The simplified description of dipole radiative strength function V.A. Plujko, E.V.Kulich, I.M.Kadenko, O.M.Gorbachenko Taras Shevchenko National University Kyiv, Ukraine CONTENT 1. Introduction and radiative strength function (RSF) definitions. 2. Closed-form description of the RSF: SLO;EGLO; GFL; MLO; SMLO. 3.Semiclassical (MSA) and microscopic (HFB- QRPA) methods of E1 calculations. 4.Calculations and comparisons with experimental data. 5.Conclusions.

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. It is very important for decreasing in computing time to have 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 investigation was to test practical methods for the calculation of E1 radiative strength functions both for  -decay and photoabsorption.

Two types of strength functions partial gamma-decay width average level spacing photoabsorption cross-section For gamma- emission process For photoabsorption

CLOSED-FORM MODELS 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)] empirical factor from fitting exp. data Infinite fermi- liquid (two-body dissipation )

Generalized Fermi liquid (GFL) model extended to GDR energies of gamma- rays [S. Mughabghab, C. Dunford PL B487(2000)] -” fragmentation” component

Modified Lorentzian approach (MLO) was obtained using expression for average gamma-width [V.A.Plujko et al., NPA649 (1999); J.Nucl.Sci Techn. (2000)] microcanonical ensemble most appropriate for closed systems like nuclei

Gamma-strength within MLO

The E1 gamma-decay strength function on 144 Nd for U=Bn EGLOSLOGFLMLO1MLO2MLO3SMLO 144 Nd

The E1 photoabsorption cross section on 144 Nd

EGLOSLOGFLMLO1MLO2MLO3SMLO 90 Zr The E1 gamma-decay strength function on 90 Zr

The E1 photoabsorption strength function on 90 Zr

The E1 gamma-decay strength function versus mass number; U=S n ; E  =0.8U EGLOSLOGFLMLO1MLO2MLO3SMLO A<= <A<= A> All nuclei

Mass number dependence of the relative deviation of photoabsorption C-S within SLO and MLO1 models E r =31.2*A -1/ *A -1/6 (MeV)Г r =0.026*E r 1.91 (MeV)

Relative deviation of RSF within different models and MLO1

Conclusions Numerical studies indicate that the calculations of E1 radiative strength functions within the closed-form models give similar results in a range of gamma-ray energies around the GDR peak. However the results within MLO(SMLO) and EGLO models are different from SLO model calculations in the low energy region. In particular, they have asymmetric shape and for E_g =7 MeV, the calculated RSF values within SLO model are about two times greater comparing to the ones obtained for MLO(SMLO) and EGLO models. The overall comparison of the calculations within different models and experimental data showed that MLO(SMLO) and GFL provide the most reliable simple methods for determining the E1 radiative strength functions over a relatively wide energy interval ranging from zero to above the GDR peak. The MLO(SMLO) and GFL are not time consuming calculational routes and can be recommended for general use; both of them can be used to predict the photoabsorption cross-sections and to extract the GDR parameters from the experimental data for nuclei of middle and heavy weights but collisional component of the GFL damping width can become negative in some deformed nuclei. Microscopic HFB-QRPA(RIPL3) model and semi-microscopic MSA approach with moving surface seems to be more adequate for estimation of the RSF in spherical light and medium-mass nuclei if reliable values of the GDR parameters are not available. The studies were performed within RIPL-2&3 projects (IAEA Research Contract #12492);