The Nuclear Level Densities in Closed Shell 205-208 Pb Nuclei

1. The Nuclear Level Densities in Closed Shell 205-208Pb 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 27,28Si. • The limit of applicability of method on closed shell nuclei was also required.

4. Experimental details • MC-35 cyclotron at OCL, • 38 MeV 3He beam bombarded on 206Pb and 208Pb targets having thickness of 4.707 and 1.4 mg/cm2. • Following reactions were studied, • 206Pb(3He, 3He´)206Pb • 206Pb(3He, )205Pb • 208Pb(3He, 3He´)208Pb • 208Pb(3He, )207Pb • The particle- coincidences were recorded while the experiment ran for 2-3 weeks.

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

6. Detector Arrangement • The charged ejectiles ----> 8 collimated Si at 45o 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. Data Analysis: Unfolding of coincidence spectra Raw Data Particle Spectra Calibration -spectra calibration and alignment Extracting Primary-  spectra Data Reduction Particle -  coincidences thickness spectrum Gating on particles

8. 3He- - Coincidence Spectra:

9. Response function of 4 MeV . Response Matrix 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, uo = r • First folded spectrum, fo = R uo • Next trial fn, u1 = uo + (r - fo) • Generally, ui+1 = ui+ (r - fi) • Iteration continues until fi ~ r Fluctuations in folded spectra Compton background are subtracted.

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, • f1 = f.g. -spectrum of highest Ex bin. • g = weighted sum of all spectra. • wi = prob. of decay from bin 1 - i. • ni = i / j

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

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

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

18. Gamma transition probability • Theoretically • Minimizing;

19. =0.634 208Pb Nuclear Level Density: • At low Ex; • comparing the extracted NLD to • At Bn deducing NLD from resonance spacing data. • BSFG level density extrapolation where a = level density parameter, U = E-E1 and E1 = back-shifted parameter,

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(Ei, E) determines the energy dependence of T(Ei, 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. Voinov Ohio university, OH, USA Andreas Schiller MSU, USA Tom Lønnroth Åbo Akademi, Finnland Jon Rekstad University of Oslo Finn Ingebretsen University of Oslo

25. Thank You