Line shape of the plasma resonance in simple metals

Gibbons, P. C.; Schnatterly, S. E.; Ritsko, John J.; Fields, J. R.

doi:10.1103/physrevb.13.2451

Cited by 161 publications

(45 citation statements)

References 27 publications

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“…However, recent inelastic X-ray scattering measurements on the plasmon dispersion in Li metal by Eisenberger et al [5] indicate that in the long wavelength limit (k = O ) , the frequency of the plasmon has a value which is x 0.90~1, instead of the classical value wPl. The measurements made by Gibbons et al [6] in metals like Al, Li, and Na, using inelastic electron scattering experiments, show similar results. A later observation by Krane [7] in polycrystalline A1 and I n has given rise to a plasmon dispersion which is of different character than that exhibited by most of the earlier measurements.…”

Section: Introductionsupporting

confidence: 87%

Estimation of plasmon dispersion‐coefficient and evaluation of the effective mass of electrons in metals

Misra

Tripathy

1987

Physica Status Solidi (b)

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Using an improved version of the Bohm-Pines effective Hamiltonian for the electron-plasmon system, the correct value is reproduced of the critical wave-vector, k,, for the plasmons in the random phase approximation (RPA) by minimizing the total energy of the system. The calculated values for the effective mass m* of the electron show a close agreement with the experimental result for sodium and potassium. By introducing a n adjustable mass-parameter, meff, in the theory not only a very good fit of the plasmon frequencies with the experimental data is obtained but also reproduced the observed value of the plasmon dispersion coefficient, a, for metals like AI, In, Na, and K. Further, an explanation for the two branch behaviour of the volume plasmon in A1 and In is given. Finally, a qualitative argument is put forth to explain the difference between the calculated values of m* and those of meff. Unter Benutzung einer verbesserten Version des effektiven Bohm-Pines-Hamiltonians fur dasElektron-Plasmon-System wird der korrekte Wert des kritischen Wellenvektors k, fur die Plasmonen in der Random-Phase-Naherung (RPA) durch Minimisierung der Gesamtenergie des Systems reproduziert. Die berechneten Werte fur die effektive Masse m* des Elektrons zeigen eine enge Dbereinstimmung mit dem experimentellen Ergebnis fur Natrium und Kalium. Durch Einfuhrung eines anpal3baren Massenparameters meff in die Theorie wird nicht nur eine sehr gute Anpassung der Plasmonfrequenzen mit den experimentellen Daten erhalten, sondern auch der beobachtete Wert des Plasmon-Dispersionskoeffizienten a, fur Metalle wie Al, In, Na und K reproduziert. Weiterhin wird eine Erklarung fur das Zwei-Zweige-Verhalten des Volumenplasmons in A1 und I n gegeben. SchlieBlich wird ein qualitatives Argument geliefert, um die Differenz zwischen den berechneten Werten von m* und denen von meff zu erklaren.

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Section: Introductionsupporting

confidence: 87%

Estimation of plasmon dispersion‐coefficient and evaluation of the effective mass of electrons in metals

Misra

Tripathy

1987

Physica Status Solidi (b)

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“…The deviation of the experimental plasmon-peak position from the free-electron value was mainly interpreted in terms of optical effective mass and is due to intraband transitions as pointed out by Paasch [ll]. The volume plasmon linewidth in lithium was interpreted as a plasmon decay via interband transitions [10,12]. So the question arises as to whether such a deviation still exists for clusters.…”

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Optical response of large lithium clusters: Evolution toward the bulk

et al. 1993

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Multistep photon absorption has been used to measure the collective excitation of free lithium clusters having up to 1500 atoms. The blueshift of the Mie resonance energy, as cluster size increases, probes the surface effects. Its absolute value is consistent with the dielectric constants of the bulk down to a 100 atom cluster. The comparison with calculations in random-phase approximation in the local approximation demonstrates that the jellium model is no longer valid for lithium clusters. PACS numbers: 78.20.Dj, 61.46.+w The optical response of small metal particles as a function of size offers the possibility to follow the development of collective effects in metallic systems. Of these, alkali clusters, and in particular sodium and potassium, are regarded as a prototype of simple metallic particles. Their dipole absorption spectra are consistent with the optical excitation predicted by the classical Mie theory treatment of collective dipole oscillation in spherical or ellipsoidal distorted metallic droplets [1][2][3][4]. A more elaborate approach was obtained from time-dependent density-functional-theory calculations to quantitatively interpret the experimental data on sodium and potassium clusters having less than 40 atoms [5]. However, it was of fundamental interest to explore large cluster sizes to bridge the gap between the free small particles and the bulk in order to know to what extent the macroscopic dielectric function describes the optical response of metallic clusters.We have developed recently an experimental procedure for extending optical absorption measurements [6] to large masses, i.e., a few thousand atoms. For large potassium clusters we have shown that the experimental value of the resonance energy evolves toward the infinite limit h(DM deduced either from the experimental volume plasmon energy hcop [7] or from the surface plasmon energy hcos [8]: hwp^=^ h(OM^^^ hcDs^.Those values are close to the free-electron values. The small difference, less than 5%, which still remains between experimental values and free-electron values is greatly reduced when core polarization and effective mass are included [7,9].Lithium metal differs from the other alkali metals. The measured volume plasmon energy is greatly shifted down from the free-electron value and its linewidth is very broad as compared to other alkali metals [10]. The deviation of the experimental plasmon-peak position from the free-electron value was mainly interpreted in terms of optical effective mass and is due to intraband transitions as pointed out by Paasch [ll]. The volume plasmon linewidth in lithium was interpreted as a plasmon decay via interband transitions [10,12]. So the question arises as to whether such a deviation still exists for clusters. The measurement of the plasmon resonance of lithium clusters is a real challenge to know to what extent the dielectric constants of the bulk are pertinent parameters to interpret the collective excitation of lithium clusters. If so, the microscopic calculation of the dynamic response o...

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“…For a typical metal, 0.02 < η 0 < 0.2 and dη/dq 2 ∼ = aη 0 , where 2 < a < 10 [18]. This experimental damping rate is successfully modeled by Sturm [17], who takes into account of the Umklapp process of electrons in the presence of the spatially periodic ions.…”

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confidence: 97%

“…(3) would be preferred for a strong pump, while a small value of η(q) is better for a weak pump. The damping rate in the warm dense matters might be accessible by the measurement of the electron energy loss in the thin heated foil experiments [18]. The effect of the phase transition on the plasmon decay is theoretically challenging to understand, yet it is important because of its relevance to the BRS x-ray compression.…”

mentioning

confidence: 99%

“…The situation is different in metals and the warm dense matters that we consider for the x-ray compression. The interaction of electrons via the inter-band transition (the Umklapp process) [16][17][18][19][20][21][22] becomes the dominant plasmon decay process, in contrast to the Landau damping in an ideal plasma. As a consequence, the decay rate of the long wavelength plasmon * Electronic address: seunghyeonson@gmail.com † Electronic address: sku@cims.nyu.edu ‡ Current address: Citigroup, 388 Greenwich St. New York, NY 10013 is much higher than the prediction of the prevalent dielectric function theory.…”

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Backward Raman compression of x-rays in metals and warm dense matters

Son

Moon

2010

Physics of Plasmas

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Experimentally observed decay rate of the long wavelength Langmuir wave in metals and dense plasmas is orders of magnitude larger than the prediction of the prevalent Landau damping theory. The discrepancy is explored, and the existence of a regime where the forward Raman scattering is stable and the backward Raman scattering is unstable is examined. The amplification of an x-ray pulse in this regime, via the backward Raman compression, is computationally demonstrated, and the optimal pulse duration and intensity is estimated.PACS numbers: 52.38.-r, 52.59. Ye, 42.60.Jf Coherent intense x-rays would enable various potential applications [1,2], however, it is very difficult to compress an x-ray pulse, or even in the UV regime. Some progress has been made in this direction, based on the recent advances in the areas of free electron laser [3] and the inertial confinement fusion [4]. It is shown that the backward Raman scattering (BRS) [5,6], where two light pulses and a Langmuir wave interact one another to exchange the energy, is one promising approach to create an ultra short light pulse (down to a few attoseconds [7,8]); a pulse gets compressed and intensified via this laser-plasma interaction. The BRS is successfully used to create intense pulses of the visible light frequencies [9,10]. It is natural to consider the same technique for the x-ray compression [7,8]. However, some physical processes in the regime where x-rays might be compressible are considerably different from those in the visible light regime. There are new physical processes to be considered, such as the Fermi degeneracy and the electron quantum diffraction [11][12][13][14], to mention a few.We consider one key aspect for the BRS in the x-ray compression regime, i.e., the damping of the Langmuir wave. In an ideal plasma, the decay rate of the Langmuir wave increases rapidly as the wavelength decreases. It poses a concern for the BRS, as the plasmon from the forward Raman scattering (FRS), having a lower wave vector than the BRS, depletes the pump. There have been various attempts to suppress the FRS in the visible light regime [15]. The situation is different in metals and the warm dense matters that we consider for the x-ray compression. The interaction of electrons via the inter-band transition (the Umklapp process) [16][17][18][19][20][21][22] becomes the dominant plasmon decay process, in contrast to the Landau damping in an ideal plasma. As a consequence, the decay rate of the long wavelength plasmon * Electronic address: seunghyeonson@gmail.com † Electronic address: sku@cims.nyu.edu ‡ Current address: Citigroup, 388 Greenwich St. New York, NY 10013 is much higher than the prediction of the prevalent dielectric function theory. In this paper, we show that a parameter regime where the BRS is unstable and the FRS is stable does exist in metals and warm dense matters, as the plasmon from the FRS strongly decays. Here, we consider metals in room temperature, and show that an x-ray pulse can be compressed in this regime. We estimate an optima...

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Line shape of the plasma resonance in simple metals

Cited by 161 publications

References 27 publications

Estimation of plasmon dispersion‐coefficient and evaluation of the effective mass of electrons in metals

Estimation of plasmon dispersion‐coefficient and evaluation of the effective mass of electrons in metals

Optical response of large lithium clusters: Evolution toward the bulk

Backward Raman compression of x-rays in metals and warm dense matters

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