Positron absorption

The rate of positron absorption in positron-atom collisions, proportional to the flux loss due to —iV, should be obtainable by solving the... 

Pair annihilation of a positron e+ and an electron e by y-ray emission was briefly explained in Section 1.3. There, the hydrogen-like system ePe, or positronium Ps, was described quantum mechanically as a QBS having a finite lifetime r because of an absorption potential —z Vabs- This potential also causes positron flux loss, or positron absorption, in collisions with atoms. 

Summarizing the previous discussion, individual forces are active along the respective rays. If test charge is negative, electron force is repulsive, whereas positron force is attractive. Also, distance de is evaluated at the time of emission te, while da is evaluated at the moment of absorption. Net force is the vector addition. 

Montgomery and LaBahn (1970). The number in parentheses following 30 eV indicates the power of ten by which the cross sections have been multiplied. Normalization to theory was done at 30° and 120° by Smith et al. (1990) and at 30° and 60° by Floeder et al. (1988). Reprinted from Physical Review Letters 64, Smith et al, Evidence for absorption effects in positron elastic scattering by argon, 1227-1230, copyright 1990 by the American Physical Society. 

Dou, L., Kauppila, W.E., Kwan, C.K., Pryzybyla, D., Smith, S.J. and Stein, T.S. (1992a). Evidence for resonances and absorption effects in positron-krypton differential-elastic-scattering measurements. Phys. Rev. A 46 R5327-R5330. 

Joachain, C.J. and Potvliege, R.M. (1987). Importance of absorption effects on fast positron-argon differential cross sections. Phys. Rev. A 35 4873-4875. 

A negative imaginary potential in the time-independent Schrodinger equation absorbs the particle flux, thus violating the law of conservation of flux, which is satisfied for real potentials [12,13]. Then, the quantum electrodynamical phenomenon of pair annihilation can be represented by particle loss due to an effective absorption potential H = —zVabs since the exact mechanism of positron loss is totally irrelevant to the study of the atomic processes in consideration [9,10,14-16]. The only important aspect of pair annihilation for the present purpose is the correct description of the loss rate. The absorption potential H is proportional to the delta function 5 (r) of the e+-e distance vector r (Section 4.2). 

Here, HQ is the Coulomb-interaction Hamiltonian similar to Eq. (3), and E is a real-valued energy of the whole system, i.e., the sum of the collision energy and the energy of the target state before collision. If the target atom contains more than one electron, the absorption potential —iVabs is to be summed over all the target electrons since the incident positron can annihilate with any of the electrons. 

Most positron collision processes can be treated with high precision by considering only the Coulomb interactions with no absorption potentials taken into account. Then, the same kind of QBSs as explained in Section 1.2 for electronic systems are possible in positron collisions too. 

Figure 4.19 The partial-wave singlet (full curves) and triplet (broken curves) absorption cross sections in e+ + H(1s) collisions, plotted versus the incident positron energy measured from the threshold energy for positronium formation. Results of hyperspherical closecoupling calculations including the absorption potential —iVabs in the Hamiltonian. Note that the thresholds Etu for the full and broken curves are different by 0.841 meV, the hyperfme splitting. Figure from Ref. [16].

A. Igarashi, M. Kimura, I. Shimamura, N. Toshima, Inseparable positron annihilation and positronium formation in positron-atom collisions Description in terms of an absorption potential, Phys. Rev. A 68 (2003) 042716. 

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