Lorentzian-like models of E1 radiative strength functions

1. Lorentzian-like models of E1 radiative strength functions V. A. Plujko, O. M. Gorbachenko,E. V. Kulich Taras Shevchenko National Kyiv University, Ukraine

2. Content • Introduction: average description of the gamma-transitions by the use of radiative strength function (RSF). • 2. Closed-form description of the dipole RSF: • SLO; EGLO; GFL; MLO (SMLO). • 3. Determination of the RSF function parameters. • 4. Calculations and comparisons with experimental data. • 5. Conclusions.

3. Introduction Gamma-emission is the most universal channel of the nuclear decay, because it is, as a rule, realized during emission of any particle or cluster. The strengths of electromagnetic transitions between nuclear states are much used for investigations of nuclear models, mechanisms of -decay, width of the collective excitations and nuclear deformations. Average strengths of  - transitions are described by radiative strength functions. It is very important for decreasing in computing time to use simple closed-form expressions for -ray strength functions, since these functions in the most cases are auxiliary quantities required for calculations of other nuclear reaction characteristics. The goal of this contribution is to overview and test practical methods for the calculation of E1 radiative strength functions both for -decay and photoabsorption.

4. partial gamma-decay width average level spacing Radiative strength functions The photoexcitation strength function The gamma-decay strength function

5. Mainclosed-form models of E1 RSF Standard Lorentzian (SLO)[D.Brink. PhD Thesis(1955); P. Axel. PR 126(1962)] Enhanced Generalized Lorentzian (EGLO) [J.Kopecky , M.Uhl, PRC47(1993)] [S.Kadmensky, V.Markushev, W.Furman, Sov.J.N.Phys 37(1983)] Infinite fermi- liquid(two-body dissipation) empirical factor from fitting exp. data

6. Generalized Fermi liquid (GFL) model (extended to GDR energies of gamma- rays) [S. Mughabghab, C. Dunford PL B487(2000); Ext.:V.A. Plujko, O.O.Kavatsyuk, Proc. 11th Int. Symp. Capture Gamma-Ray Spectr. and Related Topics (CGS 11), 2002, 793.] -” fragmentation” component

7. RSF for gamma-decay [V.A.Plujko, NPA649 (1999); Acta Phys. Pol. B31 (2000) 435. V.A. Plujko, S.N. Ezhov, M.O. Kavatsyuk et al,J.Nucl.Sci Techn. (2000); Plujko V. A., Kadenko I. M., Kulich E. V., Goriely S. et al Proc. of Workshop on photon strength functions and related topics, Prague, June 17-20, 2007, PSF07, 2008; http://arxiv.org/abs/0802.2183] Approximation of strong collective state for response function

8. MLO1 - no restriction on multipolarity of the deformation of Fermi-surface Doorway state approach for collisional relaxation time • SMLO At U=0, width is similar to that proposed by S.Coriely ( PhL. B436(1998) 10)

9. RSF for photoabsorption • SMLO Axially deformed nuclei - n=2;

10. Estimation of experimental data • If experimental or evaluated data for some nuclei is absent in data base, then the total cross section is approximated by the total photoneutron cross section • The total photoneutron cross section is estimated with partial cross sections

11. GDR parameter determination • The adjustment is performed by the least square method with minimizing • Energy dependent errors are used for estimated data: Spherical nuclei Deformed nuclei

12. Photoabsorbtion cross sections and gamma-decay strength function

13. (a) (b)

14. Systematics of GDR energies, widths and peak cross section • Systematics are found on base of resonance parameters, that are obtained from fitting of experimental data Berman B.L., Fultz S.C. // Rev. Mod. Phys. – 1975. – Vol. 47. – P. 713 – 761.

15. Comparison of systematics with fitting data

16. Conclusions • Modefied LOrentzian approach is based on general relations between the RSF and the nuclear response function. Therefore it can potentially lead to more reliable predictions among other simple models. • The energy dependence of the width is governed by complex mechanisms of nuclear dissipation and is still an open problem. • Reliable experimental information is needed to better determine the temperature and energy dependence of the Radiative Strength Function, so that the contributions of the different mechanisms responsible for the damping of the collective states can be further investigated.

17. The RSF within SLO, GFL and EGLO models for gamma-decay are not agree with general expression for radiative strengths in heated nuclei which corresponds to detailed balance principle with the canonical distribution for initial states. • In the EGLO expression for RSF includes an additional phenomenological contributions. • Gamma-ray energy dependence of widths in expressions within EGLO and GFL models is introduced formally by substitution of the gamma-ray energy instead of GDR energy. • [ T. Belgya, O. Bersillon, R. Capote, T. Fukahori, G. Zhigang, S. Goriely, M. Herman, A.V. Ignatyuk, S. Kailas. A. Koning, P. Oblozinsky, V. Plujko and P. Young. IAEA-TECDOC-1506:Handbook for calculations of nuclear reaction data: Reference Input Parameter Library-2, IAEA, Vienna, 2005, Ch.7; http://www-nds.iaea.org/RIPL-2/]