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We study the symmetric nuclear matter using bare nucleon-nucleon ($NN$) interactions with finite particle-number approach within finite cubic boxes. Due to the $NN$ correlations originating from bare $NN$ interaction, two nucleons can be excited to the high-momentum region, leading to the increase of the kinetic energy in nuclear matter. We further consider the spin excitations in the nucleon pairs, where the spin of the two nucleons are changed, and this excitation is important for the tensor correlation. The unitary correlation operator method (UCOM) is used to treat the short-range correlation. The tail correction coming from the neighbouring boxes is also included. We demonstrate the contributions of various excitations of nucleon pairs as well as the tail correction to the total energy at the normal density. We also discuss the effects of UCOM and correlated nucleon pairs on the density dependence of the total energy. We calculate the equations of state of symmetric nuclear matter using two kinds of the Argonne potentials and the results agree with those from other many-body theories. The density dependences of the Hamiltonian components are also shown., Comment: 12 pages, 11figures, 1 table

We propose a new many-body method based on the correlation functions, in which the multiple products of the correlation functions are expanded into the many-body diagrams using the cluster expansion method and every diagram is independently optimized in the total-energy variation. We apply this idea to the tensor-optimized antisymmetrized molecular dynamics (TOAMD) using the bare nucleon-nucleon interaction and show the results of the $s$-shell nuclei within the triple products of the correlation functions of tensor and central-types. We evaluate the effect of the independent optimization of the many-body diagrams on the solutions. It is found that the triple products provides the sizable effect in the present scheme, which results in the good reproduction of the total energy and the Hamiltonian components of nuclei with respect to the few-body calculations., 12 pages, 13 figures

In this paper, the properties of the symmetry energy in asymmetric nuclear matter, including the quadratic and quartic symmetry energies as well as their density slopes at the saturation density, are studied by the radioactivity of unstable nuclei. The symmetry energy was initially introduced as a quantum correction energy in the Weizsacker-Bethe liquid-drop model, which was proposed to describe the binding energies of finite nuclei. In order to systematically study the properties of the symmetry energy, the concept of the nuclear matter was introduced, which consists of neutrons and protons with finite neutron and proton densities but infinite neutron and proton numbers. By comparing the properties of the isospin symmetric nuclear matter, in which the neutron density is equal to the proton density, and those of the isospin asymmetric nuclear matter, in which the two densities are unequal, the symmetry energy is found to approximately represent the difference of the energy per nucleon in them. That is to say, the symmetry energy is an evaluation of the energy cost to convert protons in symmetric nuclear matter to neutrons in asymmetric nuclear matter. Since the symmetry energy characterizes the isospin asymmetric effect in nuclear matter, it plays critical roles in not only nuclear physics but also astrophysics. For example, the symmetry energy is closely related to the nuclear masses, the structures and properties of nuclei far away from stability line and near drip lines, the mechanism of heavy-ion reactions, the structures and component of neutron stars, the masses and radii of neutron stars, the cooling process of neutron stars, and so on. Besides of the quadratic symmetry energy, the quartic symmetry energy can have obvious effects on the properties of neutron stars as well. The quartic symmetry energy can significantly affect both the proton fraction in β-stable neutron stars and the critical density for the direct Urca process, which leads to faster cooling of neutron stars. In addition, the quartic symmetry energy is found to be very important for the location of the inner edge of crusts and the core-crust transition density and pressure in neutron stars. So the quartic symmetry energy can also have an influence on the structure of neutron stars. Because of the very important roles of the symmetry energy playing in not only nuclear physics but also astrophysics, it is of great significance to study the properties of both the quadratic and quartic symmetry energies. Based on the fundamental Hugenholtz-Van Hove (HVH) theorem, the properties of the symmetry energy are found to be closely related to the isoscalar and the isovector parts of the nucleon single-particle potentials, where the latter two parts can be extracted from the nuclear radioactivity. So by linking both the symmetry energy and the nuclear radioactivity to the nucleon single-particle potentials, the symmetry energy can be directly studied by nuclear radioactivity. In this paper, both the heavy-cluster radioactivity and the proton radioactivity are employed to constrain the properties of not only the quadratic symmetry energy but also the quartic symmetry energy. Besides, the effect of both the spectroscopic factor of proton radioactivity and the deformation in the daughter nucleus on the extracted results are also discussed, which are subsequently found to be very limited.

We extend high-momentum antisymmetrized molecular dynamics (HMAMD) by incorporating the short-range part of the unitary correlation operator method (UCOM) as the variational method of finite nuclei. In this HMAMD+UCOM calculation of light nuclei, HMAMD is mainly in charge of the tensor correlation with up to four-body correlation, while the short-range correlation is further improved by using UCOM. The binding energies of the $^3$H and $^4$He nuclei are calculated with HMAMD+UCOM using the AV8$'$ bare nucleon–nucleon ($NN$) interaction. The different roles of the short-range and tensor correlations from HMAMD and UCOM are analyzed in the numerical results. Compared with previous calculations based on different variational methods, this newly extended HMAMD+UCOM method can almost provide consistent results with ab initio results.

Based on the Hugenholtz-Van Hove theorem, six basic quantities of the EoS in isospin asymmetric nuclear matter are expressed in terms of the nucleon kinetic energy $t(k)$, the isospin symmetric and asymmetric parts of the single-nucleon potentials $U_0(\rho,k)$ and $U_{\text{\text{sym,i}}}(\rho,k)$. The six basic quantities include the quadratic symmetry energy $E_{\text{sym,2}}(\rho)$, the quartic symmetry energy $E_{\text{sym,4}}(\rho)$, their corresponding density slopes $L_2(\rho)$ and $L_4(\rho)$, and the incompressibility coefficients $K_2(\rho)$ and $K_4(\rho)$. By using four types of well-known effective nucleon-nucleon interaction models, namely the BGBD, MDI, Skyrme, and Gogny forces, the density- and isospin-dependent properties of these basic quantities are systematically calculated and their values at the saturation density $\rho_0$ are explicitly given. The contributions to these quantities from $t(k)$, $U_0(\rho,k)$, and $U_{\text{sym,i}}(\rho,k)$ are also analyzed at the normal nuclear density $\rho_0$. It is clearly shown that the first-order asymmetric term $U_{\text{sym,1}}(\rho,k)$ (also known as the symmetry potential in Lane potential) plays a vital role in determining the density dependence of the quadratic symmetry energy $E_{\text{sym,2}}(\rho)$. It is also shown that the contributions from high-order asymmetric parts of the single-nucleon potentials ($U_{\text{sym,i}}(\rho,k)$ with $i>1$) cannot be neglected in the calculations of the other five basic quantities. Moreover, by analyzing the properties of asymmetric nuclear matter at the exact saturation density $\rho_{\text{sat}}(\delta)$, the corresponding quadratic incompressibility coefficient is found to have a simple empirical relation $K_{\text{sat,2}}=K_{2}(\rho_0)-4.14 L_2(\rho_0)$., Comment: 14 pages, 8 figures, 2 tables

High-momentum components of nuclei are essential for understanding the underlying inter-nucleon correlations in nuclei. We perform the comprehensive analysis for the origin of the high-momentum components of $^4$He in the framework of Tensor-optimized High-momentum Antisymmetrized Molecular Dynamics (TO-HMAMD), which is a completely variational approach as an $ab$ $initio$ theory starting from the bare nucleon-nucleon ($NN$) interaction. The analytical derivations are provided for the nucleon momentum distribution of the Antisymmetrized Momentum Dynamics (AMD) wave functions, with subtraction of center-of-mass motion. The nucleon momentum distribution for $^4$He is calculated by applying a new expansion technique to our $ab$ $initio$ wave function, and agrees with the values extracted from experimental data up to the high-momentum region. Fine-grained analysis is performed for the high-momentum components in $^4$He with respect to different nucleon correlations. Contributions from tensor, central with short-range, and many-body correlations are extracted from the nucleon momentum distributions. The manifestation of tensor correlation around 2 fm$^{-1}$ region is explicitly confirmed by comparing the momentum distributions predicted using different types of $NN$ interactions with and without the tensor force., 7 pages, 6 figures, under review in Phys. Lett. B

We propose a new variational method for describing nuclear matter from nucleon-nucleon interaction. We use the unitary correlation operator method (UCOM) for central correlation to treat the short-range repulsion and further include the two-particle two-hole (2p2h) excitations of nucleon pair involving a large relative momentum, which is called 'high-momentum pair'(HM). We describe nuclear matter in finite size with finite particle number on periodic boundary condition and increase the 2p2h configurations until we get the convergence of the total energy per particle. We demonstrate the validity of this 'UCOM+HM' framework by applying it to the symmetric nuclear and neutron matters with the Argonne V4$^\prime$ potential having short-range repulsion. The nuclear equations of state obtained in UCOM+HM are fairly consistent to those of other calculations such as Brueckner-Hartree-Fock and auxiliary field diffusion Monte Carlo in the overall density region., Comment: 12 pages, 24 figures

By using bare Argonne V4' (AV4'), V6' (AV6'), and V8' (AV8') nucleon-nucleon (NN) interactions respectively, the nuclear equations of state (EOSs) for neutron matter are calculated with the unitary correlation operator and high-momentum pair methods. The neutron matter is described under a finite particle number approach with magic number $N=66$ under a periodic boundary condition. The central short-range correlation coming from the short-range repulsion in the NN interaction is treated by the unitary correlation operator method (UCOM) and the tensor correlation and spin-orbit effects are described by the two-particle two-hole (2p2h) excitations of nucleon pairs, in which the two nucleons with a large relative momentum are regarded as a high-momentum pair (HM). With the 2p2h configurations increasing, the total energy per particle of neutron matter is well converged under this UCOM+HM framework. By comparing the results calculated with AV4', AV6', and AV8' NN interactions, the effects of the short-range correlation, the tensor correlation, and the spin-orbit coupling on the density dependence of the total energy per particle of neutron matter are demonstrated. Moreover, the contribution of each Hamiltonian component to the total energy per particle is discussed. The EOSs of neutron matter calculated within the present UCOM+HM framework agree with the calculations of six different microscopic many-body theories, especially in agreement with the auxiliary field diffusion Monte Carlo calculations., Comment: 13 pages, 6 figures, 3 tables

Within the density-dependent cluster model (DDCM), the decay half-lives of 22 cluster emitters are calculated by using experimental decay energies. Based on our previous study on cluster radioactivity [Phys. Rev. C 90, 064310 (2014)], not only the quadratic symmetry energy ${E}_{2}({\ensuremath{\rho}}_{0})$ and its slope ${L}_{2}({\ensuremath{\rho}}_{0})$ but also the quartic symmetry energy ${E}_{4}({\ensuremath{\rho}}_{0})$ and its slope ${L}_{4}({\ensuremath{\rho}}_{0})$ at the saturation density ${\ensuremath{\rho}}_{0}$ are constrained by considering the neutron skin thicknesses in the daughter nuclei. With the extracted values of ${E}_{2}({\ensuremath{\rho}}_{0})$ and ${L}_{2}({\ensuremath{\rho}}_{0})$, the exponent $\ensuremath{\gamma}$ of the quadratic density-dependent symmetry energy ${E}_{2}(\ensuremath{\rho})={E}_{2}({\ensuremath{\rho}}_{0}){(\ensuremath{\rho}/{\ensuremath{\rho}}_{0})}^{\ensuremath{\gamma}}$ is estimated. Moreover, the symmetry energy coefficient of nuclei ${a}_{\mathrm{sym}}(A)$ and the ratio $\ensuremath{\kappa}$ of the surface symmetry coefficient to the volume symmetry coefficient are extracted as well.

Based on the newest experimentally extracted nuclear density distributions for double-magic nucleus $$^{208}\text {Pb}$$ (Tarbert et al. in Phys Rev Lett 112:242502, 2014), the sensitivity of $$\alpha $$ -decay half-life to nuclear skin thickness is explored in the vicinity of the shell closure region around $$^{208}\text {Pb}$$ , i.e., isotopes of $$Z=82$$ and isotones of $$N=126$$ . With the two-parameter Fermi (2PF) density distributions and an analytically derived formula, the $$\alpha $$ -decay half-life is found to be closely related to the magnitude of nuclear skin thickness. For $$\alpha $$ decays to the $$Z=82$$ isotopes, the $$\alpha $$ -decay half-life is found to decrease with the increasing neutron skin thickness, while the opposite behavior is found for $$\alpha $$ decays to the $$N=126$$ isotones. Therefore, it could be a possible way to extract the nuclear skin thickness from measured $$\alpha $$ -decay half-lives.