1. The Nuclear Level Densities in Closed Shell 205-208 Pb Nuclei Syed Naeem Ul Hasan

2. Introduction : Nuclear level density: Bethe Fermi gas model in 1936. For many years, measurements of NLD have been interpreted in the framework of an infinite Fermi-gas model. Gil. & Cam. CTF, BSFG were later proposed accounting shell effects etc. Shell Model Monte Carlo (SMMC)

3. Experimental NLD, Counting of neutron (proton) resonances Discrete levels counting Evaporation spectra OSLO METHOD Method has successfully been proven for a No. of nuclei. However in cases where statistical properties are less favorable the method foundation is more doubtful. A test at the lighter nuclei region has been made already for 27,28 Si. The limit of applicability of method on closed shell nuclei was also required.

4. Experimental details MC-35 cyclotron at OCL, 38 MeV 3 He beam bombarded on 206 Pb and 208 Pb targets having thickness of 4.707 and 1.4 mg/cm 2. Following reactions were studied, 206 Pb( 3 He, 3 He´) 206 Pb 206 Pb( 3 He,  ) 205 Pb 208 Pb( 3 He, 3 He´) 208 Pb 208 Pb( 3 He,  ) 207 Pb The particle-  coincidences were recorded while the experiment ran for 2-3 weeks.

5. Oslo Cyclotron Lab http://www.physics..no/ocl/intro/ CACTUS Concrete wall

6. Detector Arrangement The charged ejectiles ----> 8 collimated Si at 45 o to the beam. The  -rays detection -----> CACTUS: 28 NaI(Tl) 5”x5” detection  = 15% of 4π. Particles &  -rays are produced in rxns are measured in both particle-  coincidence & particle singles mode by the CACTUS multi-detector array.

7. thickness spectrum Gating on particles Particle -  coincidences Unfolding of coincidence spectra Extracting Primary-  spectra Raw Data  -spectra calibration and alignment Particle Spectra Calibration Data Reduction Data Analysis:

8. 3 He- -- Coincidence Spectra:

9. Unfolding: Detector response of 28 NaI detectors are determined 11 energies and interpolation is made for intermediate  -energies. Folding iteration method is used; Unfolded spectrum is starting point, such that, f = R u. –First trial fn as, u o = r –First folded spectrum, f o = R u o –Next trial fn, u 1 = u o + (r - f o ) –Generally, u i+1 = u i + (r - f i ) –Iteration continues until f i ~ r Fluctuations in folded spectra Compton background are subtracted. Response function of 4 MeV . Response Matrix

10. Raw folded unfolded Test of method:

11. Primary  -matrix: Assumption: The  -decay pattern from any Ex is independent of the population mechanism The nucleus seems to be an CN like system prior to  -emission. Method: The f.g.  -spectrum of the highest Ex is estimated by, f 1 = f.g.  -spectrum of highest Ex bin. g = weighted sum of all spectra. w i = prob. of decay from bin 1 - i. n i =  i /  j Assumption: The  -decay pattern from any Ex is independent of the population mechanism The nucleus seems to be an CN like system prior to  -emission. Method: The f.g.  -spectrum of the highest Ex is estimated by, f 1 = f.g.  -spectrum of highest Ex bin. g = weighted sum of all spectra. w i = prob. of decay from bin 1 - i. n i =  i /  j

15. Multiplicity Normalization : Algorithm: 1.Apply a trial fn w i 2.Deducing h i = f i -  g 3.Transforming h i to w j i (i.e. Unfold h, make h having same energy calibration as w i, normalize the area of h to 1). 4.If w j i (new) ≈ w j i (old) then the calculated h i would be the Primary-  function for the level E i, else proceed with (2) Some experimental conditions can introduce severe systematic errors, like pile-up effects, isomers etc.

16. f g h=f-g Ex ~ 4.5-5.5 MeV. Testing of an Experimental spectrum:

17. Brink-Axel Hypothesis; Transforming; A, B,  are free parameters. A. Schiller et al./ Nucl. Instr. & Methods in Physics Research A 447 (2000) 498-511 Extraction of NLD & GSF:  Ef f Ediff

18. Gamma transition probability Theoretically Minimizing;

19. Nuclear Level Density: At low Ex; ocomparing the extracted NLD to At B n deducing NLD from resonance spacing data. BSFG level density extrapolation where a = level density parameter, U = E-E 1 and E 1 = back-shifted parameter, 208 Pb  =0.634

21. Experimental NLD

22. Entropy:  o is adjusted to give S = ln  ~ 0 close to ground state band The ground band properties fullfil the Third law of dynamics: S(T =0) = 0;

23. Gamma Strength Function: The fitting procedure of P(E i, E  ) determines the energy dependence of T(E i, E  ). The fitting of B must be done here. Assumptions: – The decay in the continuum E1, M1. – No of states with  = ± is equal Radiative strength function is,

24. Collaborators Magne Guttormsen University of Oslo Suniva Siem University of Oslo Ann Cecilie University of Oslo Rositsa Chankova University of Oslo A. VoinovOhio university, OH, USA Andreas SchillerMSU, USA Tom LønnrothÅbo Akademi, Finnland Jon Rekstad University of Oslo Finn Ingebretsen University of Oslo

25. Thank You