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The 12 C(α, γ) 16 O reaction plays a central role in astrophysics, but its cross section at energies relevant for astrophysical applications is only poorly constrained by laboratory data. The reduced α width, γ11, of the bound 1 − level in 16 O is particularly important to determine the cross section. The magnitude of γ11 is determined via sub-Coulomb α-transfer reactions or the β-delayed α decay of 16 N, but the latter approach is presently hampered by the lack of sufficiently precise data on the β-decay branching ratios. Here we report improved branching ratios for the bound 1 − level [b β,11 = (5.02 ± 0.10) × 10 −2 ] and for β-delayed α emission [b βα = (1.59 ± 0.06) × 10 −5 ]. Our value for b βα is 33% larger than previously held, leading to a substantial increase in γ11. Our revised value for γ11 is in good agreement with the value obtained in α-transfer studies and the weighted average of the two gives a robust and precise determination of γ11, which provides significantly improved constraints on the 12 C(α, γ) cross section in the energy range relevant to hydrostatic He burning.

The Efimov effect for three bosons in three dimensions requires two infinitely large s-wave scattering lengths. We assume two identical particles with very large scattering lengths interacting with a third particle. We use a novel mathematical technique where the centrifugal barrier contains an effective dimension parameter, which allows efficient calculations precisely as in ordinary three spatial dimensions. We investigate properties and occurrence conditions of Efimov states for such systems as functions of the third scattering length, the non-integer dimension parameter, mass ratio between unequal particles, and total angular momentum. We focus on the practical interest of the existence, number of Efimov states and their scaling properties. Decreasing the dimension parameter from 3 towards 2 the Efimov effect and states disappear for critical values of mass ratio, angular momentum and scattering length parameter. We investigate the relations between the four variables and extract details of where and how the states disappear. Finally, we supply a qualitative relation between the dimension parameter and an external field used to squeeze a genuine three dimensional system.

Wave functions, phase shifts, and corresponding elastic cross sections are investigated for two short-range interacting particles in a deformed external oscillator field. For this we use the equivalent d method employing a noninteger dimension d. Using a square-well potential, we derive analytic expressions for scattering lengths and phase shifts. In particular, we consider the dimension, d E , for infinite scattering length, where the Efimov effect occurs by addition of a third particle. We give explicitly the equivalent continuum wave functions in d and ordinary three-dimensional space, and show that the phase shifts are the same in both methods. Consequently the d method can be used to obtain low-energy two-body elastic cross sections in an external field.

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