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Register a new userMass dependence and isospin dependence of short-range correlated pairs
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The target-mass number dependence of nucleon-nucleon pairs with short-range correlations is explored in a physically transparent geometrical model within a zero-range approximation. The observed $A$ dependence of 2-nucleon ejection cross sections in $(e,e)$ reactions is found to reflect the mass dependence of nuclear density distributions. A parametrization of this $A$ dependence is given. The $A$ dependence of proton-proton vs. proton-neutron pairs relative to $^{12}$C is also analyzed in this model. It can be understood using simple combinatorics without any additional isospin dependence.
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Pair densities and associated correlation functions provide a critical tool for introducing many-body correlations into a wide-range of effective theories. Ab initio calculations show that two-nucleon pair-densities exhibit strong spin and isospin dependence. However, such calculations are not available for all nuclei of current interest. We therefore provide a simple model, which involves combining the short and long separation distance behavior using a single blending function, to accurately describe the two-nucleon correlations inherent in existing ab initio calculations. We show that the salient features of the correlation function arise from the features of the two-body short-range nuclear interaction, and that the suppression of the pp and nn pair-densities caused by the Pauli principle is important. Our procedure for obtaining pair-density functions and correlation functions can be applied to heavy nuclei which lack ab initio calculations.
The nucleon momentum distribution $n_A(k)$ for $A=$2, 3, 4, 16, and 40 nuclei is systematically analyzed in terms of wave functions resulting from advanced solutions of the nonrelativistic Schr{o}dinger equation, obtained within different many-body approaches. Particular attention is paid to the separation of the momentum distributions into the mean-field and short-range correlations (SRC) contributions. It is shown that at high values of the momentum $k$ the high-momentum components ($kgtrsim 1.5-2$ fm$^{-1}$) of all nuclei considered are very similar, exhibiting the well-known scaling behavior with the mass number $A$, independently of the used many-body approach and the details of the bare $NN$ interaction. The number of $NN$ pairs in a given ($ST$) state, viz., ($ST$)=(10), (00), (01), and (11), and the contribution of these states to the nucleon momentum distributions are calculated. It is shown that, apart from the (00) state, which has very small effects, all other spin-isospin states contribute to the momentum distribution in a wide range of momenta. It is shown that that for all nuclei considered the momentum distributions in the states T=0 and T=1 exhibit at $kgtrsim 1.5-2$ fm$^{-1}$ very similar behaviors, which represents strong evidence of the A-independent character of SRCs. The ratio $n_A(k)/n_D(k)$ is analyzed in detail stressing that in the SRC region it always increases with the momentum and the origin of such an increase is discussed and elucidated. The relationships between the one- and two-body momentum distributions, considered in a previous paper, are discussed and clarified, pointing out the relevant role played by the center-of-mass motion of a correlated pair in the (10) state. The relationship of the present approach with the many-body methods based upon low-momentum effective interactions is briefly discussed.
A linear correlation is found between the magnitude of nucleon-nucleon short-range correlations and the nuclear binding energy per nucleon with pairing energy removed. By using this relation, the strengths of nucleon-nucleon short-range correlations of some unmeasured nuclei are predicted. Discussions on nucleon-nucleon pairing energy and nucleon-nucleon short-range correlations are made. The found nuclear dependence of nucleon-nucleon short-range correlations may shed some lights on the short-range structure of nucleus.
In the present paper, we explore the idea of isospin conservation in new situations and contexts based on the directions provided by our earlier works. We present the results of our calculations for the relative yields of neutron-rich fission fragments emitted in fast neutron-induced fission, 238U (n, fission) reaction by using the concept of the conservation of isospin and compare with the experimental data. Our results successfully reproduced the gross features of partition wise fission fragments distribution of 238U (n, fission). This confirms that in all kinds of fission, isospin remains pure in neutron-rich systems even at high excitations. Thus, isospin can be proven as an important quantum number for the prediction of fission fragment distribution.
The isospin dependence of the nucleon effective mass is investigated in the framework of the Dirac Brueckner-Hartree-Fock (DBHF) approach. The definition of nucleon scalar and vector effective masses in the relativistic approach is clarified. Only the vector effective mass is the quantity related to the empirical value extracted from the analysis in the nonrelatiistic shell and optical potentials. In the relativistic mean field theory, where the nucleon scalar and vector potentials are both energy independent, the neutron vector potential is stronger than that of proton in the neutron rich nuclear matter, which produces a smaller neutron vector effective mass than that of proton. It is pointed out that the energy dependence of nucleon potentials has to be considered in the analysis of the isospin dependence of the nucleon effective mass. In the DBHF the neutron vector effective mass is larger than that of proton once the energy dependence of nucleon potentials is considered. The results are consistent with the analysis of phenomenological isospin dependent optical potentials.
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