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Register a new userRole of unitary correlation operator on high-momentum antisymmetrized molecular dynamics using bare NN interaction for 3H and 4He
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We extend the 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, the HMAMD is mainly in charge of the tensor correlation with up to the four-body correlation, while the short-range correlation is further improved by using the UCOM. The binding energies of the 3H and 4He nuclei are calculated with this HMAMD+UCOM using the AV8 bare nucleon-nucleon (NN) interaction. The different roles of the short-range and tensor correlations from the HMAMD and UCOM are analyzed in the numerical results. Compared with the previous calculations based on the different variational methods, this newly extended HMAMD+UCOM method can almost provide the consistent results with the ab initio results.
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We propose a new variational method for treating short-range repulsion of bare nuclear force for nuclei in antisymmetrized molecular dynamics (AMD). In AMD, the short-range correlation is described in terms of large imaginary centroids of Gaussian wave packets of nucleon pairs in opposite signs, causing high-momentum components in nucleon pair. We superpose these AMD basis states and name this method high-momentum AMD (HM-AMD), which is capable of describing strong tensor correlation (Prog. Theor. Exp. Phys. (2017) 111D01). In this paper, we extend HM-AMD by including up to two kinds of nucleon pairs in each AMD basis state utilizing the cluster expansion, which produces many-body correlations involving high-momentum components. We investigate how much HM-AMD describes the short-range correlation by showing the results for $^3$H using the Argonne V4$^prime$ central potential. It is found that HM-AMD reproduces the results of few-body calculations and also the tensor-optimized AMD. This means that HM-AMD is a powerful approach to describe the short-range correlation in nuclei. In HM-AMD, momentum directions of nucleon pairs isotropically contribute to the short-range correlation, which is different from the tensor correlation.
We treat the tensor correlation in antisymmetrized molecular dynamics (AMD) including large-relative-momentum components among nucleon pairs for finite nuclei. The tensor correlation is described by using large imaginary centroid vectors of Gaussian wave packets for nucleon pairs with opposite directions, which makes a large relative momentum. We superpose the AMD basis states, in which one nucleon pair has various relative momenta for all directions; this new method is called high-momentum AMD (HM-AMD). We show the results for $^4$He using the effective interaction having a strong tensor force. It is found that HM-AMD provides a large tensor matrix element comparable to the case of the tensor-optimized shell model (TOSM), in which the two-particle-two-hole (2p-2h) excitations are fully included to describe the tensor correlation. The results of two methods agree with each other at the level of the Hamiltonian components of $^4$He. This indicates that in HM-AMD the high-momentum components described by the imaginary centroid vectors of the nucleon pair provide the equivalent effect of the 2p-2h excitations for the tensor correlation.
The high-momentum antisymmetrized molecular dynamics (HMAMD) is a new promising framework with significant analytical simplicity and efficiency inherited from its antisymmetrized molecular dynamics in describing the high momentum correlations in various nuclear states. In the aim of further improving the numerical efficiency for the description of nucleon-nucleon correlation, we introduce a new formulation by including a new Gaussian weighted basis of high momentum pairs in the HMAMD wave function, with which very rapid convergence is obtained in numerical calculation. It is surprising that the very high-momentum components in the new HMAMD basis are found to be almost equivalent to the contact representation of the nucleon-nucleon pairs with very small nucleon-nucleon distance. The explicit formulation for the contact term significantly improves the numerical efficiency of the HMAMD method, which shows the importance of the contact correlation in the formulation of light nuclei.
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.
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.
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