Two-phonon States Research Articles

Self-Consistent Calculations of Probabilities for the $${E}$$1 Transition between the Ground State and the $${[3_{1}^{-}\times 2_{1}^{+}]_{1^{-}}}$$ Two-Phonon State in Tin Isotopes

Self-Consistent Calculations of Probabilities for the $${E}$$1 Transition between the Ground State and the $${[3_{1}^{-}\times 2_{1}^{+}]_{1^{-}}}$$ Two-Phonon State in Tin Isotopes

Spreading Widths of Giant Monopole Resonance in the Lead Region: Random Matrix Approach

The microscopic calculation of the decay width of giant monopole resonance (GMR) anticipates the mixing of one-phonon states with configurations of increasing complexity. To this aim we develop the effective approach for description of monopole excited states that are obtained in the quasiparticle random phase approximation (QRPA), with regard of the coupling between one- and two-phonon states. Based on the QRPA one-phonon states, we generate the coupling and two-phonon states by means of the Gaussian orthogonal ensemble (GOE) distribution. Within our approach the spreading width of the GMRs in 204,206,208Pb are described by means of a random matrix approach on two energy scales. It is demonstrated that the main contribution into the decay of the GMR is determined by a small number of two-phonon states strongly coupled to low-energy surface vibrations. While a vast majority of the coupling matrix elements (that are small in value and following the GOE distribution) are responsible for the fine structure of the GMR spreading width. A remarkable agreement between the results of the full microscopic calculations (based on QRPA phonons coupled by means of the microscopic coupling matrix elements with calculated two-phonon states) with those of the developed approach confirms the vitality of the proposed ideas.

Scalable and programmable phononic network with trapped ions

Controllable bosonic systems can provide post-classical computational power with sub-universal quantum computational capability. A network that consists of a number of bosons evolving through beam-splitters and phase-shifters between different modes, has been proposed and applied to demonstrate quantum advantages. While the network has been implemented mostly in optical systems with photons, recently alternative realizations have been explored, where major limitations in photonic systems such as photon loss, and probabilistic manipulation can be addressed. Phonons, the quantized excitations of vibrational modes, of trapped ions can be a promising candidate to realize the bosonic network. Here, we experimentally demonstrate a minimal-loss phononic network that can be programmed and in which any phononic states are deterministically prepared and detected. We realize the network with up to four collective-vibrational modes, which can be straightforwardly extended to reveal quantum advantage. We benchmark the performance of the network with an exemplary algorithm of tomography for arbitrary multi-mode states with a fixed total phonon number. We obtain reconstruction fidelities of 94.5 $\pm$ 1.95 % and 93.4 $\pm$ 3.15 % for single-phonon and two-phonon states, respectively. Our experiment demonstrates a clear and novel pathway to scale up a phononic network for various quantum information processing beyond the limitations of classical and other quantum systems.

Hybrid model for the damped transient response of giant dipole resonances

We suggest the hybrid model for the description of the dipole spreading widths, in which the strength function is built on the one-phonon strength distribution folded with the energy-dependent Lorentzian. Its energy dependence is brought about by (i) the energy-dependent smearing parameter and (ii) the energy-dependent shift of the one-phonon states. These variables are estimated by means of the two-phonon density, provided by a modified Fermi gas model with uniformly spaced states, and with the aid of the weak constant interaction between the one-phonon states and the two-phonon states, considered as background states. Based on calculated one-phonon states, the model is analytically solvable. To explore the validity of the model we analyze the properties of the ${1}^{\ensuremath{-}}$ spectrum in $^{206}\mathrm{Hg}$, $^{206}\mathrm{Pb}$, and $^{210}\mathrm{Po}$ nuclei. Our results demonstrate that the description of the decay widths within the latter approach is in good agreement with that obtained in the quasiparticle random phase approximation, by means of the random distribution of the coupling between microscopic one-phonon states and two-phonon states, generated by the Gaussian orthogonal ensemble distribution.

Raman scattering in diamond nano- and microcrystals, synthesized at high temperatures and high pressures

The dependences of the Raman spectra of microdiamonds synthesized at high temperatures and high pressures on sizes in the range of 0.1–73.0 μm have been established. For samples several tens of microns in size, additional peaks of Raman scattering (1400 and 2619 cm−1) were found, which are interpreted as a manifestation of bound two-phonon states. A strong coupling between optical phonons in microdiamonds is predicted due to the resonator effect resulting from the confinement of phonons in diamond microcrystals.

Role of neutron transfer in the sub-barrier fusion cross section in O18 + Sn116

Background: In heavy-ion-induced fusion reactions, cross sections in the sub-barrier region are enhanced compared to predictions of the one-dimensional barrier penetration model. This enhancement is often understood by invoking deformation and coupling of the relative motion with low-lying inelastic states of the reaction partners. However, effects of nucleon transfer on fusion below the barrier, especially for the systems having positive $Q$ value neutron transfer (PQNT) channels, are yet to be disentangled completely.Purpose: We intend to study the role of the PQNT effect on the sub-barrier fusion of the $^{18}\mathrm{O} + ^{116}\mathrm{Sn}$ system having positive $Q$ value for the two-neutron stripping channel. Also we reflect on the interplay of couplings involved in the system around the Coulomb barrier.Method: The fusion excitation function was measured at energies from $11%$ below to $46%$ above the Coulomb barrier for $^{18}\mathrm{O} + ^{116}\mathrm{Sn}$ using a recoil mass spectrometer, viz., the Heavy-Ion Reaction Analyser (HIRA). Fusion barrier distributions were extracted from the data. Results from the experiment were analyzed within the framework of the coupled-channels model.Results: Fusion cross sections at energies below the Coulomb barrier showed strong enhancement compared to predictions of the one-dimensional barrier penetration model. The fusion process is influenced by couplings to the collective excitations with coupling to single- and two-phonon vibrational states of the target and the projectile respectively. Inclusion of the two-neutron transfer channel in the calculation along with these couplings could reproduce the data satisfactorily.Conclusions: The significant role of PQNT in enhancing the sub-barrier fusion cross section for the chosen system is not observed. It simply reduced the sub-barrier fusion cross section. Therefore, a consistent link between PQNT and sub-barrier fusion enhancement could not be established vividly while comparing the fusion excitation function from this work with the same from other $^{16,18}\mathrm{O}$-induced reactions. This clearly points to the need for more experimental as well as theoretical investigation in this field.

Nature of Lieb’s “Hole” Excitations and Two-Phonon States of a Bose Gas

It is generally accepted that the ``hole'' and ``particle'' excitations are two independent types of excitations of a one-dimensional system of point bosons. We show for a weak coupling that the Lieb's ``hole'' with the momentum $p=j2\pi/L$ is $j$ identical interacting phonons with the momentum $2\pi/L$ (here, $L$ is the size of the system, and $\hbar=1$). We prove this assertion for $j=1, 2$ by comparing solutions for a system of point bosons with solutions for a system of nonpoint bosons obtained in the limit of the point interaction. The additional arguments show that our conclusion should be true for any $j=1, 2, \ldots, N$. Thus, at a weak coupling, the holes are not a physically independent type of quasiparticles. Moreover, we find the solution for two interacting phonons in a Bose system with an interatomic potential of the general form at a weak coupling and any dimension (1, 2, or 3). It is also shown for a weak coupling that the largest number of phonons in a Bose system is equal to the number of atoms $N$. Finally, we have studied the structure of wave functions for the Tonks--Girardeau gas and found that the properties of quasiparticles in this regime are quite strange.

Effects of nuclear collective vibrations on the α -decay fine structure of vibrational nuclei with A≈220

The multichannel cluster model (MCCM) is generalized to investigate the effect of nuclear collective vibrations on the $\ensuremath{\alpha}$-decay fine structure. Vibrational excitations up to two-phonon states are taken into account and coupled-channels calculations are performed for vibrational Rn, Ra, Th, and U isotopes. Without introducing any additional adjustable parameter, the calculated $\ensuremath{\alpha}$-decay branching ratios to various vibrational states show good agreement with the experimental data. In particular, it is shown that the $\ensuremath{\alpha}$-decay fine structure is strongly correlated with vibrational excitations, offering an alternative tool to explore the phonon states in daughter nuclei. Despite the $N=126$ shell closure, the calculated $\ensuremath{\alpha}$-decay half-lives are also found to be in good agreement with the experimental data. A unified description of the $\ensuremath{\alpha}$-decay fine structure has been achieved by the MCCM for both rotational and vibrational nuclei.

Second- and Third-Order Anharmonic Effects within the Quantum Many-Body Theory

The paper presents a brief review of the results in the self-consistent theory of the anharmonic effects of the second and third orders in the phonon production amplitude, based on the quantum many-body theory. Numerical (for second-order effects) and theoretical analyses of new, i.e., three- and four-quasiparticle correlations in the ground state (backward-going graphs) in magic nuclei and in nuclei with pairing are given. A formula for the probability of transition between one- and two-phonon states is obtained and compared to the solution of a similar problem within the quasiparticle-phonon model. It is shown that the approach under consideration contains a number of new effects.

Microscopic multiphonon approach to nuclei with a valence hole in the oxygen region

An equation of motion phonon method, developed for even nuclei and recently extended to odd systems with a valence particle, is formulated in the hole-phonon coupling scheme and applied to $A=15$ and $A=21$ isobars with a valence hole. The method derives a set of equations which yield an orthonormal basis of states composed of a hole coupled to an orthonormal basis of correlated $n$-phonon states ($n=0,1,2,\ensuremath{\cdots}$), built of constituent Tamm-Dancoff phonons, describing the excitations of a doubly magic core. The basis is then adopted to solve the full eigenvalue problem. The method is formally exact but lends itself naturally to simplifying approximations. Self-consistent calculations using a chiral Hamiltonian in a space encompassing up to two-phonon and three-phonon basis states in $A=21$ and $A=15$ nuclei, respectively, yield full spectra, moments, electromagnetic and $\ensuremath{\beta}$-decay transition strengths, and electric dipole cross sections. The analysis of the hole-phonon composition of the eigenfunctions contributes to clarify the mechanism of excitation of levels and resonances and to understand the reasons of the deviations of the theory from the experiments. Prescriptions for reducing these discrepancies are suggested.

КОМБІНАЦІЙНЕ РОЗСІЮВАННЯ СВІТЛА У СКЛОПОДІБНОМУ Li2B4O7

Lithium tetraborate is a promising material to be used in the production of solid electrolytes and solid-state batteries. A powerful tool for investigating its structure in the B2O3–Li2O system is Raman spectroscopy. The Raman spectra were investigated using the XploRA PLUS (HORIBA Jobin Yvon) Raman spectrometer at the temperature of T = 300 K within the 70–2000 cm–1 range. The excitation wavelength was 785 nm, the spectral resolution was no worse than 1 cm–1. As a result of the study, we have determined the nature of vibrational modes. We detected a fine structure in the 70–400 cm–1 range, which we found to correspond to normal vibration of the lithium-oxygen structural complexes in the structure of [LiO6] frames, and also vibrations and librations of [LiO6] frame and the BO3 and BO4 groups in the structure of [B4O7]2– cluster as a whole. In the 400–800 cm–1 range the superposition of vibrations of [LiO4] clusters and [BO4] tetrahedrons takes place, whereas their normal vibrations are detected in the 800–1354 cm–1 range. In the 1300–2000 cm–1 range we observed the manifestation of two-phonon states, the normal vibrations of borate rings, and the symmetric stretching of the BO3 flat triangles, and detected two peaks that have not been observed previously. The obtained results show that the Raman spectra of glassy Li2B4O7 generally display a single-mode behavior and are caused by a combination of vibrations of different types which are interconnected via the frame structure of the glass consisting of complex boron-oxygen and lithium-oxygen structural complexes.

Damped transient response of the giant dipole resonance in the lead region

We analyze thoroughly the statistical properties of the 1- spectrum in energy interval 9.5-18.5 MeV for Hg206, Pb204,206,208, and Po210 nuclei. To this aim we use the Skyrme interaction SLy4 and the volume pairing interaction, treated in the BCS approximation, as our model Hamiltonian to create a single-particle spectrum and to analyze excited states. The excited states are obtained in the quasiparticle random phase approximation taking into account the coupling between one- and two-phonon states. The obtained spectra (studied by means of the nearest-neighbour spacing distribution, Δ3-statistics and the Porter-Thomas distribution) indicate on the onset of statistical properties close to those of the Gaussian Orthogonal Ensembles. The comparison of the results, obtained with the aid of the coupling calculated microscopically and by means of the Gaussian random distribution, demonstrates a close similarity in the description of the spreading widths of the Isovector Dipole Giant Resonanse of the considered nuclei. Furthermore, we show that employing the random distribution for the coupling between microscopic one-phonon states and two-phonon states, generated by the Gaussian Orthogonal Ensembles distribution, a good agreement is also obtained with the microscopic description of the decay widths. (Less)

Gamow-Teller and double- β decays of heavy nuclei within an effective theory

We study $\beta$ decays within an effective theory that treats nuclei as a spherical collective core with an even number of neutrons and protons that can couple to an additional neutron and/or proton. First we explore Gamow-Teller $\beta$ decays of parent odd-odd nuclei into low-lying ground-, one-, and two-phonon states of the daughter even-even system. The low-energy constants of the effective theory are adjusted to data on $\beta$ decays to ground states or Gamow-Teller strengths. The corresponding theoretical uncertainty is estimated based on the power counting of the effective theory. For a variety of medium-mass and heavy isotopes the theoretical matrix elements are in good agreement with experiment within the theoretical uncertainties. We then study the two-neutrino double-$\beta$ decay into ground and excited states. The results are remarkably consistent with experiment within theoretical uncertainties, without the necessity to adjust any low-energy constants.

Reply to “Comment on ‘Spreading widths of giant resonances in spherical nuclei: Damped transient response’ ”

We demonstrate that our approach [Phys. Rev. C 95, 061305(R) (2017)PRCHCD2469-998510.1103/PhysRevC.95.061305] serves as a useful tool to describe the gross structure of the spreading widths of the giant resonances of the doubly magic heavy nuclei. It reduces significantly the computational efforts implementing the ideas of random matrix distribution of the coupling between one-phonon and two-phonon states and generating the energies of the two-phonon states by means of the Gaussian orthogonal ensemble distribution. We show that the Comment misrepresents our paper and fails to provide plausible arguments against the description of the gross structure with the aid of the random matrix theory.

Spreading widths of giant resonances in spherical nuclei: Damped transient response

We propose the universal approach to describe spreading widths of monopole, dipole and quadrupole giant resonances in heavy and superheavy spherical nuclei. Our approach is based on the ideas of the random matrix distribution of the coupling between one-phonon and two-phonon states generated in the random phase approximation. We use the Skyrme interaction SLy4 as our model Hamiltonian to create a single-particle spectrum and to analyze excited states of the doubly magic nuclei $^{132}$Sn, $^{208}$Pb and $^{310}$126. Our results demonstrate that the universal approach enables to describe gross structure of the spreading widths of the considered giant resonances.

Near-barrier Fusion Evaporation and Fission of 28Si+174Yb and 32S+170Er

Fusion evaporation residues and fission fragments have been measured, respectively, at energies around the Coulomb barrier for the 28 Si+ 174 Yb and 32 S+ 170 Er systems forming the same compound nucleus 202 Po. The excitation function of fusion evaporation, fission as well as capture reactions were deduced. Coupled-channels analyses reveal that couplings to the deformations of targets and the two-phonon states of projectiles contribute much to the enhancement of capture cross sections at sub-barrier energies. The mass and total kinetic energy of fission fragments were deduced by the time-difference method assuming full momentum transfer in a two-body kinematics. The mass-energy and mass-angle distributions were obtained and no obvious quasi-fission components were observed in this bombarding energy range. Further, mass distributions of fission fragments were fitted to extract their widths. Results show that the mass widths decrease monotonically with decreasing energy, but might start to increase when E c.m. / V B < 0.95 for both systems.

Nuclear Spectroscopic Properties within a Selfconsistent Multiphonon Approach

The equation of motion phonon method is adopted to investigate the dipole response in neutron rich nuclei. The calculation is carried out in a space spanned by one- and two-phonon basis states. It makes direct use of a nucleon-nucleon optimized chiral potential complemented with a density dependent term simulating a three-body force and is fully selfconsistent. The inclusion of the two-phonon states induces a pronounced fragmentation of both giant and pygmy resonances consistently with recent experiments.

Gamma Decay of the Possible $1^-$ Two-phonon State in $^{140}$Ce Excited via Inelastic Scattering of $^{17}$O

Gamma Decay of the Possible $1^-$ Two-phonon State in $^{140}$Ce Excited via Inelastic Scattering of $^{17}$O

Electric Monopole Transition Strengths in62Ni

Excited states in 62 Ni were populated with a (p, p') reaction using the 14UD Pelletron accelerator at the Australian National University. Electric monopole transition strengths, ρ 2 (E0), were measured through simultaneous detection of the internal conversion electrons and γ rays emitted from the de-excitation of popu- lated states, using the Super-e spectrometer coupled with a germanium detector. The strength of the 0 + to 0 + transition has been measured to be 77 +23 −34 × 10 −3 and agrees with previously reported values. Upper limits have been placed on the 0 + to 0 + and 0 + to 0 + transitions. The measured ρ 2 (E0) value of the 2 + to 2 + transition in 62 Ni has been measured for the first time and found to be one of the largest ρ 2 (E0) values measured to date in nuclei heavier than Ca. The low-lying states of 62 Ni have previously been classified as one- and two-phonon vibrational states based on level energies. The measured electric quadrupole transition strengths are consistent with this interpretation. However as electric monopole transitions are forbidden between states which differ by one phonon number, the simple harmonic quadrupole vibrational picture is not sufficient to explain the large ρ 2 (E0) value for the 2 + to 2 + transition.

Dipole response inPb208within a self-consistent multiphonon approach

Background: The electric dipole strength detected around the particle threshold and commonly associated to the pygmy dipole resonance offers a unique information on neutron skin and symmetry energy, and is of astrophysical interest. The nature of such a resonance is still under debate. Purpose: We intend to describe the giant and pygmy resonances in 208 Pb by enhancing their fragmentation with respect to the random-phase approximation. Method: We adopt the equation of motion phonon method to perform a fully self-consistent calculation in a space spanned by one-phonon and two-phonon basis states using an optimized chiral two-body potential. A phenomenological density dependent term, derived from a contact three-body force, is added in order to get single-particle spectra more realistic than the ones obtained by using the chiral potential only. The calculation takes into full account the Pauli principle and is free of spurious center of mass admixtures. Results: We obtain a fair description of the giant resonance and obtain a dense low-lying spectrum in qualitative agreement with the experimental data. The transition densities as well as the phonon and particle-hole composi- tion of the most strongly excited states support the pygmy nature of the low-lying resonance. Finally, we obtain realistic values for the dipole polarizability and the neutron skin radius. Conclusions: The results emphasize the role of the two-phonon states in enhancing the fragmentation of the strength in the giant resonance region and at low energy, consistently with experiments. For a more detailed agreement with the data, the calculation suggests the inclusion of the three-phonon states as well as a fine tuning of the single-particle spectrum to be obtained by a refinement of the nuclear potential.