Daughter molecules wave functions

Here Mnuc, is the internal matrix element of the radioactive nucleus which we have supplied with the index n Mmol is the molecular matrix element pv, fp, and Prec are, respectively, the neutrino, the / -electron, and the recoil momenta [ o1 and noi are the wave functions of the daughter and the parent molecules which describe the electronic, vibrational, and rotational molecular degrees of freedom. 

R jm and Rq" are the equilibrium configurations of the nuclei of the parent molecule (RT) in the electron state m and of the daughter molecule (RHe)+ in the electron state n, respectively. Shown in Fig. 1 are the electron terms and the vibrational wave functions of the parent and the daughter molecules together with the transition nuclear density function... 

Fig. 1. Scheme of the electronic terms and vibrational wave functions of parent (RT) and daughter (RHe)+ molecules. 

The greater the number of functions 4 J, belonging to the orthonormal set, the more completely and in more detail the spectrum of the /(-decay-induced excitations of a molecule can be calculated. Consequently, the method for calculating the wave functions of the daughter ion must be such that at a reasonable volume of calculation we would be able to construct a sufficiently large number of multielectron wave functions of excited states. The Hartree Fock method allows one to construct the wave functions of excited states as the combinations of determinants symmetrized in a certain way. Within this method the excitation is considered to be a transition of an electron from an occupied Hartree-Fock molecular orbital into a vacant one. 

The Feynman diagram for the simplest annihilation event shows that annihilation is possible when the two particles are Ax h/mc 10 12 5 m apart, and that the duration of the event is At h/mc2 10-21 s. The distance is the geometric mean of nuclear and atomic dimensions, which is probably not significant. The distance is so much smaller than electronic wave functions that it may be assumed to be zero in computations of annihilation rates. The time is so short that, during it, a valence electron in a typical atom or molecule moves a distance of only ao/104, so that a spectator electron can be assumed to be stationary and the annihilating electron can be assumed to disappear in zero time. Thus the calculation of annihilation rates requires the evaluation of expectation values of the Dirac delta function, and the relaxation of the daughter system (post-annihilation remnant) can be understood with the aid of the sudden approximation [4], These are both relatively simple computations, providing an accurate wave function is available. 

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