Ionization by Recoil Particles from Alpha-Decay

Abstract

which can be derived from considerations of the momentum space degeneracy of the outgoing particles.In line with the suggestions of Weisskopf, Feshbach, and Peaslee, 7 Wigner 8 has shown that widths are also proportional to level spacing, D } whence (6) becomes TacEW.Relation (5) must then be considered valid only in cases of neutron capture. Since level spacings in neutron capture are about 10 ev, in general, (5) must be replaced by r/£*£~4XlO-B (ev)-*.Applying (8) to the case of alpha-decay, JS*~2.5X10 3 (ev)*, £-40* ev whence T~10 4 ev.The value of D was obtained from the measured energy differences between various energy groups in natural alpha-decay. 9 Comparison of (9) with (3) indicates that the ratio of neutron width to alpha-width without barrier is about 0.1; and comparison of (3) with the width from the one-body theory (0.8 Mev) indicates that the "probability of formation of an alpha-particle" in a nucleus (i.e., the correction for the many-body theory over the one-body theory) is about one-eighth. Either of these last two values may be in error by a factor of 10 or more. S INCE the energy loss of a slow heavy particle is predominantly to recoiling gas atoms, ionization by secondary heavy particles contributes a large fraction of the total ionization resulting from a slow heavy particle that is stopped in a gas.Let r} be the ionization efficiency o e I/E of a primary particle of energy E which gives rise to the number of ion pairs /, where c<>* is the energy loss per ion pair of a particle the energy of which is very high. The ionization efficiency satisfies an equation of the formin which ^' -oi e I'/E' is the ionization efficiency of a gas atom of energy E f in its own gas. The functions /x and X are given by ^co e <r e /(b e +b v ),where <r e is the cross section for the production of an ion pair in a collision between the primary particle and an atom of the gas including ionization by ejected electrons, and b e and b" are the stopping cross sections per atom for the loss of energy by the primary particle to excitation and ionization and to atomic recoil, respectively. The kernel k(E y E') iswhere o~(E, E') is the cross section per unit energy range for the production of a recoil atom of energy E'; the maximum energy transferred to an atom is E m '=4MM'E/(M+M') 2 .The ionization efficiency rj f of a gas atom satisfies the differential-integral equation obtained from (1) by regarding the initial particle as identical in nature with the recoil atom; the corresponding functions are designated //, X', etc.We consider a heavy particle (Z=82, M = 208 proton masses) in argon. For velocities less than about 0Av Qy where vo=e?/h, the primary scattering is very nearly spherically symmetrical in the center of gravity system and therefore k(E, E')^2E'/E m ' 2 .Deviations from spherically symmetrical secondary scattering are unimportant until velocities of the primary particle considerably greater than 0.12PO are attained (E2>7& kev). Up to these velocities b v and b v ' are practically constant, 1 except for...

Bragg-like curve for dark matter searches: Binary gases

“…It is not clear how much of such effect is included in the asymptotic form. Ling and Knipp (1950) presented a model for Pb ions in Ar similar to the power low approximation by Lindhard. They estimated that about 2/3 of the ionization is due to the secondary ions.…”

Luminescence Response and Quenching Models for Heavy Ions of 0.5 keV to 1 GeV/n in Liquid Argon and Xenon

“…The curve is intended for directional searches for WIMPs in the gas TPC. Ling and Knipp [30] presented an approximate equation for q nc for a heavy particle (24) where γ" = 2M 1 / (M 1 + M 2 ) and a , a" are constants. They found that the measurement by Madsen [27] is well represented by the following equation:…”

“…LET el for Pb recoils is as large as S T /3 in argon as shown in Figure 2a. Following Ling and Knipp [30], we use the W α /W NR ratio, (22.0 ± 0.3)/(158.8 ± 8) = 0.139, for 103 keV Pb recoils in Xe measured by Cano [29], and a semi-empirical power-law approximation may be written as…”

“…The numerical calculation for Pb recoils in LAr by Lindhard et al gives values significantly larger than the experimental values and those obtained by the power-law approximation. We took a semi-empirical power law by Ling and Knipp [30], Equation (25), which is similar to the power-law approximation by Lindhard; however, the coefficient was determined by using the measured W α /W NR ratios for a Ar + 5% air mixture by Madsen [27]. Measurements obtained for Ar by Jesse and Sadauskis [28] and measurements obtained for Ar + 2% CH 4 [29] and Ar + 2% Xe by Cano [29] are also shown.…”

Quenching factor and electronic LET in a gas at low energy

“…Ling and Knipp [7] have presented an approximate equation for a heavy particle (Z=82, A= 208) in Ar.…”