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Register a new userMatrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states
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We present new formulae for the matrix elements of one-body and two-body physical operators in compact forms, which are applicable to arbitrary Hartree-Fock-Bogoliubov wave functions, including those for multi-quasiparticle excitations. The test calculations show that our formulae may substantially accelerate the process of symmetry restoration when applied to the heavy nuclear system.
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Precision tests of the Standard Model and searches for beyond the Standard Model physics often require nuclear structure input. There has been a tremendous progress in the development of nuclear ab initio techniques capable of providing accurate nuclear wave functions. For the calculation of observables, matrix elements of complicated operators need to be evaluated. Typically, these matrix elements would contain spurious contributions from the center-of-mass (COM) motion. This could be problematic when precision results are sought. Here, we derive a transformation relying on properties of harmonic oscillator wave functions that allows an exact removal of the COM motion contamination applicable to any one-body operator depending on nucleon coordinates and momenta. Resulting many-nucleon matrix elements are translationally invariant provided that the nuclear eigenfunctions factorize as products of the intrinsic and COM components as is the case, e.g., in the no-core shell model approach. An application of the transformation has been recently demonstrated in calculations of the nuclear structure recoil corrections for the beta-decay of 6He.
In this talk, we present a framework for studying structural information of resonances and bound states coupling to two-hadron scattering states. This makes use of a recently proposed finite-volume formalism to determine a class of observables that are experimentally inaccessible but can be accessed via lattice QCD. In particular, we shown that finite-volume two-body matrix elements with one current insertion can be directly related to scattering amplitudes coupling to the external current. For two-hadron systems with resonances or bound states, one can extract the corresponding form factors of these from the energy-dependence of the amplitudes.
State-of-the-art multi-reference energy density functional calculations require the computation of norm overlaps between different Bogoliubov quasiparticle many-body states. It is only recently that the efficient and unambiguous calculation of such norm kernels has become available under the form of Pfaffians~[L. M. Robledo, Phys. Rev. C79, 021302 (2009)]. The goals of this work is (i) to propose and implement an alternative to the Pfaffian method to compute unambiguously the norm overlap between arbitrary Bogoliubov quasiparticle states and (ii) to extend the first point to explicitly correlated norm kernels at play in recently developped particle-number-restored Bogoliubov coupled-cluster (PNR-BCC) and particle-number-restored many-body perturbation (PNR-BMBPT) ab initio theories~[T. Duguet and A. Signoracci, J. Phys. G44, 015103 (2017)]. Point (i) constitutes the purpose of the present paper while point (ii) is addressed in a forthcoming companion paper. We generalize the method used in~[T. Duguet and A. Signoracci, J. Phys. G44, 015103 (2017)] to obtain the norm overlap between arbitrary Bogoliubov product states under a closed-form expression. The formula is physically intuitive, accurate, versatile and relies on elementary linear algebra operations. It equally applies to norm overlaps between Bogoliubov states of even or odd number parity. Numerical applications illustrate these features and provide a transparent representation of the content of the norm overlaps. Furthermore, the closed-form expression extends naturally to correlated overlaps at play in PNR-BCC and PNR-BMBPT. As such, the straight overlap between Bogoliubov states is the zeroth-order reduction of more involved norm kernels to be studied in the forthcoming paper.
We examine the leading effects of two-body weak currents from chiral effective field theory on the matrix elements governing neutrinoless double-beta decay. In the closure approximation these effects are generated by the product of a one-body current with a two-body current, yielding both two- and three-body operators. When the three-body operators are considered without approximation, they quench matrix elements by about 10%, less than suggested by prior work, which neglected portions of the operators. The two-body operators, when treated in the standard way, can produce much larger quenching. In a consistent effective field theory, however, these large effects become divergent and must be renormalized by a contact operator, the coefficient of which we cannot determine at present.
We study one- and two-body visibility measures under an optimization of common, i.e. global evolutions of a two-body system, and identify two different visibilities of two-body correlators, both behaving complementary to the usual onebody interference visibility. We show that only one of them satisfies the common inequality associated with a complementary relation, while the other one entails a contrary relation. This, however, can be understood in terms of entanglement between the constituents.
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