Multipolar Approach for Description of Bremsstrahlung During α -Decay and Unified Formula of the Bremsstrahlung Probability

Abstract

Model of angular bremsstrahlung of photons emitted during α-decay is presented. A special emphasis is given on development of unified formalism of matrix elements in the dipole and multipolar approaches. A probability of the emission of photons calculated on the basis of the multipole model without any normalization on experimental data (i. e. in absolute scale) is found at 90• of the angle ϑαγ between directions of motion of the α-particle (with its tunneling under barrier) and emission of photons to be in a good agreement with the newest experimental data for the 210 Po, 214 Po, and 226 Ra nuclei. The spectrum for 244 Cm is found at ϑαγ = 25• to be in satisfactory agreement with high limit of errors of experimental data of Japanese group. A comparative analysis for the spectra calculated for 210 Po by the multipole and dipole approaches in the absolute scale and with normalization on experimental data is performed. The emission of photons from the internal well in the dipole approach is found to be not small while the multipolar approach does not show such a strong dependence. Distribution of the bremsstrahlung probability on the numbers of protons and nucleons of the α-decaying nucleus in selected region close to 210 Po is obtained. An unified formula of the bremsstrahlung probability during the α-decay of arbitrary nucleus expressed directly through the Qα-value and numbers Ap, Zp of nucleons and protons of this nucleus is proposed.

Model for bremsstrahlung emission accompanying interactions between protons and nuclei from low energies up to intermediate energies: Role of magnetic emission

“…This definition for F f i is in compliance with our previous formalism in [11,32,33,[38][39][40][41][42]53,75]. In particular, for the square of the matrix element of emission we have (see Eqs.…”

“…(49), allows us to describe well enough experimental data for bremsstrahlung emission during α decay without any normalization of the calculated spectra to the experiment (see Fig. 1 in [41]). 4 A key problem in obtaining reliable bremsstrahlung spectra is the difficulty in achieving stability in calculations of the matrix elements.…”

“…(39) or (41). In particular, J m (l i , l f , n; r 1 , r 2 ) transforms to J m (l i , l f , n) at r 1 → 0 and r 2 → +∞.…”

What can we know about hypernuclei via analysis of bremsstrahlung photons?

“…From analysis of literature we conclude, that this question has not been studied yet. On the other side, we can base our new investigations on our current formalism of emission of bremsstrahlung photons in nuclear reactions [71][72][73][74][75][76][77][78][79][80][81][82][83][84].…”

Study of compound nucleus formation via bremsstrahlung emission in proton $α$-particle scattering

“…Results of such a work are used as a basis for construction of other bremsstrahlung models in nuclear physics. Our bremsstrahlung model is developed along such a line [15][16][17][18][19][20][21][22][23][24][25][26][27]. According to its logic, determination of the wave functions for the scattering states is quantum mechanical task with interacting potentials, that allows to keep maximally accurate quantum effect (that can be interesting in cases where they are strong, for example, see [28]).…”