Determination of the nuclear vertex constants for the 7Be ↔ 3He4He vertex using theN/D equations and calculation of the astrophysical S factor for the 4He(3He, γ)7Be reaction

Blokhintsev, L.D.; Irgaziev, B. F.; Mukhamedzhanov, A. M.; Safronov, A. N.; Сафронов, А. А.

doi:10.3103/s1062873808030064

Cited by 7 publications

(18 citation statements)

References 7 publications

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“…In this case the extrapolation should provide only one missing parameter -the ANC. This procedure has been realized in [2] for the α − d elastic scattering and the ANC has been found for the virtual decay 6 Li → α + d in the s-wave channel. Once we know both parameters of the bound state, binding energy and the ANC, using the experimental data we can find, according to the inverse scattering theorems, a unique two-body potential.…”

Section: Introductionmentioning

confidence: 99%

“…However, the off-shell properties of the bound states, are not necessarily correctly reproduced. Consider, for example, the s-wave elastic scattering of composite nuclei α + d. The ANC for the virtual decay of the 6 Li bound state 6 Li → α + d is the amplitude of the tail of the overlap function…”

Section: Introductionmentioning

confidence: 99%

“…The ANC of the bound state wave function is called the single-particle ANC, although it is more appropriate to call it the two-body ANC what we are going to use here. In the two-body approach the ANC and the two-body ANC are related as (applying for the 6 Li case)…”

Section: Introductionmentioning

confidence: 99%

“…Here, C 6 Li α d (01) and b α d (101) are the ANC and the two-body ANC and S α d (101) is the spectroscopic factor of the configuration (α d) 101 in the ground state of 6 Li. Note that the right-hand-side depends on the additional quantum number n = 1, which is the principal quantum number showing the number of nodes of the adopted radial α − d bound-state wave function at r > 0.…”

Section: Introductionmentioning

confidence: 99%

“…There is also a possibility to solve N/D equations, which take into account the right unitary cut and the left dynamical singularities. Using these equations one can fit the experimental scattering phase shift at given partial wave and find the bound state pole and its residue [6,7]. We note that effective field theory can also be applied to obtain binding energy (if necessary) and the ANC [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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Reexamination of the astrophysicalSfactor for theα+d→6Li

2011

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Reexamination of the astrophysicalSfactor for theα+d→6Li

2011

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Generalized Faddeev equations in the Alt-Grassberger-Sandhas form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction

2012

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Theoretical description of reactions in general, and the theory for (d, p) reactions, in particular, needs to advance into the new century. Here deuteron stripping processes off a target nucleus consisting of A nucleons are treated within the framework of the few-body integral equations theory. The generalized Faddeev equations in the AGS form, which take into account the target excitations, with realistic optical potentials provide the most advanced and complete description of the deuteron stripping. The main problem in practical application of such equations is the screening of the Coulomb potential, which works only for light nuclei. In this paper we present a new formulation of the Faddeev equations in the AGS form taking into account the target excitations with explicit inclusion of the Coulomb interaction. By projecting the (A + 2)-body operators onto target states, matrix three-body integral equations are derived which allow for the incorporation of the excited states of the target nucleons. Using the explicit equations for the partial Coulomb scattering wave functions in the momentum space we present the AGS equations in the Coulomb distorted wave representation without screening procedure. We also use the explicit expression for the off-shell two-body Coulomb scattering T -matrix which is needed to calculate the effective potentials in the AGS equations. The integrals containing the off-shell Coulomb T-matrix are regularized to make the obtained equations suitable for calculations. For N N and nucleon-target nuclear interactions we assume the separable potentials what significantly simplifies solution of the AGS equations.

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

Mukhamedzhanov

2012

Phys. Rev. C

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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 Schrödinger 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.

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Determination of the nuclear vertex constants for the 7Be ↔ 3He4He vertex using theN/D equations and calculation of the astrophysical S factor for the 4He(3He, γ)7Be reaction

Cited by 7 publications

References 7 publications

Reexamination of the astrophysicalSfactor for theα+d→6Li

Reexamination of the astrophysicalSfactor for theα+d→6Li

Generalized Faddeev equations in the Alt-Grassberger-Sandhas form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction

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

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