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 CORRECTION However Correction Factors can be found by comparison of calculated point and integrated yields. Correcting the yield is like averaging point yields over energy and angular range, –so the better the choice of mean energy/angle, Correction Factor is closer to 1. One needs as many C.F.s as gamma yields CF

9. YIELD CORRECTION Correction depends on the matrix element set so it is usually performed after satisfactory initial set is found. Minimisation is usually performed using corrected yields After minimisation, another correction should be performed with the new found matrix element set so the process is recursive but converges very well.

10. 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/cm 2 ) [Y]=mb/sr  mg/cm 2

11. 88 Kr simulation – level layout

12. One usually adds some „buffer” states on top of observed ones to avoid artificial population build-up it the highest observed state 43214321 5656

13. megen generation 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.

14. megen generation of matrix elements set parity level number spin level energy [MeV] input termination

15. 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 megen generation of matrix elements set E2 M1

16. megen output E2 M1 initial level | final level | starting value (1) | low limit | high limit

17. How to get matrix elements for 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

18. OP,THEO generation of a starting point From the GOSIA manual: OP, THEO generates only the matrix speci fi ed in the ME input and writes them to the (...) fi le. 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.

19. OP,THEO for 88 Kr 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 43214321 5656 band 1 band 2 end of band-band input end of multipolarities loop

20. 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.

21. 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!

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

23. elo screen dump iwanicki@jedrek:~/Coulex/88Kr$ elo Notes to ELO users: 1) Maximum of energy steps = 100 2) Maximum of absorbers number = 40 3) Maximum of projectiles number = 40 4) For energies less than 10 keV/u uncertainty of range (and energy loss) may be greater then 10%, especially for lighter projectiles or absorbers *** Input data *** *** Absorbers specification *** Enter number of absorbers 1 Absorber # 1: Solid of 1 components Enter mass and atomic numbers and number of atoms in component # 1 120 50 1 Element # 1: 120Sn 1 atoms Enter thickness of solid absorber ( 0 - mg/cm**2) 1 Equivalent Values : Z = 50.00, A = 120.00, Av.Ion.En. = 511.800 eV Thickness = 0.0014 mm ( 1.0000 mg/cm**2 ) *** Projectile specification *** Enter number of projectiles 1 Mass and atomic numbers of projectile # 1 88 36

24. elo screen dump *** Projectile specification *** Enter number of projectiles 1 Mass and atomic numbers of projectile # 1 88 36 Projectile # 1: 88Kr *** Energy specification *** Enter indeks, if indeks = 0 - total energy, if indeks = 1 - energy per nucleon 1 Enter minimum, maximum and step of energy 1 3 0.1 Choose output specification - enter iout iout = 1 - only energy losses iout = 2 - energy losses and ranges iout = 3 - energy losses, ranges and stopping powers 3 End of input data reading Output data will be written on file ELO.OUT

25. YIELD  COUNT RATE GOSIA is 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)

26. 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)

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

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

29. “Saturation” of the yield

30. 88 Kr on 208 Pb target, simple sensitivity to the diagonal E2 matrix element of the 2 + 1 state

31. How does GOSIA work? (1/3)

32. How does GOSIA work? (2/3)

33. How does GOSIA work? (3/3)

34. How does GOSIA work? normalisation factor calculated yield experimental yield spectroscopic data point calculated magnitude