On the Born limit of relativistic electron and positron bremsstrahlung in the field of heavy nuclei

Abstract

It is shown numerically that for high collision energies and small emission angles of the bremsstrahlung photon and the scattered particle the differential cross section as well as the polarization correlations tend to the Born limit when the photon frequency becomes small. This holds irrespective of the target nuclear charge. Thus the Born approximation is complementary to the Dirac partial-wave theory where the latter is no longer convergent.

Advances in bremsstrahlung: a review

“…Considered are small emission angles of photon and lepton, but the two particles are emitted into opposite sides of the beam axis. Justified by the applicability of the plane-wave Born approximation at small angles when the photon frequency is low, that theory is used to interpret the structures near 2.5 MeV as resulting from interference [57] between the two parts of the transition amplitude (2.1.5) which correspond to photon emission before, respectively after, the scattering from the nuclear field. The strong decrease of the positron intensity near the high-energy end of the spectrum is also clearly seen.…”

“…We have chosen the case where photon (θ k = 20 • ) and electron (ϑ f = 30 • ) are emitted in coplanar geometry to the same side of the beam axis (where the intensity is high, see, e.g. [44,57]. For emission to opposite sides, see Fig.…”

“…This is due to the strong Coulomb repulsion between the positron and the nucleus which becomes effective at the large momentum transfers necessary to create hard photons. On the other hand, for soft photons emitted into forward directions, the plane-wave Born approximation becomes valid [13], such that the electron-positron differences are very small [57].…”

Relativistic positron scattering from heavy ground-state nuclei

“…As concerns C 120 , it decreases monotonously below ω = 2 MeV in all cases, but for high frequencies, |C 120 | for electrons is much larger at ϑ f = 150 • than for 30 • , while for positrons the increase with ω near the SWL is similar for both angles. If, instead of ϕ f = 0, a coplanar geometry with ϕ f = 180 • is chosen (where lepton and photon emerge on different sides of the beam axis), there appears an interference structure in the photon spectrum for small scattering angles and photon angles (as discussed in [71]), which is also visible in the photon angular distribution near 350 • (corresponding to θ k = 10 • at ϕ f = 180 • , see Fig. 7c).…”

“…On the other hand, small angles are related to distant collisions, particularly for low photon frequencies. Under such conditions, even the PWBA describes the intensity and the polarization correlations satisfactorily [71]. The maximum value of |A| is below 1 MeV at small angles, while it is near 3 MeV for 140 • , its position increasing to about 10 MeV at the backmost angles [68,72].…”