TY - JOUR

T1 - Quantum effect in the diffusion along a potential barrier

T2 - Comments on the synthesis of superheavy elements

AU - Takigawa, Noboru

AU - Ayik, Sakir

AU - Washiyama, Kouhei

AU - Kimura, Sachie

N1 - Funding Information:
This work is supported in part by the Grant-in-Aid for Scientific Research from Ministry of Education, Culture, Sports, Science and Technology under Grant No. 12047203 and No. 13640253, also under the Special Area Research, Contract No. 08640380, and also by the U.S. DOE Grant No.DE-FG05-89ER40530. N.T. thanks Tennessee Technological University for support and hospitality during his visits. N.T. and S.A. thank also A. Gokalp and O. Yilmaz for their kind hospitality at the Middle East Technical University∕Ankara, where this work has been partly completed.

PY - 2004/5

Y1 - 2004/5

N2 - We discuss a quantum effect in the diffusion process by developing a theory, which takes the finite curvature of the potential field into account. The transport coefficients of our theory satisfy the well-known fluctuation-dissipation theorem in the limit of Markovian approximation in the cases of diffusion in a flat potential and in a potential well. For the diffusion along a potential barrier, the diffusion coefficient can be related to the friction coefficient by an analytic continuation of the fluctuation-dissipation theorem for the case of diffusion along a potential well in the asymptotic time, but contains strong non-Markovian effects at short times. By applying our theory to the case of realistic values of the temperature, the barrier curvature, and the friction coefficient, we show that the quantum effects will play significant roles in describing the synthesis of superheavy elements, i.e., the evolution from the fusion barrier to the conditional saddle, in terms of a diffusion process. We especially point out the importance of the memory effect, which increases at lower temperatures. It makes the net quantum effects enhance the probability of crossing the conditional saddle.

AB - We discuss a quantum effect in the diffusion process by developing a theory, which takes the finite curvature of the potential field into account. The transport coefficients of our theory satisfy the well-known fluctuation-dissipation theorem in the limit of Markovian approximation in the cases of diffusion in a flat potential and in a potential well. For the diffusion along a potential barrier, the diffusion coefficient can be related to the friction coefficient by an analytic continuation of the fluctuation-dissipation theorem for the case of diffusion along a potential well in the asymptotic time, but contains strong non-Markovian effects at short times. By applying our theory to the case of realistic values of the temperature, the barrier curvature, and the friction coefficient, we show that the quantum effects will play significant roles in describing the synthesis of superheavy elements, i.e., the evolution from the fusion barrier to the conditional saddle, in terms of a diffusion process. We especially point out the importance of the memory effect, which increases at lower temperatures. It makes the net quantum effects enhance the probability of crossing the conditional saddle.

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U2 - 10.1103/PhysRevC.69.054605

DO - 10.1103/PhysRevC.69.054605

M3 - Article

AN - SCOPUS:17144438902

VL - 69

SP - 054605-1-054605-5

JO - Physical Review C - Nuclear Physics

JF - Physical Review C - Nuclear Physics

SN - 0556-2813

IS - 5

M1 - 054605

ER -