Investigation Of Chiral Bands In ¹³⁰Cs

Chiral symmetry exists commonly in nature. Since the chiral symmetry broken in triaxial-deformed nuclei has been predicted by Frauendorf and Meng in 1997, nuclear chiral structure has attracted significant interest of both theoretical and experimental studies. More than 20 candidate chiral bands with the same parity and degenerate energy have been reported in odd-odd, odd-A, and even-even nuclei of the A~100,130,190 mass regions in experiments. The cores in these nuclei are soft toγ-deformation;, the proton (or neutron) Fermi surface lies in the high-j low-Ωorbital (particle-like), and the neutron (or proton) Fermi surface is located in the middle or upper of high-j subshell (hole-like). These nuclei are suggested to have stable triaxial deformation due to the different deformation-driving effects of the hole-like and particle-like valence nucleons. In the triaixal-deformed nuclei, the core's collective angular momentum will favour alignment with the intermediate"i-axis", which has the largest moment of inertia. The particle-like nucleon tends to align their angular momentum along the short"s-axis", and the hole-like nucleon tends to align their angular momentum along the long"l-axis". The total angular momentum will be aplanar, i.e. tilting away from any principal axes and from a plane defined by any two of three principal axes. The system formed by the three mutually perpendicular angular momenta contains left-handed and right-handed geometrical configurations. In the intrinsic body-fixed frame, chiral symmetry is broken. In the laboratory frame, the restoration of the chiral symmetry results in two bands which are of the same parity and almost degenerate in energy.A great number of experimental and theoretical studies have suggested some fingerprints of nuclear chiral bands. These fingerprints are as follows:1. The degenerate bands of the same parity, connected to each other via M1/E2 transitions.2. The bands should show a smooth variation of the energy staggering parameter S(I), defined as S(I)=[E(I)-E(I-1)]/2I.3. The stronger intraband M1 transitions and the weak E2 linking transitions at high spin states.4. The staggering interband B(M1)/B(E2) ratios of the partner bands with spin. In the A~100 mass region, the chiral bands are built on theπh11/2?νh11/2 configuration, the odd spin values are staggered lower compared to even spin values. In the A~130 mass region, the chiral bands are built on theπg9/2?νh11/2 positive parity configuration, the staggering phase is opposite.5. The electromagnetic transition probabilities should be similar in chiral bands. The absolute B(M1) and B(E2) transition probabilities are critical for the identification of the chiral bands.The purpose of this thesis is to extract the absolute B(M1) and B(E2) transition probabilities of the chiral bands in 130Cs by the lifetime measurements using Doppler Shift Attenuation Method (DSAM) to test whether the electromagnetic transition rates fulfill the fingerprint of the ideal chiral geometry. The odd-odd nucleus 130Cs, with 55 protons and 75 neutrons, has two valence nucleons outside theγ-soft 128Xe core. The PES (Potential Energy Surface) calculation shows that the valence proton lies in the h11/2[550]1/2- orbital and the valence neutron lies in the h11/2[514]9/2- orbital. The opposite shape-driving effects of the particle-like proton and the hole-like neutron result in the stable triaxial deformation in 130Cs. The TRS (Total Routhian Surface) calculation also confirms the conclusion, i.e.β=0.18,γ=27°. The high spin states of 130Cs have been investigated by T.Kokie and P.Joshi. The near-degenerateΔI=1 double bands with the same positive parity have been observed.In the present work, the high spin states of 130Cs were populated via the reaction of 124Sn(11B, 5n)130Cs at the beam energy of 65 MeV. The 11B beam was delivered by the HI-13 tandem accelerator at the China Institute of Atomic Energy (CIAE). The target consisted of a 7.06 mg/cm2 thick 124Sn backed on lead of 6.7mg/cm2 thickness in order to slow down and stop the recoiling nuclei. Theγ-γcoincidence events were collected by an array of 14 HPGe detectors with BGO Compton suppression shield. A total of about 220×106 coincidence events were collected. Theγ-γcoincidence events were sorted into several conventional two-dimensional matrices and analyzed using the RADWARE package base on Linux-PC system.From theγ-γcoincidence analysis, the same scheme of 130Cs as before has been reproduced in this experiment. Level lifetimes have been measured using DSAM. The Doppler Broadened peak shapes of the forward and backward angle detectors with respect to the beam axis were obtained. The stopping powers of atoms were calculated to get velocity change information of the beam and recoil nuclei traversing the target and the backing material. Electronic stopping powers were calculated with the LSS-theory and the nuclear stopping powers were used according to Ziegler et al. The velocity profile of recoiling nuclei was simulated by the Monte Carlo procedure. The line shapes ofγ-transitions are analyzed by the DSAMFT code of Gascon. Lifetime analysis was performed starting from the highest energy level. The lifetimes of seven states in yrast band and four states in side band have been determined. The best fittings were obtained on the basis of a minimization of the reducedχ2.The absolute B(M1) and B(E2) transition probabilities have been derived from the measured lifetimes. Comparison with the chiral bands, the experimental B(M1) and B(E2) values are essentially the same from the spin 14+ to 17+ in the experimental uncertainties. With the increasing spin in the chiral bands, the B(E2) values remain constant; the B(M1) values show the character of staggering, and the B(M1) values of transitions depopulating the odd spin levels are larger than that of even spin; the B(M1) values of interband transitions show the opposite odd-even spin staggering phase, and the B(M1) values of even spin are larger than those of odd spin. The main features of the experimental results support the identification of chiral partner bands.For the purpose of the current study, the Particle-Rotor Model (PRM) with one particle and one hole coupled with a triaxial rotor has been developed and used due to its advantages of the good angular momentum number and simple picture. PRM is a quantum mechanical method that describes the system in the laboratory framework and yields directly the energy splitting and tunneling between doublet bands. The excited energy spectra and the transitional probabilities of the chiral bands have been calculated. The results support the chiral bands in 130Cs. At low spins, total angular momentum is mainly contributed by the valence nucleons and remains in the plane spanned by the short and long axes. This situation can be called as weak chiral symmetry broken, and the energy splitting is large. In the spin interval of 12+≤I≤18+, with the increasing of the collective angular momentum, the rotation becomes the chiral rotation, energy of the rotational bands begin degenerate. With the increasing of rotation frequency, the particles alignments along with medium axis, contributions from the valence particle and hole become negligible compared with the total spin, the nuclei rotation becomes the axial rotation. From the comparison of the experimental and the theoretical results, it can be seen that the agreement is excellent for the excited energy at high spin region. The magnitude, staggering, and the changing trend of electromagnetic transition rates are reproduced quite well. The experimental B(M1) odd-even staggering phase is reproduced in the PRM calculation, i.e., the values at odd spins are larger than those of even spins in intraband and the values at odd spins are smaller than those of even spins in the interband.To further confirm the picture of chirality in 130Cs, the orientation of the angular momentum for the rotor as well as the valence proton and neutron are calculated for the yrast band and side band. The effective angles in body frame are also investigated. In a large spin interval of 9+≤I≤18+, the effective angles are larger than 45°. This behavior suggests a remarkable aplanar rotation in this nucleus. With respect to the high-spin states (I≥14+),The effective angles show the odd-even staggering pattern, which indicates quantum tunneling between the left-handed and right-handed system. As the total angular moment I increases, the effective angles gradually decrease and reach a constant. This behavior of the effective angles suggests that the angular momentum align along the same direction at high spin. The probability distributions for the l.i.s axes projections of the total angular momentum have been calculated. The results indicate the partner bands of 130Cs shows clearly the characteristics of static chirality at the higher spin.A systematic comparison of the candidate chiral bands in A～130 mass region has been performed. The near degenerateΔI=1 positive parity bands in odd-odd 122-132Cs isotopes have been studied. The comparisons of the excited energy, signature splitting, B(M1)/B(E2) ratios, and TRS calculations show the partner bands in the 126.128.130Cs fulfill the picture of chiral bands. The absolute electromagnetic transition probabilities of the measured level lifetimes in several candidate chiral bands have been systematic analyzed.The level lifetimes in 129Cs have been measured. The quadrupole moments of three bands have been deduced. The experimental results indicate that the Qt values of the negative parity band are smaller than those of the positive parity bands, probably due to the differentγ-deformation driving effects of different proton orbital. The Qt values exhibit a considerable change near the band crossing region in these bands. This behavior demonstrates that nuclear shape changing results from the neutron or proton alignments.As a conclusion, the level lifetimes of chiral band in 130Cs have been determined using DSAM. The absolute B(M1) and B(E2) transition probabilities were derived. The PRM calculations were performed and the results agree with the experimental results, which indicates the chiral bands of this nucleus in spin interval of 14+≤I≤17+. Systematic comparison and analysis of candidate chiral bands in A～130 mass region has been performed. The level lifetimes in 129Cs have been measured. The nuclear shapes of three bands have been investigated.