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Register a new userProton-Neutron Pairing Amplitude as a Generator Coordinate for Double-Beta Decay
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We treat proton-neutron pairing amplitudes, in addition to the nuclear deformation, as generator coordinates in a calculation of the neutrinoless double-beta decay of 76Ge. We work in two oscillator shells, with a Hamiltonian that includes separable terms in the quadrupole, spin-isospin, and pairing (isovector and isoscalar) channels. Our approach allows larger single-particle spaces than the shell model and includes the important physics of the proton-neutron quasiparticle random-phase approximation (QRPA) without instabilities near phase transitions. After comparing the results of a simplified calculation that neglects deformation with those of the QRPA, we present a more realistic calculation with both deformation and proton-neutron pairing amplitudes as generator coordinates. The future should see proton-neutron coordinates used together with energy-density functionals.
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The generator coordinate method begins with the variational construction of a set of non-orthogonal mean-field states that span a subspace of the full many-body Hilbert space. These states are then often projected onto states with good quantum numbers to restore symmetries, leading to a set with members that can be similar to one another, and it is sometimes possible to reduce this set without greatly affecting results. Here we propose a greedy algorithm that we call the energy-transition-orthogonality procedure (ENTROP) to select subsets of important states. As applied here, the approach selects on the basis of diagonal energy, orthogonality, and contribution to the matrix element that governs neutrinoless double-$beta$ decay. We present both shell-model and preliminary ab initio calculations of this matrix element for the decay of $^{76}$Ge, with quadrupole deformation parameters and the isoscalar pairing strength as generator coordinates. ENTROP converges quickly, reducing significantly the number of basis states needed for an accurate calculation.
We investigate several Pb$(n,ngamma$) and Ge$(n,ngamma$) reactions. We measure $gamma$-ray production from Pb$(n,ngamma$) reactions that can be a significant background for double-beta decay experiments which use lead as a massive inner shield. Particularly worrisome for Ge-based double-beta decay experiments are the 2041-keV and 3062-keV $gamma$ rays produced via Pb$(n,ngamma$). The former is very close to the ^{76}Ge double-beta decay endpoint energy and the latter has a double escape peak energy near the endpoint. Excitation $gamma$-ray lines from Ge$(n,ngamma$) reactions are also observed. We consider the contribution of such backgrounds and their impact on the sensitivity of next-generation searches for neutrinoless double-beta decay using enriched germanium detectors.
We study the feasibility of applying the Generator Coordinate Method (GCM) of self-consistent mean-field theory to calculate decay widths of composite particles to composite-particle final states. The main question is how well the GCM can approximate continuum wave functions in the decay channels. The analysis is straightforward under the assumption that the GCM wave functions are separable into internal and Gaussian center-of-mass wave functions. Two methods are examined for calculating decays widths. In one method, the density of final states is computed entirely in the GCM framework. In the other method, it is determined by matching the GCM wave function to an asymptotic scattering wave function. Both methods are applied to a numerical example and are found to agree within their determined uncertainties.
The onset of 1S0 proton spin-singlet pairing in neutron-star matter is studied in the framework of the BCS theory including medium polarization effects. The strong three-body coupling of the diproton pairs with the dense neutron environment and the self-energy effects severely reduce the gap magnitude, so to reshape the scenario of the proton superfluid phase inside the star. The vertex corrections due to the medium polarization are attractive in all isospin-asymmetry range at low density and tend to favor the pairing in that channel. However quantitative estimates of their effect on the energy gap do not give significant changes. Implications of the new scenario on the role of pairing in neutron-star cooling is briefly discussed.
The self-energy effect on the neutron-proton (np) pairing gap is investigated up to the third order within the framework of the extend Bruecker-Hartree-Fock (BHF) approach combined with the BCS theory. The self-energy up to the second-order contribution turns out to reduce strongly the effective energy gap, while the emph{renormalization} term enhances it significantly. In addition, the effect of the three-body force on the np pairing gap is shown to be negligible. To connect the present results with the np pairing in finite nuclei, an effective density-dependent zero-range pairing force is established with the parameters calibrated to the microscopically calculated energy gap.
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