Three-body bremsstrahlung and the rotational character of theC12spectrum

Abstract

The electric quadrupole transitions between 0 + , 2 + , and 4 + states in 12 C are investigated in a 3α model. The three-body wave functions are obtained by means of the hyperspherical adiabatic expansion method, and the continuum is discretized by imposing a box boundary condition. Corresponding expressions for the continuum three-body (3α) bremsstrahlung and photon dissociation cross sections are derived and computed for two different α-α potentials. The available experimental energy dependence is reproduced and a series of other cross sections are predicted. The transition strengths are defined and derived from the cross sections, and compared to schematic rotational model predictions. The computed properties of the 12 C resonances suggest that the two lowest bands are made, respectively, by the states {0 For the second band, the transitions are also consistent with a rotational pattern, but with the three alphas in an aligned arrangement.

Rotational character of the12Cspectrum investigated through inelastic cross sections via photon emission

“…The results are similar no matter what method is used to extract the transition strengths (B σ or B γ ), especially when taking into account the uncertainties inherent to each of the methods. Although not shown, it has also been observed that the results are, to a large extent, independent of the potential used [4]. An important result is that the 4 .…”

“…It is important to note that the summation over i and j in the Eq. (3) is not unrestricted, but limited to the initial and final energy ranges of experimental interest [4].…”

“…States arising as the result of a rotation of a reasonable rigid structure should show similar values of ρ rms . It is remarkable that, on the one side, the 0 + when the repulsion in the three-body force is diminished [4].…”

Capture reactions into Borromean two-proton systems atrpwaiting points

“…However, it is a well known fact that using only twobody potentials will usually lead to an underbound threebody structure, as shown for instance for 17 Ne and 12 C in Refs. [23,39], respectively. This problem is typically overtaken by addition of an effective three-body force, V 3b (ρ), to the adiabatic potential given in Eq.…”

“…This problem can be handled by two conceptually different methods [39,41], where the first is to specify the boundary conditions directly and solve the Schrödinger equation. The second method is to discretize the continuum in a large hyperradial box which in the present case is limited by hyperradii less than the box radius ρ max .…”