Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing an important role in nuclear physics and astrophysics. We derive a new useful relationship between ANC of the Gamow radial wave function and the renormalized (due to the Coulomb interaction) Coulomb-nuclear partial scattering amplitude. We use an analytical approximation in the form of a series for the nonresonant part of the phase shift which can be analytically continued to the point of an isolated resonance pole in the complex plane of the momentum. Earlier, this method which we call the S-matrix pole method was used by us to find the resonance pole energy. We find the corresponding fitting parameters for the

Explicit expressions of the vertex constant for the decay of a nucleus into two charged particles for an arbitrary orbital momentum l are derived for the standard expansion of the effective-range function K l (k 2 ), as well as when the function K0(k 2 ) has a pole. As physical examples, we consider the bound state of the nucleus 3 He and the resonant states of the nuclei 2 He and 3 He in the s-wave, and those of 5 He and 5 Li in the p-wave. For the systems N p and N d the pole trajectories are constructed in the complex planes of the momentum and of the renormalized vertex constant. They correspond to a transition from the resonance state to the virtual state while the Coulomb forces gradually decrease to zero.

A general method, which we call the potential S-matrix pole method, is developed for obtaining the S-matrix pole parameters for bound, virtual, and resonant states based on numerical solutions of the Schrödinger equation. This method is well known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when r → ∞. Concrete calculations are performed for the 1 + ground state of 14 N, the resonance 15 F states (1/2 + , 5/2 + ), low-lying states of 11 Be and 11 N, and the subthreshold resonance in the proton-proton system. We also demonstrate that in the case of broad resonances, their energy and width can be found from the fitting the experimental phase shifts using the analytical expression for the elastic-scattering S matrix. We compare the S-matrix pole and the R matrix methods for broad resonances in the 14 O-p and in 26 Mg-n systems.A. M. MUKHAMEDZHANOV et al. PHYSICAL REVIEW C 81, 054314 (2010)

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A new algorithm for the asymptotic nuclear coefficients calculation, which we call the ∆-method, is proved and developed. This method was proposed in Ref. [O. L. Ramírez Suárez and J.-M. Sparenberg, arXiv: 1602.04082 [nucl-th] (2016)] but no proof was given. We apply it to the bound state situated near the channel threshold when the Sommerfeld parameter is quite large within the experimental energy region. As a result, the value of the conventional effective-range function K l (k 2 ) is actually defined by the Coulomb term. One of the resulting effects is the wrong description of energy behavior of the elastic scattering phase shift δ l reproduced from the fitted total effectiverange function K l (k 2 ). This leads to an improper value of the asymptotic normalization coefficient (ANC) value. No such problem arises if we fit only the nuclear term. The difference between the total effective-range function and the Coulomb part at real energies is the same as the nuclear term. Then we can proceed using just this ∆-method to calculate the pole position values and the ANC. We apply it to the vertices 4 He + 12 C ←→ 16 O and 3 He + 4 He ←→ 7 Be. The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the 16 O bound final states as well as to the 7 Be.

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This paper presents control laws for distributed parameter systems of parabolic and hyperbolic types with unknown spatially varying parameters. These laws, based on the model reference adaptive control approach, guarantee asymptotic tracking of the output of the reference model by the output of the plant for arbitrary time invariant, but spatially varying reference input. The novel capabilities of the algorithms proposed are providing reduced sensitivity to measurement noise due to the reduced order of the spatial di!erentiation of the output data and permitting on-line estimation of the spatially varying plant parameters, constructively enforceable through the reference input and/or boundary conditions. The parameter estimation is carried out by means of an auxiliary system with the time-varying parameters that simultaneously converge in¸ to plant parameters when appropriate input signals in the reference model are used. The orthogonal expansions of these time-varying parameters, which can be computed by passing the auxiliary system parameters through the integrator block, converge to the plant parameters pointwise if the latter are su$ciently smooth. The parameter convergence is obtained by combining the adaptation laws with su$ciently rich input signals, referred to as generators of persistent excitation, which guarantee the existence of a unique steady state for the parameter errors.

This erratum corrects misprints in Sec. V and in the Conclusion (Sec. VII) of our paper. The end of Eq. (34) should read ANC = 1.032×10 14 fm −1/2 instead of ANC = 1.032×10 4 fm −1/2 . There, the given value of the squared NVCG 2 l is correct. At the end of the Conclusion (p. 7, the right column, the fifth line above the Acknowledgments) the text should read ANC = 2.106×10 4 fm −1/2 instead of ANC = 1.0323×10 4 fm −1/2 .We would like to thank J.-M. Sparenberg who pointed out these misprints in his letter concerning his new preprint. 2469-9985/2016/93(5)/059901(1) 059901-1