GOSIA

2. GOSIA As a Simulation Tool J.Iwanicki, Heavy Ion Laboratory, UW

3. OUTLINE Our goal is to estimate gamma yieds • What the yield is • Point Yield vs. Integrated Yield • What they are needed for • What is needed to calculate it • Definition of the nucleus considered • Definition of the experiment

4. YIELD GOSIA recognizes two types of yields: • Point yields calculated for: • Excited levels layout • Collision partner • Matrix element values • CHOSEN particle energy and scattering angle • Integrated yields calculated for: • (... as above but ...) • A RANGE of scattering angles and energies

5. POINT YIELD How GOSIA does it? • Assumes nucleus properties and collision partner; • starts with experimental conditions (angle, energy) and matrix element set • solves differential equations to find level populations; • calculates deexcitation using gamma detection geometry, angular distributions, deorientation and internal conversion into acount.

6. POINT YIELD Point yields: • are fast to be calculated... • ...so they are used at minimisation stage • OP,POIN – if one needs a quick look • but are good for one energy and one(particle scattering)angle

7. INTEGRATED YIELD Integrated yields • are something close to reality • but quite slow to calculate Useful integration options: • axial symmetry option • circular detector option • PIN detector option (multiple particle detectors)

8. YIELD • GOSIA calculates yields as differential cross sections, integrated over in-target particle energies and particle scattering angles • ‘differential’ in  but integrated for particles • The ‘GOSIA yield’ may be understood as a mean differential cross section multiplied by target thickness (in mg/cm2) [Y]=mb/sr  mg/cm2

9. 88Kr simulation – level layout

10. 88Kr simulation – level layout 5 6 4 3 2 1 One usually adds some „buffer” states on top of observed ones to avoid artificial population build-up it the highest observed state

11. megengeneration of matrix elements set Apply  transition selection rules to create a set of all possible matrix elements involved in excitation. • This is easy but takes time and any error will corrupt the results of simulation! • Tomek quickly wrote a simple code to do the job which uses data in GOSIA format.

12. megengeneration of matrix elements set level number parity spin level energy [MeV] input termination

13. megengeneration of matrix elements set iwanicki@buka:~/Coulex/88Kr$ megen 1 Create setup for this multipolarity (y/n) n 2 Create setup for this multipolarity (y/n) y Do you want them coupled ? n Please give limit value -1.5 1.5 3 Create setup for this multipolarity (y/n) n (…) 7 Create setup for this multipolarity (y/n) y Do you want them coupled ? n Please give limit value -1 1 8 Create setup for this multipolarity (y/n) n E2 M1

14. How to get matrix elementsfor simulation from? • Check the literature for published values • Get all the available spectroscopic data (lifetimes, E2/M1 mixing ratios, branching ratios) • Ask a theoretician • Use OP,THEO to generate the rest from rotational model • Do some fitting with spectroscopic data only

15. OP,THEOgeneration of a starting point From the GOSIA manual: • OP, THEO generates only the matrix specified in the ME input and writes them to the (...) file. • For in-band or equal-K interband transitions only one (moment) marked Q1 is relevant. For non-equal K values generally two moments with the projections equal to the sum and difference of K’s are required (Q1 and Q2), unless one of the K’s is zero, when again only Q1 is needed. • For the K-forbidden transitions a three parameter Mikhailov formula is used.

16. OP,THEO for 88Kr OP,THEO 2 0,4 1,2,3,4 2,2 5,6 2 1,1 0.3,0,0 1,2 0.05,0,0 0,0 7 1,2 0.05,0,0 0,0 0 number of bands (2) First band, K and number of states band member indices Second band, K and number of states Multipolarity E2 Bands 1 and 1 (in-band) Moment Q1 of the rotational band Multipolarity M1 band 1 band 2 4 3 2 1 5 6 end of band-band input end of multipolarities loop

17. Minimisation with OP,MINI • Some minimisation would be in order but minimisation itself is a bit complex subject... • Let’s assume we have some best possible Matrix Elements set. • Next step is the integration over particle energy and angle.

18. Integration with OP,INTG Few hints: • READ THE MANUAL, it is not easy! • Integration over angles: assume axial symmetry if possible (suboption of EXPT) • Theta and energy meshpoints have to be given manually, do it right or GOSIA will go astray!

19. Integration with OP,INTG • Yield integration over energies: stopping power used to replace thickness with energy for integration: • One has to find projectile energy Eminat the end of the target to know the energy range for integration.

20. YIELD COUNT RATE • GOSIAis aware of gamma detectors set-up • Gamma yield depends on detector angle (angular distribution) • However, angular distributions are flattened by detection geometry (both for particle and gamma ) • Gamma detector geometry is calculated at the initial stage (geometry correction factors are calculated and stored for yield calculation)

21. YIELD COUNT RATE • One may try to reproduce gamma detector set-up of the intended experiment • or assume the symmetry of the detection array and calculate everything with a virtual gamma detector covering 2 of the full space (huge radius, small distance to target)

22. YIELD COUNT RATE • Taking into account the solid angle, Avogadro number, barns etc, beam current, total efficiency... Count Rate = target yield  count rate y2c code

23. Having the yields calculated... GOSIA GOSIA spectroscopic data • Kasia is going to show the way to estimate experimental errors of matrix elements to be measured: generated yields matrix element errors estimate

24. “Saturation” of the yield