Fragmentation of giant multipole resonances in deformed nuclei

The fragmentation of the giant monopole resonance in deformed nuclei is first studied by coupling the monopole oscillation with the quadrupole oscillation by means of the variational procedure for resonance frequencies. It is shown that, for non-axial symmetry, the monopole oscillation couples with both m = 0 and 2 modes of the quadrupole oscillation and the giant monopole resonance is split into three components, whereas for axial symmetry, the fragmentation is given by E₀(1 + 0.86δ² ± 1.25δ³) and E₀(0.74 ± 0.22δ ? 0.21δ² ± 0.57δ³), where E₀ is the g monopole resonance energy for spherical nuclei, δ is the deformation parameter, and the upper and lower signs stand for prolate and oblate deformations, respectively. The initial fragmentation of the giant quadrupole resonance is seen to be little modified by the coupling, except for the m = 0 mode which is split into two components. The variational method is extended to general multipoles for an ellipsoid and the fragmentation of giant multipole resonances in deformed nuclei is investigated for both axial and non-axial symmetries. A brief discussion is also made about the meaning of the energy eigenvalue involved in the model wave equation in terms of multipole sum rules. The giant dipole resonance for the static octupole deformation is shortly considered. The giant E0 and E3 resonances for largely deformed nuclei are finally examined by solving the spheroidal eigenvalue equation and they are compared with the results of the giant dipole and quadrupole resonances.     

Doublet splitting in even-A deformed nuclei

The doublet splittings between excited two-quasiparticle states with parallel and antiparallel angular-momentum coupling in some even-A deformed rare earth nuclei have been calculated and compared with the experimental values. The influence of the various exchange forces is investigated, and results with both finite-range and zerorange forces are presented. Qualitative agreement is obtained when finite-range forces are used; but the SDI results—especially the spin-dependent ones—are also satisfactory if the states of the doublets are sufficiently pure two-quasiparticle states. This condition seems to be fulfilled by the doublet states considered in¹⁶²Dy, but not by those considered in the nuclei¹⁶⁸Er and¹⁷²Yb for which the experimental level splittings are rather large (about 450 keV) and could not reproduced at all. These discrepancies are discussed. It is argued that they are not due do the choice of the residual interactions but rather are due to configuration mixing, which is expected to be strong in these high-lying states.     

Vibrational states in odd deformed nuclei

The energies and wave functions of the nonrotational states in odd deformed nuclei are calculated in the quasiparticle-phonon model of the nucleus. It is shown that the number of vibrational states in odd nuclei is many times larger than the number of vibrational states in even-even nuclei. The wave functions of the overwhelming majority of these states with excitation energies in the range 1.5–2.5 MeV possess a dominant term of the type quasiparticle⊗phonon. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 575–578 (25 April 1996)     

Double giant dipole excitations in deformed nuclei

A calculation is presented for the excitation spectra of two superimposed dipole resonances for deformed nuclei by using theSU(3) limit of the interaction boson model for the case of many bosons. The results indicate that experiments to test the model may be feasible.     

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.     

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.     

Semimicroscopic description of giant octupole resonances in deformed nuclei

The strength functions b(E3, ω) are calculated, and the positions and widths of giant octupole resonances in deformed nuclei are found. It is shown that the giant octupole isoscalar resonances have energies (19–20) MeV for the rare-earth nuclei and (17–18) MeV for the actinides and the widths (5–7) MeV. The energies of the giant octupole isovector resonances are defined by the value of the isovector constant κ⁽³⁾₁.     

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.     

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.     

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.     

Excitation of multiple giant dipole resonances: from spherical to deformed nuclei

The effect of deformation on the excitation of multiple giant dipole resonances is studied. Analytical expressions are derived in the framework of the interacting boson model for the energies and E1 properties of giant dipole resonances in spherical and deformed nuclei, and a numerical treatment of transitional nuclei is proposed. Coulomb-excitation cross sections are calculated in ²³⁸U and in the samarium isotopes.     

The decay width of higher multipole giant resonances

The decay width of higher multipole giant resonances is described within the framework of the newly developed Fourier-Bessel random-phase approximation. We calculate the distribution of the isoscalar and isovector multipole strength for electric resonances up to $\text{J}{}^{\mathrm{\pi }}\text{= 7}{}^{\mathrm{?}}$. In our model we find no concentrated multipole strength beyond the hexadecapole.     

On the coupling of the giant multipole resonances to the surface quadrupole oscillations of nuclei

Within the framework of the hydrodynamic model the exact coupling constants of the coupling of the giant multipole resonances to the surface quadrupole oscillations of nuclei are derived. The differences to former variational calculations are discussed. It is found that the coupling constants for the terms linear in the surface variables are almost the same whereas the coupling constants for the quadratic terms differ appreciably. The influence on the photon absorption and scattering cross sections of spherical nuclei is discussed.