Radioactive beams by fragmentation and ISOL techniques - CERN

(5)
(4,)
A A -A B
69 = % = Gfumi IV ET`
Z _ Sym DE V A;(Ap—l) Ap’Af
Rewriting equation (4) gives
YOc E?/2/UXP-1
S (X)) P ‘ Af 3/2
A quantitative formula can be easily obtained from the considerations above with
of,ag=l()()MeV/c and Ei in units of MeV/nucleon
YS=opmd.tOp[.(l) 3/2 Q?—.&.
4,,) H G9 GQ? 6Ap/p
Z 4.08 (5,,,.,., . t.,,,,(§§
where SS, os, (Ap/p)S are the half acceptances of the spectrometer in units of
radians and percent respectively This formula is valid as long as the acceptance is small
as compared to the respective o—values of equation (5). Otherwise the gaussian
distribution should be integrated using the error function. The final intensities can be
obtained multiplying with the intensity of the incident beam.
b) Choice of the beam
A rough idea about the influence of the choice of the incident beam may be
obtained by the following considerations.
3/2 i*’l 30
9, (D, . Ei
The number of nuclei which will be produced can be approximated by the fact that
the width of the isotope chains is approximately proportional to the atomic number Zbcam.
Therefore for a constant total cross-section the cross-section will be devided by a number
of channels which increases as Zi. As the energy loss is AE/E = cAZbcami/(EE)
Zbeam for a given energy per nucleon we expect that the yield for a given channel in a
fragmentation process will decrease as l/Zjbcam. This simple prediction is once again
checked with respect to the codes LISE and Intensity on fig. 2.
Thus, the beam should be choosen as light as possible to produce a given final
product. However, one should not forget that more complicated processes than
fragmentation contribute. Pick—up reactions for example may give significant yields. as OCR Output
Q