https://doi.org/10.1140/epja/i2015-15109-9
Regular Article - Theoretical Physics
The energy-weighted sum rule and the nuclear radius
Aleph-Consulting GmbH Verlag, Wiesentalstr. 19, D-65207, Wiesbaden, Germany
* e-mail: hans-peter.schroeder@web.de
Received:
29
May
2015
Revised:
31
July
2015
Accepted:
13
August
2015
Published online:
9
September
2015
The energy-weighted integrated cross-section for photon absorption --known as sum rule 
-- is under certain conditions proportional to the mean square nuclear radius (Levinger, Bethe (Phys. Rev. 78, 115 (1950))). Due to the energy weight factor the low-energy absorption components are emphasized and the dipole transitions in the region of giant resonances contribute enhanced at . Thus, the cross-section of the full interaction can be replaced in good approximation by the dipole cross-section. Under these aspects, we have calculated and the radii of various gg-nuclei. For our purpose, we have chosen a simple shell model where the integrals can be solved analytically, and the contributions of uncorrelated functions and correlation corrections can be shown explicitly. The mean square radius as a function of differs by a factor of 1.5/0.87 from the previous result of Levinger and Kent (Phys. Rev. 95, 418 (1954)) without correlation corrections. Plotting the function of the correlation corrections 
and the uncorrelated function 
as a ratio it shows that 
tends towards a limit. Finally, our results for the radii of gg-nuclei are in good agreement with recent experiments (I. Angeli, K.P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)).
© SIF, Springer-Verlag Berlin Heidelberg, 2015
