It has been shown [1] that Order Statistics [2] (OS) combined with experimental tools like Energy Ordered Spectra [3] (EOS) and the Hk-technique [4] may help obtaining physical parameters that describe nuclei at high excitation energy over a wide spin region. The experimental quantities to analyze are spectra formed by the most energetic transitions in each cascade of the continuum gamma decay after e.g. fusion-evaporation reactions. OS gives formulas to calculate the spectral shape of EOS according to any given nuclear statistical model under the assumption that (i) the statistical variable is unbound, whereas in our case, the corresponding random quantity, the transition energy E_gamma, is bound; (ii) the order parameter is a fixed number, whereas in continuum gamma decay the corresponding quantity, the multiplicity of the given cascade, M, is a random number; (iii) the statistical variables are independent and identically distributed, which in our case, alone because they are bound, do not hold these conditions.

Approximations of the OS formulation that circumvent the three previous conditions have been tried with limited success [5]. We present here a new way to calculate EOS that by including correctly the relative contribution of the different multiplicities produces spectral shapes identical to those from Monte Carlo simulations.

The deduced analytical expression (fitting function) is used for the constant temperature level density and the classical dipole gamma strength. Conclusions regarding the capability of this formulation for improving the agreement with simulated spectra when higher multiplicity is included.


References

[1] F. Cristancho, Heavy Ion Physics 2 (1995), 299.
[2] B. C. Arnold et al., A First Course in Order Statistics, John Wiley, 1992.
[3] C. Baktash et al., Nucl. Phys. A520 (1990), 555c.
[4] M. Jääskeläinen et al., Nucl. Inst. Meth. 204 (1983), 385.
[5] F. Cristancho and J. P. Urrego, Heavy Ion Physics, 16 (2002), 75.