Radioactive beams by fragmentation and ISOL techniques - CERN

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(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
1010 8 10 -A— —~ —Y‘ nd ES. 1 ) E? S 10° 104 106 105 104 1000 100 % 100 10 100 1000 E (MeV/nuclcon) Fig 1: Prediction of secondary beam intensities by the programs LISE and Intensity for a constant spectrometer acceptance compared tothe 7/2 E1aw,equ. (4). Z beam Fig 2: yield of 61-Ie as a function ofthe atomic number ofthe incident beum from LISE and Intensity codes(open circles) compared to the Z ‘—‘ lawttriunglesl. OCR Output 10 \\ AV / _ . / c, / Z \\ 100
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Radioactive beams by fragmentation and ISOL techniques - CERN

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