Rotational bands in the light odd-mass Tl nuclei

The odd-mass nuclei ^191–197Tl have been formed in a variety of (HI, xn) reactions and studied by in-beam spectroscopic techniques. The decay of the high-spin Pb isomers, also formed in (HI, xn) reactions, leading to ^193–197Tl has also been investigated. Evidence is presented for the existence of levels of the previously proposed $\text{9}\text{2}{}^{\mathrm{?}}\text{[505]}$rotational bands in the nuclei. Tentative evidence is given for the existence of oblate rotational bands, based on the $\text{13}\text{2}{}^{\mathrm{+}}\text{[606]}$ state, in ^191–195Tl.     

Solution of Bohr's collective Hamiltonian for transitional odd-mass nuclei

A numerically feasible method, based on the use of deformed phonons, is developed for the diagonalization of the collective quadrupole Hamiltonian for a system with an odd particle coupled to an anharmonic even core. Examples: the transition from prolate to oblate via γ-unstable shapes and furthermore the $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ spectra of the nuclei ¹⁸⁷Ir and ¹⁹⁷Tl.     

Quasi-gamma bands in even-mass Xe AND Ba nuclei

Low-lying excited states of ^124,126Xe and ¹³²Ba have been studied by means of in-beam γ-ray spectroscopy in (p, xny) reactions. Excitation functions, angular distributions and γ-γ coincidence spectra were obtained. The 2₂⁺ , 3⁺, 4₂⁺ and 5⁺ levels were observed at the following excitation energies in keV: 846.4(2₂⁺), 1247.5(3⁺), 1437.3 (4₂⁺), 1836.6(5⁺) in ¹²⁴Xe, 879.7(2₂⁺), 1317.3(3 ⁺), 1488.2(4₂⁺), 1903.1(5 ⁺) in ¹²⁶Xe and 1032.1(2₂⁺), 1511.3(3⁺), 1729.9(4₂⁺) in ¹³²Ba. The 2214.3 and 2561.7 keV levels in ¹²⁶Xe were tentatively assigned as the 6₂⁺ and 7⁺ levels, respectively. These 2₂⁺, 3 ⁺, 4₂⁺, 5⁺, 6₂⁺and 7⁺ levels are interpreted as members of a quasi-γ band. The E2/M1 mixing ratios of the 2₂⁺ → 2₁⁺ transitions in ^124,126Xe and ¹³²Ba were obtained as + 6.3^+5.3_?2.0 + 10.8^7.8_?3.2 and + 8.3^+4.9_?2.2, respectively.     

Decoupled bands in odd-mass mercury isotopes

The schemes of the low-lying high-spin states in mercury isotopes with A = 195, 197, and 199 have been studied by γ-ray spectroscopy following (α, xn) reactions on separated platinum targets. Two bands have been excited in each Hg nucleus, one with positive parity based on the isomeric i$\text{13}\text{2}$. state and one, probably with negative parity, starting at spin $\text{case21}\text{2}$. The positive-parity states are interpreted with the rotation-aligned coupling scheme as decoupled bands; this implies oblate deformation in these three Hg isotopes. The negative-parity states are discussed as a decoupled i$\text{13}\text{2}$ neutron state coupled to the 5^?, 7^?, 9^?,…states, recently discovered in doubly even mercury isotopes.     

Nuclear shapes of the transitional nuclei 186, 188, 190, 192Os

Excitation functions at θ_lab = 130° have been measured for inelastic scattering of 13–24 MeV alpha particles from ^{186,188,190,192}Os. Data have been obtained for 0⁺, 2⁺, 4⁺, 2⁺' states in ^186,188,192Os and for 0⁺, 2⁺ states in ¹⁹⁰Os. Charge and mass quadrupole deformations, β₂^c and β₂^N, were deduced from coupled-channels analysis of the 2⁺ data. No simple model could provide good fits to the 4⁺ data over the entire energy range but the very deep interference minima observed establish the charge and mass hexadecapole moments, β₄^c and β₄^N, to be negative. The energies of the interference minima for the 4⁺ states could be reproduced by coupled-channels calculations only if large differences in β₄^c and β₄^N were allowed. Data for the (J, K)^π = (2, 2)⁺ states are inconsistent with an asymmetric rotational model.     

The droplet model energy of axially asymmetric nuclei

The shape dependent factors of the droplet model energy are evaluated for the special case of an ellipsoid and expressed in terms of four incomplete elliptic integrals. Generalization to other axially asymmetric shapes is considered.     

Magnetic moments of isomeric bandheads in transitional nuclei: 119I and 192Tl

Nuclear g-factors of isomeric bandheads in the transition nuclei ¹¹⁹I and ¹⁹²Tl have been measured to be $\text{g[}{}^{119}\text{I}\text{(}\text{9}\text{2}{}^{\mathrm{+}}\text{)] = 1.20(3)}$ and $\text{g[}{}^{192}\text{Tl}\text{(8}{}^{\mathrm{?}}\text{)] = 0.207(5)}$. These values are in agreement with a model of one or two quasiparticles coupled to a deformed core. This interpretation is also supported by a preliminary quadrupole moment determination of $\text{Q[}{}^{192}\text{Tl}\text{(8}{}^{\mathrm{?}}\text{)] = 45(9)}\text{fm}{}^2$. The lifetimes were remeasured to be $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 34.6(5)}\text{ns}$ and $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 296(5)}\text{ns}$ for the ¹¹⁹I and the ¹⁹²Tl isomers, respectively.     

Target fragments in collisions of 1.8 GeV/nucleon Fe nuclei with photoemulsion nuclei, and the cascade-evaporation model

Nuclear photographic emulsion is used to study the dependence of the characteristics of target-nucleus fragments on the masses and impact parameters of interacting nuclei. The data obtained are compared in all details with the calculation results made in terms of the Dubna version of the cascade-evaporation model (DCM).     

Beta decay log ft values for transitional odd-mass nuclei

Using the wave functions yielded by the asymmetric rotor model with a decoupled odd nucléon with variable moment of inertia the absolute log ft values for some transitional odd-mass nuclei have been calculated. The dependence on the γ-deformation is important in a few cases. A great improvement is obtained in comparison with a pure spherical shell-model calculation.     

Rotational bands in odd hafnium nucleides

Rotational bands up to high-spin members in odd-neutron Hf nucleides are studied by in-beam spectroscopy using (α, xn) reactions on isotopically enriched Yb targets. The $\text{1}\text{2}{}^{\mathrm{?}}$ [521], $\text{5}\text{2}{}^{\mathrm{?}}$ [512], and the $\text{7}\text{2}{}^{\mathrm{+}}$ mixed positive-parity (mainly $\text{7}\text{2}{}^{\mathrm{+}}$ [633]) bands were observed in ¹⁷³Hf and ¹⁷⁵Hf while the $\text{7}\text{2}{}^{\mathrm{?}}$ [514], $\text{9}\text{2}{}^{\mathrm{+}}$ (mainly $\text{9}\text{2}{}^{\mathrm{+}}$[624]), and the $\text{3}\text{QP}\text{(K =}\text{23}\text{2}$⁺) bands were studied in ¹⁷⁷Hf. The analysis of the band structure within the Nilsson model is extended to also include adjacent odd Hf nuclei making it possible to follow these bands through five isotopes of Hf.     

A phenomenological woods-saxon potential for p-shell nuclei

The parameters of a Woods-Saxon potential well have been determined for ten p-shell nuclei by fitting the electron scattering form factors and single-particle binding energies. The resulting radius shows, for all but very light nuclei, a regular $\text{A}\text{1}\text{3}$ dependence while the depth smoothly decreases with the increasing proton energy. The observed energy dependence may be ascribed to the non-locality of the HF potential. An energy-independent non-local potential, compatible with elastic electron and proton scattering, is proposed in the energy range ?50 to +50 MeV.     

Study of the inertial functions for rare-earth nuclei

Vibrational (B_ββ, B_βγ, B_γγ) and rotational (B_x, B_y, B_z) inertial functions of Bohr's collective Hamiltonian are studied microscopically as functions of deformation. The study is extended to the inertial functions of the Hamiltonian appropriate for the phonon expansion treatment. The cranking approximation is used. The results are compared with those of the pairing-plus-quadrupole model. Non-adiabatic effects are discussed.     

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.     

Solution of Hartree-Fock equations in coordinate space for axially symmetric nuclei

As an alternative to the conventional deformed harmonic oscillator basis expansion, a method is developed in which the coupled integro-differential Hartree-Fock equations are solved directly in coordinate space for a simple effective interaction. The single particle wave functions are obtained on a finite mesh by minimizing a discretized energy functional and solving the resulting finite difference equations using the Lanczos algorithm. Expressions to correct the total energy to second order in the mesh spacing are derived, and the accuracy of the method is demonstrated by numerical comparison with spherical results. Applications and advantages of this new technique are briefly discussed.     

Search for highly excited states in light nuclei with three-body reactions

Various three-body break-up reactions resulting from the bombardment of ⁷Li with 120 MeV ³He have been measured simultaneously in a kinematically complete experiment. Missing-mass spectra have been deduced for ⁴H, ⁴He, ⁴Li, ⁵He, ⁵Li, ⁶He, ⁶Li and ⁷Li. The ground states of ⁴H and ⁵He are well described as n-t and n-α P-wave final-state interactions, respectively. Evidence is found for relatively narrow states at very high excitation energies in several nuclei. The results are compared with those of other authors and with various theoretical predictions.     

Rotation-induced shape transitions in Dy nuclei

Lifetimes of states with spins up to 30? have been measured in the nuclei ¹⁵⁶Dy, ¹⁵⁷Dy, and ^ll58Dy using the recoil-distance technique together with inverse reactions of the type $\text{Mg}\text{(}{}^{136}\text{Xe}\text{, x}\text{n}\text{)}$. The applied method, which benefited from the high velocities of the fusion residues as well as from improvements of the recoil-distance technique, allowed us to determine lifetimes and feeding times down to 0.1 ps. Below the first backbending the resultant B(E2) values in the ground-state band of ^{156, 158}Dy increase faster with increasing rotational frequency than expected for rigid rotors, reaching values similar to those observed for the well-deformed neutron-rich Dy isotopes. In contrast to this, the E2-transition probabilities between high-spin states are clearly retarded. The retardation gradually evolves from the rotation alignment of nucléons and indicates deformation changes most likely towards a triaxial shape. From the analysis of the side-feeding times of the high-spin yrast states it could be furthermore deduced that the E2 component of the preyrast γ-decay stems from transitions along highly collective bands.     

Gamma-ray spectra and positive parity bands in 158Gd

A Ge(Li)-NaI(Tl) pair spectrometer and a Ge(Li)-NaI(Tl) anti-Compton spectrometer were used to measure γ-rays from the reaction ¹⁵⁷Gd(n, γ)¹⁵⁸Gd. A detailed decay scheme for levels of ¹⁵⁸Gd was constructed up to an excitation energy of 2504 keV. Branching ratios for transitions from members of the positive parity bands to members of the ground state band were determined. It is shown that a single band-mixing parameter is not sufficient to explain the experimental results, and that even a four-band-mixing calculation does not provide satisfactory agreement. The binding energy of the last neutron is determined to be 7937.4±0.7 keV.     

Hexadecapole deformation in the wolfram nuclei

The (τ, α) and (d, t) reactions have been used to investigate the positive-parity intrinsic excitations in ^{179, 181, 183, 185}W stemming form the i_{$\text{13}\text{2}$} spherical shell-model state. The $\text{13}\text{2}{}^{\mathrm{+}}$ members of the rotational bands built on each of these orbitals are expected to be populated strongly in neutron-transfer reactions due to the near-unity values of the $\text{C}{}_{\mathrm{j}}\text{=}\text{13}\text{2}$ coefficients. These states were populated in the (τ, α) reaction which favours transfer of high angular momentum. The assignments of l-values were based on the measured ratio of (τ, α) to (d, t) cross sections populating the same state. The Nilsson model, with the inclusion of pairing and Coriolis mixing, was unable to account for the experimental results, namely the observation of all the expected strength localized in only two or four states below 2 MeV of excitation. Much better agreement with experiment was obtained if the extended Nilsson model including a hexadecapole deformation of ε₄ ≈ +0.06 was used as a starting point for a Coriolis-coupling calculation.     

One-nucleon transfer reactions in deformed nuclei

The one-nucleon transfer reaction on deformed nuclei has been computed with the inclusion of indirect inelastic transitions that go through intermediate rotational states. The specific examples considered are¹⁷¹Yb(d, p), ¹⁷²Yb(p, d) and ¹⁸⁶W(p, d). Anomalies in the shapes of of experimental angular distributions with respect to predictions of the distorted-wave Born approximation are shown to be reproduced when these higher-order inelastic processes are taken into account. Consideration is also given to the deuteron optical potential needed for these studies.