Using method equal square triangle" for calculation of nucleus temperature and energy levels density, taking into account vibrational states in the frame of statistical approach. Beloshenko Nikita St. Gorbachenko Oleksandr Ph. D Ukraine 2007 Kyev Taras Shevchenko national university Dubna, NTAA07

Introduction We proposed the new method, called "equal square triangle", for calculation roots of the algebraic equations, which allows to simplify calculation of the nucleus temperature. We calculated nucleus temperature from the thermodynamical state equation in the frame of statistical approach.

Method "equal square triangle". Search solution of the equation. Function must be : Where x in the. 1. Continuous, 2. Strongly grows up, 3. Strongly convexity up. For any x1,x2 with [a,b]:.

- barrier" distance - square of the figure - length of the snippet

The main iteration formula of the method "equal square triangle" is

Compare velocity of the convergence with chord method

Compare velocity of the convergence with the dihotomia method

Asymptotic estimation of convergence of the method "equal square triangle".

Coefficient of the amplification of the energy levels density. - density of the energy levels with taking into account vibrational states and without it, corresponding. Density of the energy levels

Method saddle point - entropy of the nucleus; - statistical sum; The thermodynamical equation of state: - thermodynamical potential; - temperature;- chemical potential;

Vibration change of the statistical sum Response function method

Solution termodynamical equation of state with help equal square triangle method Fermi gas model

Calculation influence vibrational states to the temperature of the nucleus.

Calculation coefficient of the amplification of the energy levels density

Conclusions : We propose method "equal square triangle", which allows search roots of equation faster than standard methods such as "chord" and dichotomia. This method has advantages for functions which has analytical possibility to calculate integral. This method allows simplify calculations of the temperature of nucleus from the thermodynamical equation of state. Temperature and energy levels density (of nucleus) changed under influence of the vibrational states was analysed. Dependence coefficient of the amplification of the energy levels density from energy excitation (with take into account change of temperature) was explored, when change statistical sum calculated in the frame of response function method.

Acknowledgments Volodimir Savchenko who helped me make this presentation. Basov D.S. who help me make my first presentation of this method. Morozova R.P. - my first mathematical teacher. And all who helped me. Thank you for attention.