Journal of Physical Studies 19(3), Article 3001 [19 pages] (2015) DOI: https://doi.org/10.30970/jps.19.3001 TUNNELING THROUGH THE ALBRECHT'S BARRIERS WITH DISSIPATIVE TERMS S. P. Maydanyuk Institute for Nuclear Research of the National Academy of Sciences of Ukraine Kyiv, UA-03680, Ukraine

We present a new method for the determination of the wave function for a particle tunneling through one-dimensional Albrecht potential barriers with a dissipative term constructed on the basis of evolving non-stationary wave packets. The intensity of the influence of the dissipative forces of such a type on the tunneling process can be controlled via an arbitrary parameter $\gamma$. The properties of the dissipative forces in tunneling are investigated in the task of capture of the $\alpha$-particle by the nucleus $^{44}{\rm Ca}$ with the rectangular barrier (whose parameters were extracted from modern approaches for the description of the interaction between the $\alpha$-particle and nucleus without any dissipation in this $\alpha$-capture reaction).

Understanding the influence of dissipation on the tunneling processes can be better obtained on the basis of the characteristics which are not dependent on the arbitrary dissipative parameter $\gamma$. A dissipative correction $\Delta T$ of the penetrability without dissipation $T_{0}$ or its ratio to the penetrability without dissipation $\Delta T / T_{0}$ provides such information. We performed calculations of this characteristic in dependence on the energy of the $\alpha$-particle, and we conclude:

• The dissipative correction $\Delta T$ is negative, i.e. the inclusion of a dissipative term $W_{A}$ of Albrecht type into the potential suppresses barrier penetrability. This result is natural, but it was obtained on the basis of the developed method.
• We observe the presence of clear minimum in dependence of the dissipative correction $\Delta T / T_{0}$ on the energy of the incident $\alpha$-particle at $E=5.27$ MeV where the influence of the dissipative forces on the tunneling processes is maximal. At a further increase of the energy the role of the dissipative forces is decreased.
• At decreasing of the energy of the $\alpha$-particle (from 5.27 MeV) the dissipative correction $\Delta T / T_{0}$ is decreased. This indicates at the suppression of the influence of the dissipative forces on the tunneling process deeply under the barrier.
• A general dependence of the dissipative correction $\Delta T / T_{0}$ on energy of the $\alpha$-particle has an oscillatoric character. We can explain such a behavior by the wave nature of the tunneling processes under the barrier (where most of characteristics have a harmonic energy dependence).

PACS number(s): 03.65.-w, 03.65.Xp, 25.40.Lw

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