1. V. A. Plujko Taras Shevchenko National University, Kyiv, Ukraine
CLOSED-FORM E1 RADIATIVE STRENGTH FUNCTIONS FOR PHOTOABSORPTION AND GAMMA-DECAY
V. A. Plujko
Taras Shevchenko National University, Kyiv, 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. Radiative strength functions
The photoexcitation strength function
The gamma-decay strength function
partial gamma-decay
width
average level
spacing

5. MAIN CLOSED-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. 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;

8. RSF within modified Lorentzian (MLO)
MLO is based on expression for average gamma-width averaged
on microcanonical ensemble of initial states
[V.A.Plujko (Plyuiko), Sov.J.Nucl.Phys. 52 (1990) 639; Proc. 9th Inter. Conf. Nucl. Reaction Mechanisms, Varenna, June 5-9, 2000, edited by E. Gadioli, (Universita degli Studi di Milano, Suppl. N.115, 2000),113]

9. 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;
Approximation of strong collective state for response function

10. 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)

11. RSF for photoabsorption
Axially deformed nuclei - n=2 ;

12. 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

13. The E1 photoabsorption cross section on 144Nd

14. (a)
(b)

15. The E1 gamma-decay strength function on 144Nd for U=Bn
Model
EGLO
SLO
GFL
MLO1
MLO2
MLO3
SMLO
2.2
22.9
2.6
6.47
6.52
7.16
6.06

16. (a)
(b)

17. (a)
(b)

18. (a)
(b)

20. (a)
(b)

21. (a)
(b)

22. Model
EGLO
SLO
GFL
MLO1
SMLO
5.0
105
5.27
7.55
2.0

23. Systematics of GDR energies and widths
Systematics are found on base of resonance parameters, that are obtained from fitting of experimental data

24. Comparison of systematics with fitting data

25. Conclusions
MLO approach with asymmetric shape of the RSF provide unified and rather reliable simple methods to estimate the dipole RSF both for gamma-decay and for photoabsorption over a relatively wide energy interval ranging from zero to slightly above the GDR peak; EGLO approach is also rather reliable for description of gamma-decay RSF.
MLO 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 RSF, so that the contributions of the different mechanisms responsible for the damping of the collective states can be further investigated.