No abstract

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.

In this work we study the r-mode instability windows and the gravitational wave signatures of neutron stars in the slow rotation approximation using the equation of state obtained from the density dependent M3Y effective interaction. We consider the neutron star matter to be βequilibrated neutron-proton-electron matter at the core with a rigid crust. The fiducial gravitational and viscous timescales, the critical frequencies and the time evolutions of the frequencies and the rates of frequency change are calculated for a range of neutron star masses. We show that the young and hot rotating neutron stars lie in the r-mode instability region. We also emphasize that if the dominant dissipative mechanism of the r-mode is the shear viscosity along the boundary layer of the crust-core interface, then the neutron stars with low L value lie in the r-mode instability region and hence emit gravitational radiation.

Dipole and quadrupole polarizabilities and shielding factors for 10-electron closed-shell ions from O-to Si 4+ have been calculated following the self-consistent perturbation procedure. Results are accurate in the coupled Hartree-Fock scheme. Interpolation relations have been obtained which may be used to relate these quantities to the radius of maximum electron density for ions in actual crystals.

We study the properties of the neutron-nucleus total and reaction cross sections for several nuclei. We have applied an analytical model, the nuclear Ramsauer model, justified it from the nuclear reaction theory approach, and extracted the values of 12 parameters used in the model. The given parametrization has an advantage as phenomenological optical model potentials are limited up to 150-200 MeV. The present model provides good estimates of the total cross sections for several nuclei particularly at high energies.