Nuclear Theory

Repko, A.;Nesterenko, V. O.;Kvasil, J.;Reinhard, P. -G.

doi: 10.1140/epja/i2019-12770-xpmid: N/A

Abstract: We analyze the relation between isoscalar toroidal modes and so-called pygmy dipole resonance (PDR) which both appear in the same region of low-energy dipole excitations. To this end, we use a theoretical description within the fully self-consistent Skyrme quasiparticle random-phase approximation (QRPA). Test cases are spherical nuclei $^{40,48}$Ca, $^{58,72}$Ni, $^{90,100}$Zr, and $^{100,120,132}$Sn which cover four different elements and for each element at least two isotopes with different neutron excess, one small and another large. The structure of the modes is investigated in terms of strength functions, transition densities (TD) and transition currents (TC). For all considered nuclei, we see that, independently on whether PDR strength exists or not, the flow pattern in the lower part of the "PDR energy region" is basically the isoscalar vortical toroidal motion with a minor irrotational fraction. A one-to-one correspondence between calculated TD and TC can be established. The toroidal flow appears already in the uncoupled two-quasiparticle (2qp) excitations and becomes definitively strong for the QRPA modes. Altogether, we find that low-lying dipole strength often denoted as isoscalar PDR is actually an oversimplified imitation of the basically toroidal motion in nuclei with a sufficient neutron excess.

Reichert, Tom;Hillmann, Paula;Limphirat, Ayut;Herold, Christoph;Bleicher, Marcus

doi: 10.1088/1361-6471/ab34fapmid: N/A

Abstract: The HADES experiment at GSI will soon provide data on the production and properties of $\Delta$(1232) baryons from Au+Au reactions at 1.23 AGeV. Using the UrQMD model, we predict the yield and spectra of $\Delta$(1232) resonances. In addition we show that one expects to observe a mass shift of the $\Delta$(1232) resonance on the order of 50 MeV in the reconstructable $\Delta$(1232) mass distribution. This mass shift can be understood in terms of late stage $\Delta$(1232) formation with limited kinetic energy. We show how the mass shift can be used to constrain the kinetic decoupling temperature of the system.

Lynn, J. E.;Lonardoni, D.;Carlson, J.;Chen, J. -W.;Detmold, W.;Gandolfi, S.;Schwenk, A.

doi: 10.1088/1361-6471/ab6af7pmid: N/A

Abstract: High-energy scattering processes, such as deep inelastic scattering (DIS) and quasielastic (QE) scattering provide a wealth of information about the structure of atomic nuclei. The remarkable discovery of the empirical linear relationship between the slope of the European Muon Collaboration (EMC) effect in DIS and the short-range-correlation (SRC) scaling factors $a_2$ in QE kinematics is naturally explained in terms of scale separation in effective field theory. This explanation has powerful consequences, allowing us to calculate and predict SRC scaling factors from ab initio low-energy nuclear theory. We present ab initio calculations of SRC scaling factors for a nucleus $A$ relative to the deuteron $a_2(A/d)$ and relative to $^3\rm He$ $a_2(A/^3\rm He)$ in light and medium-mass nuclei. Our framework further predicts that the EMC effect and SRC scaling factors have minimal or negligible isovector corrections.

Yakovlev, S. L.

doi: 10.1007/s00601-019-1490-3pmid: N/A

Abstract: The formal scattering theory is developed for the three-particle differential Faddeev equations. The theory is realised along the same line as in the standard two-body case. The solution of the scattering problem is expressed in terms of the matrix T-operator constructed from the matrix resolvent of the differential Faddeev equations. The relationships of the matrix T-operator with elements of transition operators and Faddeev T-matrix components have been established.

Pérez, R. Navarro;Schunck, N.

doi: 10.1088/1742-6596/1308/1/012014pmid: N/A

Abstract: While ab initio many-body techniques have been able to successfully describe the properties of light and intermediate mass nuclei based on chiral effective field theory interactions, neutron-rich nuclei still remain out of reach for these methods. Conversely, energy density functional approaches can be used to calculate properties of heavy nuclei but rely mostly on phenomenological interactions. A usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces was presented recently. The first component of this new set of functionals corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. The exchange term, which is a functional of the non-local density, is transformed into a local functional by applying the density matrix expansion. In order to reduce the computational cost due to the direct implementation of non-separable, local interactions in the Hartree term, we use an approximation to represent the regularized Yukawa functions in terms of a sum of (separable) Gaussian functions. These proceedings analyze the accuracy of such an approximation in terms of the number of Gaussian functions and look for an optimal value that gives an acceptable level of accuracy while maintaining the computational memory requirements in a many-body calculation as low as possible.

Hernandez, Oscar J.;Bacca, Sonia;Barnea, Nir;Nevo-Dinur, Nir;Ekström, Andreas;Ji, Chen

doi: N/Apmid: N/A

Abstract: The charge radius of the deuteron (D), was recently determined to three times the precision compared with previous measurements using the measured Lamb shift in muonic deuterium (muD). However, the muD value is 5.6 $\sigma$ smaller than the world averaged CODATA-2014 value [1]. To shed light on this discrepancy we analyze the uncertainties of the nuclear structure calculations of the Lamb shift in muD and conclude that nuclear theory uncertainty is not likely to be the source of the discrepancy.

Timofeyuk, N. K.

doi: 10.1088/1361-6471/ab0992pmid: N/A

Abstract: The change in mass of a nucleon, arising from its interactions with other nucleons inside the target, results in velocity-dependent terms in the Schrödinger equation that describes nucleon scattering. It has recently been suggested in a number of publications that introducing and fitting velocity-dependent terms improves the quality of the description of nucleon scattering data for various nuclei. The present paper discusses velocity-dependent optical potentials in a context of a three-body problem used to account for deuteron breakup in the entrance channel of $(d,p)$ reactions. Such potentials form a particular class of nonlocal optical potentials which are a popular object of modern studies. It is shown here that because of a particular structure of the velocity-dependent terms the three-body problem can be formulated in two different ways. Solving this problem within an adiabatic approximation results in a significant difference between the two approaches caused by contributions from the high $n$-$p$ momenta in deuteron in one of them. Solving the three-body problem beyond the adiabatic approximation may remove such contributions, which is indirectly confirmed by replacing the adiabatic approximation by the folding Watanabe model where such contributions are suppressed. Discussion of numerical results is carried out for the $^{40}$Ca($d,p)^{41}$Ca reaction where experimental data both on elastic scattering in entrance and exit channels and on nucleon transfer are available.

Benhar, Omar

doi: N/Apmid: N/A

Abstract: The scale-dependence of the nucleon-nucleon interaction, which in recent years has been extensively analysed within the context of chiral effective field theory, is, in fact, inherent in any potential models constrained by a fit to scattering data. A comparison between a purely phenomenological potential and local interactions derived from chiral effective field theory suggests that--thanks to the ability to describe nucleon-nucleon scattering at higher energies, as well as the deuteron momentum distribution extracted from electro-disintegration data--phenomenological potentials are best suited for the description of nuclear dynamics at the scale relevant to neutron star matter.

Bertsch, G. F.

doi: N/Apmid: N/A

Abstract: The nuclear compressibility has a role in nuclear physics in several ways. Its relationship to the giant monopole is well known and has been subject of much theoretical work. Less well known is its affect on in nuclear structure, namely monopole transitions between low-lying states in the spectrum. Here I revisit the relationship between monopole and quadrupole moments in deformed nuclei. It has often been assumed without any microscopic justification that the nucleus can be treated as an incompressible fluid. An analytic formula is derived here for the resulting relationship between monopole and quadrupole moments. The formula is shown to be well satisfied within self-consistent mean-field theory calculated with several energy functionals. The formula can be tested when both monopole and quadrupole matrix elements of band-to-band transitions are known. Data is available for the decay of the first excited $K^\pi = 0^+$ band to the ground-state band in $^{156}$Gd, and the extracted matrix elements are found to be consistent with the incompressible fluid picture.

Kopeliovich, Vladimir B.

doi: N/Apmid: N/A

Abstract: The angular dependence of the cumulative particles production off nuclei near the kinematical boundary for multistep process is defined by characteristic polynomials in angular variables, describing spatial momenta of the particles in intermediate and final states. Physical argumentation, exploring the small phase space method, leads to the appearance of equations for these polynomials in $cos (\theta/N)$, where $\theta$ is the polar angle of the momentum of final (cumulative) particle, the integer $N$ being the multiplicity of the process (the number of interactions). It is shown explicitly how these equations appear, and the recurrent relations between polynomials with different $N$ are obtained. Factorization properties of characteristic polynomials found previously, are extended, and their connection with known in mathematics Chebyshev polynomials of 2-d kind is established. As a result, differential cross section of the cumulative particle production has characteristic behaviour $d\sigma \sim 1/ \sqrt {\pi - \theta}$ near the strictly backward direction ($\theta = \pi$, the backward focusing effect). Such behaviour takes place for any multiplicity of the interaction, beginning with $n=3$, elastic or inelastic (with resonance excitations in intermediate states), and can be called the nuclear glory phenomenon, or 'Buddha's light' of cumulative particles.