Subatomic Physics

E/A(MeV)
16.3. Heavy Ion Reactions 509
200
150
100
50
Realistic potentials
Fermi gas
� �
0.2 0.4 0.6 0.8
����fm �
3
Figure 16.5: Sketch of calculations of energy per nucleon as
a function of density at a temperature of 0 K. The ‘Fermi
gas’ curve assumes no interaction appart from Pauli blocking.
The other curves that show minima around the observed
nuclear density come from realistic potentials with
different ingredients. [After A. Akmal, V.R. Pandharipande,
and D.G. Ravenhall, Phys. Rev. C 58, 1804 (1998).
Some typical plots of the energy
dependence on density
are shown in Fig. 16.5 for nuclear
matter. Nuclear matter
consists of an equal and
infinite number of neutrons
and protons distributed uniformly
throughout space, but
with the neglect of Coulomb
forces. At low densities, nuclear
matter is unbound because
nuclear forces are only
felt at short range. A minimum
energy is reached at normal
nuclear matter density,
ρn ≈ 0.17 nucleons/fm 3 ,the
central density of finite nuclei.
The minimum energy corresponds to the volume energy of Eq. (16.4), about
−15.6 MeV per nucleon. The curvature at the minimum, δ 2 E/δρ 2 , is related to
the incompressibility of nuclear matter,
�
K =9 ρ 2 δ2E/A δρ2 �
. (16.21)
min
The value of K is ∼ 210 MeV and can be obtained from the excitation energy of
the collective 0 + “breathing” mode (8) (Section 18.6) and from kaon production in
heavy ion collisions. (9)
The series of drawings in Fig. 16.6 show typical events in heavy ion collisions as
the energy is increased. The dynamics are determined by the competition between
the Coulomb force, the centrifugal barrier, and the nuclear force. Owing to these
forces, the shapes of the nuclei change as they approach each other and surface
modes of motion are excited (see Chapter 18). For energies below the Coulomb
barrier, Coulomb excitation dominates the interaction. Above the Coulomb barrier,
many nuclear processes occur. Examples are particle transfers, fusion reactions,
and nuclear excitations, often with large angular momenta, particularly for grazing
collisions. To see that very high angular momenta can be reached and to study the
collisions in more detail, we note that semi-classical approaches can be used because
prc/� ≫ 1, where p is the relative momentum of the two colliding ions and rc is
the approximate distance of closest approach. For energies close to the Coulomb
barrier, this distance can be found by assuming that the nuclei remain undistorted.
8 Youngblood et al., Phys. Rev. Lett. 82, 691 (1999).
9 Hartnack et al, Phys. Rev. Lett. 96, 012302 (2006).