Session R11: Nuclear Theory II

Microscopic folding potentials based on NCSM nonlocal densities for elastic proton scattering off light nuclei

A microscopic effective (optical) potential for describing elastic scattering of protons (neutrons) from nuclei can be formulated consistently using multiple scattering theory and the spectator expansion. In first order the use of the nucleon-nucleon t-matrix accounts for the short range interaction between the projectile and a target nucleon, and the non-local one-body density matrix describes the nucleus. Here we employ translationally invariant non-local one-body densities derived from NCSM calculations~\footnote{M.Burrows, Ch. Elster, G. Popa, K.D. Launey, A. Nogga, P. Maris, arXiv:1711.07080} in constructing the effective proton-nucleus interaction and will show elastic scattering observables for the closed shell nuclei $^4$He and $^{16}$O for laboratory kinetic energies for 200~MeV and below. We also explore the observables for the open-shell nucleus $^{12}$C.   

Sensitivity of Nuclear Optical Potentials to Similarity Renormalization Group Transformations

Recent work has shown that incorporating nonlocality in (d,p) scattering introduces sensitivity to high n-p momenta. This leads to the question of how the similarity renormalization group (SRG) impacts optical potentials. We explore the effects of SRG and other unitary transformations on simple models of optical potential.   

Neutron Transfer Reactions for Deformed Nuclei Using Sturmian Basis States

Transfer reactions leading to nuclear excitations of several MeV are of interest to indirect measurements of cross sections. The spin-parity distribution P(J$\pi $,E) of $^{\mathrm{156}}$Gd excited states above the neutron separation energy Sn $=$ 8.536 MeV expected to be populated via a 1-step neutron pickup reaction $^{\mathrm{157}}$Gd($^{\mathrm{3}}$He,$^{\mathrm{4}}$He)$^{\mathrm{156}}$Gd are studied. Excited states in $^{\mathrm{156}}$Gd are viewed as rotational excitations built on intrinsic states consisting of a neutron hole in the $^{\mathrm{157}}$Gd core; that is, a neutron removal from a deformed Woods-Saxon type single-particle states. The reaction cross section to each excited state is calculated as coherent contribution using a standard reaction code based on spherical basis states. The spectroscopic factor associated with each state is the expansion coefficient of the deformed neutron state in a spherical Sturmian basis along with the spherical form factors. The total cross section is generated using Lorentzian smearing distribution function. Our calculations show that, within the assumptions and computational modeling, the reaction has a smooth formation probability P(J$\pi $,E) within the energy range relevant to the desired reaction. The formation probability P(J$\pi $,E) resembles a Gaussian distribution with centroids and widths that differ for positive and negative parity states.   

Analysis of neutron skins using a nonlocal Dispersive Optical Model

A nonlocal dispersive optical model (DOM) analysis of the $^{40}$Ca,$^{48}$Ca, and $^{208}$Pb nuclei has been implemented. The real and imaginary potentials are constrained by fitting to elastic-scattering data, total and reaction cross sections, energy level information, particle number, and the charge densities of each nuclei. The nonlocality of these potentials permits a proper dispersive self-energy which accurately describes both positive and negative energy observables. $^{48}$Ca and $^{208}$Pb are of particular interest because they are doubly magic and have neutron skins due to the excess of neutrons. The DOM neutron skin radius in $^{48}$Ca is found to be $r^{48}_{skin} = 0.245$, which is the largest calculated value of this skin using any method. The $^{208}$Pb neutron skin is compared with the value obtained from PREX of $r^{208}_{skin} = 0.302$. The neutron skin is closely related to the symmetry energy which is a crucial part of the nuclear equation of state. The combined analysis of the nuclear energy densities provides a clear description of the symmetry energy which is then compared with the neutron skin.   

Neutron width statistics in a realistic resonance-reaction model

The statistical model of compound nucleus reactions is widely used in nuclear science, astrophysics, and nuclear technology. A recent experiment [1] found that the distributions of reduced neutron widths for Pt isotopes deviate from the Porter-Thomas distribution (PTD). This finding contradicts the statistical model expectation, and several explanations have been proposed [2-4]. We have studied resonance width statistics for $s$-wave neutron scattering off $^{194}$Pt within a model that combines the statistical description of the compound nucleus with a realistic description of the neutron channel [5]. We find that the reduced neutron width distribution agrees with the PTD for a large range of the model parameters, if the energy dependence of the average neutron widths is correctly described. We identify a parameter range where a near-threshold bound or virtual state of the neutron channel distorts the average neutron width [2], leading to apparent PTD violation if the usual analysis is used. [1] P.E. Koehler {\em et al}, PRL {\bf 105}, 072502 (2010) [2] H.A. Weidenm\"uller, PRL {\bf 105}, 232501 (2010) [3] G.L. Celardo {\em et al}, PRL {\bf 106}, 042501 (2011) [4] A. Volya {\em et al.}, PRL {\bf 115}, 052501 (2015) [5] P. Fanto, G.F. Bertsch, and Y. Alhassid, arXiv:1710.00792   

Analysis of low-energy corrections to the eikonal approximation

Exotic nuclei are mostly studied through reactions. To extract valuable structure information from measured cross sections, a reliable reaction model is needed. At high-enough energy, the eikonal approximation provides an excellent description of the collision, while being numerically efficient. Unfortunately, its validity is limited to energies above $50A$MeV. Various facilities will soon deliver exotic beams at about $10A$MeV, e.g., ReA12 at FRIB. To help experimenters in the analysis of their data, we study various corrections to the eikonal approximation to low energies [1,2,3]. Some of them efficiently correct the description of the elastic scattering of one-body projectiles. When extended to two-body projectiles, these corrections are still able to improve the eikonal prediction [4]. They could therefore provide good alternatives to coupled-channel reaction models.\\ References:\\ {[1]} S. J. Wallace, Ann. Phys. 78, 190 (1973).\\ {[2]} C. E. Aguiar, F. Zardi, and A. Vitturi, Phys. Rev. C 56, 1511 (1997).\\ {[3]} J. M. Brooke, J. S. Al-Khalili, and J. A. Tostevin, Phys. Rev. C 59, 1560 (1999).\\ {[4]} C. Hebborn and P. Capel, Phys. Rev. C 96, 054607 (2017).   

Nuclear Polarization Corrections to the Lamb Shift in Muonic Deuterium

As an electron or muon orbits a nucleus, it can excite the nucleus, and these excited nuclear states in turn affect the atomic states of the lepton-nucleus system. The resulting nuclear polarization corrections to the Lamb shift can be large and difficult to calculate accurately. We calculate these corrections in muonic deuterium in order to address their important impact on the measured finite size of the deuteron, which is relevant to the proton radius puzzle and a range of measurements taken at institutions such as the Paul Scherrer Institute. To approach the problem, we utilize pionless effective field theory and include relativistic and higher order finite range corrections. Muonic deuterium lends itself well to this approach because the muon wave function does not change much across the physical extent of the nucleus and is approximately free. This enables us to calculate the polarization correction to the Lamb shift using the forward virtual Compton amplitude, which then allows us to address the finite radius of the deuteron ground state.   

Role of fluctuations on the pairing properties of nuclei in the random spacing model

Exploiting the similarity between the bunched single-particle energy levels of nuclei and of random distributions around the Fermi surface, pairing properties of the latter are calculated to establish statistically-based bounds on the basic characteristics of the pairing phenomenon. The influence of thermal fluctuations, expected to be large for systems of finite number of particles [1,2], were investigated using a semiclassical treatment of fluctuations. When the average pairing gaps along with those differing by one standard deviations are used, the characteristic discontinuity of the specific heat at $T_c$ in the BCS formalism was transformed to a shoulder-like structure indicating the suppression of a second order phase transition as experimentally observed in nano-particles and several nuclei. To the extent that the sp levels of the RS model resemble those of nuclei that exhibit considerable dependence on choices of the energy density functionals and pairing schemes used, our results indicate the variation to be expected in the basic characteristics of the pairing phenomenon in nuclei. [1] L. G. Moretto, Phys. Lett. B 40, 1 (1972). [2] Al Hassid, in "50 years of Nuclear BCS: Pairing in Finite Systems", edited by R. A. Broglia and V. Zelevinsky, p. 608, Singapore, 2013.