Citation for published version (APA): Hoefman, M. (1999). A study of coherent bremsstrahlung and radiative capture s.n.

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1 University of Groningen A study of coherent bremsstrahlung and radiative capture Hoefman, Marieke IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 999 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Hoefman, M. (999). A study of coherent bremsstrahlung and radiative capture s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to maximum. Download date:

2 A. Abbreviations AGOR BBS BPM CFD CPV DC2B FERA FWHM GANIL GSI IMF IPN KVI LCP LED MLU MWPC PLF PM PPLF QDC RDV SALAD SPA TAPS TDC TETAS TSL Accelerateur Groningen ORsay Big{Bite Spectrometer Bremsstrahlung described within the potential model Constant{Fraction Discriminator Charged{Particle Veto Direct Capture to Bound States Fast Encoding and Readout ADC Full Width at Half Maximum Grand Accelerateur National d'ions Lourds Gesellschaft fur Schwerionenforschung Intermediate{Mass Fragment Institut de Physique Nuclaire d'orsay Kernfysisch Versneller Instituut Light Charged Particle Leading{Edge Discriminator Memory{Lookup Unit Multi{Wire Proportional Chamber Projectile{Like Fragment PhotoMultiplier Primary Projectile{Like Fragment Charge(Q){to{Digital Converter Retard a Duree Variable Small{Angle Large{Acceptance Detector Soft{Photon Approximation Two{Arm Photon Spectrometer Time{to{Digital Converter Special Two{Energy Two{Angle The Svedberg Laboratory 5

3 B. Phase shifts of 5 Li The four most relevant phase shifts of the +p system are shown here. They are used in the SPA prediction which is discussed in this thesis. The phase shifts have been obtained from data by [Dod77, Hou78, Hal98]. In the gures labelled a) the phase shifts are shown as a function of the proton energy (i.e. assuming the {particle at rest). The gures labelled b) show the Argand diagrams of e i. The unit circle is indicated by the thin line. The s/2 phase shift: phase shift (deg.) a) b) - - E p 6

4 7 The p/2 phase shift: phase shift (deg.) a) b) - - E p The p3/2 phase shift: phase shift (deg.) a) b) - - E p The d3/2 phase shift: phase shift (deg.) E p a) b) - -

5 C. Values of tted legendre polynomials gure (b) a a 2 a 3 a 4 a) { b) { c) d) { { Table C.: Overview of coecients of Legendre{polynomial ts of gure 5.6. In the gure, a) has been tted with 3 rd order Legendre polynomial. An extra point to guide the t at has an error which is equal to the one at 7. b) Like a), but with larger error for the extra point at. c) Fitted with 4 th order Legendre polynomial. Besides the extra point at also the value for a 4 is restricted. d) Like c), but with the larger error at. The values of the last row in the table represent the results of a 3 rd order Legendre{polynomial t, without the above mentioned extra point. 8

6 9 Energy a a 2 a 3 a 4 Energy a a 2 a 3 a 4 Data Classical > 22 > > { > { { 3{ { { 25{ { { 2{ { { { SPA BPM > > > > { { { { { { { { { { { { DC2B Table C.2: Overview of coecients of Legendre{polynomial ts for dierent photon energy selections. The entry for E > 22 MeV refers to the energy{integrated distributions shown in gure 5.8. The other entries refer to gure 5.2.

7 D. Table of results System +p Energy (MeV/nucleon) 5 Inclusive results (E >22 MeV) 3.6. b statistical error.4 b systematic error as a result of 4 extrapolation.39 b systematic error due to uncertainties of target thickness.6 b el 245 mb P p(e >22) ;5 Exclusive results coh (E > MeV) 9 b incoh (< E <2 MeV) 2 b Table D.: Table of results of the +p experiment. The error of b for the exclusive data reects the sensitivity to the dierent analysis methods.

8 E. New SPA predictions Since the completion of this thesis errors were found in the code used for the prediction of the Soft Photon Approximation that was used in this thesis (subsection and further). In this appendix, the latest status of this model prediction, dσ/de (µb/mev) E γ Figure E.: Exclusive photon energy spectrum (triangles) with model predictions: BPM (.6, solid), SPA (latest results.26, dashed) and classical (dash-dotted).

9 2 Appendix E: New SPA predictions prior to printing, is shown and compared with the data and other model predictions. In gure E. the most recent SPA energy distribution is shown in comparison with the exclusive data, the prediction of the bremsstrahlung within the potential model (BPM) and the classical calculation. This gure can be considered as an update of gure 5.7 in chapter 5 of this thesis. The SPA prediction is shown as the dashed line and the calculated absolute cross sections have been normalized to the data by multiplying them with a factor of.26. As shown in chapter 5, the BPM calculation has been normalized to the data with a factor of.6 Note that now the SPA and BPM coincide in shape in the resonance region. As was already known, the SPA predicts the peak position at the high photon dσ/dω (µb/sr) Θ γ (deg.) Figure E.2: Measured and calculated angular distribution of bremsstrahlung in +p. Filled circles are the data. The lines are the results of dierent model calculations: classical (dash-dotted, 2.5), BPM (solid,.6), SPA (dashed,.26) and DC2B (dotted, scaled).

10 3 Legendre polynomial coefficients data SPA a a2 a3 a4 classical BPM DC2B E γ Figure E.3: Comparison of Legendre polynomial coecients obtained by tting the angular distributions for dierent energy windows and dierent calculations. energies very well, but still it underpredicts the data for the low{energy photons, where the photons show a classical dependence. The fact that both the BPM and the SPA calculations underpredict the photon yield at the high energies cannot be attributed to the data. In this energy region, no other `contaminating' sources of photon production exist. The updated SPA prediction for the angular distribution has a surprisingly dierent shape as the other predictions. It is shown as the dashed line in gure E.2, which should be considered as the latest version of gure 5.8. Like in the energy distribution, the SPA prediction has been multiplied with a factor of.26 in this gure. Especially if the energy{dependent angular distribution of the SPA is studied

11 4 Appendix E: New SPA predictions the deviation of the other models and the data become clearer. This is shown in gure E.3, which compares the Legendre polynomial coecients obtained by tting the angular distributions for dierent energy selections. Towards the higher photon energies, it does nog converge anymore to the result of the direct capture prediction (DC2B). The origin of these inconsistencies are presently being studied [Tim98].