Kramers Diffusive Mechanism of Alpha Decay, Proton/Cluster Radioactivity and Spontaneous Fission, Induced by Vacuum Zero-point Radiation Vitaliy Rusov Department of Theoretical and Experimental Nuclear Physics, Odessa National Polytechnic University, Ukraine with with S. . Mavrodiev Mavrodiev (INRNE, BAS, Sofia, Bulgaria (INRNE, BAS, Sofia, Bulgaria D. . Vlasenko (NPU, Odessa, Ukraine) Vlasenko (NPU, Odessa, Ukraine) M. . Deliyergiyev (NPU, Odessa, Ukraine) Deliyergiyev (NPU, Odessa, Ukraine)
Nucleus nonlinear dynamics Nucleus nonlinear dynamics tunneling tunneling superfluidity and superconductivity superfluidity and superconductivity Josephson nuclear effect, Josephson nuclear effect, - condensate condensate dynamical supersymmetry and nuclear dynamical supersymmetry and nuclear quantum phase transition quantum phase transition quantum, dynamical and constructive quantum, dynamical and constructive chaos chaos nuclear stochastic resonance nuclear stochastic resonance
Tunneling or jumping over ? Tunneling or jumping over ?
On Chetaev’s theorem and its On Chetaev’s theorem and its consequence consequences b s briefly riefly Chetaev’s theorem: Chetaev’s theorem: Stability condition for Hamiltonian systems Stability condition for Hamiltonian systems in in the presence of dissipative forces has the following the form the presence of dissipative forces has the following the form (1) (1) where where S is the action, is the action, q is generalized coordinate. is generalized coordinate. N.G. Chetaev N.G. Chetaev , Scientific proceedings of Kazan Aircraft Institute, № 5, ( , Scientific proceedings of Kazan Aircraft Institute, № 5, ( 1936 1936 ) 3; ) 3; N.G. Chetaev N.G. Chetaev , Motion stability. Resear. on the analyt. mechanics, Nauka, Moscow , Motion stability. Resear. on the analyt. mechanics, Nauka, Moscow 1962 1962 .
The The Schrödinger equation as the stability condition Schrödinger equation as the stability condition of trajectories in classical mechanics of trajectories in classical mechanics
The Bohm The Bohm-Madelung system of equations Madelung system of equations Hence it follows that the Bohm Bohm-Madelung Madelung quantum potential is equivalent to Chetaev’s dissipation energy Q where S is the action; h = 2 is Plank constant; А is amplitude, which in the general case is the real function of the coordinates q i and time t.
Diffusion mechanism of alpha decay, cluster Diffusion mechanism of alpha decay, cluster Diffusion mechanism of alpha decay, cluster Diffusion mechanism of alpha decay, cluster radioactivity and spontaneous fission radioactivity and spontaneous fission radioactivity and spontaneous fission radioactivity and spontaneous fission where W = W ( x,p,t ) is the probability density distribution in phase space x , p .
The transition rate over the potential barrier looks like where E * is the heat excitation energy; а = А /(8 1 ) MeV -1 is the parameter of the density of one-particle levels.
The Kramers’s channel of -decay, cluster The Kramers’s channel of decay, cluster radioactivity and spontaneous fission radioactivity and spontaneous fission The dependence of nuclear particle potential energy on distance to nuclear center Kramers transition rate
Kramers’s transition time Kramers’s transition time where T 1/2 is half-life; Kramers is the effective frequency of daughter particle appearance on the nuclear surface of radius R; A and Z are mass number and the charge of parent nucleus ; Z cl is the charge of outgoing particle ; (Z-Z cl ) is the charge of the daughter nucleus ; R Coul is minimal Coulomb radius , Fm.
Comparing theory with experiment Comparing theory with experiment It It is is necessary to to solve solve the the inverse inverse nonlinear nonlinear problem, problem, which which represents the system of nonlinear equations of of following following type type: for which we have applied parameterization of functions R Kramers , Kramers , with respect to quantum numbers A , Z , A cl , Z cl , which determine the mass numbers and the charges of parent nucleus and cluster, and energies Е TKE , Q cl , which determine the kinetic and total energy of decay.
Using the Alexandrov dynamic regularization method we have obtained Using the Alexandrov dynamic regularization method we have obtained , Kramers and : the parameterization of functions the parameterization of functions R Kramers Kramers , Kramers and
The theoretical and experimental values of half-life for even-even nuclei as a function of the total kinetic energy Е TKE for decay, cluster and proton radioactivity, spontaneous fission.
The theoretical and experimental values of the half-life of even-even nuclei as function of fission total kinetic energy Е TKE for decay of superheavy nuclei with Z =114, 116, 118.
CONCLUSIONS CONCLUSIONS In In the the framework framework of of Bohmian Bohmian quantum quantum mechanics mechanics supplemented supplemented with with the the Chetaev Chetaev theorem theorem on on stable stable trajectories trajectories in in dynamics dynamics in in the the presence presence of of dissipative dissipative forces forces we we have have shown shown the the possibility possibility of of the the classical classical (without (without tunneling) tunneling) universal universal description description of of radioactive radioactive decay decay of of heavy heavy nuclei, nuclei, in in which which under under certain certain conditions conditions so so called called noise noise-induced induced transition transition is is generated generated or, or, in in other other words, words, the the stochastic stochastic channel channel of of alpha alpha decay, decay, cluster cluster radioactivity radioactivity and and spontaneous spontaneous fission fission conditioned conditioned by by the the Kramers Kramers diffusion diffusion mechanism mechanism. Based Based on on the the ENSDF ENSDF database database we we have have found found the the parametrized parametrized solutions solutions of of the the Kramers Kramers equation equation of of Langevin Langevin type type by by Alexandrov Alexandrov dynamic dynamic auto auto-regularization regularization method method (FORTRAN (FORTRAN program program REGN REGN-Dubna) Dubna). These These solutions solutions describe describe with with high high-accuracy accuracy the the dependence dependence of of the the half half-life life (decay (decay probability) probability) of of heavy heavy radioactive radioactive nuclei nuclei on on total total kinetic kinetic energy energy of of daughter daughter decay decay products products. The verification The verification of of inverse inverse problem problem solution solution in in the the framework framework of of the the universal universal Kramers description Kramers description of of the the alpha alpha decay, decay, cluster cluster radioactivity radioactivity and and spontaneous spontaneous fission, fission, which which was was based based on on the the newest newest experimental experimental data data for for alpha alpha-decay decay of of even even-even even super super heavy heavy nuclei nuclei ( Z =114 114, 116 116, 118 118 ) have have shown shown the the good good coincidence coincidence of of the the experimental experimental and and theoretical theoretical half half-life life depend depend on on of of alpha alpha- decay decay energy energy.
The principle of least action of dissipative forces The principle of least action of dissipative forces The The statement statement that that P ( x , y , z, z, t ) indeed indeed is is the the probability probability density density function function of of particle particle trajectory trajectory number number is is substantiated substantiated as as follows follows. Let Let us us assume assume that that the the influence influence of of the the perturbation perturbation forces forces generated generated by by the the potential potential Q on on the the wave wave packet in packet in an an arbitrary arbitrary point point in in the the phase phase space space is is proportional proportional to to the the density density of of trajectories ( = A 2 ) at the the particle particle trajectories at this this point point. From From where where follows follows that that the the wave wave packet packet is is practically practically not not perturbed perturbed when when the the following following condition condition is is fulfilled fulfilled
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