Coulomb breakup of 6Li^6\rm{Li} into α + d\alpha\,+\,\rm{d} in the field of ion 208Pb^{208}\rm{Pb}

The triple differential cross section of $^{208}\rm{Pb}(^6\rm{Li};\alpha,\rm{d})^{208}\rm{Pb}$ elastic Coulomb breakup is calculated using the semiclassical method. We fit the parameters of the Woods-Saxon potential using the experimental $\alpha-\rm{d}$ phase shifts for different states to describe the relative motion of $\alpha$-particle and deuteron. In order to check the validity of the two particle approach for $\alpha-d$ system we apply a potential model to describe the $^2\rm{H}(\alpha,\gamma)^6\rm{Li}$ radiative capture. Our results for the Coulomb breakup of $^6\rm{Li}$ show large value of the forward-backward asymmetry of the $\alpha$-particle and deuteron emission around zero energy in the $^6\rm{Li}$ center-of-mass (c.m.) system. Comparison of the results of our calculation with experimental data gives evidence for the dominance of the Coulomb dissociation mechanism at the $\alpha-d$ relative energy larger than $E_{\alpha\,d}>300\,\rm{keV}$ and sufficiently big contribution of nuclear distortion at $E_{\alpha\,d}$ near zero energy, but essentially smaller than the value reported in Ref.[F. Hammache et al. Phys.Rev. C82, 065802 (2010)].Comment: 11 pages, 5 figures (one figure removed), added the results of new calculations and performed the audit of the tex

Coulomb renormalization and ratio of proton and neutron asymptotic normalization coefficients for mirror nuclei

Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing important role in nuclear reactions, nuclear structure and nuclear astrophysics. In this paper the physical reasons of the Coulomb renormalization of the ANC are addressed. Using Pinkston-Satchler equation the ratio for the proton and neutron ANCs of mirror nuclei is obtained in terms of the Wronskians from the radial overlap functions and regular solutions of the two-body Schr\"odinger equation with the short-range interaction excluded. This ratio allows one to use microscopic overlap functions for mirror nuclei in the internal region, where they are the most accurate, to correctly predict the ratio of the ANCs for mirror nuclei, which determine the amplitudes of the tails of the overlap functions. Calculations presented for different nuclei demonstrate the Coulomb renormalization effects and independence of the ratio of the nucleon ANCs for mirror nuclei on the channel radius. This ratio is valid both for bound states and resonances. One of the goals of this paper is to draw attention on the possibility to use the Coulomb renormalized ANCs rather than the standard ones especially when the standard ANCs are too large.Comment: 20 pages, 14 figure

Asymptotic Normalization Coefficients for 13C+p->14N

The $^{13}C(^{14}N,^{13}C)^{14}N$ proton exchange reaction has been measured at an incident energy of 162 MeV. Angular distributions were obtained for proton transfer to the ground and low lying excited states in $^{14}N$. Elastic scattering of $^{14}N$ on $^{13}C$ also was measured out to the rainbow angle region in order to find reliable optical model potentials. Asymptotic normalization coefficients for the system $^{13}C+p\to {}^{14}N$ have been found for the ground state and the excited states at 2.313, 3.948, 5.106 and 5.834 MeV in $^{14}N$. These asymptotic normalization coefficients will be used in a determination of the S-factor for $^{7}Be(p,\gamma)^{8}B$ at solar energies from a measurement of the proton transfer reaction $^{14}N(^{7}Be,^{8}B)^{13}C$.Comment: 5 pages, 6 figure

Are spectroscopic factors from transfer reactions consistent with asymptotic normalisation coefficients?

It is extremely important to devise a reliable method to extract spectroscopic factors from transfer cross sections. We analyse the standard DWBA procedure and combine it with the asymptotic normalisation coefficient, extracted from an independent data set. We find that the single particle parameters used in the past generate inconsistent asymptotic normalization coefficients. In order to obtain a consistent spectroscopic factor, non-standard parameters for the single particle overlap functions can be used but, as a consequence, often reduced spectroscopic strengths emerge. Different choices of optical potentials and higher order effects in the reaction model are also studied. Our test cases consist of: $^{14}$C(d,p)$^{15}$C(g.s.) at $E_d^{lab}=14$ MeV, $^{16}$O(d,p)$^{17}$O(g.s.) at $E_d^{lab}=15$ MeV and $^{40}$Ca(d,p)$^{41}$Ca(g.s.) at $E_d^{lab}=11$ MeV. We underline the importance of performing experiments specifically designed to extract ANCs for these systems.Comment: 15 pages, 12 figures, Phys. Rev. C (in press

Asymptotic normalization coefficients (nuclear vertex constants) for p+7Be→8Bp+^7Be\to ^8B and the direct 7Be(p,γ)8B^7Be(p,\gamma)^8B astrophysical S-factors at solar energies

A new analysis of the precise experimental astrophysical S-factors for the direct capture $^7Be(p,\gamma)$ $^8B$ reaction [A.J.Junghans et al.Phys.Rev. C 68 (2003) 065803 and L.T. Baby et al. Phys.Rev. C 67 (2003) 065805] is carried out based on the modified two - body potential approach in which the direct astrophysical S-factor, ${\rm S_{17}(E)}$, is expressed in terms of the asymptotic normalization constants for $p+^7Be\to ^8B$ and two additional conditions are involved to verify the peripheral character of the reaction under consideration. The Woods-Saxon potential form is used for the bound ($p+^7Be$)- state wave function and for the $p^7Be$- scattering wave function. New estimates are obtained for the ^{\glqq}indirectly measured\grqq values of the asymptotic normalization constants (the nuclear vertex constants) for the $p+^7Be\to ^8B$ and $S_{17}(E)$ at E$\le$ 115 keV, including $E$=0. These values of $S_{17}(E)$ and asymptotic normalization constants have been used for getting information about the ^{\glqq}indirectly measured\grqq values of the $s$ wave average scattering length and the $p$ wave effective range parameters for $p^7Be$- scattering.Comment: 27 pages, 6 figure

Tests of Transfer Reaction Determinations of Astrophysical S-Factors

The ${}^{16}O ({}^{3}He,d) {}^{17}F$ reaction has been used to determine asymptotic normalization coefficients for transitions to the ground and first excited states of ${}^{17}F$. The coefficients provide the normalization for the tails of the overlap functions for ${}^{17}F \to{}^{16}O + p$ and allow us to calculate the S-factors for ${}^{16}O (p,\gamma){}^{17}F$ at astrophysical energies. The calculated S-factors are compared to measurements and found to be in very good agreement. This provides the first test of this indirect method to determine astrophysical direct capture rates using transfer reactions. In addition, our results yield S(0) for capture to the ground and first excited states in $^{17}F$, without the uncertainty associated with extrapolation from higher energies.Comment: 6 pages, 2 figure

Asymptotic normalization coefficients for 8B->7Be+p from a study of 8Li->7Li+n

Asymptotic normalization coefficients (ANCs) for 8Li->7Li+n have been extracted from the neutron transfer reaction 13C(7Li,8Li)12C at 63 MeV. These are related to the ANCs in 8B->7Be+p using charge symmetry. We extract ANCs for 8B that are in very good agreement with those inferred from proton transfer and breakup experiments. We have also separated the contributions from the p_1/2 and p_3/2 components in the transfer. We find the astrophysical factor for the 7Be(p,gamma)8B reaction to be S_17(0)=17.6+/-1.7 eVb. This is the first time that the rate of a direct capture reaction of astrophysical interest has been determined through a measurement of the ANCs in the mirror system.Comment: 5 pages, 3 figures, 2 table

How unique is the Asymptotic Normalisation Coefficient (ANC) method?

The asymptotic normalisation coefficients (ANC) for the vertex $^{10}$B $\to$ $^9$Be + p is deduced from a set of different proton transfer reactions at different energies. This set should ensure the peripheral character of the reaction and availability of data for the elastic channels. The problems associated with the characteristics of the data and the analysis are discussed. For a subgroup of the set of available data, the uniqueness property of the extracted ANC is fulfilled. However, more measurements are needed before a definite conclusion can be drawn.Comment: 19 pages, 11 figures, to be published in Phys Rev

An Alternative Parameterization of R-matrix Theory

An alternative parameterization of R-matrix theory is presented which is mathematically equivalent to the standard approach, but possesses features which simplify the fitting of experimental data. In particular there are no level shifts and no boundary-condition constants which allows the positions and partial widths of an arbitrary number levels to be easily fixed in an analysis. These alternative parameters can be converted to standard R-matrix parameters by a straightforward matrix diagonalization procedure. In addition it is possible to express the collision matrix directly in terms of the alternative parameters.Comment: 8 pages; accepted for publication in Phys. Rev. C; expanded Sec. IV, added Sec. VI, added Appendix, corrected typo

Scattering theory with the Coulomb potential

Basic features of a new surface-integral formulation of scattering theory are outlined. This formulation is valid for both short-range and Coulombic long-range interactions. New general definitions for the potential scattering amplitude are given. For the Coulombic potentials the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the amplitudes of breakup, direct and rearrangement scattering in a Coulomb three-body system are presented