Multiphonon Excitations Research Articles

A new scattering kernel for superfluid helium at low temperatures

We present a scattering kernel to describe the interactions of low-energy neutrons in superfluid 4He at temperatures below ∼1.3K. The kernel was developed on the basis of the separation of the single-phonon and multi-phonon excitations. The single-phonon excitations are described exactly by the dispersion relation and the multi-phonon excitations are included using the phonon expansion approach in the Gaussian approximation. For this purpose, a weighted frequency distribution, derived from the experimentally observed phonon-roton excitations, is used as input. We demonstrate that this approach reproduces very well the measured total cross-sections, scattering functions, and ultra-cold neutron production spectrum, including both the single-phonon and multi-phonon components.

Multiphonon diffuse scattering in solids from first principles: Application to layered crystals and two-dimensional materials

Time-resolved diffuse scattering experiments have gained increasing attention due to their potential to reveal non-equilibrium dynamics of crystal lattice vibrations with full momentum resolution. Although progress has been made in interpreting experimental data on the basis of one-phonon scattering, understanding the role of individual phonons can be sometimes hindered by multi-phonon excitations. In Ref. [{\it arXiv:2103.10108}] we have introduced a rigorous approach for the calculation of the all-phonon inelastic scattering intensity of solids from first-principles. In the present work, we describe our implementation in detail and show that multi-phonon interactions are captured efficiently by exploiting translational and time-reversal symmetries of the crystal. We demonstrate its predictive power by calculating the scattering patterns of monolayer molybdenum disulfide (MoS$_2$), bulk MoS$_2$, and black phosphorus (bP), and we obtain excellent agreement with our measurements of thermal electron diffuse scattering. Remarkably, our results show that multi-phonon excitations dominate in bP across multiple Brillouin zones, while in MoS$_2$ they play a less pronounced role. We expand our analysis for each system and examine the effect of individual atomic and interatomic vibrational motion on the diffuse scattering signals. We further demonstrate the high-throughput capability of our approach by reporting all-phonon scattering maps of 2D MoSe2, WSe2, WS2, graphene, and CdI2, rationalizing in each case the effect of multi-phonon processes. As a side point, we show that the special displacement method reproduces the thermally distorted configuration that generates precisely the all-phonon diffuse pattern.

Dark Matter Detection with Bound Nuclear Targets: The Poisson Phonon Tail.

Dark matter (DM) scattering with nuclei in solid-state systems may produce elastic nuclear recoil at high energies and single-phonon excitation at low energies. When the DM momentum is comparable to the momentum spread of nuclei bound in a lattice, q_{0}=sqrt[2m_{N}ω_{0}] where m_{N} is the mass of the nucleus and ω_{0} is the optical phonon energy, an intermediate scattering regime characterized by multiphonon excitations emerges. We study a greatly simplified model of a single nucleus in a harmonic potential and show that, while the mean energy deposited for a given momentum transfer q is equal to the elastic value q^{2}/(2m_{N}), the phonon occupation number follows a Poisson distribution and thus the energy spread is ΔE=qsqrt[ω_{0}/(2m_{N})]. This observation suggests that low-threshold calorimetric detectors may have significantly increased sensitivity to sub-GeV DM compared to the expectation from elastic scattering, even when the energy threshold is above the single-phonon energy, by exploiting the tail of the Poisson distribution for phonons above the elastic energy. We use a simple model of electronic excitations to argue that this multiphonon signal will also accompany ionization signals induced from DM-electron scattering or the Migdal effect. In well-motivated models where DM couples to a heavy, kinetically mixed dark photon, we show that these signals can probe experimental milestones for cosmological DM production via thermal freeze-out, including the thermal target for Majorana fermion DM.

Exploring the fusion hindrance phenomenon: the case of 32,34S + 89Y

The sub-barrier fusion data of 32,34S + 89Y colliding systems are analyzed using the coupled-channels (CC) calculations, including couplings to the low-lying 2+ and 3− states in reacting nuclei as well as mutual and multi-phonon excitations of these states, based on the proximity potential model. In this scheme, we focus upon the the effect of surface energy coefficient γ and also thermal properties of liquids and hot nuclei on the inner part of the nuclear potential and thus on the fusion cross sections at bombarding energies far below the Coulomb barrier. As expected, our primary calculations using the original proximity potential 1977 show that this model underestimates the measured fusion cross sections at the whole energy region. It is shown that the mentioned physical effects bring significant cross sections enhancements for both reactions. The indications of the fusion hindrance phenomenon in the fusion cross sections at energies far below the Coulomb barrier show up. The observed S factors for the above-mentioned systems develop a maximum at low energies which can also be predicted by the phenomenological extrapolations. Our results within the framework of the modified form of the proximity potential reveal that the calculated fusion cross sections, S factors, and logarithmic slopes for the two systems are in good agreement with the corresponding experimental data even at the lowest energies.

Erratum: Multiphonon excitations from dark matter scattering in crystals [Phys. Rev. D 101 , 036006 (2020)

Received 23 June 2020DOI:https://doi.org/10.1103/PhysRevD.102.019904Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasParticle dark matterTechniquesDark matter detectorsGravitation, Cosmology & AstrophysicsParticles & Fields

Multiphonon excitations from dark matter scattering in crystals

For direct detection of sub-MeV dark matter, a promising strategy is to search for individual phonon excitations in a crystal. We perform an analytic calculation of the rate for light dark matter (keV $<m_{DM}<$ MeV) to produce two acoustic phonons through scattering in cubic crystals such as GaAs, Ge, Si and diamond. The multiphonon rate is always smaller than the rate to produce a single optical phonon, whenever the latter is kinematically accessible. In Si and diamond there is a dark matter mass range for which multiphonon production can be the most promising process, depending on the experimental threshold.

Pygmy and core polarization dipole modes in 206Pb: Connecting nuclear structure to stellar nucleosynthesis

A high-resolution study of the electromagnetic response of 206Pb below the neutron separation energy is performed using a (γ→,γ′) experiment at the HIγ→S facility. Nuclear resonance fluorescence with 100% linearly polarized photon beams is used to measure spins, parities, branching ratios, and decay widths of excited states in 206Pb from 4.9 to 8.1 MeV. The extracted ΣB(E1)↑ and ΣB(M1)↑ values for the total electric and magnetic dipole strength below the neutron separation energy are 0.9±0.2 e2fm2 and 8.3±2.0μN2, respectively. These measurements are found to be in very good agreement with the predictions from an energy-density functional (EDF) plus quasiparticle phonon model (QPM). Such a detailed theoretical analysis allows to separate the pygmy dipole resonance from both the tail of the giant dipole resonance and multi-phonon excitations. Combined with earlier photonuclear experiments above the neutron separation energy, one extracts a value for the electric dipole polarizability of 206Pb of αD=122±10 mb/MeV. When compared to predictions from both the EDF+QPM and accurately calibrated relativistic EDFs, one deduces a range for the neutron-skin thickness of Rskin206=0.12–0.19 fm and a corresponding range for the slope of the symmetry energy of L=48–60 MeV. This newly obtained information is also used to estimate the Maxwellian-averaged radiative cross section Pb205(n,γ)Pb206 at 30 keV to be σ=130±25 mb. The astrophysical impact of this measurement—on both the s-process in stellar nucleosynthesis and on the equation of state of neutron-rich matter—is discussed.

Multiphonon excitation and quantum decoherence in neon scattering from solid surfaces

We present angle- and energy-resolved analysis of Ne scattering from a Ni(111) surface at moderate beam energy and surface temperature. Variation of the surface temperature allows the transition from a pure quantum regime, where single-phonon events are observed, to the classical regime, where multiphonon excitations are observed. The latter can be reproduced by classical calculations. Therefore, our data lie on the border between the coherent quantum regime and the incoherent classical regime.

Absorption of light dark matter in semiconductors

Semiconductors are by now well-established targets for direct detection of MeV to GeV dark matter via scattering off electrons. We show that semiconductor targets can also detect significantly lighter dark matter via an absorption process. When the dark matter mass is above the band gap of the semiconductor (around an eV), absorption proceeds by excitation of an electron into the conduction band. Below the band gap, multi-phonon excitations enable absorption of dark matter in the 0.01 eV to eV mass range. Energetic dark matter particles emitted from the sun can also be probed for masses below an eV. We derive the reach for absorption of a relic kinetically mixed dark photon or pseudoscalar in germanium and silicon, and show that existing direct detection results already probe new parameter space. With only a moderate exposure, low-threshold semiconductor target experiments can exceed current astrophysical and terrestrial constraints on sub-keV bosonic dark matter.

Role of triple phonon excitations in large angle quasi-elastic scattering of very heavy mass systems

We study the effect of multi-phonon excitations on large-angle quasi-elastic scattering of massive systems using the full order coupled-channels formalism. We especially investigate the role of triple phonon excitations of the target and projectile nuclei on the quasi-elastic scattering cross-section as well as the barrier distribution for [Formula: see text]Cr, [Formula: see text]Fe, [Formula: see text]Ni and [Formula: see text]Zn + [Formula: see text]Pb systems. It is shown that the calculations taken into account, the triple octupole phonon excitations of the target and triple quadrupole phonon excitations of the projectile for these systems can explain the experimental data of the quasi-elastic cross-section and the quasi-elastic barrier distribution. These results indicate that the coupled-channels formalism is still valid even for the very heavy mass systems.

Revised analysis ofCa40+Zr96fusion reactions

Fusion data for $^{40}$Ca+$^{96}$Zr are analyzed by coupled-channels calculations that are based on a standard Woods-Saxon potential and include couplings to multiphonon excitations and transfer channels. The couplings to multiphonon excitations are the same as used in a previous work. The transfer couplings are calibrated to reproduce the measured neutron transfer data. This type of calculation gives a poor fit to the fusion data. However, by multiplying the transfer couplings with a $\sqrt{2}$ one obtains an excellent fit. The scaling of the transfer strengths is supposed to simulate the combined effect of neutron and proton transfer, and the calculated one- and two-nucleon transfer cross sections are indeed in reasonable agreement with the measured cross sections.

Present status of coupled-channels calculations for heavy-ion subbarrier fusion reactions

The coupled-channels method has been a standard tool in analyzing heavy-ion fusion reactions at energies around the Coulomb barrier. We investigate three simplifications usually adopted in the coupled-channels calculations. These are i) the exclusion of non-collective excitations, ii) the assumption of coordinate independent coupling strengths, and iii) the harmonic oscillator approximation for multi-phonon excitations. In connection to the last point, we propose a novel microscopic method based on the beyond-mean-field approach in order to take into account the anharmonic effects of collective vibrations.

The pygmy quadrupole resonance and neutron-skin modes in 124Sn

We present an extensive experimental study of the recently predicted pygmy quadrupole resonance (PQR) in Sn isotopes, where complementary probes were used. In this study, (α,α′γ) and (γ,γ′) experiments were performed on 124Sn. In both reactions, Jπ=2+ states below an excitation energy of 5 MeV were populated. The E2 strength integrated over the full transition densities could be extracted from the (γ,γ′) experiment, while the (α,α′γ) experiment at the chosen kinematics strongly favors the excitation of surface modes because of the strong α-particle absorption in the nuclear interior. The excitation of such modes is in accordance with the quadrupole-type oscillation of the neutron skin predicted by a microscopic approach based on self-consistent density functional theory and the quasiparticle-phonon model (QPM). The newly determined γ-decay branching ratios hint at a non-statistical character of the E2 strength, as it has also been recently pointed out for the case of the pygmy dipole resonance (PDR). This allows us to distinguish between PQR-type and multiphonon excitations and, consequently, supports the recent first experimental indications of a PQR in 124Sn.

Pygmy resonances and radiative nucleon captures for stellar nucleosynthesis

The impact of low-energy multipole excitations and pygmy resonances on radiative neutron and proton-capture cross sections in nuclei close to the $\ensuremath{\beta}$-stability line is investigated. For this purpose, a microscopic theoretical approach based on self-consistent density functional theory and quasiparticle-random-phase-approximation formalism extended with multiphonon degrees of freedom is implemented in a statistical reaction model. The advantage of the method is the microscopic nuclear structure input for unified description of low-energy multiphonon excitations and pygmy and giant resonances. This is found to be important for the understanding of the fine structure and dynamics of the nuclear response function at low energies, which strongly influences nuclear reaction rates of astrophysical relevance. Calculations of the radiative capture cross sections of the reactions $^{85}\mathrm{Kr}(n,\ensuremath{\gamma})^{86}\mathrm{Kr}, ^{87}\mathrm{Sr}(n,\ensuremath{\gamma})^{88}\mathrm{Sr}$, and $^{89}\mathrm{Y}(p,\ensuremath{\gamma})^{90}\mathrm{Zr}$ are discussed in comparison with experimental data. For the reactions $^{89}\mathrm{Zr}(n,\ensuremath{\gamma})^{90}\mathrm{Zr}$ and $^{91}\mathrm{Mo}(n,\ensuremath{\gamma})^{92}\mathrm{Mo}$ theoretical predictions of the reaction cross sections are made.

Multi-Phonon Excitations in Fe 2p RIXS on Mg2FeH6

Multi-phonon excitations, indicating a strong electron–phonon coupling, were observed by soft X-ray resonant inelastic X-ray scattering of Mg2FeH6 and Mg2FeD6. The Fe–H/D stretch and bend modes are selectively activated by the tuned electron excitation to eg brach of Fe 3d states in octahedral symmetry. The energy deviation with the factor of \( {\sim} \sqrt{2} \) due to the isotope effect was clearly observed.

Nuclear response theory with multiphonon coupling in a covariant framework

Background: Nuclear excited states within a wide range of excitation energies are formally described by the linear response theory. Besides its conventional formulation within the quasiparticle random phase approximation (QRPA) representing excited states as two correlated quasiparticles (2q), there exist extensions for 4q configurations. Such extended approaches are quite successful in the description of gross properties of nuclear spectra, however, accounting for many of their fine features requires further extension of the configuration space. Purpose: This work aims at the development of an approach which is capable of such an extension as well as of reproducing and predicting fine spectral properties, which are of special interest at low energies. Method: The method is based on the covariant density functional theory and time blocking approximation, which is extended for couplings between quasiparticles and multiphonon excitations. Results: The covariant multiphonon response theory is developed and adopted for nuclear structure calculations in medium-mass and heavy nuclei. The equations are formulated in both general and coupled forms in the spherical basis. Conclusions: The developed covariant multiphonon response theory represents a new generation of the approaches to nuclear response, which aims at a unified description of both high-frequency collective states and low-energy spectroscopy in medium-mass and heavy nuclei.

Pygmy resonances and nucleosynthesis

A microscopic theoretical approach based on a self-consistent density functional theory for the nu- clear ground state and QRPA formalism extended with multi-phonon degrees of freedom for the nuclear excited states is implemented in investigations of new low-energy modes called pygmy resonances. Advantage of the method is the unified description of low-energy multiphonon excitations, pygmy resonances and core polariza- tion effects. This is found of crucial importance for the understanding of the fine structure of nuclear response functions at low energies. Aspects of the precise knowledge of nuclear response functions around the neutron threshold are discussed in a connection to nucleosynthesis.

Single-phonon and multi-phonon excitations of theγvibration in rotating odd-Anuclei

Multi-phonon excitations in atomic nuclei were observed very rarely although collective motions in quantum many-body systems are described as bosonic excitations. In particular, the first two-phonon $\gamma$ vibrational ($2\gamma$) excitation in odd-$A$ nuclei was reported in 2006 and only a few have been known. Quite recently, conspicuously enhanced $B(E2)$s feeding $2\gamma$ states were observed in $^{105}$Nb and conjectured that their parent states are candidates of $3\gamma$ states. In the present work, the model space is enlarged from the present author's previous calculation for $^{103}$Nb. The purpose is twofold: One is to see how the description of $2\gamma$ states is improved, and the other is to examine the existence of collective $3\gamma$ states, and when they exist, study their collectivity through calculating interband $B(E2)$s. The particle-vibration coupling model based on the cranking model and the random-phase approximation is used to calculate the vibrational states in rotating odd-$A$ nuclei. Interband $B(E2)$s are calculated by adopting the method of the generalized intensity relation. The present calculation reproduces the observed spectra of $0\gamma$ - $2\gamma$ states well and gives collective $3\gamma$ states with enhanced $B(E2)$s to $2\gamma$ states in $^{103}$Nb and $^{105}$Nb. The most collective $3\gamma$ state with the highest $K$ at zero rotation is thought to be the main component of the observed band.

Influence of multiphonon excitations and transfer on the fusion of Ca+Zr

Fusion data for $^{48}$Ca+$^{90,96}$Zr are analyzed by coupled-channels calculations that are based on the M3Y+repulsion, double-folding potential. By applying a previously determined nuclear density of $^{48}$Ca, the neutron densities of the zirconium isotopes are adjusted to optimize the fit to the fusion data, whereas the proton densities are determined by electron scattering experiments. It is shown that the fusion data can be explained fairly well by including couplings to one- and two-phonon excitations of the reacting nuclei and to one- and two-nucleon transfer reactions but there is also some sensitivity to multiphonon excitations. The neutron skin thicknesses extracted for the two zirconium isotopes are consistent with anti-proton measurements. The densities of the zirconium isotopes are used together with the previously determined nuclear density of $^{40}$Ca to calculate the M3Y+repulsion potentials and predict the fusion cross sections of $^{40}$Ca+$^{90,96}$Zr. The predicted cross sections for $^{40}$Ca+$^{90}$Zr are in reasonable agreement with the data when the influence of multiphonon excitations and a modest transfer is considered. The prediction of the $^{40}$Ca+$^{96}$Zr fusion cross section, on the other hand, is poor and under-predicts the data by 30 to 40%. Although couplings to transfer channels with positive $Q$ values were expected to play an important role, they are not able to explain the data, primarily because the predicted Coulomb barrier is about 1.5 MeV too high. Possible reasons for this failure are discussed.

Analysis of heavy-ion fusion reactions at extreme sub-barrier energies using the proximity formalism

The recent measured values of the fusion excitation functions of the heavy-ion colliding systems ${}^{28}$Si${+}^{100}$Mo, ${}^{58}$Ni${+}^{54}$Fe, and ${}^{64}$Ni${+}^{64}$Ni are investigated using the original version of the proximity formalism. The fusion cross sections are calculated based on the coupled-channels approach, including couplings to the low-lying ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states in both target and projectile nuclei. The comparison between the calculated and the measured values of the fusion excitation functions indicates that the potential Prox.77 needs to be modified considerably at sub-barrier energies. In the present study, the role of the surface energy coefficient $\ensuremath{\gamma}$ and also the temperature $T$ of the compound nucleus in nuclear potential and fusion cross section has been explored for our colliding systems. Moreover, the mutual and the multiphonon excitations of the lowest ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states are considered in the coupled-channels calculations. It is demonstrated that the potential Prox.77 with these corrective effects can reproduce the experimental data of the fusion cross section, the $S$ factor and the logarithmic derivative for fusion reactions ${}^{28}$Si${+}^{100}$Mo, ${}^{58}$Ni${+}^{54}$Fe, and ${}^{64}$Ni${+}^{64}$Ni with good accuracy especially at below-barrier energies.