If we consider the nucleus as a relativistic composite, then we are able to derive from a many-particle Dirac model a coupling between the center of mass motion and internal nuclear degrees of freedom. This interaction can be rotated out in free space, but has the potential to give rise to new physics when two or more nuclei exchange phonons with a common vibrational mode. The simplest example of such a system is a homonuclear diatomic molecule in a frozen matrix, for which we are able to develop an expression for the second-order phonon–nuclear interaction that can result in a splitting of the nuclear energy levels as a result of excitation transfer between the nuclei. The phonon-nuclear coupling is an E1 interaction, so the low energy 6.237 keV E1 transition in 181Ta is special; this motivates an interest in molecular 181Ta2 as a candidate for a Mössbauer experiment where the splitting might be observable. We also consider excitation transfer in the case of a macroscopic a Ta plate.
If we consider the nucleus as a relativistic composite, then we are able to derive from a many-particle Dirac model a coupling between the center of mass motion and internal nuclear degrees of freedom. This interaction can be rotated out in free space, but has the potential to give rise to new physics when two or more nuclei exchange phonons with a common vibrational mode. The simplest example of such a system is a homonuclear diatomic molecule in a frozen matrix, for which we are able to develop an expression for the second-order phonon–nuclear interaction that can result in a splitting of the nuclear energy levels as a result of excitation transfer between the nuclei. The phonon-nuclear coupling is an E1 interaction, so the low energy 6.237 keV E1 transition in 181Ta is special; this motivates an interest in molecular 181Ta2 as a candidate for a Mössbauer experiment where the splitting might be observable. We also consider excitation transfer in the case of a macroscopic a Ta plate.
Atomic nuclei are complex, quantum many-body systems whose structure manifests itself through intrinsic quantum states associated with different excitation modes or degrees of freedom.Collective modes (vibration and/or rotation) dominate at low energy (near the ground-state).The associated states are usually employed, within a truncated model space, as a basis in (coherent) coupled channels approaches to low-energy reaction dynamics.However, excluded non-collective states can be essential, and their effects on the open (nuclear) system dynamics are usually treated through complex potentials.Is this a complete description of open system dynamics?Does it include effects of quantum decoherence?Can decoherence be manifested in reaction observables?This paper discusses these issues and the main ideas of a coupled-channels density-matrix approach that makes it possible to quantify the role and importance of quantum decoherence in low-energy nuclear reaction dynamics.Some topical applications are highlighted.
We consider a composite system consisting of coupled particles, and investigate decoherence due to coupling of the center-of-mass degree of freedom to the internal vibrational degrees of freedom. For a composite system of bound particles, we show that in general such a decoherence effect exists, and leads to suppression of interference between different paths of the center-of-mass. For the special case of harmonically-bound particles moving in an external potential, we show that the coupling between the center-of-mass and internal degrees of freedom takes the form of parametric driving of the vibrational degrees of freedom, and that nontrivial coupling depends on the second derivative of the external potential. We find a solution to this parametric driving problem in one dimension for a fixed center-of-mass trajectory. We also propose a measure of compositeness, which quantifies the extent to which such a composite system cannot be approximated as a single, indivisible particle. We perform numerical simulations for a simple interference experiment, consisting of two wave packets scattering off of a square well, and show a close connection between suppression of interference and entanglement between the center-of-mass and internal degrees of freedom, which depends on the initial state of the internal mode. We also calculate the measure of compositeness for this system.
We are interested in the energy-momentum relation for a moving composite in relativistic quantum mechanics in many-particle Dirac models. For a manifestly covariant model one can apply the Lorentz transform to go from the rest frame to a moving frame to establish an energy-momentum relation of the form (M∗c2)2+c2∣P∣2 where M∗ is the kinematic mass. However, the many-particle Dirac model is not manifestly covariant, and some other approach is required. We have found a simple approach that allows for a separation of relative and center of mass contributions to the energy. We are able to define the associated kinematic energy and determine the energy-momentum relation. Our result can be expressed as a modified deBroglie relation of the form ℏω(P)=[M∗(P)c2]2+c2∣P∣2 where the kinematic mass M∗ will depend on the total momentum P for a general noncovariant potential. The prefactor that occurs we associate with a time dilation effect, the existence of which has been discussed previously in the literature.
Abstract A generalization of the quantum mechanical representation transformation is presented, in this paper. It is shown that, as an important example, the Boson-expansion method, commonly employed in nuclear physics, corresponds to such a generalized transformation. Using this generalization, we were able to construct a special representation called the “Composite Particle Representation”. In the composite, particle representation, the composite particle degrees of freedom are included, as well as the original particle degrees of freedom. The former is introduced in order that the motion of certain particle clusters can be described as separate entities in a many-body system. This representation is shown to be exactly equivalent to the usual quantum mechanical representation which includes only the original particle degrees of freedom. Many applications of this theory are expected, in particular in the study of hadrons from the quark point of view and the Interacting Boson Model in nuclei.
Efforts to describe nuclear structure and dynamics from first principles have advanced significantly in recent years. Exact methods for light nuclei are now able to include continuum degrees of freedom and treat structure and reactions on the same footing, and multiple approximate, computationally efficient many-body methods have been developed that can be routinely applied for medium-mass nuclei. This has made it possible to confront modern nuclear interactions from Chiral Effective Field Theory, that are rooted in Quantum Chromodynamics with a wealth of experimental data. Here, we discuss one of these efficient new many-body methods, the In-Medium Similarity Renormalization Group (IMSRG), and its applications in modern nuclear structure theory. The IMSRG evolves the nuclear many-body Hamiltonian in second-quantized form through continuous unitary transformations that can be implemented with polynomial computational effort. Through suitably chosen generators, we drive the matrix representation of the Hamiltonian in configuration space to specific shapes, e.g., to implement a decoupling of low-and high-energy scales, or to extract energy eigenvalues for a given nucleus. We present selected results from Multireference IMSRG (MR-IMSRG) calculations of open-shell nuclei, as well as proof-of-principle applications for intrinsically deformed medium-mass nuclei. We discuss the successes and prospects of merging the (MR-)IMSRG with many-body methods ranging from Configuration Interaction to the Density Matrix Renormalization Group, with the goal of achieving an efficient simultaneous description of dynamic and static correlationsin atomic nuclei.
Efforts to describe nuclear structure and dynamics from first principles have advanced significantly in recent years. Exact methods for light nuclei are now able to include continuum degrees of freedom and treat structure and reactions on the same footing, and multiple approximate, computationally efficient many-body methods have been developed that can be routinely applied for medium-mass nuclei. This has made it possible to confront modern nuclear interactions from Chiral Effective Field Theory, that are rooted in Quantum Chromodynamics with a wealth of experimental data. Here, we discuss one of these efficient new many-body methods, the In-Medium Similarity Renormalization Group (IMSRG), and its applications in modern nuclear structure theory. The IMSRG evolves the nuclear many-body Hamiltonian in second-quantized form through continuous unitary transformations that can be implemented with polynomial computational effort. Through suitably chosen generators, we drive the matrix representation of the Hamiltonian in configuration space to specific shapes, e.g., to implement a decoupling of low-and high-energy scales, or to extract energy eigenvalues for a given nucleus. We present selected results from Multireference IMSRG (MR-IMSRG) calculations of open-shell nuclei, as well as proof-of-principle applications for intrinsically deformed medium-mass nuclei. We discuss the successes and prospects of merging the (MR-)IMSRG with many-body methods ranging from Configuration Interaction to the Density Matrix Renormalization Group, with the goal of achieving an efficient simultaneous description of dynamic and static correlationsin atomic nuclei.