Nuclear-matter radii of 7Be and 7Li and astrophysical S-factors for radiative alpha-capture reactions

The nuclear-matter radii of ⁷Be and ⁷Li measured in high-energy heavy-ion reactions have been calculated and applied to the estimate of astrophysical S-factors for the ³He(α,γ)⁷Be and ³G(α,γ)⁷Li reactions. The absolute S(O) values in the KeV b are constrained to be 0.36<S(0)<0.63 and 0.083<S(0)<015 for the ³He(α,γ)⁷Be and ³H(α,γ)⁷Li reactions, respectively.     

Consistent cluster model description of the electromagnetic properties of lithium and beryllium nuclei

We calculate the electromagnetic properties of lithium and beryllium nuclei within a resonating group model using bare charges and g-factors. For ⁶Li we give results for reduced transition strengths and explain the tiny quadrupole moment. For ⁷Li and ⁷Be we compute electromagnetic moments and transitions between bound states. Furthermore we reproduce the existing data on the radiative captures ³He(α, γ)⁷Be and ³H(α, γ)⁷Li. In the ⁷Li case the calculations indicate an increase of the astrophysical S- factor for decreasing energy which might have astrophysical consequences. We show that closed channels do not influence results on the astrophysical S-factor at low energy. Finally we demonstrate that the polarisability of ⁷Li originates from the virtual break-up at low energies. In this case, the ⁶Li + n channels contribute appreciably.     

The 3He(α, γ)7Be and 3He(α, γ)7Li reactions at astrophysical energies

The radiative capture cross sections for ³He(α, γ)⁷Be and ³He(α, γ)⁷Li at astrophysical energies have been studied microscopically in terms of the resonating group method. It was found that the astrophysical S-factors correlate strongly to the nuclear size and deformation of ⁷Be and ⁷Li. With the help of measured nuclear properties of these nuclei, a safety range of the absolute values of the S-factor was determined; the most recommended S(0)-values are 0.50 ± 0.03 keV · b for the ³He(α, γ)⁷Be reaction and 0.098 ± 0.006 keV · b for the ³H(α, γ)⁷Li reaction.     

Reaction efficiencies in nucleon channels for 7Li and 9Be nuclei

Reaction cross sections of the radiative capture of nucleons ⁶Li(n, γ)⁷Li, ⁶He(p, γ)⁷Li, and ⁸Li(p, γ)⁹Be in the region of low astrophysical energies are calculated using the dynamic potential cluster model. The results are compared to the available experimental and theoretical data. The yields of these reactions are also calculated, based on the established theoretical results.     

Photoproduction of π + p pairs on nuclei

The photoproduction of pion-nucleon pairs on nuclei was analyzed. The contributions of both nucleonic and isobar configurations in the ground state of nuclei were taken into account. The cross section for the photoproduction of pion-proton pairs in the reactions ¹⁶O(??, ?? ⁺ p)¹⁵C and ¹²C(??, ?? ⁺ p)¹¹Be were calculated.     

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     

Experimental investigation of highly excited states of the 5,6He and 5,6Li nuclei in the (6Li, 7Be) and (6Li, 7Li) one-nucleon pickup reactions

The (⁶Li, ⁷Be) and (⁶Li, ⁷Li) reactions on ⁶Li and ⁷Li nuclei were investigated in the angular interval 0°–20° in the laboratory system at a ⁶Li energy of 93 MeV. In addition to low-lying states of the ^5,6He and ^5,6Li nuclei, broad structures were observed near the t(³He)+d and t(³He)+t thresholds at the excitation energies of 16.75 (3/2⁺) and ～20 MeV (for ⁵He), 16.66 (3/2⁺) and ～20 MeV (⁵Li), 14.0 and 25 MeV (⁶He), and ～20 MeV (⁶Li). The angular distributions measured in the ⁷Li(⁶Li, ⁷Be)⁶He reaction for transitions to the ground state (0⁺) and excited states at E _x=1.8 MeV (2⁺) and 14.0 MeV of the ⁶He nucleus were analyzed by the finite-range distorted-wave method assuming the 1p-and 1s-proton pickup mechanism. The (⁶Li, ⁷Be) and (⁶Li, ⁷Li) reactions were shown to proceed predominantly through the one-step pickup mechanism, and the broad structures observed at high excitation energies are considered as quasimolecular states of the t(³He)+d and t(³He)+t types.     

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

N/D equations taking into account the Coulomb interaction effects are used to consider the phase analysis data on ³He⁴He scattering and determine the nuclear vertex constants for the ⁷Be ? ³He⁴He vertex, where the beryllium nucleus is in the ground (3/2^?) or first excited (1/2^?) states. Information about the asymptotic normalization coefficients of the wave functions of the ⁷Be nucleus in the noted states is derived. The data obtained are used to calculate the astrophysical S factor for the ⁴He(³He, γ)⁷Be reaction.     

One-nucleon spectroscopy of light nuclei

The capabilities and limitations of the conventional many-particle shell model and modern potential cluster models are discussed. New revaluated and more accurate calculations of one-nucleon spectroscopic characteristics of the light nuclei of 1p shell are presented. In many-particle shell model for nuclei with A = 7, 9, 11, 13, and 15 nucleon partial widths of highly excited states with the isotopic spin T = 3/2 were calculated both for “allowed” and “forbidden” transitions. One-nucleon spectroscopic factors were calculated in threebody multicluster models of ⁶Li{αnp}, ⁸Li{αtn}, and ⁹Be{ααn} nuclei. For isobar-analogue nuclei ⁷Li and ⁷Be, the spectroscopic proton S _p and neutron S _n factors for transitions to the ground and excited states of corresponding residue nuclei of the triplet ⁶Li-⁶He-⁶Be were calculated in the framework of binary potential αtand ατ models. Integral, differential and polarization characteristics of photonuclear processes ⁷Li(γ, n ₀)⁶Li, ⁶He(p, γ_{0 + 1})⁷Li, ⁷Li(γ, p ₀)⁶He, and ⁹Be(γ, p _{0 + 1})⁸Li were calculated in this approach.     

Total cross-section measurements for the production of nuclear gamma rays from light nuclei by low-energy deuterons

The thick target yields of the reactions ⁶Li, ⁹Be, ¹⁰B(d, nγ) for specific final nucleus γ-rays have been measured between deuteron bombarding energies of 48 and 170 keV. The measured thick target yields are used, together with recently published values of the stopping power of low-energy deuterons in matter, to infer the total reaction cross sections for the production of the specific γ-rays between deuteron energies of 65 and 160 keV. The cross sections are compared to appropriate Coulomb barrier penetration probabilities and the astrophysical functions S(E) are deduced.     

New approach to analyzing and evaluating cross sections for partial photoneutron reactions

The presence of substantial systematic discrepancies between the results of different experiments devoted to determining cross sections for partial photoneutron reactions??first of all, (??, n), (??, 2n), and (??, 3n) reactions??is a strong motivation for studying the reliability and authenticity of these data and for developing methods for taking into account and removing the discrepancies in question. In order to solve the first problem, we introduce objective absolute criteria involving transitional photoneutron-multiplicity functions F ₁, F ₂, F ₃, ??; by definition, their values cannot exceed 1.0, 0.5, 0.33, ??, respectively. With the aim of solving the second problem, we propose a new experimental-theoretical approach. In this approach, reaction cross sections are evaluated by simultaneously employing experimental data on the cross section for the total photoneutron yield, ?? ^expt(??, xn) = ?? ^expt(??, n) + 2?? ^expt(??, 2n) + 3?? ^expt(??, 3n) + ??, which are free from drawbacks plaguing experimental methods for sorting neutrons in multiplicity, and the results obtained by calculating the functions F _theor ¹ , F _theor ² , F _theor ³ , ?? on the basis of the modern model of photonuclear reactions. The reliability and authenticity of data on the cross sections for (??, n), (??, 2n), and (??, 3n) partial reactions???? ^eval(??, in) = F _i ^theor ?? ^expt(??, xn)??were evaluated for the ⁹⁰Zr, ¹¹⁵In, ^{112,114,116,117,118,119,120,122,124}Sn, ¹⁵⁹Tb, and ¹⁹⁷Au nuclei.     

Effects of 8B size on the low-energy 7Be(p,γ)8B cross section

We calculate several “size-like” ⁸B observables within the microscopic three-cluster model and study their potential constraints on the zero-energy astrophysical S₁₇(0) factor of the ⁷Be(p,γ)⁸B reaction. We find within our three-cluster model that a simultaneous reproduction of the experimental data for the ⁸B radius and quadrupole moment and of the ⁸B⁸Li Coulomb displacement energy implies S₁₇(0) = (23–25) eV b.     

Activation measurement of the3He(4He,γ)7Be reaction

The energy integrated absolute cross section of the³He(⁴He,γ)⁷Be reaction has been determined by an activation measurement, using the branching of the⁷Be 53.44d β-decay to the 478 keV state in⁷Li and its subsequentγ-decay. Depending on the branching ratio used (10.4% or 15.4%) we obtain a zero-energy nuclear cross section factor ofS(0)=0.56±0.03 keV·barn orS(0)=0.38±0.03 keV·barn, respectively.     

Electric and magnetic response to the continuum for A = 7 isobars in a dicluster model

The mirror isobars ⁷Li and ⁷Be are investigated in a dicluster model. The magnetic dipole moments and the magnetic dipole response to the continuum are calculated in this framework. The magnetic contribution is found to be small with respect to electric dipole and quadrupole excitations even at astrophysical energies, at a variance with the case of the deuteron. Energy-weighted molecular sum rules are evaluated and a formula for the molecular magnetic dipole sum rule is found which matches the numerical calculations. Cross-sections for photo-dissociation and radiative capture as well as the S -factor for reactions of astrophysical significance are calculated with good agreement with known experimental data.     

The astrophysical S-factor of the reaction 7Be (p, γ)8B in the direct capture model

The astrophysical S-factor for the reaction ⁷Be(p, γ)⁸B up to an energy of 2 MeV (c.m.) and the capture cross section of ⁷Li(n,γ)⁸Li up to 1 MeV (c.m.) are calculated using the Direct Capture model (DC). Both calculations are in good agreement with experimental data.     

Study of complete and incomplete fusion for loosely bound projectiles 6He and 6Li on 165Ho and 166Er targets

Complete fusion (CF) and incomplete fusion (ICF) reactions were studied for the cases of the loosely bound ⁶He and ⁶Li projectiles bombarding ¹⁶⁶Er and ¹⁶⁵Ho targets at energy of about 10 MeV/nucleon. Experiments were carried out to test an approach exploiting the measured intensities of ?? rays emitted at the transitions between the yrast-band levels of reaction products formed after the termination of neutron evaporation. Partial waves feeding the CF reactions ¹⁶⁵Ho (⁶Li, ⁵ n) ¹⁶⁶Yb and ¹⁶⁶Er(⁶He, ⁶ n) ¹⁶⁶Yb as well as ICF ¹⁶⁵Ho (⁶Li, ??3n) ¹⁶⁴Er and ¹⁶⁶Er(⁶He, ??4n) ¹⁶⁴Er reaction channels were revealed from the obtained ??-ray data. The method of exit channel identification via the triple coincidence (??1-??2-light charged particle) was employed for these reactions study.     

A microscopic multi-channel calculation for the reactions 7Li(p,p)7Li and7Li(p,n)7Be

Based on a refined resonating group method a microscopic multi-channel calculation for the reactions ⁷Li(p, p)⁷Li and ⁷Li(p, n)⁷Be has been performed. Diagonal S-matrix elements and differential cross sections are presented from the ⁷Li-p threshold up to E = 2.5 MeV c.m. and compared with experimental data.     

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