Projectile-charge dependence of quasi-free-electron bremsstrahlung

Abstract

Continuum x rays induced by bombardments of a Be target with 20.14-MeV/amu protons and He2+ ions have been measured with a Si(Li) detector in the direction of 90' with respect to the incident beam. Differences in the x-ray -production cross sections multiplied by the x-ray energy 8'ay Pro [o-I, (tao)/4 -oz(leo) jJ and ratio of the cross sections R (A'au) f= -o&(Aced) j4az(has)] for the proton and He +-ion impact, where (7&(fo)) and o. z(A'e) are the x-ray -production cross sections for proton and He2+-ion impact, respectively, were obtained as a function of the x-ray energy. Both the difference and the ratio show peaks in the region where the x-ray energy is equal to the relative kinetic energy between the projectile and the inner-shell electron to be scattered by the projectile. From the comparison with a theory of quasi-free-electron bremsstrahlung based on the impulse approximation, it is found that this peak corresponds to the maximum of the velocity-distribution function of the inner-shell electron. Furthermore, the contribution of the radiative electron-capture process in the case of proton and 3He2+ impact is clearly found.Recently, ' we have bombarded targets of Be, C, and Al with 6 -40-MeV protons and have found a new component of continuum x rays. These continuum x rays are predominant in the region where the x-ray energy tao is smaller than the energy T, = --,m, V»', where m, is the electron mass and V~is the projectile velocity, and the Doppler effect is definitely observed in the angular distributions of these x rays. From these experimental results, the x rays have been well understood in terms of the bremsstrahlung produced by the orbital electrons scattered by the projectile Coulomb field; we call this process the quasi-free-electron bremsstrahlung (QFEB). The lllIX r '1/2 projectile-energy dependence and the angular dependence of QFEB have been well explained by a simple theory assuming that the orbital electrons are free.Further, a calculation taking into account the velocity distribution of orbital electrons has been developed, ' and it was found that the spectrum of QFEB in the vicinity of the high-energy limit of Ace = T, is sensitively dependent on the velocity distribution of orbital electrons.On the basis of the impulse approximation which Jakubassa and Kleber have developed for the bremsstrahlung in heavy-ion reaction, 3 a more accurate formula for the cross section of QFEB can be given by with v, '"= -, '

Continuous X-rays produced in light-ion–atom collisions

“…The calculated angular distribution are compared with experiment at proton energy of 4.0 MeV in Fig. 15 and a satisfactory agreement is obtained (Ishii et al, 1977). It should be noted that the angular distribution of SEB plays an important role in the detection limit of PIXE analysis, resulting in higher sensitivity in backward than in forward direction.…”

“…20 in form of Eq. (32a) (Ishii and Morita, 1987). The three lines in the figure are calculated AB for 0.5, 1.0, and 4.0 MeV protons.…”

“…In accordance with the formulae described above, the production cross sections of AB, SEB and QFEB can be approximately scaled and are expressed by Ishii and Morita, 1987) …”

“…In other words, the spectral shape of the high-energy limit of QFEB provides for a sensitive and direct measurement of the velocity distribution of target electrons. Moreover, the variation in QFEB cross sections using projectiles with different nuclear charge contains even more detailed information on the velocity distribution of target electrons in the atom (Ishii et al, 1983).…”

“…To explain this asymmetry in the bremsstrahlung production, a factor of relativistic retardation i.e. 1/(1Àb cos y Br ) 4 must be taken into account and this factor can be approximated by, 1=ð1 À b cos y Br Þ 4 % 1 þ 4b cos y Br , then, the angular distribution of SEB is modified as follows (Ishii et al, 1977): The coefficients C R 1 and C R 2 are given by Eq. (26) shows that the contribution from the relativistic retardation vanishes at an observation angle of 901.…”