Microscopic study of odd-A nuclei

The odd-proton nucleus¹⁵⁵Tb and odd-neutron nucleus¹⁵⁵Dy are studied along with doubly-even nucleus¹⁵⁶Dy using microscopic method of variation after projection of angular momentum and conservation of nucleon number in each projected state. The calculated energies of the ground band in¹⁵⁶Dy and the ground and excited bands in¹⁵⁵Dy and¹⁵⁵Tb are in good agreement with the corresponding experimental data. The role played by thei _13/2 neutron pair in these nuclei is discussed.     

Variation of interband interaction strength in odd-A nuclei

Bandcrossing in 31 rotational bands of 25 different odd-A nuclei in the rare-earth region has been analysed by using a two-band mixing formalism with a constant band interaction within the framework of the effective decoupling picture. The interband interaction strengthV between the one-quasiparticle band and the three-quasiparticle band exhibits a variation with the neutron number which is not different from the oscillatory behaviour observed in even-even nuclei and does not show signs of any appreciable phase shifting as predicted by theory. However, the overall range of variation ofV is greater than that observed in even-even systems.     

Study of weakly-bound odd-A nuclei with quasiparticle blocking

The coordinate-space Hartree-Fock-Bogoliubov(HFB) approach with quasiparticle blocking has been applied to study the odd-A weakly bound nuclei ~(17,19)B and ~(37)Mg,in which halo structures have been reported in experiments.The Skyrme nuclear forces SLy4 and UNEDF1 have been adopted in our calculations.The results with and without blocking have been compared to demonstrate the emergence of deformed halo structures due to blocking effects.In our calculations,~(19)B and ~(37)Mg have remarkable features of deformed halos.     

Coupled-cluster and configuration-interaction calculations for odd-A heavy nuclei

We compare coupled-cluster (CC) and configuration-interaction (CI) results for 55Ni and 57Ni obtained in the pf-shell basis, focusing on the practical equation-of-motion (EOM) CC approximations that can be applied to systems with dozens of correlated fermions. The weight of the reference state and the strength of correlation effects are controlled by the gap between the f7/2 orbit and the f5/2, p3/2, p1/2 orbits. Independent of the gap, the CC methods with up to 2p-2h components in the cluster operator and 3p-2h/3h-2p components in the EOMCC excitation operator are more accurate than the computationally more demanding CI approach with up to 3p-3h excitations and almost as accurate as the even more demanding CI approach truncated at 4p-4h excitations.     

Algebraic realization of the quantum rotor — odd-A nuclei

An algebraic realization of the quantum rotor for non-zero spin values (integer as well as half-integer) is established by constructing a model Hamiltonian out of rotationally invariant functions of the generators ofSU(3). The eigenvalues of this Hamiltonian in the leading normal-SU(3) symmetry for²⁵Mg and the so-called leading pseudo-SU(3) symmetries for¹⁵⁹Dy and¹⁶⁵Er are compared with the corresponding rotor results. For spinfree systems the internal symmetry group of the rotor and itsSU(3) realization are known to be D₂, the Vierergruppe. This symmetry extends to integral spin values, while for half-integer spins the rotor and itsSU (3) realization are shown to display an internal quaternion group symmetry. The theory points to a microscopic (many-particle shell-model) picture of nuclear rotational motion with spin degrees of freedom taken fully into account. An algebraic realization of the many-particle Nilsson model for odd-A nuclei, with the orbit-orbit and spin-orbit terms included, is given and applied to²³Na.     

Rotational motion of triaxial shape in unfavoured-signature states of odd-A nuclei

In the region of the angular momentum where the intrinsic energy (namely, the odd-quasiparticle energy) plays a more important role than the collective rotational energy, we point out that the way of rotation in unfavoured-signature states of odd-A nuclei, which is clearly different from that in the usual cranking approximation, can be realized for triaxial intrinsic shape and leads to a peculiar signature dependence of B(E2;I→I - 1) values.     

An investigation of the odd-A rare-earth nuclei using rotational models

Using recently compiled data for band-head energies of 53 odd-A rare-earth nuclei, rotational models for strongly deformed nuclei have been used to determine the variation of deformations, spin-orbit parameter κ and the l² parameter, μ, in these nuclei. The deformation is found to be consistent with experimental deformations within 20 %. The spin-orbit parameter, κ, is found to vary from 0.037 up to 0.070, a 25 % variation from Nilsson's 0.050. The l² parameter μ is found to vary from 0.30 up to 0.71, a 30 % variation from Nilsson's 0.45. The trends observed in the values of spin-orbit strength C indicate a correlation with deformation, δ. Simultaneous shifts of the l² strength D for neutron numbers 95–97 and 101–103 may be interpreted as a sudden shift in the squareness of the potential well possibly caused by shell filling. Inclusion of hexadecapole deformation greatly improves the band-head energies for the mass region 150 ≦ A ≦ 165.     

Systematid study on the Even-Even nuclei and odd-A nuclei calculating error with Relativistic Mean-Field Theory

The ground state properties of the four isotope chains, ²⁸Ni,⁵⁴Xe,⁷⁸Pt,⁹⁴Pu are studied in the relativistic mean-field theory by using two sets of parameters, NL-3 and NL-Z. We find that the binding energies of odd-A nuclei are even closer to the corresponding experimental results, compared with those of the even-even nuclei. Our results indicate that it is reliable to neglect the space component of the vector meson fields in calculating binding energies of odd-A nuclei in the relativistic mean-field theory.     

Deformation properties of the neutron-deficient odd-A Pt and Hg nuclei

Nuclear and atomic spectroscopy measurements have provided a great number of data on the neutron-deficient Pt and Hg nuclei. The odd-A Pt and Hg with A<186 have a prolate shape, and the even-even isotopes have a triaxial shape, while the nuclear shape of the odd-A Pt and Hg with A>186 is still an open question. The energy of the low-lying levels and the nuclear moments have been calculated in the framework of a semimicroscopic “axial-rotor + 1 quasiparticle” coupling model. The predictions are compared with the experimental data and discussed. The results strongly suggest a prolate shape for the negative-parity low-lying states of the odd-A ^187–191Pt and ^187–193Hg isotopes.     

Coriolis coupling and electromagnetic properties of rotational bands in odd-A Yb nuclei

Influence of a Coriolis coupling on the properties of¹⁷³Yb has been studied using the quasi-particle-phonon model of Soloviev. The energy and structure of the rotational levels, reduced E 2 and M 1 transition probabilities and E 2/M 1 multipole mixing ratios have been calculated. A comparison between theory and experiment is on the whole successful.     

Collective properties of A = 117−127 odd-A I nuclei

Systematic ΔJ = 2 bands have been observed on the $\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ quasi-proton states in A = 117?127 odd-I nuclei. The ΔJ = 2 energy spacings decrease (relative to the Te cores) as A decreases for the $\text{h}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ band but not for the others. Also ΔJ = 1 bands on unsually low-lying $\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton-hole states exist.     

Influence of the pairing parameter rotation dependence on signature splitting in odd-A nuclei

The influence of the rotation dependence of the pairing correlations on the signature splitting is analysed in terms of the core quasiparticle coupling model. The quenching of the pairing parameter with increasing the rotational angular momentum, and the different rotational structures of the favoured and unfavoured states cause a rising of the signature splitting. An additional growth of the signature splitting results from the different particle-hole structures of the favoured and unfavoured states and from the fact that theA?1 andA+1 cores, to which the quasiparticle is coupled in the odd-A nucleus, have different moments of inertia. The calculated results are in agreement with experiment.     

The collective bands of positive parity states in odd-A (fp) shell nuclei

The low-lying collective bands of positive parity states in (fp) shell nuclei are described in the deformed Hartree-Fock method by projecting states of definite angular momenta from ‘the lowest energy intrinsic states in (sd)⁻¹ (fp) ⁿ⁺¹ configurations. The modified Kuo-Brown effective interaction for (fp) shell and modified surface delta interaction (MSDI) for a hole in (sd) shell with a particle in (fp) shell have been used. The collective bands of states are in general well reproduced by the effective interactions. The excitation energies of the band head states are however off by about one MeV. The calculated magnetic moments of the band headj=3/2⁺ states are in reasonable agreement with experiment. Using effective chargese _p=1.33e ande _n=0.64e we get fairly good agreement forE(2) transitions. The hinderedM(1) transition strengths are reproduced to the correct order however they are slightly higher compared to experiment.     

Collective model description of transitional odd-A nuclei: (I). The triaxial-rotor-plus-particle model

The energy spectrum of an odd nucléon coupled to a triaxial rotating core has been calculated as a function of the deformation β, the asymmetry γ and the Fermi energy λ_f. Results are presented in a series of plots with the odd nucleon restricted to a single j-shell and the parameters covering the area which is of most interest for transitional odd-A nuclei in the A = 135 and the A = 190 mass regions. The results apply to unique-parity spectra which are based either on particle or hole states in a. $\text{j =}\text{11}\text{2}$ shell, but hold also for $\text{j =}\text{9}\text{2}\text{and}\text{j =}\text{13}\text{2}$. In addition, results on moments and transition probabilities are given. The quasiparticle-rotor Hamiltonian is derived with special emphasis on the particle-hole symmetry. The analytic solution for the even triaxial rotor at γ = 30° is given. Concerning the odd-A spectrum, characteristics which can be tested experimentally are discussed, and a qualitative physical interpretation is given. In particular, band structures in the triaxial region and their approximate classification are pointed out.     

A DWBA formalism for knockout-exchange reactions of composite nuclei

A DWBA formulation of the knockout-exchange scattering of composite projectiles having zero internal orbital angular momentum is presented. The model problem assumes a target nucleus heavy enough to allow the neglect of its recoil. The formalism accommodates any form of nucleon-nucleon potential containing central, tensor and spin-orbit terms which are treated on the same footing, with no multipole expansions. The nonlocal radial integrals assume transition nucleon exchange density matrices characteristic of finite potential well shell-model target and cluster model projectile wave functions. The usefulness of the formalism is demonstrated with a PWBA numerical application to the ²⁶Mg(⁶Li, ⁶He)²⁶Al reaction.     

New coupling scheme in the interacting boson-fermion model: O(6) spectra in odd-A nuclei

We suggest that a new coupling scheme, based on the O(6) boson symmetry, may be useful in describing the spectra of odd-A nuclei towards the end of major shells. We describe the main properties of this scheme and show one example of it.     

The structure of the odd-A nuclei withA≈130 and the problem ofγ-softness

The negative parity states in the^{123, 125, 131}Cs and the¹³¹La nuclei are described in the framework of the particle-core coupling model. In order to study the problem of gamma softness, the following two core models are used:(1) the rigid triaxial rotor model, and(2) theγ-unstable model withγ-dependent inertial functions. The properties of the odd-A nuclei with rigid and soft cores are compared with the experimental data. The results do not allow to draw a definite conclusion about the softness. When seeking properties which could help to distinguish between soft and rigid nuclei it has been found that some spectroscopic factors for the proton stripping reaction are sensitive to the gamma softness.