Yu.L. Ratis

Projectile delta excitation in alpha-proton scattering

Abstract The (α, α′) reaction in the Δ-region is a clear example of projectile delta excitation. We study the reaction theoretically and compare the results to a recent experiment. The agreement is rather good. On the other hand the reaction offers a test for models of coherent pion production. Finally, the use of the present model should provide the appropriate background to extract the excitation strength of the Roper resonance observed in the same reaction.

A code to evaluate modified bessel functions based on thecontinued fraction method

Abstract We present an algorithm to evaluate the modified Bessel functions I v and K v of integral and half-integral order based onthe calculation of the continued fraction for the I v I s , the Wronskian and the application of forward recurrence relations for the K v I s and backward recurrence for the I v I s . The main feature of the algorithm is that it does not require recalculations using normalization relations nor trial values to start the recurrences; the code evaluates in each step (already normalized) Bessel functions. The accuracy of the method (10 −16 for half-integral order and better than 2×10 −7 for integral order in our code) is limited only by the precision in the initial values for the recurrence and the maximum order available for a given value of the argument is restricted only by the maximum real number available in the computer.

Evaluation of Fresnel integrals based on the continued fractions method

Abstract We present a simple algorithm for evaluating Fresnel integrals based on the continued fractions method: we use the relation between these integrals and first-kind Bessel functions of fractional order, and we apply a fast code to calculate them based on the continued fractions method. This latter code is especially useful for evaluating high order Bessel functions because it does not require recalculations using normalization relations. Comments on the same procedure but using Miller’s algorithm to evaluate the required Bessel functions are presented and a comparison with a standard code for evaluating Fresnel integrals ( Numerical Recipes program FRENEL) is provided.

A code to calculate (high order) Bessel functions based on the continued fractions method

Abstract We have developed a fast code to calculate Bessel functions of integer and fractional order based on the continued fractions method. This algorithm is specially useful in the case of Bessel functions of high order because it does not require any recalculation using normalization relations.

Heat transfer between a gas and an ultralow thermal conductivity porous structure

The analytical solution of a one-dimensional problem of heat transfer between an inert gas and an ultralow thermal conductivity porous medium is obtained by means of the Laplace transform method. The solution shows a sharp heat front propagation through the medium during its heating or cooling depending on its initial temperature.

New quantization rule in the world of resonances of elementary particles

A simple mass formula for hadronic resonances is proposed based on the representation of the resonances as semi‐classical radiating systems. The Bohr‐Sommerfeld quantization rule is used to single out mass eigenvalues as a function of an integer‐valued parameter. Authors claim strong correlation with the experimental data. (AIP)