Dependence of Coulomb capture ratio and x-ray intensities on the mesonic-particle energy spectrum

Abstract

The dependence of the per-atom capture ratio A(Z1, Z2) and the x-ray intensity pattern on the spectral flux density n(W) of slow mesonic particles in the target is calculated in closed form with a semiclassical theory. The intensity pattern turns out to vary only slightly with n(W) whereas the capture ratio shows a more pronounced dependence.Numerical results are presented.There are basically two quantities which enter into the capture ratio and the initial angular momentum distribution of the mesonic particles Coulomb captured in a given element in the case of a homo- where R denotes the cut-off radius of the atomic potential ~u, for an energy loss -A W > W andfor -A W < W. It is the aim of this note to calculate the effect of a deviation of n(W) from a white spectrum on peratom capture ratio A(Z1, Zz) in the case of a homogeneous target consisting of elements with atomic numbers Z 1 and Z2, and on angular momentum distribution P(I). Also, variations in the shape of the atomic potential ~u will be allowed for. The deviation from a white spectral flux density shall be described by a linear term only,

An experimental investigation of the pressure and concentration dependence of muonic Coulomb capture and cascade in gases

“…It was shown [18] that in a binary mixture the component with low atomic concentration sees a spectrum different from that seen by the component with high atomic concentration. The influence of n(W) on A(Z1,Z2) has recently been treated in the framework of the semiclassical theory [20]. Up to now no experiments were performed to explicitly establish a concentration dependence of A(ZI, Z2) in gases.…”

“…[1][2][3] only few experiments have been performed on the muonic (and pionic) Coulomb capture and cascade in gases [4][5][6][7]. Nevertheless most of the theoretical treatments of muonic Coulomb capture -either semiclassical [8][9][10][11][12][13][14][15][16][17][18][19][20] or purely quantum-mechanical [21][22][23][24][25][26][27][28][29] -use spherically symmetric electron densities and atomic potentials which are best realized in noble gases. One particularly interesting question connected with the Coulomb capture of muons is that of a possible concentration dependence of the per atom Coulomb capture probability P(Z), where Z denotes the atomic number.…”

Muonic x-ray intensity measurements on a highT c superconductor

“…The muon Coulomb capture in the individual elements of a chemical compound and the x-ray intensities in the individual cascades are strongly determined by the energy spectrum of the slow muons in the sample before Coulomb capture [5]. This spectrum is governed by the stopping power S, and S itself depends on the electronic band structure in a similar way as the electric conductivity [1,6].…”