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Suche nach „[C.] [Eltschka]“ hat 6 Publikationen gefunden
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    Angewandte Naturwissenschaften und Wirtschaftsingenieurwesen

    Beitrag (Sammelband oder Tagungsband)

    H. Friedrich, Michael Moritz, C. Eltschka

    Near-Threshold Quantization and the Semiclassical Limit

    Sitzung Q14.3

    DPG-Tagung 2001

    2001

    Angewandte Naturwissenschaften und Wirtschaftsingenieurwesen

    Zeitschriftenartikel

    H. Friedrich, Michael Moritz, C. Eltschka

    Near-threshold quantization and level densities for potential wells with weak inverse-square tails

    Physical Review A - atomic, molecular and optical physics, vol. 64

    2001

    DOI: 10.1103/PhysRevA.64.022101

    Abstract anzeigen

    For potential tails consisting of an inverse-square term and an additional attractive 1/rm term, V(r)∼[ħ2/(2M)][(γ/r2)-(βm-2/rm)], we derive the near-threshold quantization rule n=n(E) which is related to the level density via ρ=dn/dE. For a weak inverse-square term, -14<γ<34 (and m>2), the leading contributions to n(E) are n=E→0A-B(-E)γ+1/4√, so ρ has a singular contribution proportional to (-E)γ+1/4√-1 near threshold. The constant B in the near-threshold quantization rule also determines the strength of the leading contribution to the transmission probability through the potential tail at small positive energies. For γ=0 we recover results derived previously for potential tails falling off faster than 1/r2. The weak inverse-square tails bridge the gap between the more strongly repulsive tails, γ>~3/4, where n(E)=E→0A+O(E) and ρ remains finite at threshold, and the strongly attractive tails, γ<-1/4, where n=E→0Bln(-E/A), which corresponds to an infinite dipole series of bound states and connects to the behavior n=E→0A+BE(1/2)-(1/m), describing infinite Rydberg-like series in potentials with longer-ranged attractive tails falling off as 1/rm, 0<m<2. For γ=-1/4 (and m>2) we obtain n(E)=E→0A+C/ln(-E/B), which remains finite at threshold.

    Angewandte Naturwissenschaften und Wirtschaftsingenieurwesen

    Zeitschriftenartikel

    H. Friedrich, Michael Moritz, C. Eltschka

    Comment on “Breakdown of Bohr's Correspondence Principle”

    Physical Review Letters - moving physics forward, vol. 86

    2001

    DOI: 10.1103/PhysRevLett.86.2693

    Angewandte Naturwissenschaften und Wirtschaftsingenieurwesen

    Zeitschriftenartikel

    H. Friedrich, Michael Moritz, C. Eltschka

    Threshold properties of attractive and repulsive 1/r2 potentials

    Physical Review A - atomic, molecular and optical physics, vol. 63

    2001

    DOI: 10.1103/PhysRevA.63.042102

    Abstract anzeigen

    We study the near-threshold (E⃗ 0) behavior of quantum systems described by an attractive or repulsive 1/r2 potential in conjunction with a shorter-ranged 1/rm (m>2) term in the potential tail. For an attractive 1/r2 potential supporting an infinite dipole series of bound states, we derive an explicit expression for the threshold value of the pre-exponential factor determining the absolute positions of the bound-state energies. For potentials consisting entirely of the attractive 1/r2 term and a repulsive 1/rm term, the exact expression for this prefactor is given analytically. For a potential barrier formed by a repulsive 1/r2 term (e.g., the centrifugal potential) and an attractive 1/rm term, we derive the leading near-threshold behavior of the transmission probability through the barrier analytically. The conventional treatment based on the WKB formula for the tunneling probability and the Langer modification of the potential yields the right energy dependence, but the absolute values of the near-threshold transmission probabilities are overestimated by a factor which depends on the strength of the 1/r2 term (i.e., on the angular momentum quantum number l) and on the power m of the shorter ranged 1/rm term. We derive a lower bound for this factor. It approaches unity for large l, but it can become arbitrarily large for fixed l and large values of m. For the realistic example l=1 and m=6, the conventional WKB treatment overestimates the exact near-threshold transmission probabilities by at least 38%.

    Angewandte Naturwissenschaften und Wirtschaftsingenieurwesen

    Zeitschriftenartikel

    H. Friedrich, Michael Moritz, C. Eltschka

    Near-threshold quantization and scattering for deep potentials with attractive tails

    Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 33

    2000

    DOI: 10.1088/0953-4075/33/19/315

    Abstract anzeigen

    Near-threshold properties of bound and continuum states in a deep potential with an attractive tail depend essentially on a few `tail parameters', which are determined by the properties of the potential tail beyond the region of r-values where WKB wavefunctions are accurate solutions of the Schrödinger equation. One of these tail parameters is a length parameter which defines the singular contribution to the level density just below threshold and the reflectivity of the tail of the potential just above threshold; another is a phase difference which, together with the length parameter, determines the mean scattering length. The near-threshold quantization rule and the actual scattering length are determined by the tail parameters together with a dimensionless constant depending on the zero-energy value of the WKB action integral. We study potentials with tails consisting of two inverse-power terms, V(r)~-Cα/rα-Cα1/rα1,α1>α>2 and we derive exact analytical expressions for the tail parameters in the special case α1 = 2(α-1). This enables us to demonstrate the effect of a significant non-homogeneity of the potential tail on the results derived previously for homogeneous tails.

    Angewandte Naturwissenschaften und Wirtschaftsingenieurwesen

    Zeitschriftenartikel

    H. Friedrich, J. Trost, Michael Moritz, C. Eltschka

    Tunneling near the base of a barrier

    Physical Review A - atomic, molecular and optical physics, vol. 58, no. 2, pp. 856-861

    1998

    DOI: 10.1103/PhysRevA.58.856

    Abstract anzeigen

    Generalized WKB connection formulas are used to derive the transmission amplitude describing tunneling through a potential barrier via two isolated classical turning points. The resulting formulas correctly reproduce the behavior in the vicinity of the base of the barrier where the tunneling probability vanishes exactly, and where formulas available to date fail.