Lorentzian like models of e1 radiative strength functions
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Lorentzian-like models of E1 radiative strength functions. V. A. Plujko, O. M. Gorbachenko, E. V. Kulich Taras Shevchenko National Kyiv University, Ukraine. Content. Introduction: average description of the gamma-transitions by the use of radiative strength function (RSF).

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Lorentzian-like models of E1 radiative strength functions

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Lorentzian like models of e1 radiative strength functions

Lorentzian-like models of E1 radiative strength functions

V. A. Plujko, O. M. Gorbachenko,E. V. Kulich

Taras Shevchenko National Kyiv University, Ukraine


Lorentzian like models of e1 radiative strength functions

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.


Lorentzian like models of e1 radiative strength functions

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.


Radiative strength functions

partial gamma-decay

width

average level

spacing

Radiative strength functions

The photoexcitation strength function

The gamma-decay strength function


Lorentzian like models of e1 radiative strength functions

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


Lorentzian like models of e1 radiative strength functions

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


Lorentzian like models of e1 radiative strength functions

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


Lorentzian like models of e1 radiative strength functions

  • 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)


Lorentzian like models of e1 radiative strength functions

RSF for photoabsorption

  • SMLO

Axially deformed nuclei - n=2;


Estimation of experimental data

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


Gdr parameter determination

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


Photoabsorbtion cross sections and gamma decay strength function

Photoabsorbtion cross sections and gamma-decay strength function


Lorentzian like models of e1 radiative strength functions

(a)

(b)


Systematics of gdr energies widths and peak cross section

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.


Comparison of systematics with fitting data

Comparison of systematics with fitting data


Conclusions

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.


Lorentzian like models of e1 radiative strength functions

  • 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/]


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