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Register a new userDoorway States in the Random-Phase Approximation
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Authors
A. De Pace
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By coupling a doorway state to a see of random background states, we develop the theory of doorway states in the framework of the random-phase approximation (RPA). Because of the symmetry of the RPA equations, that theory is radically different from the standard description of doorway states in the shell model. We derive the Pastur equation in the limit of large matrix dimension and show that the results agree with those of matrix diagonalization in large spaces. The complexity of the Pastur equation does not allow for an analytical approach that would approximately describe the doorway state. Our numerical results display unexpected features: The coupling of the doorway state with states of opposite energy leads to strong mutual attraction.
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As a function of energy E, the average strength function S(E) of a doorway state is commonly assumed to be Lorentzian in shape and characterized by two parameters, the peak energy E_0 and the spreading width Gamma. The simple picture is modified when the density of background states that couple to the doorway state changes significantly in an energy interval of size Gamma. For that case we derive an approximate analytical expression for S(E). We test our result successfully against numerical simulations. Our result may have important implications for shell--model calculations.
A characteristic feature of collective and particle-hole excitations in neutron-rich nuclei is that many of them couple to unbound neutron in continuum single-particle orbits. The continuum random phase approximation (cRPA) is a powerful many-body method that describes such excitations, and it provides a scheme to evaluate transition strengths from the ground state. In an attempt to apply cRPA to the radiative neutron capture reaction, we formulate in the present study an extended scheme of cRPA that describes gamma-transitions from the excited states under consideration, which decay to low-lying excited states as well as the ground state. This is achieved by introducing a non-local one-body operator which causes transitions to a low-lying excited state, and describing a density-matrix response against this operator. As a demonstration of this new scheme, we perform numerical calculation for dipole, quadrupole, and octupole excitations in $^{140}$Sn, and discuss E1 and E2 transitions decaying to low-lying $2^{+}_{1,2}$ and $3^{-}_{1}$ states. The results point to cases where the branching ratio to the low-lying states is larger than or comparable with that to the ground state. We discuss key roles of collectivity and continuum orbits in both initial and final states.
The self-consistent random phase approximation (RPA) based on a correlated realistic nucleon-nucleon interaction is used to evaluate correlation energies in closed-shell nuclei beyond the Hartree-Fock level. The relevance of contributions associated with charge exchange excitations as well as the necessity to correct for the double counting of the second order contribution to the RPA ring summation are emphasized. Once these effects are properly accounted for, the RPA ring summation provides an efficient tool to assess the impact of long-range correlations on binding energies throughout the whole nuclear chart, which is of particular importance when starting from realistic interactions.
The Random Phase Approximation theory is used to calculate the total cross sections of electron neutrinos on $^{12}$C nucleus. The role of the excitation of the discrete spectrum is discussed. A comparison with electron scattering and muon capture data is presented. The cross section of electron neutrinos coming from muon decay at rest is calculated.
The Quasiparticle Random Phase Approximation (QRPA) is used in evaluation of the total muon capture ratesfor the final nuclei participating in double-beta decay. Several variants of the method are used, depending on the size of the single particle model space used, or treatment of the initial bound muon wave function. The resulting capture rates are all reasonably close to each other. In particular, the variant that appears to be most realistic, results in rates in good agreement with the experimental values. There is no necessity for an empirical quenching of the axial current coupling constant $g_A$. Its standard value $g_A$ = 1.27 seems to be adequate.
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