Two-phonon States Research Articles

Fermi resonance in the phonon spectra of copper halides.

Several theoretical concepts such as two-phonon bound states, off-center ions, and Fermi resonances have been suggested to explain the strong anomalies in the phonon spectra of copper halides, with no conclusive results. We take into account the anharmonic coupling of the $TO(\ensuremath{\Gamma})$ phonons with the two-phonon states and calculate the line shapes in the framework of an anharmonic valence-shell model. We show that the anomalies are Fermi resonances; other mechanisms need not be invoked.

Nonlinear response function in case of polariton Fermi resonance

A response function describing processes with three electromagnetic waves (polaritons) in crystals has been defined. This function has been calculated by a specific method for the case of polariton Fermi resonance, i.e. when one of the polaritons interacts with the two-phonon states of a non-degenerate polar vibration. Some features of the three-polariton interaction in the two-phonon band have been investigated, like modulation and broadening of the spectrum, anti-resonance and wave-vector mismatch. The information obtained from nonlinear optical spectra about polariton and two-phonon states has been analysed.

Time-resolved nonlinear spectroscopy of a fermi doublet: The { nu 1,2 nu 2} Fermi resonance in CO2 solid.

It is shown that the intramolecular Fermi doublet {${\ensuremath{\nu}}_{1}$,2${\ensuremath{\nu}}_{2}$} in crystalline ${\mathrm{CO}}_{2}$ arising from resonant anharmonic coupling between a single-phonon state and a quasibound two-phonon state can be coherently driven and its dynamics determined by time-resolved nonlinear optical techniques. Coherence relaxation times for both components of the doublet are measured between 9 K and the fusion point (217 K). A mechanism for loss of coherence is proposed which involves modulation by low-lying intermolecular modes.

Time-resolved nonlinear spectroscopy of two-phonon states in molecular crystals

It is shown that time-resolved nonlinear optical techniques can be extended to the selective study of the dynamics of vibrational overtones and two-phonon states in condensed media. In a primary application the first experimental demonstration of coherent anti-Stokes higher order Raman scattering (CAHORS) on the overtone and bound two-phonon state of the v2 vibration in liquid and crystalline CS2 , respectively. Is presented. The CAHORS technique is subsequently employed to measure the coherence relaxation times of both components of the Fermi doublet {v1 ,2v2 } in condensed CO2 , as a function of temperature up to and across the melting point. Several possible mechanisms for the loss of coherence of bound two-phonon states are described and discussed.

Calculation of Phonon-Phonon Interactions and the Absence of Two-Phonon Bound States in Diamond

We demonstrate that anharmonic phonon-phonon coupling constants can be extracted from frozen-phonon total-energy calculations. The method is applied to the optical modes of diamond. The zone-center coupling constants are completely determined through fourth order, and are used to compute an effective four-phonon vertex including virtual optical-phonon exchange. The interaction is found to have the wrong sign to allow formation of a two-phonon bound state.

Transversal E1-Resonance in Spherical Nuclei

The spin-flip E1-states in medium and heavy spherical nuclei are investigated within the quasiparticle-phonon nuclear model. The RPA-calculations predict the existence of a collective 1--state formed by the isovector spin-dipole force. Its excitation energy is about 20 MeV. This state is intensively excited by the inelastic electron scattering at momentum transferred q ≈ 0.5-0.7 fm-1, at the scattering angles θ > 60° the main contribution to its excitation comes from the transversal form factor. Therefore, it can be recognized as the transversal E1-resonance. The interaction with two-phonon states causes a very strong spreading of the resonance, thus making its experimental observation hardly probable.

Spreading width of giant resonances in fluid-dynamical approximation

On the basis of a semiclassical argument a fluid-dynamical expression is derived for the coupling matrix element between a giant multipole state and a two-phonon state responsible for the spreading width. Significance of effective three-body forces originating from the density-dependent potential energy functional is pointed out in the description of the coupling.

Time-Resolved Spectroscopy of Vibrational Overtones and Two-Phonon States

The authors propose the application of time-resolved nonlinear optical techniques to the selective study of the dynamics of vibrational overtones and two-phonon states in condensed media. They present the first experimental demonstration of picosecond coherent anti-Stokes higher-order Raman scattering on the first overtone and the bound two-phonon state of the ${\ensuremath{\nu}}_{2}$ mode in liquid and crystalline C${\mathrm{S}}_{2}$, respectively, and describe its dynamics and deexcitation channel in terms of a simple effective Hamiltonian.

Search for two-octupole-phonon states in 208Pb

A search for two-phonon octupole vibrational states in 208Pb was carried out using the 207Pb(n th, γ) reaction at the High Flux Reactor of the Institut Laue-Langevin. The conversion electron spectrum was scanned with the spectrometer BILL with a sensitivity of 20 μb in the 4–6 MeV interval. Coincidence and singles γ-ray measurements were performed at the end of the thermal neutron beam guide H22-F reaching a sensitivity of 80 μb for energies above 0.511 MeV. In addition the singles spectrum was investigated with the pair spectrometer at the tangential beam facility. Levels have been observed at (energies in keV and parenthesis for tentative level identification and spin-parity assignments): 2614.4, 3 −; 3997, (3 −); 4084.7, 2 +; 4253, (2 −, 3 −); 4704, (2 −, 3 −); (4882.0), (0 +); (4904.9), (0 +); 4935, 2 +; (6343), (2 +) and the 0 −, 1 − capture state at 7367.9 keV. The 4882.0 keV level probably corresponds to the known two-neutron pairing vibration. Possible candidates for two-phonon octupole excitations are the (0 +)(4904.9) and 2 + 4935 keV states. The nuclear field theory formalism is used to calculate branching ratios and energies for states in 208Pb under several assumptions. The most inimportant result of the comparison of theory and experiment is that the experimental properties of the 2 + 4935 keV state favour the interpretation of this state as a two-phonon octupole vibration rather than as a one-phonon non-collective quadrupole state.

High-resolution investigation of the 116Sn(p, p') reaction

Angular distributions for states up to 4.0 MeV excitation energy have been measured with the 116Sn(p, p') reaction at E p = 25 MeV. They were compared with macroscopic DWBA calculations in order to extract L-values and deformation parameters. Coupled-channels calculations were performed to investigate two-phonon excitations and the mixing between one- and two-phonon states. The results of the present study are compared with other experimental results and with model calculations.

Search for two-phonon vibrations inEr168

The low-lying level structure of $^{168}\mathrm{Er}$ has been examined by the (n, ${\mathrm{n}}^{\ensuremath{'}}\ensuremath{\gamma}$) reaction and all known levels with $J<7$ and ${E}_{x}<~2.0$ MeV are observed. The discovery of a level at 1893 keV calls for a reexamination of the completeness of the level scheme assumed previously for this nucleus. No new low-lying candidates for two-phonon $\ensuremath{\gamma}$ vibrations are observed.NUCLEAR REACTIONS $^{168}\mathrm{Er}(\mathrm{n}, {\mathrm{n}}^{\ensuremath{'}}\ensuremath{\gamma})$, ${E}_{\mathrm{n}}=1.0\ensuremath{-}3.5$ MeV; measured ${E}_{\ensuremath{\gamma}}$, ${I}_{\ensuremath{\gamma}}$, $\ensuremath{\sigma}(E, {E}_{\ensuremath{\gamma}}, {\ensuremath{\theta}}_{\ensuremath{\gamma}})$. Searched for two-phonon states.

Resonance of one-phonon and two-phonon states in mixed semiconductors

RESONANCE OF ONE-PHONON AND TWO-PHONON STATES IN MIXED SEMICONDUCTORS V. V. Artamonov, M. Ya. Valakh, A. P. Litvinehuk, V. I. Sidorenko, and A. M. Yaremko UDC 535.343.2 Studies in recent years have revealed multifaceted resonance phenomena in the interaction of exeitons, biexcitons, plasmons, electronic excitations, and phonons in solid materials [1-5]. Interesting anomalies in the resonant anharmonic interactions have been observed in a study of polar[ton Raman scattering in crystals which lack a center of inversion symmetry [6] and in "soft" phonon modes in ferroelectric crystals [7]. In the case of polariton resonance the energy mismatch of the resonating excitations may be varied by changing the scattering angle, which in turn changes the polariton frequency. The resonance conditions in ferroelee- trics are varied by changing the crystal temperature. In this work we present the results of experimental and theoretical studies of the anharmonic resonance of phonon excitations in mixed II-VI semiconductors. In semiconducting crystals the phonon branches typically exhibit significant dispersion and, consequently, there is a broad band with a complex frequency distribution function. Therefore the spectral manifestation of the resonance of discrete and continuous excitations in such materials is rather complex and in many cases may exhibit a Fano contour [8 ] with its characteristically asymmetric bandshapes and a sharp valley in the intensity between them (the so-called "Fano antiresonance"). Since the resonant interaction is determined to a significant degree by the energy mismatch and by the relationship of the intensities of the resonating states [ 1, 8, 9], mixed sere[conducting crystals are conve- nient systems for study. In crystals with a one-mode character the rearrangement of the phonon spectrum as the composition is changed includes a significant change in the frequency of the long wavelength optic phonons. Therefore, it is most likely that in some interval of composition the one-phonon state will cross a band of two- phonon excitations of the appropriate symmetry. In the case of crystals with a two-mode character, the rear- rangement of the spectrum consists mainly of a redistribution of the intensities of the phonon lines due to scattering by the individual components, which also may influence the resonance phenomena. EXPERIMENTAL RESULTS Experimental studies of Raman scattering were carried out in a right angle geometry on an apparatus based on a DFS-24 spectrometer. The light source utilized was a He-Ne laser (~ = 632.8 nm). An FEU-79 photomultiplier was used as a detector, with a photon-counting system. In Fig. 1 we show the tlaman spectra of crystals of Zn1_xCdxSe for various compositions. In the compo- sition range 0 _< x _< 0.4 they are characterized by the structure of sphalerite. ]Preliminary experimental data on the resonance phenomena in this system have been reported previously [10]. In Zn0.89Cd0.11Se lines are ob- served at ~ = 140, 186, 204, and 250 cm -1 (curve 1, Fig. la). The latter two are due to scattering by the long lines (symmetry A1) are due to scattering processes involving simultaneous excitation of two TA phonons at the special points X and W in the Brillouin zone [11]. In the polarization studied (yy), corresponding to the fully symmetric component A1, the two-phonon peak at ~ = 140 cm -1 has a significant intensity. The appear- ance of the bands of F2 symmetry in the spectra is due to incomplete polarization of the exciting and scatter- ing light and also to some lifting of the selection rules caused by the disorder of the mixed crystals. As the CD content of the mixed crystals is increased the frequency of the long wavelength LO phonons decreases monotonically to ~ = 232 cm -t for x = 0.60 (curves 1-3, Fig. la). No significant change in the in- tensiW, halfwidth, or shape of this band is observed as this takes place. At the same time the changes in the vicinity of the transverse optical vibrations are significant. The TO band, which approaches the sharp two- phonon peak at 186 cm -~, causes a significant increase in the intensity of the latter (curve 2, Fig. la). In other words, there is a transfer of intens[ W between the one-phonon and two-phonon peaks. Such a process is known Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 38, No. 2, pp. 272-279, February, 1983. Original article submitted January 4, 1982. 0021-9037/83/3802-0223507.50 9 1983 Plenum Publishing Corporation 223

The effect of two-magnon two-phonon interactions on the two-magnon Raman spectra of antiferromagnets

An effect of magnon-phonon interactions on two-magnon Raman spectra is studied using Green function methods developed by Elliott and Thorpe. Green functions associated with two-phonon states are included. Two-magnon two-phonon interactions modify the shape of two-magnon Raman spectra appreciably.

Search For the Two-Phonon 0+ Strength in 64Zn

The two-phonon 0+ strength in 64Zn has been searched for by obtaining experimental results for the E0 and E2 transitions depopulating the excited 02+ and 03+ states. The previous identification of the 02+ state in 64Zn at 1910.3 keV as a two-phonon state is completely washed out through the present experimental results: B(E2;02+ → 21+) = 0.058(3) W.u., B(E2;02+ → 22+) = 62(8) W.u. and ρ2(E0;02+ → 01+) = 3.9(4) × 10-3.

Anharmonicities of Gamma Vibration in168Er

Properties of the r·vibration in Er are examined both in a macroscopic and in a microscopic approach with special emphasis on the anharmonicities of two-phonon states. It is found that in order to account for recent ex­ perimental evidence it is necessary to assume large anharmonic components both in the collective potential energy surface and in the mass parameters. Points which are not clear in our present understanding of the gamma-motion are described. § l. Introduction The investigation of vibrational anharmonicities was a popular subject about 15''20 years ago. Systematic methods for the treatment of anharmonic effects have been developed by many people,1> mainly in connection with low­ frequency quadrupole vibrational excitations in nuclei. The an­ harmonicities manifest themselves through shifts and/or splittings of the multi­ phonon levels and through transition matrix-elements for the multipole operators that violate the selection rules implied by the harmonic picture. Roughly speaking, there are two cases in which the anharmonicities are large; either the collectivity of the vibration is so strong that the system is approaching to the instability of the corresponding degree of freedom, or the excitation mode has a single-particle character. The case of low-frequency quadrupole vibrations in nuclei belongs often to the former case. Consequently, it is often difficult to make a quantitative analysis of available data in terms of the basic coupling of the vibrational modes to other degrees of freedom, both collective and single-particle. A nice example of low-frequency octupole vib­ rations in spherical nuclei is the 3- state at 2.6 MeV in 208Pb. Although observed octupole vibrations in the neighbouring odd-A nuclei have been suc­ cessfully understood2> in terms of particle-vibration coupling8> which is a basic tool in the understanding of vibrational anharmonicities, none of the double octupole-phonon states have ever been detected experimentally in 208Pb. In the case of the octupole vibration in 147Gd (I;,.= 7 /2-) a member with the

Macroscopic and microscopic analysis of gamma motion in 168Er

The γ-vibrations in 168Er are analysed in a macroscopic and in a microscopic model with special emphasis on the anharmonicities of two-phonon states. It is found that in order to account for recent experimental evidence it is necessary to assume large anharmonic components both in the collective potential energy surface and in the mass parameters. The possibility that the quadrupole energy function has a minimum at γ ≠ 0 is also considered.

Magnetic dipole and quadrupole states of58Ni

The cross sections for the inelastic scattering of electrons with excitation of the 1+ and 2- states of 58Ni are calculated using the DWBA. Their structure is calculated within the quasiparticle-phonon nuclear model taking the interaction of one- and two-phonon states into account. The interaction is shown to be important for the explanation of the experimental data of Lindgren et al. (1976).

High-lyingM 1-states of spherical nuclei

The cross section of inelastic scattering of slow electrons at large angles with excitation of high-lying 1+-states in208Pb are calculated in DWBA. The calculations are carried out both in the random-phase approximation and with the interaction of one-and two-phonon states in the framework of semi-microscopic quasi-particle-phonon model. A group of noncollective 1+-states with a large excitation probability in backward (e, e)-scattering is found in the excitation energy region of 17–21 MeV. We discuss also the problem of existence, properties, and possibility of discovery the high-lying collective 1+-states (2ħωM 1-resonance) predicted by Speth et al.

Comment on "Isospin and strong-coupling effects in neutron scattering from even-ASe isotopes"

The effect of coupling of the two-phonon states on elastic and ${2}^{+}$ inelastic cross sections is calculated for 8 MeV neutrons incident on $^{76,80,82}\mathrm{Se}$. Isospin optical parameters and deformation parameters are determined from comparison with data. The values of $\ensuremath{\beta}$ are larger than one would expect on the basis of measured values from ($p$,${p}^{\ensuremath{'}}$) and Coulomb excitation.NUCLEAR REACTIONS $^{76,80,82}\mathrm{Se}$ ($n$,$n$) and ($n$,${n}^{\ensuremath{'}}$); cross sections calculated with coupled channels; effects of two-phonon coupling.

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.