Two-phonon Configurations Research Articles

The model for describing the width of double-gamma decay of the quadrupole state of spherical nuclei

We study the competitive γγ-decay of the state of an even-even spherical nucleus. An influence of the phonon-phonon coupling on the double γ-decay width is analysed within the microscopic model based on the Skyrme energy density functional. It is shown that the γγ-decay width is sensitive to the interaction of the one- and two-phonon configurations of the giant dipole resonance.

Microscopic Model to Take into Account Complex Configurations for Pygmy and Giant Resonances

A microscopic model for taking into account quasiparticle–phonon interaction in magic nuclei is considered within nuclear quantum many-body theory. This model is of interest for constructing a microscopic theory of pygmy and giant multipole resonances—first of all, a description of their fine structure. This article reports on a continuation and development of our earlier study [1]. Basic physics results of that study are confirmed here, and new results are obtained: (i) exact (not approximate, as in [1]) expressions for the first and second variations of the vertex in the phonon field are found and employed; (ii) a new equation involving, in addition to the known effective interaction, the total amplitude for particle–hole interaction is derived for the vertex, which is the main ingredient in the theory of finite Fermi systems; (iii) the required two-phonon configurations are obtained owing to the last result. The new equation for the vertex now contains complex configurations such as 1p1hotimestextrm{phonon} and two-phonon ones, along with numerous ground-state correlations.

On Statistical Properties of the Gamow–Teller Strength Distribution in $${}^{\mathbf{60}}$$Ca

The $$\beta$$ -decay half-life and the delayed neutron emission of $${}^{60}$$ Ca are studied within a microscopic model, which is based on the Skyrme interaction T45 to construct single-particle and phonon spaces. We observe a redistribution of the Gamow–Teller strength due to the phonon-phonon coupling and the tensor correlations, considered in the model. For $${}^{60}$$ Sc, the spin-parity of the ground state is found to be $$1^{+}$$ . We predict that the half-life of $${}^{60}$$ Ca is 0.3 ms, while the total probabilities of the $$\beta xn$$ emission is 6.1%. To elucidate the obtained results, the random matrix theory has been applied to analyse the statistical properties of the $$1^{+}$$ spectrum populated in the $$\beta$$ -decay. We found a remarkable agreement between the GT strength distribution, obtained within the microscopic approach, and the ones, generated by means of the random coupling between the one- and two-phonon configurations.

Effect of Dynamical Pairing of the Beta-Decay Properties of Neutron-Rich Nuclei

The influence of an effective spin—isospin interaction in the particle—particle channel on the beta-decay half-lives and multineutron-emission probabilities is studied. The contributions of tensor correlations and coupling of the one- and two-phonon configurations are taken into account within a self-consistent approach that relies on the quasiparticle random-phase approximation and which employs Skyrme interaction. The beta-decay properties of neutron-rich cadmium isotopes are calculated.

Quasiparticle formulation of a multiphonon method and its application to the 20O nucleus

We outline briefly the quasiparticle formulation of a microscopic multiphonon approach known as equation of motion phonon method and discuss its application to the neutron rich semi-magic 20O. Our calculation emphasizes the crucial role of the two-phonon configurations, responsible for establishing an almost one to one correspondence between theoretical and experimental energy levels and for fragmenting the dipole strength, in qualitative agreement with the data. In particular, the fragmentation yields two dipole levels below the neutron threshold which correspond to the two peaks recently observed.

Effects of 2 particle–2 hole configurations on dipole states in neutron-rich N = 80–84 isotones

Starting from the Skyrme interaction SLy4 we study the effects of 2 particle–2 hole configurations on the low-energy electric dipole response in$^{130–134}$Sn. It is shown that the pygmy dipole resonance properties are correlated with the neutron skin thickness. The two-phonon configurations give a considerable contribution to the low-lying E1 strength.

Ground-state correlations within a nonperturbative approach

The contribution of the two-phonon configurations to the ground state of $^{4}\mathrm{He}$ and $^{16}\mathrm{O}$ is evaluated nonperturbatively using a Hartree-Fock basis within an equation-of-motion phonon method using a nucleon-nucleon optimized chiral potential. Convergence properties of energies and root-mean-square radii versus the harmonic oscillator frequency and space dimensions are investigated. The comparison with the second-order perturbation theory calculations shows that the higher-order terms have an appreciable repulsive effect and yield too-small binding energies and nuclear radii. It is argued that four-phonon configurations, through their strong coupling to two phonons, may provide most of the attractive contribution necessary for filling the gap between theoretical and experimental quantities. Possible strategies for accomplishing such a challenging task are discussed.

Effects of 2p-2h configurations on low-energy dipole states in neutron-rich N=80, 82 and 84 isotones

Starting from the Skyrme interaction SLy4 we study the effects of phonon-phonon coupling on the low-energy electric dipole response in 130−134 Sn, 132−136 Te and 134−138 Xe. Our calculations are performed within the finite-rank separable approximation, which enables one to perform quasiparticle random phase approximation calculations in very large two-quasiparticle configuration spaces. A dependence of the pygmy dipole resonance strengths on the neutron skin thickness is found. The inclusion of the two-phonon configurations gives a considerable contribution to the low-lying strength.

Effects of Phonon--Phonon Coupling on Properties of Pygmy Resonance in $^{132}$Sn

Starting from an effective Skyrme interaction, we study the effects of phonon–phonon coupling on the low-energy spectrum of the 1− states in 132Sn. The calculations are performed within a finite rank separable approximation for the particle-hole interaction. The inclusion of two-phonon configurations brings a sizeable contribution to the low-lying strength. Comparison with available experimental data shows a reasonable agreement for the low-energy E1 strength distribution.

Relativistic two-phonon model for the low-energy nuclear response

A two-phonon version of the relativistic quasiparticle time-blocking approximation introduces a new class of many-body models for nuclear structure calculations based on the covariant energy density functional. As a fully consistent extension of the relativistic quasiparticle random phase approximation, the relativistic two-phonon model implies fragmentation of nuclear states over two-quasiparticle and two-phonon configurations coupled to each other. In particular, we show how the lowest two-phonon ${1}^{\ensuremath{-}}$ state, identified as a member of the $[{2}^{+}\ensuremath{\bigotimes}{3}^{\ensuremath{-}}]$ quintuplet, emerges from the coherent two-quasiparticle pygmy dipole mode in vibrational nuclei. The inclusion of the two-phonon configurations into the model space allows a quantitative description of the positions and the reduced transition probabilities of the lowest ${1}^{\ensuremath{-}}$ states in tin isotopes ${}^{112,\phantom{\rule{0.16em}{0ex}}116,\phantom{\rule{0.16em}{0ex}}120,\phantom{\rule{0.16em}{0ex}}124}$Sn as well as the low-energy fraction of the dipole strength below the giant dipole resonance without any adjustment procedures. The model is applied to the low-lying dipole strength in neutron-rich ${}^{68,\phantom{\rule{0.16em}{0ex}}70,\phantom{\rule{0.16em}{0ex}}72}$Ni isotopes. Recent experimental data for ${}^{68}$Ni are reproduced fairly well.

Effects of phonon-phonon coupling on properties of pygmy resonance in124-132Sn

Starting from an effective Skyrme interaction we study effects of phonon-phonon coupling on the low-energy electric dipole response in $^{124-132}$Sn. The QRPA calculations are performed within a finite rank separable approximation. The inclusion of two-phonon configurations gives a considerable contribution to low-lying strength. Comparison with available experimental data shows a reasonable agreement for the low-energy $E1$ strength distribution.

Mode Coupling and the Pygmy Dipole Resonance in a Relativistic Two-Phonon Model

A new class of many-body models, based on covariant density functional theory for excited states, is presented. It allows a parameter free description of the fragmentation of nuclear states induced by mode coupling of two-quasiparticle and two-phonon configurations. As compared to earlier methods it provides a consistent and parameter free theory of the fine structure of nuclear resonances. The method is applied very successfully to investigate the newly discovered low-lying dipole excitations in Sn and Ni isotopes with large neutron excess.

ON THE TFD TREATMENT OF COLLECTIVE VIBRATIONS IN HOT NUCLEI

The approach in a theory of collective excitations in hot nuclei exploring the formalism of thermo field dynamics and the model Hamiltonian consisting of a mean field, the BCS paring interaction, and long-range particle–hole effective forces is reexamined. In contrast with earlier studies, it is found that a wave function of a thermal phonon is depended not only on the Fermi–Dirac thermal occupation numbers of the Bogoliubov quasiparticles consisting the phonon but also on the Bose thermal occupation numbers of the phonon. This strongly affects a thermal phonon coupling due to the renormalization of a phonon–phonon interaction and enlarging the number of thermal two-phonon configurations coupled with one-phonon ones. Moreover, it is shown that the formulation of the double tilde conjugation rule for fermions proposed by I. Ojima is more appropriate in the context of the present study than the original one by H. Umezawa and co-workers.

Quasiparticle time blocking approximation within the framework of generalized Green function formalism

The problem of the microscopic description of excited states of the even-even open-shell atomic nuclei is considered. A model is formulated which allows one to go beyond the quasiparticle random phase approximation. The physical content of the model is determined by the quasiparticle time blocking approximation (QTBA) which enables one to include contributions of the two-quasiparticle and the two-phonon configurations, while excluding (blocking) more complicated intermediate states. In addition, the QTBA ensures consistent treatment of ground state correlations in the Fermi systems with pairing. The model is based on the generalized Green function formalism (GGFF) in which the normal and the anomalous Green functions are treated in a unified way in terms of the components of generalized Green functions in a doubled space. Modification of the GGFF is considered in the case when the many-body nuclear Hamiltonian contains two-, three-, and other many-particle effective forces.

Two-Phonon Background for the Double Giant Resonance

The direct excitation of a "sea" of two-phonon configurations above 15 MeV from the ground state is considered. It is concluded that these configurations form a flat physical background in photoexcitation cross sections and Coulomb excitation in heavy ion reactions at relativistic energies. The contribution of the background to the total cross section in Coulomb excitation of Pb-208 in the DGDR energy region is about 15%. This shows that It should be considered while drawing out conclusions on anharmonicities effects for the DGDR.

Study of the Gamow-Teller resonance in 90Nb and 208Bi

An approach is proposed for studying the spreading properties of the Gamow-Teller resonance (GTR) in heavy nuclei including the coupling to 2 p2 h configurations and the ground-state correlations beyond RPA. The GTR is generated by a proton p-neutron h ( πp- νh) phonon within the renormalized RPA. The second-order configuration mixing beyond RPA is realized by constructing two-phonon configurations, in which one of two intermediate phonon states is a πp- νh phonon. The numerical calculations are performed in the parent nuclei 90Zr and 208Pb making use of M3Y nucleon-nucleon interaction and the single-particle wave functions obtained in the standard harmonic oscillator potential. The single-particle energies around the Fermi surface are substituted with the empirical values or those given by a Woods-Saxon potential. The results obtained provide a reasonable account for recent experimental findings on the GTR in these nuclei. The extension of the present approach to highly excited (hot) nuclei is also provided. The GTR is found to be stable against temperatures up to T = 6 MeV.

On single and double resonances in spherical nuclei

Microscopic calculations of the fine structure of single and double giant dipole resonances (GDR) in 136Xe are presented. The single GDR is treated by a wave function that takes into account a coupling of one-phonon with two-phonon configurations while for the double GDR we mix two-phonon and three-phonon configurations.

Description of low-lying vibrational and two-quasiparticle states in 166Er.

The energies and wave functions of nonrotational states below 2.3 MeV in $^{166}\mathrm{Er}$ are calculated within the quasiparticle-phonon nuclear model. It is shown that the wave functions have a dominating one-phonon component. The contribution of the two-phonon configurations to the wave function of ${\mathit{K}}^{\mathrm{\ensuremath{\pi}}}$\ensuremath{\ne}${0}^{+}$ and ${4}^{+}$ states below 2.3 MeV is less than 6%. The existence of the double-\ensuremath{\gamma} vibrational state with ${\mathit{K}}^{\mathrm{\ensuremath{\pi}}}$=${4}^{+}$ at 2.0-2.2 MeV in $^{166}\mathrm{Er}$ is predicted. The calculated excitation energies and B(E2) and B(E3) values for transitions from the ground state are found to be in agreement with experimental data. Large spectroscopic factors of one-nucleon transfer reactions are explained by the large two-quasiparticle components of the one-phonon terms of the wave functions.

Microscopic description of low-lying one- and two-phonon states and application to 96Zr

A self-consistent approach to finite Fermi systems is expanded for the description of two-phonon states in non-magic nuclei with weak anharmonicity. It is based on a density-functional approach, the quasi-particle random-phase approximation (QRPA) and the Green's function method, the latter enabling one to calculate the diagrams of the phonon-phonon interaction in the coordinate representation. This approach is applied to the low-lying excitations in 96Zr. The transition density of the two-phonon state [3 1 −⊗3 1 −] 6+ in 96Zr is calculated. It is shown that interplay of one-phonon and two-phonon configurations may lead to the origin of two 6 + states with strongly different excitation probabilities. Mixing coefficients and energy splitting of these states are estimated microscopically. The transition probabilities of the one-phonon states 3 1 − and 6 + and the mixing coefficients of the one- and two-phonon 6 + states resulting from the microscopic calculations are used as input for DWBA and coupled-channels calculations for inelastic scattering of 22 MeV polarized deuterons. Calculated cross sections for the 6 + states are compared with experimental data.

Description of low-lying vibrational states and gamma-ray transitions between excited states in 156Gd and 158Gd

The energies and wave functions of the nonrotational states below 2.3 MeV in 156Gd and 158Gd are calculated within the quasiparticle-phonon nuclear model. It is shown that the wave functions have the dominating one-phonon component. The contribution of the two-phonon configurations to the wave function of the excited states is less than 10%. The calculated excitation energies and B(E; λ = 2, 3, 4) values for transition from the ground state are found to be in agreement with experimental data. High intensities of the one-nucleon transfer reactions are explained by the corresponding large two-quasiparticle components of the one-phonon terms of the wave functions. The calculated intensities and reduced probabilities of the E1, E2, and M1 transitions between excited states are in reasonably good overall agreement with experimental data.