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Register a new userReflection asymmetric relativistic mean field approach and its application to the octupole deformed nucleus $^{226}$Ra
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A Reflection ASymmetric Relativistic Mean Field (RAS-RMF) approach is developed by expanding the equations of motion for both the nucleons and the mesons on the eigenfunctions of the two-center harmonic-oscillator potential. The efficiency and reliability of the RAS-RMF approach are demonstrated in its application to the well-known octupole deformed nucleus $^{226}$Ra and the available data, including the binding energy and the deformation parameters, are well reproduced.
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We report the recent progress in relativistic mean-field (RMF) and beyond approaches for the low-energy structure of deformed hypernuclei. We show that the $Lambda$ hyperon with orbital angular momentum $ell=0$ (or $ell>1$) generally reduces (enhances) nuclear quadrupole collectivity. The beyond mean-field studies of hypernuclear low-lying states demonstrate that there is generally a large configuration mixing between the two components $[^{A-1}Z (I^+) otimes Lambda p_{1/2}]^J$ and $[^{A-1}Z (Ipm2 ^+) otimes Lambda p_{3/2}]^J$ in the hypernuclear $1/2^-_1, 3/2^-_1$ states. The mixing weight increases as the collective correlation of nuclear core becomes stronger. Finally, we show how the energies of hypernuclear low-lying states are sensitive to parameters in the effective $N Lambda $ interaction, the uncertainty of which has a large impact on the predicted maximal mass of neutron stars.
Electron scattering methods, involving nucleus which have little or no intrinsic deformation suggest nucleon distribution to be of Fermi type. This distribution is further parameterised as Wood Saxon (WS) distribution, where an uniform charge density with smoothed-out surface have been implemented. Incorporating shape modification in WS, earlier attempts were made to explain observables in deformed nuclear collisions, such as charged particle multiplicity. In this work, we use an alternate approach known as Nilsson model or Modified Harmonic Oscillator (MHO), to explain charged particle multiplicity in U+U collisions at top RHIC energy. We have implemented the formalism in HIJING model and we found that the model describes the experimental data to an extent.
$K^-$ atomic data are used to test several models of the $K^-$ nucleus interaction. The t($rho$)$rho$ optical potential, due to coupled channel models incorporating the $Lambda$(1405) dynamics, fails to reproduce these data. A standard relativistic mean field (RMF) potential, disregarding the $Lambda$(1405) dynamics at low densities, also fails. The only successful model is a hybrid of a theoretically motivated RMF approach in the nuclear interior and a completely phenomenological density dependent potential, which respects the low density theorem in the nuclear surface region. This best-fit $K^-$ optical potential is found to be strongly attractive, with a depth of 180 pm 20 MeV at the nuclear interior, in agreement with previous phenomenological analyses.
For the first time, we apply the temperature dependent relativistic mean field (TRMF) model to study the ternary fission of heavy nucleus using level density approach. The probability of yields of a particular fragment is obtained by evaluating the convolution integrals which employ the excitation energy and the level density parameter for a given temperature calculated within the TRMF formalism. To illustrate, we have considered the ternary fissions in 252Cf, 242Pu and 236U with fixed third fragment A3 = 48Ca, 20O and 16O respectively. The relative yields are studied for the temperatures T = 1, 2 and 3 MeV. For the comparison, the relative yields are also calculated from the single particle energies of the finite range droplet model (FRDM). In general, the larger phase space for the ternary fragmentation is observed indicating that such fragmentations are most probable ones. For T = 2 and 3 MeV, the Sn + Ni + Ca is the most probable combination for the nucleus 252Cf. However, for the nuclei 242Pu and 236U, the maximum fragmentation yields at T = 2 MeV differ from those at T = 3 MeV. For T = 3 MeV, the closed shell (Z = 8) light mass fragments with its corresponding partners has larger yield values. But, at T = 2 MeV Si/P/S are favorable fragments with the corresponding partners. It is noticed that the symmetric binary fragmentation along with the fixed third fragment for 242Pu and 236U are also favored at T = 1 MeV. The temperature dependence of the nuclear shape and the single particle energies are also discussed.
In this paper, we compare the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We obtain an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. We find: (1) Potential $V_{RMF}$ of the RMF theory for nucleons has the wave functions $f$ and $g$ with joint part $h$ coincident exactly with the nucleon wave function of DOS model with potential $V_{rm shell}$. But, a difference between $V_{RMF}$ and $V_{rm shell}$ is essential for any nucleus. (2) The nucleon wave functions and densities obtained by the DOS and RMF theories are essentially different. The nucleon densities of the RMF theory contradict to knowledge about distribution of the proton and neutron densities inside the nuclei obtained from experimental data. This indicates that $g$ and $f$ have no sense of the wave functions of quantum physics. But, $h$ provides proper description of quantum properties of nucleons inside the nucleus. (3) We calculate meson function $w^{0}$ and potential $V_{w}$ in RMF theory based on the found nucleon density. (4) $f$ and $g$ are not solutions of Dirac equation with $V_{w}$. If the meson theory describes quantum properties of nucleus well, then a difference between $V_{w}$ and $V_{RMF}$ should be as small as possible. We introduce new quantum corrections characterizing difference between these potentials. We find that (a) The function $w^{0}$ should be reinforced strongly, (b) The corrections are necessary to describe the quantum properties of the nuclei.
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