The geometric nature of cross section we find considering the collisions of point
particles with other bodies derived from the model used to describe the dynamic part
of the process.
The cross section calculus in the case of Coulomb interactions of point-like
bodies with Z, Z
0 charge is then suggested in the case in which one of the two bodies
(scatterer) is much bigger than the other (incident), so that its position does not vary
in the collision process and we can therefore consider it still at rest as in the case of
scattering experiments to explore a solid system and in particular Rutherford Backscattering Spectroscopy (RBS) (Corni and Michelini 2018). The calculation of the
differential cross section for this process is done in the same way as for the previous
section: calculation of the relationship between the collision parameter and scattering
angle and subsequent application of the definition. The detailed proposal is
published in the path dedicated to RBS (Corni and Michelini 2018).
The discussion of the nuclear cross section and relative difficulties conclude the
proposal for the last part of the curriculum. Due to the high number of nucleons
involved in a nuclear reaction, we are not able to write down a simple expression for
the nuclear force, then a simple expression for the cross section cannot be simply
derived, but taking into account that we could have, at the same time, Coulombian
and nuclear interactions for different nuclei, we can write: σ NUC ¼ Aσ R N NU /N R ,
where σ R the Rutherford cross section, N NUC the number of nuclear events, N R the
number of Rutherford events, and A a parameter depending on detectors’ solid
angles and intrinsic efficiencies. The N NU number depends on the observed nuclear
process we observe. In the case of a nuclear reaction where the two nuclei come
close enough to fuse, one of these nuclei dissipate the extra energy and angular
momentum removing nucleons from high energy levels to lower energy ones and
emitting γ photons with energy equal to the difference of the two levels. For each
nuclear fusion event, we will have a γ ray cascade from the first excited state to the
ground state. The fusion cross section σ FUS depend by the total number of transitions
N γ and by Rutherford scattering events as follows: σ FUS ¼ Aσ R N γ /N R .
Students learn how in a similar way it is possible to measure the cross section for
other nuclear processes and understand why there are research fields on cross
section.
10.4 A Conceptual Explorative Path to Superconductivity
Superconductivity is one of the most relevant topics of the twentieth-century physics. It is an important research field in material science for different kind of research,
its application changes almost all the way in which magnetism is employed in
technologies and produces new technologies as for the case of Maglev train, its
theoretical interpretation founded a new theory (Bardeen et al. 1957). It can be
explained at different level and in different interpretive frames (González-Jorge and
Domarco 2004; Essén and Fiolhais 2012). From educational point of view, we offer
to secondary school students the opportunity to experience how to perform a
10 Innovation of Curriculum and Frontiers of Fundamental Physics in Secondary. . .
109
particles with other bodies derived from the model used to describe the dynamic part
of the process.
The cross section calculus in the case of Coulomb interactions of point-like
bodies with Z, Z
0 charge is then suggested in the case in which one of the two bodies
(scatterer) is much bigger than the other (incident), so that its position does not vary
in the collision process and we can therefore consider it still at rest as in the case of
scattering experiments to explore a solid system and in particular Rutherford Backscattering Spectroscopy (RBS) (Corni and Michelini 2018). The calculation of the
differential cross section for this process is done in the same way as for the previous
section: calculation of the relationship between the collision parameter and scattering
angle and subsequent application of the definition. The detailed proposal is
published in the path dedicated to RBS (Corni and Michelini 2018).
The discussion of the nuclear cross section and relative difficulties conclude the
proposal for the last part of the curriculum. Due to the high number of nucleons
involved in a nuclear reaction, we are not able to write down a simple expression for
the nuclear force, then a simple expression for the cross section cannot be simply
derived, but taking into account that we could have, at the same time, Coulombian
and nuclear interactions for different nuclei, we can write: σ NUC ¼ Aσ R N NU /N R ,
where σ R the Rutherford cross section, N NUC the number of nuclear events, N R the
number of Rutherford events, and A a parameter depending on detectors’ solid
angles and intrinsic efficiencies. The N NU number depends on the observed nuclear
process we observe. In the case of a nuclear reaction where the two nuclei come
close enough to fuse, one of these nuclei dissipate the extra energy and angular
momentum removing nucleons from high energy levels to lower energy ones and
emitting γ photons with energy equal to the difference of the two levels. For each
nuclear fusion event, we will have a γ ray cascade from the first excited state to the
ground state. The fusion cross section σ FUS depend by the total number of transitions
N γ and by Rutherford scattering events as follows: σ FUS ¼ Aσ R N γ /N R .
Students learn how in a similar way it is possible to measure the cross section for
other nuclear processes and understand why there are research fields on cross
section.
10.4 A Conceptual Explorative Path to Superconductivity
Superconductivity is one of the most relevant topics of the twentieth-century physics. It is an important research field in material science for different kind of research,
its application changes almost all the way in which magnetism is employed in
technologies and produces new technologies as for the case of Maglev train, its
theoretical interpretation founded a new theory (Bardeen et al. 1957). It can be
explained at different level and in different interpretive frames (González-Jorge and
Domarco 2004; Essén and Fiolhais 2012). From educational point of view, we offer
to secondary school students the opportunity to experience how to perform a
10 Innovation of Curriculum and Frontiers of Fundamental Physics in Secondary. . .
109