Investigation of cascade processes of antiprotonic deuterium at low temperature
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ORIGINAL PAPER
Investigation of cascade processes of antiprotonic deuterium at low temperature S M Motevalli*, O N Ghodsi and S Sheikhian Department of Physics, Faculty of Sciences, University of Mazandaran, P. O. Box 47415-416, Babolsar, Mazandaran, Iran Received: 24 June 2012 / Accepted: 03 October 2012 / Published online: 26 October 2012
Abstract: In this paper, all transition rates of antiprotonic deuterium de-excitation processes have been studied in various initial states and kinetic energies. We have investigated Stark mixing effects in Borie–Leon model. The best experimental data on shift and width of 1S and 2P state have been used to obtain logical rate. Keywords:
Transition rate; Antiprotonic deuterium; De-excitation process; Borie–Leon model
PACS Nos.: 36.10.-k; 36.10.Gv
1. Introduction One of the known effects in cascade processes is formation of the exotic atoms in low temperature fusion reactions. The formation of these atoms is due to the kinetic energy deposit of the heavy negatively charged particles such as muon, pion, kaon, and antiproton when moving through the electron clouds [1–9]. In this process the exotic atoms form in highly excited states and at radius comparable to the outer most electrons Bohr radius [10, 11]. Therefore, cascade processes begin from initial state. Because of large amount of degrees of freedom, many cascade models consider statistical distribution pl / ð2l þ 1Þeal for angular momentum states that pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi have started from n ¼ mX =me . This initial population is 14, 16, 31 and 40 for muon, pion, kaon and antiproton, respectively [12]. Cascade processes fundamentally depend on the radiation and collisional de-excitation after the formation of exotic atom. The known collisional de-excitation processes are chemical dissociation, external Auger transition, Coulomb de-excitation, elastic scattering, Stark mixing [13–19]. These de-excitation processes follow until hadrons capture with hydrogen isotopes or weak decay process occurs [20, 21]. It should be mentioned that weak decay process does not occur for antiprotonic atom [22]. The transition rate estimation of these processes plays fundamental role on X-ray yield calculation [23]. Until now the
transition rates of antiprotonic deuterium have not been presented, therefore we have calculated all transition rates of cascade processes under kinetic energy evolution. We have also taken into account the density dependence of Stark mixing with Borie–Leon model [24]. Then we have estimated the standard cascade transition rates in various initial states. It should be mentioned that at low energy the strong interaction of antiprotonic deuterium has to be considered [25]. Hence, the energy levels of the antiprotonic deuterium are shifted and broadened due to the strong interaction between nucleus and antiproton. These strong interactions, shifts and widths affect the absorption during the cascade processes. In this paper we have only used experimental widths and shifts; parameters that are listed in ref. [26–28].
2. Cas
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