Relation between total cross sections from elastic scattering andα-induced reactions: The example of64Zn

Abstract

The total reaction cross section is related to the elastic scattering angular distribution by a basic quantum-mechanical relation. We present new experimental data for α-induced reaction cross sections on 64 Zn which allow for the first time the experimental verification of this simple relation at low energies by comparison of the new experimental reaction data to the result obtained from 64 Zn(α,α) 64 Zn elastic scattering.PACS numbers: 24.10. Ht,24.60.Dr, A main application of quantum mechanics is nuclear physics. Here basic theoretical relations can be tested experimentally with high precision. An interesting example is the simple relation between the total (non-elastic) reaction cross section σ reac and the elastic scattering cross section:Here k = √ 2µE c.m. /h is the wave number, E c.m. is the energy in the center-of-mass (c.m.) system, and η L and δ L are the real reflexion coefficients and scattering phase shifts which define the angular distribution dσ dΩ (ϑ) of elastic scattering. Eq. (1) is derived from a partial wave analysis using the standard two-body Schrödinger equation. This Eq. (1) is widely used, in particular in the calculation of reaction cross sections using the statistical model (StM; to avoid confusion with the widely used abb. "SM" for "shell model"). In the following discussion we will focus on α-induced reactions at low energies.In the StM the reaction cross section of an α-induced (α,X) reaction is calculated in two steps. In the first step the total reaction cross section σ reac is calculated using Eq. (1); the reflexion coefficients η L are determined by solving the Schrödinger equation using a global α-nucleus potential, e.g. the widely used potential by McFadden and Satchler [1]. Compound formation is the dominating absorption mechanism at energies from a few MeV up to about several tens of MeV; thus, it is assumed that the compound formation cross section is approximately given by the total reaction cross section: σ compound ≈ σ reac . In the second step σ compound is distributed among all open channels. The decay branching is obtained from the transmission factors into the various open channels which are again calculated using global potentials for each (outgoing particle + residual nucleus) channel or from the photon strength function in the case of the (α,γ) channel. Further details of the StM can be found in the recent review [2].To our knowledge, the underlying basic relation in Eq. (1) has never been verified experimentally for α-induced reactions at low energies around or below the Coulomb barrier. Although there is no special reason to suspect to Eq. (1) for the particular case of α-induced reactions, an experimental verification assures its application for the calculation of reaction cross sections which has turned out to be difficult especially at low energies (see discussion below). Alternatively, if the validity of Eq. (1) is assumed a priori, it can be used as a stringent test for consistency between different methods for the determination of σ reac . σ reac has ...

α scattering and α -induced reaction cross sections of Zn64 at low energies

“…The activation cross-section measurements have been already carried out and published in full detail [37]. In the present work only one additional data point was determined since in Ref.…”

“…Using the activation technique, the cross sections of the 64 Zn(α,γ ) 68 Ge, 64 Zn(α,n) 67 Ge, and 64 Zn(α,p) 67 Ga reactions were also measured at the same energies. Since the experimental techniques of both the scattering and activation experiments were already described in detail elsewhere [9,37], here only the most important features of the measurements and the results are presented.…”

“…In the present work only one additional data point was determined since in Ref. [37] no measurement was carried out at 16.12 MeV α energy, which is one of the energies where the scattering cross section was measured in the present work and the total cross section σ reac is determined.…”

“…The new measurement at 16.12 MeV α energy was carried out with exactly the same conditions as the experiments of [37]. The cyclotron accelerator provided the α beam which bombarded a thin natural isotopic composition Zn target on Al foil backing.…”

“…This avoids any complications from the extrapolation of the energy-dependent α-nucleus potential. In our previous study [37] such experimental data were used for a sensitive test of the basic quantum-mechanical equation which relates the total reaction cross section σ reac to the reflection coefficients η L of elastic scattering. In the present work the reduced experimental uncertainties allow one to use the quantum-mechanical relation for σ reac to constrain the cross sections of unobserved nonelastic channels.…”