Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms
Doppler broadened γ-lines from exotic nuclei
Introduction
The Doppler effect is employed in several techniques for determining lifetimes of excited nuclear states. In most of these techniques the excited state of the nucleus is created in a nuclear reaction employing a unidirectional beam of at least several MeV and consequently the Doppler effect will cause a shift of the emitted γ-ray. This is the case for the recoil distance method (RDM), the Doppler shift attenuation method (DSAM) and the Doppler broadened line shape analysis method (DBLA), see [1] for a review of these techniques.
We have developed a method for using the Doppler effect for γ-rays emitted after β-delayed neutron emission in the β-decay of 11Li. In this case the recoil direction after neutron emission is isotropic and hence the Doppler effect induces a broadening of the γ-peak in contradistinction to the usual shift. The size of this Doppler broadening is directly related to the energy of the emitted neutron and consequently by performing a detailed fit of the peak shape, information may be extracted which would otherwise require a β–γ–n triple coincidence experiment [2], [3], [4].
We have realized that the formulas derived for this method may be of interest for a larger class of phenomena where similar Doppler broadening occurs. In the inverted Doppler shift attenuation method (IDSA), which is used to determine stopping powers [5], [6], [7], [8], a thermal neutron induced reaction 10B(n,α)7Li* is used to produce a γ-decaying state in 7Li and the analysis of the Doppler broadened line shape is then used to extract information about the stopping power. These authors give very good illustrations of the physics behind the shape of Doppler broadened peaks but give no expression for the shape. A completely different application was suggested by Grenacs et al. [9] in connection with μ-capture. γ-rays emitted after μ-capture are Doppler broadened due to the emission of a neutrino with typically 50 MeV energy. If the lifetime of the γ-emitting state is sufficiently short to neglect the slowing down of the recoiling nucleus, the shape of the Doppler broadened peak is directly related to the neutrino-gamma angular correlation, which is of fundamental interest. Later Pratt [10] gave some approximations for how to take into account the energy loss of the recoiling ions. There has recently been some very interesting applications of this method [11], [12], [13], [14], but none of these authors describes how the energy loss is accounted for. Finally, in the Gamma Ray Induced Doppler Effect method (GRID) the tiny recoil from the emission of the first γ-ray in a γ–γ cascade induces a Doppler broadening of the peak shape of the second γ-ray [15]. Although the energy scale is very different for this method some of the relevant formulas are similar.
Here we give our results for the shape of such Doppler broadened γ-peaks to remedy the fact that, to our knowledge, no consistent derivation is available in the literature. In Section 2 we present our derivation of the peak shape of Doppler broadened γ-peaks and in Section 3 we discuss different treatments of the stopping power and give some useful analytical results. In Section 4 we discuss the qualitative features of the peak shape and its dependence on the main determining parameters and finally in Section 5 we discuss the occurrence and application of Doppler broadened γ-lines in the decay spectra of exotic nuclei.
Section snippets
Derivation of Doppler broadened -peak shapes
We consider the general case of a nucleus generated in some medium in a γ-emitting excited state and with a velocity (recoil) distribution which is isotropic in the laboratory system.
It is instructive to consider first the case where energy loss to the medium is neglected. In this case the nuclei move through the medium with constant energy Ei and the line shape dn/dEγ is determined as follows:where Eγ is the energy of the γ-ray. The dependence of the angular
Treatment of stopping power
There is a long and ongoing interest in the calculation of energy loss of ions in matter which has resulted in various parameterizations for the stopping power which are amenable to practical applications.
Pratt [10] gives some analytical results for Doppler broadened peak shapes for two parameterizations of the stopping power dE/dx=Mβ/α1 and dE/dx=(knβ0/β)+(keβ/β0) with β=v/c the velocity of the recoiling ion and β0 the Bohr-velocity. These expressions are only valid when the electronic
Peak shapes
To get a qualitative understanding of Eq. (6) we show in Fig. 2 the peak shape calculated for lifetimes of 50, 500 and 5000 fs for the case of the 2170 keV line from the deexcitation of the 2201.5 keV level in 28Al fed in μ-capture on 28Si. For simplicity we assume the angular correlations to be isotropic, as is often the case. The detector response function has been included through a Gaussian convolution with a resolution of 0.5 keV (sigma). For each lifetime the peak shape is calculated
Application to the -decay of 11Li
Doppler broadened γ-lines have been found in the decay spectra of exotic nuclei near the neutron drip line [22]. In these cases the β-decay feeds neutron unbound states in the daughter which, after neutron emission, can feed excited states in the βn-daughter. The γ-lines from the deexcitation of these states are Doppler-broadened by the recoil from the neutron emission and the magnitude of the effect is directly related to the energy of the neutron. Hence, by analysing the Doppler broadened
Summary and outlook
We have presented a general derivation of Doppler broadened γ-lines which takes into account energy loss to the stopping medium, angular correlations and the statistical deexcitation process of the γ-ray emission. Essential for the calculation of the peak shape is the availability of the relevant stopping power. We discuss various estimates of this quantity and illustrate how the uncertainty in its magnitude affects the calculated peak shapes. Our analytical results extend on previous work
Acknowledgements
The author gratefully acknowledges K. Riisager for suggesting this problem and for useful discussions and comments on the manuscript, P. Sigmund for kindly providing his predictions from binary theory and S. Egorov for discussions on the use of Doppler-broadening in μ-capture.
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