Level density for doubly odd deformed nuclei

The level density for doubly odd deformed nuclei near B_n is calculated within the framework of the semi-microscopic approach. The calculated values are found to be in good agreement with the experimental ones. It is shown that for the I ? 1 states it is important to take into account rotational motion.     

Electromagnetic transitions in some doubly odd deformed nuclei

Nanosecond lifetimes of excited states in doubly odd deformed nuclei have been determined by in-beam measurements applying the method of delayed γ-γ coincidences as well as by experiments in the radioactive decay with the method of delayed γ-ce coincidences, respectively. Analysing the time distributions and delayed γ-ray spectra, the following half-lives of isomeric states could be obtained for the first time: $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(63.7}\text{keV in}{}^{160}\text{Tb}\text{) = 60 ± 5}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(138.7}\text{keV in}{}^{160}\text{Tb}\text{) = 5.7 ± 0.5}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(82.0}\text{keV in}{}^{156}\text{Ho}\text{) = 1.25 ± 0.20}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(87.2}\text{keV in}{}^{156}\text{Ho}\text{) = 58.5 ± 3.5}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(139.2}\text{keV in}{}^{158}\text{Ho}\text{) = 1.85 ± 0.10}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(38.3}\text{keV in}{}^{162}\text{Ho}\text{) = 1.2 ± 0.2}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(179.9}\text{keV in}{}^{162}\text{Ho}\text{) = 8.7 ± 0.2}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(342.8}\text{keV in}{}^{164}\text{Ho}\text{) = 2.6 ± 0.2}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(295.1}\text{keV in}{}^{166}\text{Ho}\text{) = 1.10±0.15}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(44.6}\text{keV in}{}^{162}\text{Tm}\text{) = 1.40±0.15}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{,(163.4}\text{keV in}{}^{162}\text{Tm}\text{) = 1.1 ± 0.1}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(220.1}\text{keV in}{}^{178}\text{Ta}\text{) = 8.5 ± 1.0}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(289.5}\text{keV in}{}^{178}\text{Ta}\text{) = 2.0 ± 0.5}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(392.8}\text{keV in}{}^{178}\text{Ta) ≈ 1 ns, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(316.5}\text{keV in}{}^{186}\text{Re}\text{) = 0.20 ± 0.10}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(300.2}\text{keV in}{}^{188}\text{Re}\text{) = 1.5 ± 0.2}\text{ns and}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(482.2}\text{keV in}{}^{188}\text{Re}\text{) = 0.26 ± 0.10}\text{ns}$. Furthermore, upper limits for the half-lives of fifteen excited states in ¹⁶⁰Tb, ^{164, 166}Ho and ^{186, 188}Re have been estimated. For eight isomeric levels in ^{186, 188}Re, the lifetimes earlier determined have been remeasured. Unlike previous studies, the existence of isomeric states at 87.2 keV in ¹⁵⁶Ho and at 179.9 keV in ¹⁶²Ho is suggested. Absolute γ-ray transition probabilities are deduced and compared with single-particle estimates according to Weisskopf and Nilsson, the latter also including pairing correlations. The K-, Ω- and f-forbidden transitions can qualitatively be explained in terms of configuration mixings. Experimental El, ΔK= 1 transition matrix elements in odd-odd deformed nuclei are supposed to be appreciably influenced by higher-order vibrational admixtures coupled via RPC and p-n interaction mixings.     

Possible rotational states in odd In nuclei

Levels and transitions in ¹⁰⁷In and ¹⁰⁹In have been studied in in-beam spectroscopy on the reactions ¹⁰⁶Cd(d, nγ)¹⁰⁷In and ¹⁰⁸Cd(d, nγ)¹⁰⁹In. Low-lying $\text{1}\text{2}{}^{\mathrm{+}}\text{and}\text{3}\text{2}{}^{\mathrm{+}}$ states resembling the possible rotational bands observed in the heavier In isotopes are seen in both nuclei. The potential energy has been calculated for ^107–121In with the odd proton in different orbitals, using the Strutinsky normalization procedure. A prolate minimum at a deformation ε ≈ 0.2 is obtained for the lowest $\text{1}\text{2}{}^{\mathrm{+}}$ orbital, which is in good agreement with the experimental data for ^115–119In. The excitation energy of the $\text{1}\text{2}{}^{\mathrm{+}}$ minimum shows a fairly good agreement with experimental data.     

On collective two-phonon states in deformed nuclei

The centroid energies of the two-phonon states in doubly even deformed nuclei are calculated within the quasiparticle-phonon nuclear model taking into account the Pauli principle in the two-phonon components of the wave functions. It is shown that the collective two-phonon energies are shifted by 1–2 MeV to higher energies due to the Pauli principle. A strong fragmentation of the two-phonon collective states over many nuclear levels occurs at the excitation energies of 3–4 MeV. It is concluded that the two-phonon states cannot exist in deformed nuclei. The analysis of the available experimental data on the two-phonon states shows that the experimental data do not contradict the results of these calculations.     

Negative parity yrast states in deformed nuclei

The negative parity yrast states in even-even deformed nuclei are studied. For low I values these states are interpreted as octupole states. At high spin values, however, the coupling of participating quasiparticles is change; their angular momenta become parallel and aligned with the rotational axis. The transition between the two regimes occurs at I ≈ 21–25 in light actinide nuclei and as low as I ≈ 9–11 in light rare-earth nuclei.     

Excited states of deformable nonaxial odd nuclei

Rotationally single-particle and vibrational excitations of deformable nonaxial odd nuclei are investigated with allowance for the interaction of collective and single-particle states. The ratios of excitation energies, of reduced probabilities of E2 transitions, and of quadrupole moments for deformed nonaxial odd nuclei are calculated up to high-spin states.     

Extension of the multiphonon method to odd mass deformed nuclei

The multiphonon method based on one type of phonon is extended to odd mass nuclei. The formulas for the matrix elements of one and two body operators are given.     

Equations for O+ states in deformed nuclei

The quasiparticle-phonon nuclear model equations are derived for describing theKπ=O⁺ states in doubly even deformed nuclei taking account of particle-hole and particle-particle interactions between quasiparticles. Inclusion of particle-particle interactions complicates the RPA equations. Equations for the functions of monopole and quadrupole pairing are derived from the condition of eliminating spurious RPA solutions. In the QPNM, inclusion of a particle-particle interaction does not lead to very complicated calculations. The obtained equations can serve as a basis for calculating characteristics of the O⁺ excited states of doubly even deformed nuclei.     

Clustering aspects of nuclei in highly deformed states

The potential energies, the moments of inertia, and the quadrupole and octupole moments of dinuclear systems are compared with corresponding values for the highly deformed nuclear states. The idea is advocated that hyperdeformed states of nuclei are close to near-symmetric dinuclear systems. The superdeformed states are considered as asymmetric dinuclear systems. The cluster superdeformed and hyperdeformed states have quite a large octupole deformation. Measurement of octupole deformations of highly deformed nuclei can answer the question of whether these nuclei exist in cluster configurations.     

Aligned rotation of octupole-vibrational states in deformed nuclei

Analysis of level energies in aligned octupole bands in even-even deformed nuclei using the VMI-model expressed in terms of the rotational angular momentumR, show that almost complete alignment is reached at low spin values. It is shown that the alignment is almost spin independant. Using the ground-state band VMI-parameters only a renormalization of the alignment parameter 〈J _⊥〉 is enough to reproduce the level energies of the NPB's.     

Single-particle quasistationary states in spherical and deformed nuclei

A method is presented for investigation of single-particle quasistationary states of spherical and deformed nuclei in the sub-barrier energy region. The wave functions and energy levels of quasistationary sates are found as eigensolutions of the Schrödinger equation using a continuous analog of the Newton method. The formalism and the numerical results are compared to those of other methods of treating potential resonances.     

Heavy-ion excitation of 3− states in deformed nuclei

Previously measured data for 70.4 MeV ¹²C excitation of 3^? states in ^{148, 150}Nd are reanalyzed using a third-order rotational-vibrational model. Calculations using 3^? quadrupole moments which are expected if they are K = 0 states are in reasonable agreement with the magnitude of the large-angle data, but the quality of the fit in the Coulomb-nuclear interference region is only fair. It is found that the matrix element 〈2⁺∥M(E3)∥3^?〉 plays an important role in the calculations making the “measurement” of the 3^? quadrupole moments very difficult, if not impossible.     

Half-life measurements of intrinsic states in deformed odd-mass nuclei

The half-lives of the following intrinsic states in deformed odd-mass nuclei has been measured by delayed coincidences with a time-to-amplitude converter:

1. 5/2 5/2⁺[642] at 86.5 keV in¹⁵⁵Gd:T _1/2=6.7±0.3 ns, which results in the determination of theE1,ΔK=1 transition probability to the ground state 3/2 3/2^?[521] and first rotational state 5/2 3/2^?[521], yielding hindrance factors ofF _N ≈5.5 and ≈1.8 (F _W =3.1×10⁴ and 2.3×10⁴) respectively.
2. (3) 5/2 5/2^?[512] at 191.4 keV in¹⁶⁹Yb:T _1/2=3.35±0.15 ns and at 122.39 keV in¹⁷¹Yb:T _1/2=265±20 ns which results in the determination of the transition probabilities of theE1,ΔK=1 transitions to the ground states 7/2 7/2⁺[633], of theK-forbiddenM1 transitions to the 5/2 and 3/2 1/2^?[521] and of theE2 transitions to the 5/2, 3/2 and 1/2 1/2^?[521] states in both nuclei.

TheE1 transition probabilities are compared to the transitions between the same Nilsson states in¹⁷³Yb and¹⁷⁵Hf discussing the influence of the position of the Fermi surface — obtained from recent stripping and pick-up reactions — on these transition probabilities. Additional information on the decay scheme of¹⁷¹Lu→¹⁷¹Yb is obtained by delayed coincidence measurements. For testing the used time-to-amplitude converter the well known half-lives of the 482 keV level in¹⁸¹Ta (T _1/2=10.4±0.3 ns) and of the 279 keV level in²⁰³Tl (T _1/2=0.285 ±0.015 ns) were measured, in good agreement with other measurements.     

Magnetic moments of low-lying states in medium weight odd nuclei

The magnetic moments of several short-lived states in¹⁰³Rh,^1111113Cd and^1231125Te isotopes have been measured by the transient field technique. The results, together with those obtained earlier in the^1071109Ag isotopes, have been compared to predictions of various models and calculations. In the Z=45, 47 isotopes, the odd proton seems to deform the vibrational core. The data are best explained within the framework of a triaxially deformed nucleus. In the odd neutron isotopes with 50<N<82, and Z=48, 52, weak coupling states coexist with single particle states in a mix of configurations.     

The splitting of giant multipole states of deformed nuclei

A vibrating potential model is applied to deformed nuclei with a deformed harmonic oscillator potential in order to discuss the splitting of isoscalar giant quadrupole states. Eigenfrequencies of the collective states are estimated to be $\text{√2ω(1 ?}\text{1}\text{3}\text{δ)}$, $\text{√2ω(1 ?}\text{1}\text{6}\text{δ)}\text{and}\text{√2ω(1 +}\text{1}\text{3}\text{δ)}\text{fo and 2}{}^{\mathrm{+}}$ modes, respectively. The splitting of isovector dipole and isovector quadrupole states is also studied according to a schematic model as proposed by Bohr and Mottelson. It is shown that. isovector dipole states are split, as in a hydrodynamic model, while isovector quadrupole states with the same scaling factors as those of isoscalar quadrupole modes.