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/s11954-008-3006-z

Cited by 7 publications

(13 citation statements)

References 7 publications

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“…[25] can influence the extracted values of the ANCs. The present results differ strongly also from the values C 2 1 3/2 = 7.95-14.3 fm −1 and C 2 1 1/2 = 6.45-7.45 fm −1 [42], which were obtained by the analytical continuation of the corresponding bound ( 3 He + α) state pole of the Coulomb-modified effective-range theory expansion for α-3 He scattering. But this method has faced difficulties in correctly estimating the extrapolation errors [43].…”

Section: A the Asymptotic Normalization Coefficients For 3 He + α → contrasting

confidence: 99%

Determination of the3He+α→7Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of the
Tursunmahatov
¹
,
Yarmukhamedov
²

2012
Phys. Rev. C
18
2
16
1
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A new analysis of the modern astrophysical S factors for the direct-capture 3 He(α, γ ) 7 Be reaction, precisely measured in recent works [B.S. Nara Singh et al., Phys. Rev. Lett. 93, 262503 (2004); D. Bemmerer et al., ibid. 97, 122502 (2006); F. Confortola et al., Phys. Rev. C 75, 065803 (2007), Gy. Gyrky et al., ibid. 75, 035805 (2007), T. A. D. Brown et al., ibid. 76, 055801 (2007), and A. Di Leva, et al., Phys. Rev. Lett. 102, 232502], has been carried out within the modified two-body potential approach. New estimates are obtained for the "indirectly determined" values of the asymptotic normalization constants and the respective nuclear vertex constants for 3 He + α → 7 Be(g.s.) and 3 He + α → 7 Be(0.429 MeV) as well as the astrophysical S factors S 34 (E) at E 90 keV, including E = 0. The values of asymptotic normalization constants have been used to obtain the values of the ratio of the α-particle spectroscopic factors for the mirror ( 7 Li 7 Be) pair.

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Section: A the Asymptotic Normalization Coefficients For 3 He + α → contrasting

confidence: 99%

Determination of the3He+α→7Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of the
Tursunmahatov
¹
,
Yarmukhamedov
²

2012
Phys. Rev. C
18
2
16
1
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“…The value obtained here for the asymptotic normalization constant, C 2 T = 2.866, agrees well with the corresponding experimental values of C 2 T = 2.6 ± 0.3 [31], 2.78 ± 1.10 [32], and 2.74 ± 0.079 [32,33] and with the value of C 2 T = 2.96, which was determined in [34] on the basis of the S-wave analysis of proton-deuteron scattering by means of the N/D dispersion method.…”

Section: Results Of Numerical Calculationssupporting

confidence: 91%

10.1007/s11450-008-1005-z

2010

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On the basis of the Bargmann representation of the S matrix, the pole approximation is obtained for the effective-range function k cot δ. This approximation is optimal for describing the neutrondeuteron system in the doublet spin state. The values of r 0 = 412.469 fm and v 2 = −35 495.62 fm 3 for the doublet low-energy parameters of neutron-deuteron scattering and the value of D = 172.678 fm 2 for the respective pole parameter are deduced by using experimental results for the triton binding energy E T , the doublet neutron-deuteron scattering length a 2 , and van Oers-Seagrave phase shifts at energies below the deuteron-breakup threshold. With these parameters, the pole approximation of the effective-range function provides a highly precise description (the relative error does not exceed 1%) of the doublet phase shift for neutron-deuteron scattering at energies below the deuteron-breakup threshold. Physical properties of the triton in the ground (T ) and virtual (v) states are calculated. The results are B v = 0.608 MeV for the virtuallevel position and C 2 T = 2.866 and C 2 v = 0.0586 for the dimensionless asymptotic normalization constants. It is shown that, in the Whiting-Fuda approximation, the values of physical quantities characterizing the triton virtual state are determined to a high precision by one parameter, the doublet neutron-deuteron scattering length a 2 . The effective triton radii in the ground (ρ T = 1.711 fm) and virtual (ρ v = 74.184 fm) states are calculated for the first time.

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“…( 12), but the terms have opposite signs. Calculations of the ANC for the 3/2 − and 1/2 − bound state wave functions were carried out by several authors [24][25][26][27][28] using the different methods. We would like to stress that the solution of the Schrödinger equation using the phase equivalent potentials leads to a value of the ANC within quite a large range.…”

Section: Application Of the ∆-Methods To The Bound States Ofmentioning

confidence: 99%

Algorithm for calculations of asymptotic nuclear coefficients using phase-shift data for charged-particle scattering

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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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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

Determination of the3He+α→7Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of the
Tursunmahatov
¹
,
Yarmukhamedov
²

2012
Phys. Rev. C
18
2
16
1
View full text Add to dashboard Cite

Determination of the3He+α→7Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of the
Tursunmahatov
¹
,
Yarmukhamedov
²

2012
Phys. Rev. C
18
2
16
1
View full text Add to dashboard Cite

10.1007/s11450-008-1005-z

Algorithm for calculations of asymptotic nuclear coefficients using phase-shift data for charged-particle scattering

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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

Determination of the3He+α→7Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of theTursunmahatov1, Yarmukhamedov2 2012Phys. Rev. C182161View full textAdd to dashboardCite

Determination of the3He+α→7Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of theTursunmahatov1, Yarmukhamedov2 2012Phys. Rev. C182161View full textAdd to dashboardCite

10.1007/s11450-008-1005-z

Algorithm for calculations of asymptotic nuclear coefficients using phase-shift data for charged-particle scattering

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Product

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Determination of the3He+α→7Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of the
Tursunmahatov
¹
,
Yarmukhamedov
²

2012
Phys. Rev. C
18
2
16
1
View full text Add to dashboard Cite

Determination of the3He+α→7Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of the
Tursunmahatov
¹
,
Yarmukhamedov
²

2012
Phys. Rev. C
18
2
16
1
View full text Add to dashboard Cite