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Theoretically, the absorption cross-sections σ_abs of hadrons interacting with target nuclei have been measured by several groups of scientists over widely range of energy on a large number of target nuclei from He to U, by considering de-Broglie's wavelength of incident hadrons. Later, a parameter, called transmission coefficient T was introduced by some other physicists. In the present work, nuclear Transparency has been studied in Antiproton - Nucleus Interactions, using black disc formula along with transmission coefficient T. The nuclei are assumed to be completely black for T=1 and completely transparent for T=0. The agreement between the calculated and experimental values of σ_abs is achieved in all cases, considered in the present work.

The motivation for taking up the present work arises from the abiding interest in high energy hadron-nucleus collisions. One could like to understand how the antiproton – nucleus interactions are related to the basic particle – particle interactions, and thus, to the quark – quark interactions. Since the antiproton is the antiparticle of proton, the present study may help to compare features of nuclear reactions at high energies, initiated by a proton and by an antiproton. The present study may provide an opportunity to understand the phenomenon of the blackness of the target nuclei. In the present work, the main aspects of the present study includes the investigation of transmission of antiprotons through the target nucleus and to understand the mechanism of nuclear reactions. A simple and unambiguous parameterization of nuclear transmission coefficient T of antiprotons through the target nucleus, is presented, which is able to predict the different values of transmission coefficient T for various target nuclei over the wide range of incident energy. It would be fruitful in further studies in the field of nuclear reactions and nuclear structure.

When an antiproton interacts with a target nucleus, there are generally three channels, in which the reaction may take place; 1. the antiproton may be captured by the target nucleus and a compound nucleus is formed. 2. the antiproton may come out from the target nucleus losing some energy. 3. the antiproton may come out from the target nucleus without losing some energy. In the third case the target nucleus may be assumed to be transparent to the incident antiproton. Many of the earlier reaction cross-section studies [1- 14 ] at energies up to 100MeV have been considered with the behavior of absorption cross-section σ_abs as a function of nuclear mass number (A) at a single energy value. However several studies [15-30] have now been done in which energy dependence of σ_abs has been investigated. The nuclear absorption cross-section σ_abs of antiproton (□(p ̅ ) ) at various values of its momentum 0.193 GeV/c ≤ 〖□(p ̅ )〗_mom ≤ 280 GeV/c, has been measured by several workers [1-6, 8-14]. Attempts have also been made to fit the values of absorption cross-section, the expression used for this purpose is, σ_abs = σ_o A^α ……… (1) Here σ_o and α are parameters, whose values are adjusted to obtain the fit of experimental data. The values of σ_o and α estimated by many workers are given in the following Table-1.

Table – 1: Values of the parameters   and  α  for various    values;

 

According to Allebay et-al. [1] the value of the parameter α depends on the type of particle and decreases with the increase of total cross-section for interaction of the particles with nucleus, and for a black nucleus α =2/3 and for completely transparent nucleus α = 1, since does have values ∽ 2/3 for antiproton  in the range 20 - 40 GeV/c. According Abrams et-al., [2], while increases for the particles  with larger reaction cross-section decreases and for black nucleus, α =2/3. Their experiments on measurements  meson andabsorption cross-section in the momentum range 1.0 - 3.3 GeV/c  yielded results consistent with theoretical results. The calculated values of  absorption cross-section for a few nuclei with antiproton  range 0.193 - 0.900 GeV/c  were reported [3] to be in reasonable agreement with corresponding experimental values. The calculations were done by using the black disc formula,

 …….  (2)

 where ʎ is the wavelength associated with the incident particle and R is the interaction range and R = , also rₒ = 1.5. The analytical works [4,5] show that the values of tends to increase with the values of  and should at still higher values of    to be expected to approach 1 ,where the nucleus is supposed to become transparent to antiprotonsp ̅. The situation also leads to the inference that the statement that nuclei are black to . seems to be valid only for low values of , where α ≤ 2/3 . Since the response of nuclear matter to incomingis of great interest, an attempt is made in this work to further examine the behavior of nuclei, when the projectilehas momentum in excess of 1 GeV/c.

The nuclei are not likely to become completely transparent to antiprotons no matter how high momentum it is given.

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