Vitaliy Rusov Department of Theoretical and Experimental Nuclear - - PowerPoint PPT Presentation

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)

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

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

• f trajectories in classical mechanics
• f 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 qi and time t.

Diffusion mechanism of alpha decay, cluster Diffusion mechanism of alpha decay, cluster radioactivity and spontaneous fission radioactivity and spontaneous fission Diffusion mechanism of alpha decay, cluster Diffusion mechanism of alpha decay, cluster 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 The Kramers’s channel of -decay, cluster decay, cluster radioactivity and spontaneous fission radioactivity and spontaneous fission

Kramers transition rate The dependence of nuclear particle potential energy

• n distance to nuclear center

Kramers’s transition time Kramers’s transition time

where T1/2 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; Zcl is the charge of outgoing particle; (Z-Zcl) is the charge of the daughter nucleus; RCoul 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

• f following

following type type: for which we have applied parameterization of functions RKramers, Kramers,  with respect to quantum numbers A, Z, Acl , Zcl , which determine the mass numbers and the charges of parent nucleus and cluster, and energies ЕTKE , Qcl , 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 the parameterization of functions the parameterization of functions RKramers

Kramers,

,  Kramers

Kramers and

and  :

The theoretical and experimental values of half-life for even-even nuclei as a function of the total kinetic energy ЕTKE 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 ЕTKE for decay of superheavy nuclei with Z=114, 116, 118.

CONCLUSIONS CONCLUSIONS



In In the the framework framework of

• f Bohmian

Bohmian quantum quantum mechanics mechanics supplemented supplemented with with the the Chetaev Chetaev theorem theorem on

• n stable

stable trajectories trajectories in in dynamics dynamics in in the the presence presence of

• f

dissipative dissipative forces forces we we have have shown shown the the possibility possibility of

• f the

the classical classical (without (without tunneling) tunneling) universal universal description description of

• f radioactive

radioactive decay decay of

• f 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,

• r, in

in

• ther
• ther words,

words, the the stochastic stochastic channel channel of

• f 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

• n the

the ENSDF ENSDF database database we we have have found found the the parametrized parametrized solutions solutions of

• f the

the Kramers Kramers equation equation of

• f 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

• f the

the half half-life life (decay (decay probability) probability) of

• f heavy

heavy radioactive radioactive nuclei nuclei on

• n total

total kinetic kinetic energy energy of

• f daughter

daughter decay decay products products.



The The verification verification of

• f inverse

inverse problem problem solution solution in in the the framework framework of

• f the

the universal universal Kramers Kramers description description of

• f the

the alpha alpha decay, decay, cluster cluster radioactivity radioactivity and and spontaneous spontaneous fission, fission, which which was was based based on

• n the

the newest newest experimental experimental data data for for alpha alpha-decay decay of

• f

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

• f the

the experimental experimental and and theoretical theoretical half half-life life depend depend on

• n of
• f 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

• f

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

• f the

the perturbation perturbation forces forces generated generated by by the the potential potential Q on

• n the

the wave wave packet packet in 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

• f

the the particle particle trajectories trajectories ( =A2) at 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