuclear structure research. The first is related to the breaking of rotational symmetry by the current distribution in nearly spherical nuclei, while the second is related to the breaking of the left-right symmetry in the intrinsic system of triaxial nuclei. The TAC model (created by S. Frauendorf) is a generalization of the Cranking model for a rotational axis tilted with respect to the principal axes of the moment of inertia of a deformed nucleus. It is particularly suited for the description of high-K (the projection of the total angular momentum on the longest deformation axis) bands, which are characterized by magnetic dipole transitions and negligible or absent signature splitting.

Magnetic rotation is characterized by the existence of rotational-like bands in nearly spherical nuclei, also known as shears bands, and has already been observed and studied in various regions of the nuclide chart. On the other hand, in a few regions of triaxially deformed nuclei, valence particles and holes and collective angular momenta tend to align at high spin along the three perpendicular axes of the deformed core, breaking chiral symmetry. Chiral bands appear experimentally as a pair of nearly degenerate M1 bands, and have only been reportedly observed in the $A\approx130$ region. They are also predicted for the triaxial nuclei around$^{106}$Ru, where the active high-j orbits are $h_{11/2}$ for neutrons and $g_{9/2}$ holes for protons. However, the production of these neutron-rich nuclei is difficult or impossible by standard fusion-evaporation reactions with stable isotopes. Several magnetic dipole bands have already been observed in the $A\approx\textrm{100}$ mass region, particularly in the neutron deficient side, more easily accessible. Some of these bands, in weakly deformed nuclei, have been interpreted as magnetic rotation. The region is transitional and therefore rich in variety of nuclear deformations.

We propose to study the high-spin nuclear states of $^{104,106}$Rh, $^{103,104}$Ru, e $^{106}$Pd, among others, by in-beam gamma-ray spectroscopy of heavy-ion reactions at the Pelletron accelerator of the Laboratório Aberto de Física Nuclear (LAFN), IFUSP-DFN. We expect to find magnetic dipole bands, which are experimental probes of the TAC model predictions, including the existence of chiral bands. For this purpose, we propose to use the Saci-Perere spectrometer, which has recently produced new results for the $^{105}$Rh and $^{108}$Pd nuclei.

The nucleus of $^{105}$Rh has been recently studied by $\gamma-\gamma-$charged-particle coincidences of the $^{100}$Mo($^{11}$B,$\alpha$2n) reaction at 43 MeV, with the Saci-Perere spectrometer, which consists of 4 Compton-suppressed high-resolution $\gamma-$ray germanium detectors, and an ancillary system of 11 plastic phoswich telescopes with nearly 4$\pi$ total detection solid angle. Four M1 bands were observed at high-spin, including a pair of nearly degenerate bands, the first candidates for chiral bands in an odd nucleus, probably of $\pi g_{9/2}^{-1}\otimes\nu(h_{11/2}g_{7/2})$ configuration. Specific TAC calculations for this nucleus are being performed. We propose to measure the neighboring nuclei, essentially with the same techiques, equipment and analysis methods. The main production reactions are: $^{100}$Mo($^{9}$Be,3n); $^{100}$Mo($^{9}$Be,$\alpha$2n); $^{100}$Mo($^{9}$Be,p2n); $^{100}$Mo($^{7}$Li,3n); e $^{100}$Mo($^{7}$Li,p2n), for the study of $^{106}$Pd; $^{103}$Ru; $^{106}$Rh; $^{104}$Rh; e $^{104}$Ru, respectively, at high spin. The heaviest Mo isotope will be used as a target for the production of these near stability-line nuclei. The contribution of incomplete fusion reactions appears to be important for the secondary channels, increasing the production intensities. The expected cross sections should be sufficient for the proposed measurements, in analogy to the $^{105}$Rh case. The published level schemes for these nuclei are relatively poor at high spins. They have been studied long ago with simpler experimental setups, or recently by means of fusion-fission reactions, which are very difficult to measure even with the most sophisticated spectrometers presently available due to the fragmentation of the cross-sections.

Another region which we propose to measure is near $A=60$, where magnetic rotation is predicted by the TAC model. This work has already been initiated with the study of $^{58}$Co, and $^{61-60}$Ni , produced in the $^{51}$V($^{10}$B,p2n), e$^{51}$V($^{16}$O,$\alpha$p1-2n) reactions, respectively.

The requested funding for the present plan will be used mainly in the improvement of electronic equipment which will increase the detection efficiency and reduce the acquisition dead-time, and decrease the experiment setup time, allowing for better adjustments with increase of the quality and statistics of the data. In addition, it helps to preserve the experience and knowledge already acquired by the research group, and initiates the upgrade for the coupling of the system to other equipment, which can be used as ancillary systems to the spectrometer, and the new accelerator facility which are being built in the laboratory.