Direct observation of systematic deviations from the Bethe stopping theory for relativistic heavy ions

Scheidenberger, C.; Geißel, H.; Mikkelsen, H.H.; Nickel, F.; Brohm, T.; Folger, H.; Irnich, H.; Magel, A.; Mohar, M. F.; Münzenberg, G.; Pfützner, M.; Roeckl, E.; Schall, I.; Schardt, D.; Schmidt, Karl‐Heinz; Schwab, W.; Steiner, M.; Stöhlker, Th.; Sümmerer, K.; Vieira, D.J.; Voss, B.; Weber, M.

doi:10.1103/physrevlett.73.50

Cited by 52 publications

(19 citation statements)

References 25 publications

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“…Experimental data are shown as letters taken from Refs. [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. The results obtained in this study are in good agreement with the experimental data in all energy regions.…”

supporting

confidence: 93%

“…The dashed lines are obtained from HU90 [43] and SRIM96 [24] computer code. The letters are the experimental data taken from Rea87 [25], Po61a [26], Fa66 [27], Wr79 [28], Sa92 [29], Me78 [30], Ab92 [31], BG65 [32], Ga 87 [33], Sa79 [34], Ch68 [35], Hk96 [36], Shk96 [37], Sb94 [38], Bi90 [39], Hof76 [40], Or63 [41], Hv68 [42], Rä90 [43], Wr72 [45], Rä87 [46], R160 [47], BG65 [32], Bi78 [48], Ga87 [33], Bt66 [49] and Sd74 [50].…”

Section: Results and Comparison With Experimentsmentioning

confidence: 99%

“…The results indicated with solid lines are the present results obtained by our model. The S T results, obtained in this study are compared with the experimental data [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] and the other theoretical calculations, HU90 [43] and SRIM96 [24]. In Figure 1a stopping powers for oxygen ion on C is shown as a function of projectile energy (MeV=amu).…”

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confidence: 87%

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Effective stopping charges and stopping power calculations for heavy ions

Gümüş

Köksal

2002

Radiation Effects and Defects in Solids

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In this study the model suggested by Sugiyama has been developed and applied for the calculation of the stopping powers for nonrelativistic heavy ions in various target materials. Sugiyama's model has been expanded to low and high energy regions in our work. Analytical expressions are obtained in the modified BB stopping power formula for the effective charge and effective mean excitation energies. In the modified LSS formula, a quasi-molecule criterion has been applied to both the projectiles and the target atoms. Electronic excitation contribution, S e0 , and quasi-molecule contribution, S ei , to stopping power were found for a wide energy region. It is observed that in intermediate energy region both contributions have maxima. The stopping power due to excitation-ionization in the intermediate and higher energy region is found to be dominant, whereas quasi-molecule contribution is dominant in the lower energy region. The calculated results of stopping power are in good agreement with experimental data for various ions and targets within a few percent in a wide projectile energy range.

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supporting

confidence: 93%

Section: Results and Comparison With Experimentsmentioning

confidence: 99%

mentioning

confidence: 87%

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Effective stopping charges and stopping power calculations for heavy ions

Gümüş

Köksal

2002

Radiation Effects and Defects in Solids

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“…It was modified by Bloch [3], and it was shown that at relativistic velocities a "Mott" correction for spin changing collisions [4] was required. The proper combination of these effects was shown to match quantitatively with experiments on the stopping power of heavy ions with energies from 700 to 1000 MeV A [5].…”

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confidence: 63%

Effect of Nuclear Size on the Stopping Power of Ultrarelativistic Heavy Ions

Datz

et al. 1996

Phys. Rev. Lett.

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A new formulation for the theory of electronic stopping power of ions at relativistic energies has been proposed by Lindhard and Sørensen (LS). In it, they find that, at sufficiently high energy, nuclear size effects should act to reduce the momentum transfer to electrons and hence the stopping power. To test this result, we passed beams of 33. Pb ions ͑g 168͒ from the CERN-SPS through targets of C, Si, Cu, Sn, and Pb, and measured energy loss and beam broadening. The LS theory for stopping power is confirmed, but with a slight drift upward from theory for high-Z targets. A drastic decrease in energy straggling (factor of ϳ4) predicted by LS cannot be deconvoluted from the multiple Coulomb scattering distribution. [S0031-9007(96) Bloch [3], and it was shown that at relativistic velocities a "Mott" correction for spin changing collisions [4] was required. The proper combination of these effects was shown to match quantitatively with experiments on the stopping power of heavy ions with energies from 700 to 1000 MeV A [5].The energy loss DE of a totally stripped ion Z 1 passing through a thickness Dx with an electron density n e can be expressed asAt relativistic energies the term L is given bywhere g is the Lorentz factor ͑1 2 b 2 ͒ 21͞2 , b y͞c, m 0 is the electron rest mass, and I is the mean ionization potential of the target electrons. The term d arises from the so-called density effect [6,7] due to the relativistic increase in the transverse field and the attendant target screening of the projectile charge in distant collisions. For g $ 100 as in our experiments, the density effect correction can be closely approximated bywhere v p is the plasmon frequency of the total density of the electrons of the medium. Then with b Х 1 andandThe new term here is DL NS , the correction for nuclear size effect that has just recently been proposed by Lindhard and Sørensen [8,9]. Lindhard and Sørensen (LS) performed exact quantum mechanical calculations on the basis of the Dirac equation to produce values for the average energy loss and straggling which are stated to be accurate for any value of projectile charge. Note that the various DL terms are just a consequence of the calculation. Using a point Coulomb potential, they are able to reproduce the results of Bohr, Bethe, Bloch, and Mott. However, they show that at sufficiently high energies the finite nuclear size effects the stopping power.It is convenient to view the projectile nucleus as a stationary scattering point for a flux of electrons moving at the velocity of the ion in the laboratory system. According to LS, an electron will encounter the nucleus when its angular momentum pR Х gm 0 cR where R is the nuclear radius (R ϳ 1.2 3 10 213 A 1͞3 cm, where A is the atomic weight). When pR ϳh͞2 modification of the first few quantum phase shifts will be needed, i.e., nuclear size effects should be important when 2gm 0 cR͞h gA 1͞3 ͞160 Х 1. Alternatively, one may consider that the effect will become important when the deBroglie wavelength of the electron l -h͞gm 0 c beco...

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“…But the use of the LS program will hardly be necessary for radiation therapy, since even for oxygen ions at 690 MeV/u, there is no difference between LS theory and Bethe theory (eq. 1) (Scheidenberger et al 1994).…”

Section: Tables and Programsmentioning

confidence: 99%

The Stopping Power of Matter for Positive Ions

Paul¹

2012

Modern Practices in Radiation Therapy

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Direct observation of systematic deviations from the Bethe stopping theory for relativistic heavy ions

Cited by 52 publications

References 25 publications

Effective stopping charges and stopping power calculations for heavy ions

Effective stopping charges and stopping power calculations for heavy ions

Effect of Nuclear Size on the Stopping Power of Ultrarelativistic Heavy Ions

The Stopping Power of Matter for Positive Ions

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