Orbit-integral corrections to the Lindhard atomic stopping power for classically scattered heavy atoms

Latta, B.M.; Scanlon, P. J.

doi:10.1103/physreva.10.1638

Cited by 28 publications

(6 citation statements)

References 10 publications

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“…is higherthanfFHB(t1l2) fore < O.land fWHB(W, E ) islowerthan fFHB(t112) for E > 0.1, and finally these functions coincide with each other for high energies E. The same dependences are observed in the same T F calculations performed in [15]. As it is seen from Pig.…”

Section: The Elastic Scattering Cross-section and Nuclear Stopping Powersupporting

confidence: 78%

“…This difference is responsible for the considerable underestimation of the low-energy range and straggling calculated with fEF(t1/2). It should be pointed out that the scattering function f T F ( t 1 I 2 , E ) obtained on the basis of the T F potential in [15] is distinguished from f W H B ( t l / 2 , E ) to an even greater degree than the function fEF(t112). Thus utilization of the wide-angle extrapolation in numerous range calculations with the TF potential not only allowed to simplify the calculations but also prevented from greater discrepancies between theory and experiment.…”

Section: The Elastic Scattering Cross-section and Nuclear Stopping Powermentioning

confidence: 93%

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Influence of the Interatomic Potential and the Elastic Scattering Cross‐Section Approximation on the Spatial Distribution of Implanted Ions

Burenkov

Komarov

Temkin

1981

Physica Status Solidi (b)

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The elastic scattering cross-sections are calculated both in the framework of Lindhard wideangle extrapolation method and on the basis of an exact solution of the classical equation of motion of a particle in a central-force potential. Using a direct method for the numerical solution of integro-differential equations governing the ion implantation spatial distribution parameters, the projected ranges, projected and lateral stragglings, and skewnesses are calculated in a wide interval of reduced energies. It is shown that for incident energies E < 0.1 all these parameters are affected by the choice of both the interatomic potential and elastic scattering cross-section approximation.PaccwiTbmamTcR ceveHnR ynpyroro paccemmrr KaK B p a m a x nuHnxapnoBcKoii an-npoKcmarpm Ha 6 o n~r u~e YrJIbI, T a K II c noMoubm Toworo pewems maccmecKoro YPaBHeHElR nBUmeHllH YaCTUqbI B UeHTpaJIbHOM CUJIOBOM none. MCnOJIb3yH pa3pa60TaH-HbIM aBTOpaMH IIPHMOB YUCJIeHHbIfi MeTOA PeIIIeHMR IIHTerpO-AIIQ)Q)epe€I~IIanbHbIX ypa-THPOBaHHOfi IlpHMeCH, PaCCsHTaHbI ItpOeKTIIBHble npo6era, IlpOAOJIbHbIe kI IlOtIepesHbIe pas6pocb1 npo6e1-OB M aCllMMeTpllll B IIIMPOKOM HHTepBaJIe npllBeAeHHbIX 3HepTHfi. nOKa3aH0, 9 T O ~b160p KPH MeHlaTOMHOrO IIOTeHUHaJIa, TaK EI ~~U~J I H~~H U H , B KOTOPOM BHeHdi, onzicbmam~nx napaMeTpM npocTpaHcTseHrxoro pacnpeaeaeaarr HoHHo-HMnaaH-paccwTbIBanocL ceqeme ynpyroro pacceaHm BJIHReT Ha Bce napaMeTpbi pacnpene-neHm npm & < 0 , l .

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Section: The Elastic Scattering Cross-section and Nuclear Stopping Powersupporting

confidence: 78%

Section: The Elastic Scattering Cross-section and Nuclear Stopping Powermentioning

confidence: 93%

Influence of the Interatomic Potential and the Elastic Scattering Cross‐Section Approximation on the Spatial Distribution of Implanted Ions

Burenkov

Komarov

Temkin

1981

Physica Status Solidi (b)

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Section: Projectile Pathmentioning

confidence: 99%

“…The limits of integration are then from R,, the point of closest approach (obtained by setting cosq equal to zero), out to r,. The singularity in the integration arising from the cosine at Ro is removed by the transformation [32] The energy loss for a given impact parameter, s, thus becomes For separations from ro to 2r0 the impulse approximation was used. Since the cross-section for a close encounter with a neighbouring atom is small and in the region ro to 2r, the projectile is generally deflected back towards the target atom being considered, an impulse approximation would be less in error than an orbit centered on the target atom.…”

Section: Projectile Pathmentioning

confidence: 99%

Average Electronic Energy Loss in the Modified Firsov Theory

Latta

Scanlon

1976

Physica Status Solidi (b)

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Calculations of the average electronic stopping power S, for heavy ions in solids are performed within the framework of the modified Firsov theory. Consideration is given to the effect of the usual approximations of straight line trajectories, free-atom electron densities, and the positioning of the dividing surface between the atoms a t a fixed fraction of their separation. When He is averaged over all impact parameters, for classical orbits, the variation of S, as a function of target atomic number 2, is much smaller than the variation previously determined by other authors for forward-scattered particles. The use of a simple approximation for the electron densities in solids, in conjunction with a Thomas-Fermi estimate of their velocities during the interaction, leads to results that are very similar to the free-atom case.Nous avons procede B des calculs du pouvoir d'arrbt electronique moyen dans le cas d'ions lourds dans un solide dans le contexte de la theorie de Firsov modifih. Nous avons pris en consideration les effets des approximations usuelles des trajectoires en ligne droite, des densites electroniques basbes sur le modde de l'atome libre et de l'effet de la position de la surface sbparant les atomes comme se trouvant A une fraction de leur sbparation.Lorsqu'on fait la moyenne de He Bur tous les parametres d'impact, dans le cas d'orbites classiques, la variation de 8, en fonction de Z,, le nombre atomique de la cible, est de beancoup infbrieure A celle determinee prbcbdemment par d'autres auteurs dans le cas de particules diffusbes vers I'avant. Nous montrons qu'une simple approximation des densites electroniques dans les solides, en conjonction avec une estimation de leur vitesse durant l'interaction utilisant le modhle de Thomas-Fermi, conduit it des resultats qui s'avhrent tr&s similaires A ceux obtenus dans le cas du mod6le d'un atome libre. IntroductionThe Firsov theory [ 13 for the electronic stopping cross-sections of low-velocity heavy ions has been modified by various authors [Z to 51 to account for oscillatory structure in the electronic stopping cross-section S , as a function of the atomic number of both the projectile 2 , [6 to 131 and target 2 , [ 14 to 201. Since the experimentally observed oscillations have generally been for either forwardscattered particles or for channeled particles, the theoretical calculations have approximated the trajectories of the incident particles by straight lines (impulse approximation). This approximation is valid in cases where close encounters do not contribute to the phenomena being observed.In some experiments, however, the energy loss averaged over all impact parameters is required. Such is the case, for example, in the measurement of nuclear decay lifetimes by the Doppler shift attenuation method (DSAM). In this method an excited nucleus moves in an energy absorbing medium and the energy of the emitted gamma radiation is Doppler shifted in a manner that depends both on the lifetime of the state and the stopping power of the medium. Broude et al. [21...

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“…In short, for a given set of experimental parameters, it is not easy to understand damage cascade formation and evolution without conducting cascade dynamics simulations. A simplified approximation may be applied based on the work of Norgett, et al [49] and Lindhard [45,50,51] and summarized in [42], in which the relative size, l (i.e. effective diameter) of a single damage cascade for each irradiation condition may be estimated using [42]:…”

Section: Charged Particles As Surrogates For Neutron Irradiationmentioning

confidence: 99%

The Mechanism of Radiation-Induced Nanocluster Evolution in Oxide Dispersion Strengthened and Ferritic-Martensitic Alloys

Swenson¹

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Orbit-integral corrections to the Lindhard atomic stopping power for classically scattered heavy atoms

Cited by 28 publications

References 10 publications

Influence of the Interatomic Potential and the Elastic Scattering Cross‐Section Approximation on the Spatial Distribution of Implanted Ions

Influence of the Interatomic Potential and the Elastic Scattering Cross‐Section Approximation on the Spatial Distribution of Implanted Ions

Average Electronic Energy Loss in the Modified Firsov Theory

The Mechanism of Radiation-Induced Nanocluster Evolution in Oxide Dispersion Strengthened and Ferritic-Martensitic Alloys

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