Asymptotic normalization coefficients and astrophysical direct capture rates

Peripheral transfer reactions can be used to determine asymptotic normalization coefficients (ANCs). These coefficients, which specify the normalization of the tail of the nuclear overlap function, determine S-factors for direct capture reactions at astrophysical energies. A variety of proton transfer reactions involving both stable and radioactive beams have been used to measure ANCs. Tests have demonstrated that ANCs determined from proton transfer reactions can be used to calculate astrophysical direct capture rates to within 9%. The ¹⁰B(⁷Be, ⁸B)⁹Be and ¹⁴N(⁷Be, ⁸B)¹³C reactions have been used to measure the ANC appropriate for determining the ⁷Be(p,γ)⁸B rate, and the ¹⁴N(¹¹C, ¹²N)¹³C reaction has been used to measure the ANC required to calculate the ¹¹C(p,γ)¹²N rate. Received: 1 May 2001 / Accepted: 4 December 2001     

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

A new analysis of the precise experimental astrophysical S factors for the direct-capture reaction ⁷Be(p, γ)⁸B [A.J. Junghans et al., Phys. Rev. C 68, 065803 (2003) and L.T. Baby et al., Phys. Rev. C 67, 065805 (2003)] is carried out on the basis of a modified two-body potential approach in which the direct astrophysical S factor, S ₁₇(E), is expressed in terms of the asymptotic normalization constants for p + ⁷Be → 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 p ⁷Be-scattering wave function. New estimates are obtained for the “indirectly measured” values of the asymptotic normalization constants (the nuclear vertex constants) for the p + ⁷Be → ⁸B and S ₁₇(E) at E ≤ 115 keV, including E = 0. These values of S ₁₇(E) and asymptotic normalization constants have been used for obtaining the indirectly measured values of the s-wave average scattering length and the p-wave effective-range parameters for p ⁷Be scattering. The text was submitted by the authors in English.     

Determination of nuclear vertex constants (asymptotic normalization coefficients) for the virtual decays 3He → d + p and 17F → 16O + p and their use for extrapolating astrophysical S -factors of the radiative proton capture by the deuteron and the 16O nucleus at very low energies

Experimental astrophysicalS-factors for the direct radiative capture processes d(p,γ)³He and ¹⁶O(p,γ)¹⁷F are analyzed using the modified two-body potential approach. The values of the asymptotic normalization coefficients (nuclear vertex constants) are found for the wave functions of the ³He and ¹⁷F nuclei in the (d + p) and (¹⁶O + p) channels respectively and are then used to extrapolate the astrophysical S-factor to the region of very low energies. Original Russian Text ? S.V. Artemov, S.B. Igamov, K.I. Tursunmakhatov, R. Yarmukhamedov, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 176–181.     

Study of the 3He(4He,γ)7Be and 3H(4He,γ)7Li Reactions in an Extended Two-Cluster Model

 The ³He(⁴He, γ)⁷Be and ³H(⁴He, γ)⁷Li reactions are studied in an extended two-cluster model which contains α + h/t and ⁶Li + p/n clusterizations. We show that the inclusion of the ⁶Li + p/n channels can significantly change the zero-energy reaction cross sections, S(0), and other properties of the ⁷Be and ⁷Li nuclei, like the quadrupole moments Q. However, the results agree with the known correlation trend between S(0) and Q. Moreover, we demonstrate that the value of the zero-energy derivatives of the astrophysical S-factors are more uncertain than currently believed. Received June 17, 1999; revised February 22, 2000; accepted for publication April 17, 2000     

Nuclear vertex constants for the virtual decay <Superscript>7</Superscript>Be → <Superscript>3</Superscript>He + <Superscript>4</Superscript>He of the 7Be bound states from a phase-shift analysis in the effective-range theory

The phase-shift-analysis data for the ³He⁴He scattering are analyzed using the effective-range theory, with the Coulomb interaction taken into account. We find both the renormalized nuclear vertex constants for the vertex ⁷Be → ³He + ⁴He in the ground (3/2⁻) and in the first excited (1/2⁻) bound states of ⁷Be, and the corresponding asymptotic normalization constants of the radial wave functions in these states. The results obtained can be used in an astrophysical S-factor calculation for radiative capture reaction ⁴He(³He, γ)⁷Be     

Breakup of 8B and the 7Be(p, γ)8B reaction

The calculated rate of events in some of the existing solar neutrino detectors is directly proportional to the rate of the ⁷Be(p, γ)⁸B reaction measured in the laboratory at low energies. However, the low-energy cross sections of this reaction are quite uncertain as various measurements differ from each other by 30–40%. The Coulomb dissociation process which reverses the radiative capture by the dissociation of ⁸B in the Coulomb field of a target, provides an alternate way of accessing this reaction. While this method has several advantages (like large breakup cross sections and flexibility in the kinematics), the difficulties arise from the possible interference by the nuclear interactions, uncertainties in the contributions of the various multipoles and the higher order effects, which should be considered carefully. We review the progress made so far in the experimental measurements and theoretical analysis of the breakup of ⁸B and discuss the current status of the low-energy cross sections (or the astrophysical S-factor) of the ⁷Be(p, γ)⁸B reaction extracted therefrom. The future directions of the experimental and theoretical investigations are also suggested. Work supported by EPSRC, UK, grant nos J/95867 and L/94574.     

Extrapolation of astrophysical <Emphasis Type="Italic">S</Emphasis> factors for the reaction <Superscript>14</Superscript>N((<Emphasis Type="Italic">p, γ</Emphasis>) <Superscript>15</Superscript>O to near-zero energies

The astrophysical S factors for the radiative-capture reaction ¹⁴N(p, γ)¹⁵O in the region of ultralow energies were calculated on the basis of the R-matrix approach. The values of the radiative and protonic widths were fitted to new experimental data. The contribution of direct radiative capture to bound states of the ¹⁵O nucleus was determined with the aid of asymptotic normalization coefficients, whose values were refined in the present study on the basis of the results obtained from an analysis of the reaction ¹⁴N(³He, d)¹⁵O at three different energies of incident helium ions. A value of S(0) = 1.79 ± 0.31 keV b was obtained for the total astrophysical S factor, and the reaction rate was determined for the process ¹⁴N(p, γ)¹⁵O.     

Coulomb breakup of 8B and the flux of 8B neutrinos from the Sun

A kinematically complete measurement was made of the Coulomb dissociation of ⁸B nuclei on a Pb target at 83 MeV/nucleon. The cross-section was measured at low relative energies in order to infer the astrophysical S-factor for the ⁷Be(p,γ)⁸B reaction. A first-order perturbation theory analysis of the reaction dynamics including E1, E2, and M1 transitions was employed to extract the E1 strength relevant to neutrino-producing reactions in the solar interior. By fitting the measured cross-section from E _rel = 130 keV to 400 keV, we find S ₁₇(0) = 17.8^+1.4 _-1.2 eV b. Semiclassical 1st-order perturbation theory and fully quantum-mechanical continuum-discretized coupled-channels analyses yield nearly identical results for the E1 strength relevant to solar-neutrino flux calculations, suggesting that theoretical reaction mechanism uncertainties need not limit the precision of Coulomb-breakup determinations of the ⁷Be(p,γ)⁸B S-factor. A recommended value of S ₁₇(0) based on a weighted average of this and other measurements is presented. This recommendation implies a revised value for the theoretical flux of ⁸B solar neutrinos, which is also given.-1 Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"Present address: Kernfysisch Versneller Instituut, Zernikelaan 25, 9747 AA Groningen, The Netherlands; e-mail: davids@kvi.nl     

Initiation of the (<Emphasis Type="Italic">γ, n</Emphasis>) and (<Emphasis Type="Italic">p,n</Emphasis>) nuclear reactions in the picosecond laser plasma at a laser intensity of 2 × 10<Superscript>18</Superscript> W/cm<Superscript>2</Superscript>

The experimental results on the initiation of various (γ, n) and (p, n) nuclear reactions in the picosecond laser plasma are presented. It is demonstrated that the following (γ, n) and (p, n) nuclear reactions can be initiated at a laser intensity of 2 × 10¹⁸ W/cm² with the threshold energies of γ-quanta ranging from 1.67 to 7.56 MeV and the threshold energies of protons ranging from 1.88 to 5 MeV: ⁹Be(γ, n)2α, ¹⁸¹Ta(γ, n)¹⁸⁰Ta, ⁷Li(p, n)⁷Be, ⁶³Cu(p, n)⁶³Zn, ⁴⁸Ti(p, n)⁴⁸V. The method based on the detection of fast neutrons using the 3He counters is employed for the measurement of the number of the initiated (γ, n) and (p, n) nuclear reactions. The measured yield of the (γ, n) and (p, n) nuclear reactions ranges from 5 × 10¹ to 10⁵ reactions per laser pulse.     

Astrophysical <Emphasis Type="Italic">S</Emphasis>-factor of the <Emphasis Type="Italic">p</Emphasis><Superscript>7</Superscript>Li → <Superscript>8</Superscript>Beγ capture at low energies

The interaction potentials describing some phases of elastic p ⁷Li scattering for energies up to 0.8 MeV and the ground bound P ₀ state of the ⁸Be nucleus in the p ⁷Li cluster channel are obtained. The astrophysical S-factor of the p ⁷Li → ⁸Beγ radiative capture is considered for the potential cluster model.     

The characteristics of the <Superscript>8</Superscript>Be ground state in the effective-range approximation

We find the vertex constant for the synthesis α + α → ⁸Be and the corresponding asymptotic normalization coefficient of the Gamov wave function for ⁸Be in the ground state. We use modern data on the position and width of the narrow resonance of this state as well as the energy dependence of the αα scattering phase shift in the s-wave known from the literature. The effective-range theory was applied with the Coulomb interaction taken into account. The parameters of the standard effective-range function expansion up to the member with k ⁴ (k being the relative momentum) were found.     

Phenomenological applications of<Emphasis Type="Italic">k</Emphasis><Subscript>T</Subscript>factorization

We discuss applications of the perturbative QCD approach in the exclusive non-leptonic two-bodyB-meson decays. We briefly review its ingredients and some important theoretical issues on the factorization approach. PQCD results are compatible with present experimental data for charmless B-meson decays. We predict the possibility of large direct CP asymmetry in B⁰ → π⁺π⁻ (23 +7%) and B⁰ →K ⁺π⁻ (− 17 ± 5%). We also investigate the branching ratios, CP asymmetry and isospin symmetry breaking in radiativeB →(K*/ρ)γ decays.     

Quark-Antiquark states and their radiative transitions in terms of the spectral integral equation: Bottomonia

In the framework of the spectral integral equation, we consider the states and their radiative transitions. We reconstruct the interaction on the basis of data for the levels of the bottomonium states with J ^PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺ as well as the data for the radiative transitions γ (3S) → _γχbJ(2P) and γ(2S) → _γχbJ(1P) with J = 0, 1, 2. We calculate bottomonium levels with the radial quantum numbers n ≤ 6, their wave functions, and corresponding radiative transitions. The ratios Br[_χbJ(2P) → _γγ(2S)]/Br[_χbJ(2P) → _γγ(1S)] for J = 0, 1, 2 are found to be in agreement with data. We determine the component of the photon wave function using the data for the e ⁺ e ⁻ annihilation, e ⁺ e ⁻ → γ(9460), γ(10 023), γ(10 036), γ(10 580), γ(10 865), γ(11 019), and predict partial widths of the two-photon decays ηb0 → γγ, χb0 → γγ, χb2 → γγ for the radial excitation states below the threshold (n ≤ 3). The text was submitted by the authors in English.     

Further measurement of the 7Be(p,γ)8B cross section at low energies with the coulomb dissociation of 8B

We have measured the dissociation of ⁸B in the Coulomb field of ²⁰⁸Pb at E_in=51.9 MeV/nucleon and extracted the cross section of the ⁷Be(p,γ)⁸B reaction at 0.4 ≤ E_rel≤ 3 MeV, which is of importance for the ⁸B solar-neutrino production rate. The extracted astrophysical S₁₇ factors are consistent with our earlier Coulomb dissociation measurement, and agree with the values deduced from the direct capture measurements by Filippone et al., Vaughn et al. and Hammache et al. The S factor at zero energy was extracted to be 18.9±1.8 eV-b with the help of theoretical energy-dependence. Received: 15 August 1998     

Comments on preliminary data on the reactions e + e −→φ→γ f 0(980)→γπ0π0

Preliminary data on the reactions e ⁺ e ⁻→φ→γ f ₀(980)→γπ⁰π⁰ together with data on ππ scattering and the reactions J/ψ→φπ⁺π⁻ and K ⁻ p→π ⁺π⁻(Λ,Σ) are analyzed. The analysis shows that the mass of the f ₀(980) meson is = 950 MeV, and BR(φ→γf ₀→γπ⁰π⁰)≃ 1× 10⁻⁴, indicating that the f ₀(980) resonance is of a four-quark nature. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 445–449 (10 April 1998)     

Low–energy photodisintegration of 9Be and α+α+n→9Be +γ reactions at astrophysical conditions

A semi–microscopic model for the low–energy photodisintegration of the ⁹Be nucleus is constructed, and the experimental data are analyzed with its help. The older radioactive isotope data are supported by this analysis. The theoretical photodisintegration cross section is derived. The astrophysical rates for the reaction α+α+n→⁹Be+γ and the reverse photodisintegration of ⁹Be are calculated. The new reaction rate for α+α+n→⁹Be+γ is compared with previous estimations. Received: 19 January 1998     

Microscopic three-cluster study of the low-energy 9 Be photodisintegration

The ⁹Be and ⁹B nuclei are investigated in a microscopic three-cluster model involving α + α + n (or α + α + p) configurations. The ⁸Be (0 ⁺ , 2 ⁺ ) + n and ⁵He (3/2 ^- , 1/2 ^- ) + α (or mirror) channels are included by taking account of the unstable nature of ⁸Be and ⁵He. Spectroscopic properties of ⁹Be and ⁹B are analyzed. We show that the ⁵He + α configurations cannot be neglected to derive accurate results. The ⁹Be(γ,αα)n photodisintegration cross-section is shown to be mainly determined by ⁸Be + n channels at low energies, but ⁵He + α channels become important beyond E _γ≈ 4 MeV. Received: 7 September 2001 / Accepted: 19 November 2001     

Two photons into π<Superscript>0</Superscript>π<Superscript>0</Superscript>

We perform a theoretical study based on dispersion relations of the reaction γγ → π ⁰ π ⁰ emphasizing the low-energy region. We discuss how the ƒ ⁰(980) signal emerges in γγ → ππ within the dispersive approach and how this fixes to a large extent the phase of the isoscalar S-wave γγ → ππ amplitude above the threshold. This allows us to make sharper predictions for the cross-section at lower energies and our results could then be used to distinguish between different ππ isoscalar S-wave parameterizations with the advent of new precise data on ππ → π ⁰ π ⁰. We compare our dispersive approach with an updated calculation employing the unitary chiral perturbation theory (U _gC PT). We also pay special attention to the role played by the σ-resonance in γγ → ππ and calculate its coupling and width to γγ, for which we obtain Γ(σ → γγ) = (1.68 ± 0.15) keV.     

Isospin symmetry breaking in ρ→πγ decay

In terms of effective field theory and mixed-propagator approach, we show that there is a larger hidden effect of isospin breaking in ρ→πγ decay due to a ω exchange, ρ→ω→πγ. The branching ratio is predicted as B(ρ→πγ) = (11.67±2.0)×10^-4, which is much larger than Particle Data Group's datum (6.8±1.7)×10^-4 and one of charged mode, B(ρ^±→π^±γ) = (4.5±0.5)×10^-4. Received: 7 January 2002 / Accepted: 2 April 2002