PROGRESS IN THE MICROSCOPIC DESCRIPTION OF NUCLEON- NUCLEUS ELASTIC SCATTERING AT LOW ENERGY

In this brief report, we make a short review of progress in developing the microscopic optical potential in recent years. In particular, we present our current studies and plans on building the microscopic optical potential based on the so-called nuclear structure models at low energies.


Introduction
In nuclear physics studies, we still have two unsolvable problems: the many-body problem and the nuclear interaction. To avoid these difficulties, we use phenomenological approaches as the most efficient way to describe nuclear systems, for example, the great success of using effective phenomenological interaction in nuclear structure and phenomenological optical potential in nuclear reactions. However, the limit of phenomenological approaches is the unexpected separation between the structure and reactions communities. Also, due to the fits with experimental data, these approaches do not have prediction powers, especially for the nuclear reactions off-targets outside the range of validity of the fits, e.g., the exotic nuclei produced in the r-process. However, the microscopic optical potential is expected to have prediction powers and a link between the nuclear structure and reactions studies. This link allows us to learn the physics meaning from analysing the experimental data from the studies of nuclear reactions.
In the last five years, tremendous efforts have been devoted to developing the microscopic optical potential. This potential is identified with the nucleon self-energy Σ( , ′, ) , which is a complex non-local energy-dependent function.
Recently, the combination of the Green's function approach with the couple-cluster method [2] has been used to generate the microscopic optical potential for neutron elastic scattering of 40 Ca and 48 Ca. This success is based on the progress of the ab initio nuclear reaction community in many aspects: mass number, precision, and accuracy. They can now have reliable predictions for nuclei as heavy as 120 Sn by using modern nucleon-nucleon (NN) and three-nucleon forces (3NFs) from the chiral effective field theory. In Ref. [2], the microscopic optical potential is defined as where Σ * ( , , ) is the self-energy, which can be calculated from and is the HF potential. The Green's function where (0) is the first-order approximation to However, because Eq. (2) is complicated, the imaginary part (the absorption from the nonelastic channel) of the optical potential is dropped.
Another way to calculate nucleon selfenergy is to use the nuclear matter approach [3,4].
Since this method is only valid for infinite nuclear matter, the local density approximation has been used. For getting the local optical potential, the solution of the self-consistent equation is folded with the resulting density-dependent mean-field with a realistic point-nucleus density distribution.
In this approach, the first order of Σ is the Hartree-Fock contribution which is real, energy-independent, and ̃2 is the anti-symmetrization of 2 .
The second order Σ HF (1) ( , ; ) is both a real and imaginary part. The direct and exchange terms are calculated from the particle states above the Fermi level.
The microscopic optical potential calculations have been applied to study the real and imaginary part for incident energies lower than 100 MeV within the above formalism.
However, no comparison with experimental data has been made. Also, it is well known that the local density approximation cannot capture the physics of the collective surface modes, shell structure effects, and the spin-orbit interaction.
Later, several improvements have been proposed.
The improved local density approximation has been used to consider the nonzero range of where ̂ is the kinetic energy operator, and ̂2 , ̂3 are the two-body and three-body interactions.
The partial wave decomposition of the selfenergy, which is the optical potential, is According to Refs. [10,[18][19][20], the MOPs are given as where In Eqs. (9) and (10), HF is the real, local, momentum-dependent, energy-independent Skyrme HF mean-field potential, and is the nucleon incident energy. The polarization potential, ΔΣ( ), is non-local, complex, and energy-dependent. Σ( ) is the contribution from the particle-hole correlations generated from fully self-consistent particle-vibration coupling (PVC) calculations [10,18]  Using the partial wave expansion, we express the partial wave decomposition of the self-energy as where ̂= (2 + 1) 1/2 . The self-energy is nonlocal, energy-dependent, complex, and separated.
In conclusion, the microscopic optical potential is expected to be a vehicle to study nuclear reactions in unstable regions. However, the main challenge of this potential is its low precision compared with the phenomenological one, even in the stable region. As it is well known, this challenge results from the too complicated many-body problem underlying. Therefore, the combination of phenomenological and microscopic optical potential could be a promising research direction.