We present a modification of the wall formula for one body dissipation in order to include the effect of irregularity in the shape of the one body potential on the dissipation mechanism. We arrive at a dissipation rate which is a scaled version of the wall formula developed earlier by Blocki et al. We show that the scaling factor is determined by a measure of chaos in the single particle motion. As an illustration, we obtain this measure of chaos for particles in a multipole deformed cavity with a view to use the scaled wall formula to calculate the damping widths of multipole vibrations of the cavity wall. Considering the amplitudes of the vibrations typical of the giant resonances in nuclei, it is observed that the effect of the shape dependence is to strongly suppress the damping caused by the original wall formula. ͓S0556-2813͑96͒04809-1͔PACS number͑s͒: 24.60. Lz, 21.60.Ev, 05.45.ϩb, 24.30.Cz
The chaos weighted wall formula developed earlier for systems with partially chaotic single-particle motion is applied to large amplitude collective motions similar to those in nuclear fission. Considering an ideal gas in a cavity undergoing fissionlike shape evolutions, the irreversible energy transfer to the gas is dynamically calculated and compared with the prediction of the chaos weighted wall formula. We conclude that the chaos weighted wall formula provides a fairly accurate description of one-body dissipation in dynamical systems similar to fissioning nuclei. We also find a qualitative similarity between the phenomenological friction in nuclear fission and the chaos weighted wall formula. This provides further evidence for the one-body nature of the dissipative force acting in a fissioning nucleus.
The first equation of Eqs.(3) in [1] was used to describe the mass number and energy dependence of experimental total neutron cross sections for the first time in [2], while the second and third ones were used for scattering and reaction cross sections in [3]. The omissions of these two references were unintended. We derived these equations and Eq. (4) of Ref.[4] (Ref.[12] of our paper [1]) as follows. From partial wave analysis of scattering theory, we know the standard expressions for scattering σ sc and reaction σ r cross sections as, where the quantity η l = e 2iδ l . With the assumption that the phase shift δ l is independent of l and the summation over partial waves l is up to kR only, it follows that σ sc = π (R + λ -) 2 (1 + α 2 − 2α cos β), σ r = π (R + λ -) 2 (1 − α 2 ), and σ tot = σ sc + σ r = 2π (R + λ -) 2 (1 − α cos β), where λ -= 1/k, R is the channel radius beyond which partial waves do not contribute, β = 2Reδ l = 2Reδ, α = e −2Imδ l = e −2Imδ , and summing over l from 0 to kR yielded l (2l + 1) = (kR + 1) 2 .We used the name "nuclear Ramsauer model" from Ref.[12] of our paper [1]. Carpenter and Wilson [5] were the first to call the structure found in total neutron cross * tkm@veccal.ernet.in † joy@veccal.ernet.in ‡ dnb@veccal.ernet.in sections the nuclear Ramsauer effect. This name was adopted by subsequent authors, although the nature of the oscillation in fast-neutron cross sections is essentially different from that observed for slow electrons by Ramsauer. In other works the names "semiclassical optical model" [3] or "diffraction effect" [6] were used, which are more appropriate. From the model of [1] one cannot expect the accuracy of a complete quantummechanical optical model. However, the simple semiclassical optical model [1] obtained to calculate cross sections up to 600 MeV are of relevance as phenomenological optical model potentials are limited up to 150-200 MeV.In fact, the radius of the potential well is just r 0 A 1 3 = r 1 A 1 3 +γ and r 1 = constant. The parameter γ is a very small number (0.00793) compared to the 1 3 needed for fine tuning. It should, therefore, be emphasized that, as mentioned in our paper [1], it is r 0 which is used for fixing β 0 . It is the channel radius which is energy dependent. Channel radius is the radius [appearing in Eqs. (3) of our paper] beyond which no partial waves contribute. It is well known from R-matrix theory that the channel radius is less than the nuclear (potential) radius, which is precisely the case here.Obviously, these omissions do not affect the results and conclusion of the original manuscript [1].We thank Drs. I. Angeli and J. Csikai for bringing this matter to our attention.[1] T.
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