The Fifth Conference “ Nuclear Science and Its Application”, 14-17 October 2008
ASYMPTOTIC NORMALIZATION COEFFICIENTS FO R 3H e+a-»7Be AND
p+7Be ->8BANDTHE DIRECT 3He(a,y)7Be AND 7Be (p, y)8B ASTROPH Y SIC AL
S-FACTORS AT SOLAR ENERGIES
S.B. IGAMOV, K. TURSUNMAKHATOV AND R.YARMUKHAMEDOV
‘Institute o f Nuclear Physics, Uzbekistan Academy o f Sciences, Tashkent, Uzbekistan
The 7Be(p, y)8B and 3He(a,y)7Be reaction rates given by in terms of the zero-energy astrophysical S-factors (AS) S17(0) and SJO) are one of the main input data in the solar neutrino problem because the high energy neutrinos are produced via the decay 8B—>7Be+e+ + ve [1] Despite the steady progress was made in correct direct measurements of AS at extremely low energies [2-4], ambiguities ( up to about 35%) associated with prediction for S^O) however still exist, and it may considerably influence the predictions o f the standard solar model.
In this work the modified two - body potential approach [5] is applied for a new analysis of the highly precise experimental astrophysical S-factors for the direct capture 7Be(p, y)8B and 3He(a,y)7Be reactions at extremely low energies [3-4] to obtain “indirectly measured” values both of the asymptotic normalization coefficients (ANC’s) for p+7Be-*8B and 3H e+a—>7Be and of AS
S17(E) and S34(E) at E<100 keV, including E=0. In this approach S (E) is expressed in the terms of
ANC C~j .u but not in the terms of the usual spectroscopic factor Z u , which is related to the ANC C u as ZiyU - Cl.jj / b]yLJ [6], where b..,u is the single-particle ANC for the wave function of the bound state calculated within the shell model using the phenomenological Woods-Saxon potential with the geometric parameters ( a radius rg and a diffuseness a ).
The analysis of the experimental AS S f v(E) [3-4] is performed by verying values of the parameters ra and a in the wide range. It is demonstrated that these reactions are strongly peripheral and they allowed one to determine values of the ANC’s for p+7Be—>8B and 3H e+a—>7Be. The weighted mean of the ANC’s are C,27.13/2 + C127;11/2=0.628±0.017 fn r1 for p+7Be->8B and C34;13/2 =21.24+0.66 fftr1 and C3*2;11/2=14.55±0.43 fu r1 for 3H e+a-+7Be(g.s.) and 3H e+a-+7Be(0.429 MeV), respectively. It is also shown that they have fairly weak dependence on the values (rg , a )-pair. The obtained values of the ANC’s are used to extrapolate value of S..(E) at stellar energies (< 100 keV), including £=0. In particular, the values of Sl7(0)~ 23.40+0.63 eVb and S3/0 )= 0.56+0.02 keV b are obtained. The uncertainties obtained for the value of the ANC’s and of the S (0) involve the experimental uncertainties for the corresponding (E) and the theoretical uncertainties
connected with the model dependence of the calculated AS on the geometric parameters ro and a of the Woods - Saxon potentials. A comparison of the values of the ANC’s and S.fO)) with the data obtained other authors is done.
The work has been support by AS of The Republic of Uzbekistan (Grant FA-F2-F077). 1 2 3 4 5 6 1. E.G. Adelberger et al. Rev. Mod. Phys. 70 (1998) 1265.
2. A.R. Junghans et al. Phys.Rev. C 68(2003) 065803. 3. L.T. Baby et al. Phys.Rev. C 67(2003) 065805. 4. F.Confortola et al. Phys.Rev.C75(2007)065803
5. S.B. Igamov and R.Yarmukhamedov, A 781 (2007) 247. 6. L.D. Blokhintsev et al. Sov.J.Part.Nucl. 8(1977)485.
Section II. Basic Problems O f Nuclear Physics
