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Systematic study of the low-lying electric dipole strength in Sn isotopes and its astrophysical implications
The 𝛾-ray strength functions (GSFs) and nuclear level densities (NLDs) below the neutron threshold have been extracted for 111–113,116–122,124-Sn from particle-𝛾 coincidence data with the Oslo method. The evolution of bulk properties of the low-lying electric dipole response has been investigated on the basis of the Oslo GSF data and results of a recent systematic study of electric- and magnetic dipole strengths in even-even Sn isotopes with relativistic Coulomb excitation. The obtained GSFs reveal a resonance-like peak on top of the tail of the isovector giant dipole resonance centered at ≈8 MeV and exhausting ≈2% of the classical Thomas-Reiche-Kuhn (TRK) sum. For mass numbers ≥118 the data suggest also a second peak centered at ≈6.5 MeV. It corresponds to 0.1%–0.5% of the TRK sum rule and shows an approximate linear increase with the mass number. In contrast with predictions of the relativistic quasiparticle random-phase and time-blocking approximation calculations, no monotonic increase in the total low-lying 𝐸1 strength was observed in the experimental data from 111-Sn to 124-Sn, demonstrating rather similar strength distributions in these nuclei. The Oslo GSFs and NLDs were further used as inputs to constrain the cross sections and Maxwellian-averaged cross sections of (𝑛,𝛾) reactions in the Sn isotopic chain using TALYS. The obtained results agree well with other available experimental data and the recommended values from the JINA REACLIB, BRUSLIB, and KADoNiS libraries. Despite relatively small exhausted fractions of the TRK sum rule, the low-lying electric dipole strength makes a noticeable impact on the radiative neutron-capture cross sections in stable Sn isotopes. Moreover, the experimental Oslo inputs for the 121,123-Sn(𝑛,𝛾)122,124-Sn reactions were found to affect the production of Sb in the astrophysical 𝑖 process, providing new constraints on the uncertainties of the resulting chemical abundances from multizone low-metallicity asymptotic giant branch stellar models.
Calculated dipole strengths for 112,116,118-Sn. (a), (c), (e): The low-lying E1 transitions computed with the 20-keV (thin solid line) and 200-keV (thick dashed line) widths are shown up to 10 MeV. (b), (d), (f): The strengths computed with the 200-keV width are also shown up to 22 MeV. The blue and orange bands indicate the corresponding Oslo and (p,p') data [S. Bassauer 2020].
Low-lying dipole response of 64-Ni
Two complementary real-photon scattering experiments were conducted on the proton-magic 64-Ni nucleus to study the dipole response up to its neutron-separation energy of 𝑆𝑛 = 9.7 MeV. By combining both measurements, 87 𝐸1 and 23 𝑀1 transitions were identified above 4.3 MeV. The results of the observed 𝑀1 transitions were compared to shell-model calculations using two different model spaces. It was found that the inclusion of excitations across the 𝑍=28 shell gap in the calculations has a large impact. Furthermore, average cross sections for decays to the ground state (elastic transitions) as well as to lower-lying excited states (inelastic decays) were determined. The corresponding 𝐸1 channel was compared to calculations within the relativistic equation of motion (REOM) framework. Whereas the calculations of highest possible complexity reproduce the fragmentation and overall behavior of the 𝐸1 average elastic cross section well, the predicted absolute cross sections are approximately twice as high as the experimental upper limits even though the latter also include an estimate of the inelastic-decay channel.
M. Müscher, E. Litvinova, R. Schwengner, ..., and A. Zilges, Phys. Rev. C 109, 044318 (2024).
The E1 photoabsorption cross section σ(E1) of 64-Ni in the three many-body approximations of growing complexity: relativistic QRPA (RQRPA) (gray), relativistic 2q⊗1phonon EOM (REOM2) (dashed black), and relativistic 2q⊗2phonon EOM (REOM3) (solid black), compared to data.
Fine structure of the isoscalar giant monopole resonance
Over the past two decades high energy-resolution inelastic proton scattering studies were used to gain an understanding of the origin of fine structure observed in the isoscalar giant quadrupole resonance (ISGQR) and the isovector giant dipole resonance (IVGDR). Recently, the isoscalar giant monopole resonance (ISGMR) in 58-Ni, 90-Zr, 120-Sn, and 208-Pb was studied at the iThemba Laboratory for Accelerator Based Sciences (iThemba LABS) by means of inelastic 𝛼-particle scattering at very forward scattering angles (including 0∘). The good energy resolution of the measurement revealed significant fine structure of the ISGMR. To extract scales by means of wavelet analysis characterizing the observed fine structure of the ISGMR in order to investigate the role of different mechanisms contributing to its decay width. Characteristic energy scales are extracted from the fine structure using continuous wavelet transforms. The experimental energy scales are compared to different theoretical approaches performed in the framework of quasiparticle random phase approximation (QRPA) and beyond-QRPA including complex configurations using both non-relativistic and relativistic density functional theory. All models highlight the role of Landau fragmentation for the damping of the ISGMR especially in the medium-mass region. Models which include the coupling between one-particle–one-hole (1p-1h) and two-particle–two-hole (2p-2h) configurations modify the strength distributions and wavelet scales indicating the importance of the spreading width. The effect becomes more pronounced with increasing mass number. Wavelet scales remain a sensitive measure of the interplay between Landau fragmentation and the spreading width in the description of the fine structure of giant resonances. The case of the ISGMR is intermediate between the IVGDR, where Landau damping dominates, and the ISGQR, where fine structure originates from coupling to low-lying surface vibrations.
A. Bahini et al., Phys. Rev. C 109, 014325 (2024)
Left column: Experimental IS0 strength in 120-Ni (top row) in comparison with model predictions (rows 2–5) folded with the experimental energy resolution. The vertical dashed lines indicate the summation region of the wavelet coefficients (11–24 MeV) to determine the power spectra. Right column: Corresponding power spectra. Scales are indicated by filled circles with the associated errors, and for the experimental results additionally by vertical grey bars.
Quantum benefit of the quantum equation of motion for the strongly coupled many-body problem
We investigate the quantum equation of motion (qEOM), a hybrid quantum-classical algorithm for computing excitation properties of a fermionic many-body system, with a particular emphasis on the strong-coupling regime. The method is designed as a stepping stone towards building more accurate solutions for strongly coupled fermionic systems, such as medium-heavy nuclei, using quantum algorithms to surpass the current barrier in classical computation. Approximations of increasing accuracy to the exact solution of the Lipkin-Meshkov-Glick Hamiltonian with N=8 particles are studied on digital simulators and IBM quantum devices. Improved accuracy is achieved by applying operators of growing complexity to generate excitations above the correlated ground state, which is determined by the variational quantum eigensolver (VQE). We demonstrate explicitly that the qEOM exhibits a quantum benefit due to the independence of the number of required quantum measurements from the configuration complexity. Post-processing examination shows that quantum device errors are amplified by increasing configuration complexity and coupling strength. A detailed error analysis is presented, and error mitigation based on zero noise extrapolation is implemented.
M. Q. Hlatshwayo, J. Novak, and E. Litvinova, Phys. Rev. C 109, 014306 (2024)
On the dynamical kernels of fermionic equations of motion in strongly-correlated media
On the dynamical kernels of fermionic equations of motion in strongly-correlated media
Two-point fermionic propagators in strongly-correlated media are considered with an emphasis on the dynamical interaction kernels of their equations of motion (EOM). With the many-body Hamiltonian confined by a two-body interaction, the EOMs for the two-point fermionic propagators acquire the Dyson form and, before taking any approximation, the interaction kernels decompose into the static and dynamical (time-dependent) contributions. The latter translate to the energy-dependent and the former map to the energy-independent terms in the energy domain. We dwell particularly on the energy-dependent terms, which generate long-range correlations while making feedback on their short-range static counterparts. The origin, forms, and various approximations for the dynamical kernels of one-fermion and two-fermion propagators, most relevant in the intermediate-coupling regime, are discussed. Applications to the electromagnetic dipole response of Ni and low-energy quadrupole response of Sn are presented.
PANDORA project: photo-nuclear reactions below A=60
PANDORA project: photo-nuclear reactions below A=60
Photo-nuclear reactions of light nuclei below a mass of A=60 are studied experimentally and theoretically by the PANDORA (Photo-Absorption of Nuclei and Decay Observation for Reactions in Astrophysics) project. Two experimental methods, virtual-photon excitation by proton scattering and real-photo absorption by a high-brilliance gamma-ray beam produced by laser Compton scattering, will be applied to measure the photo-absorption cross sections and the decay branching ratio of each decay channel as a function of the photon energy. Several nuclear models, e.g. antisymmetrized molecular dynamics, beyond-mean-field type models, a large-scale shell model, and ab initio models, will be employed to predict the photo-nuclear reactions. The uncertainty in the model predictions will be evaluated from the discrepancies between the model predictions and the experimental data. The data and the predictions will be implemented in a general reaction calculation code TALYS. The results will be applied to the simulation of the photo-disintegration process of ultra-high-energy cosmic rays in inter-galactic propagation.
Relativistic approach to the nuclear breathing mode
Relativistic approach to the nuclear breathing mode
Microscopic theory of the nuclear response based on the relativistic meson-nucleon Lagrangian is applied to the description of the isoscalar giant monopole resonance (ISGMR) in a variety of nuclear systems. It is shown that the inclusion of beyond-mean-field correlations of the quasiparticle-vibration coupling (qPVC) type in the leading approximation allows for a simultaneous realistic description of the ISGMR in nuclei of led, tin and nickel mass regions, which is difficult on the mean-field level. The calculations are based on the NL3* parametrization of the relativistic finite-range meson-nucleon Lagrangian, which, in combination with the qPVC, have consistently demonstrated the ability to reliably describe many other nuclear structure phenomena. Systematic ISGMR calculations for nickel isotopes help reveal the central role of its coupling to the low-energy quadrupole states in the placement of the ISGMR centroids.
E. Litvinova, Phys. Rev. C 107, L041302 (2023): Editor's Suggestion
Microscopic response theory for strongly-coupled superfluid fermionic systems
Microscopic response theory for strongly-coupled superfluid fermionic systems
A consistent microscopic theory for the response of strongly-coupled superfluid fermionic systems is formulated. After defining the response as a two-point two-fermion correlation function in the basis of the Bogolyubov's quasiparticles, the equation of motion (EOM) method is applied using the most general fermionic Hamiltonian with a bare two-body interaction, also transformed to the quasiparticle space. As a superfluid extension of the case of the normal phase, the resulting EOM is of the Bethe-Salpeter-Dyson form with the static and dynamical interaction kernels, where the former determines the short-range correlations and the latter is responsible for the long-range ones. Both kernels as well as the entire EOM have the double dimension as compared to that of the normal phase. Non-perturbative approximations via the cluster decomposition of the dynamical kernel are discussed, with the major focus on a continuous derivation of the quasiparticle-phonon coupling variant of the latter kernel, where the phonons (vibrations) are composite correlated two-quasiparticle states unifying both the normal and pairing modes. The developed theory is adopted for nuclear structure applications, such as the nuclear response in various channels. In particular, the finite-amplitude method generalized beyond the quasiparticle random phase approximation, taking into account the quasiparticle-vibration coupling, is formulated for prospective calculations in non-spherical nuclei.
Beyond-mean-field calculations of allowed and first-forbidden β− decays of r-process waiting-point nuclei
Beyond-mean-field calculations of allowed and first-forbidden β− decays of r-process waiting-point nuclei
β-decay rates of neutron-rich nuclei, in particular those located at neutron shell closures, play a central role in simulations of the heavy-element nucleosynthesis and resulting abundance distributions. We present β-decay half-lives of even-even N=82 and N=126 r-process waiting-point nuclei calculated in the approach based on relativistic quasiparticle random phase approximation with quasiparticle-vibration coupling. The calculations include both allowed and first-forbidden transitions. In the N=82 chain, the quasiparticle-vibration coupling has an important impact close to stability, as it increases the contribution of Gamow-Teller modes and improves the agreement with the available data. In the N=126 chain, we find the decay to proceed dominantly via first-forbidden transitions, even when the coupling to vibrations is included.
C. Robin, E. Litivnova and G. Martínez-Pinedo, EPJ Web Conf. 260, 03002 (2022).
Damping of the isovector giant dipole resonance in 40,48Ca
Damping of the isovector giant dipole resonance in 40,48Ca
The fine structure of the IsoVector Giant Dipole Resonance (IVGDR) in the doubly-magic nuclei 40,48Ca observed in inelastic proton scattering experiments under the zero degree angle is used to investigate the role of different mechanisms contributing to the IVGDR decay width. Characteristic energy scales are extracted from the fine structure by means of wavelet analysis. The experimental scales are compared to different theoretical approaches allowing for the inclusion of complex configurations beyond the mean-field level. Calculations are performed in the framework of RPA and beyond-RPA in a relativistic approach based on an effective meson-exchange interaction, with the UCOM effective interaction and, for the first time, with realistic two- plus three-nucleon interactions from chiral effective field theory employing the in-medium similarity renormalization group. All models highlight the role of Landau fragmentation for the damping of the IVGDR, while the differences in the coupling strength between one particle-one hole (1p-1h) and two particle-two hole (2p-2h) correlated (relativistic) and non-correlated (non-relativistic) configurations lead to very different pictures of the importance of the spreading width resulting in wavelet scales being a sensitive measure of their interplay. The relativistic approach with particle-vibration coupling, in particular, shows impressive agreement with the number and absolute values of the scales extracted from the experimental data.
J. Carter, L.M. Donaldson, E. Litivnova, H. Wibowo et al., Physics Letters B833, 137374 (2022).
Theory of nuclear collective vibrations
Theory of nuclear collective vibrations
We review the theory of nuclear collective vibrations evolved over decades from phenomenological quasiclassical picture to sophisticated microscopic approaches. The major focus is put on the underlying microscopic mechanisms of emergent effects, which define the properties of giant resonances and soft modes. The response of atomic nuclei to electromagnetic and weak fields is discussed in detail. Astrophysical implications of the giant resonances and soft modes are outlined.
H.-Z. Liang and E. Litvinova, Handbook for Nuclear Physics, Chapter 7, Springer Nature 2022.
Exact dynamical kernel of the response function in an interacting many-body fermionic system.
Simulating excited states of the Lipkin model on quantum computer
Simulating excited states of the Lipkin model on quantum computer
The energy spectrum as a function of the interaction strength for N = 4 particles calculated by a simulator (left) and an IBM quantum computer (right).
The energy spectrum as a function of the interaction strength for N = 2 particles calculated by an IBM quantum computer.
We simulate the excited states of the Lipkin model using the recently proposed Quantum Equation of Motion (qEOM) method. The qEOM generalizes the EOM on classical computers and gives access to collective excitations based on quasi-boson operators of increasing configuration complexity α. The method is applied for increasing particle number. We show that the accuracy strongly depend on the fermion to qubit encoding. Standard encoding leads to large errors but the use of symmetries and the Gray code reduces the quantum resources and improve significantly the results on current noisy quantum devices. With this encoding scheme, we use IBM quantum machines to compute the energy spectrum for a system of N = 2, 3 and 4 particles and compare the accuracy against the exact solution. We show that the results for α = 2, the equivalent to second RPA, are notably more accurate than α = 1 (RPA) for large coupling strengths. Thus, we can use our scheme to implement an algorithm with complexity α > 3, which is an analogue for medium-mass and heavy nuclei, to pave the way towards achieving nuclear spectroscopic accuracy.
Nuclear Shell Structure in a Finite-Temperature Relativistic Framework
Nuclear Shell Structure in a Finite-Temperature Relativistic Framework
The shell evolution of neutron-rich nuclei with temperature is studied in a beyond-mean-field framework rooted in the meson-nucleon Lagrangian. The temperature-dependent Dyson equation with the dynamical kernel taking into account the particle-vibration coupling (PVC) is solved for the fermionic propagators in the basis of the thermal relativistic mean-field Dirac spinors. The calculations are performed for 68−78-Ni in a broad range of temperatures 0≤T≤4 MeV. The special focus is put on the fragmentation pattern of the single-particle states, which is further investigated within toy models in strongly truncated model spaces. Such models allow for quantifying the sensitivity of the fragmentation to the phonon frequencies, the PVC strength and to the mean-field level density. The model studies provide insights into the temperature evolution of the PVC mechanism in real nuclear systems under the conditions which may occur in astrophysical environments.
H. Wibowo and E. Litvinova, Phys. Rev. C 106, 044304 (2022).
A many-body approach to superfluid nuclei in axial geometry
A many-body approach to superfluid nuclei in axial geometry
Starting from a general many-body fermionic Hamiltonian, we derive the equations of motion (EOM) for nucleonic propagators in a superfluid system. The resulting EOM is of the Dyson type formulated in the basis of Bogoliubov’s quasiparticles. As the leading contributions to the dynamical kernel of this EOM in strongly-coupled regimes contain phonon degrees of freedom in various channels, an efficient method of calculating phonon’s characteristics is required to successfully model these kernels. The traditional quasiparticle random phase approximation (QRPA) solvers are typically used for this purpose in nuclear structure calculations, however, they become very prohibitive in non-spherical geometries. In this work, by linking the notion of the quasiparticle-phonon vertex to the variation of the Bogoliubov’s Hamiltonian, we show that the recently developed finite-amplitude method (FAM) can be efficiently employed to compute the vertices within the FAM-QRPA. To illustrate the validity of the method, calculations based on the relativistic density-dependent point- coupling Lagrangian are performed for the single-nucleon states in heavy and medium-mass nuclei with axial deformations. The cases of 38-Si and 250-Cf are presented and discussed.
Nuclear superfluidity at finite temperature
Nuclear superfluidity at finite temperature
The equation of motion for the two-fermion two-time correlation function in the pairing channel is considered at finite temperature. Within the Matsubara formalism, the Dyson-type Bethe-Salpeter equation (Dyson-BSE) with the frequency-dependent interaction kernel is obtained. Similarly to the case of zero temperature, it is decomposed into the static and dynamical components, where the former is given by the contraction of the bare interaction with the two-fermion density and the latter is represented by the double contraction of the four-fermion two-time correlation function, or propagator, with two interaction matrix elements. The dynamical kernel with the four-body propagator, being formally exact, requires approximations to avoid generating prohibitively complicated hierarchy of equations. We focus on the approximation where the dynamical interaction kernel is truncated on the level of two-body correlation functions, neglecting the irreducible three-body and higher-rank correlations. Such a truncation leads to the dynamical kernel with the coupling be- tween correlated fermionic pairs, which can be interpreted as emergent bosonic quasibound states, or phonons, of normal and superfluid nature. The latter ones are, thus, the mediators of the dynamical superfluid pairing. In this framework, we obtained the closed system of equations for the fermionic particle-hole and particle-particle propagators. This allows us to study the temperature dependence of the pairing gap beyond the Bardeen-Cooper-Schrieffer approximation, that is implemented for medium-heavy nuclear systems. The cases of 68-Ni and 44,46-Ca are discussed in detail.
Many-body theory for quasiparticle states in superfluid fermionic systems
Many-body theory for quasiparticle states in superfluid fermionic systems
We present a formalism for the fermionic quasiparticle propagator in a superfluid fermionic system. Starting from a general many-body Hamiltonian confined by the two-body instantaneous interaction, the equation of motion for the fermionic propagator is obtained in the Dyson form. Before making any approximation, the interaction kernel is found to be decomposed into static and dynamical (time-dependent) contributions, where the latter translates to the energy-dependent and the former maps to the energy-independent terms in the energy domain. The three-fermion correlation function, being the heart of the dynamical part of the kernel, is factorized into the two-fermion and one-fermion ones. With the relaxed particle number constraint, the normal propagator is coupled to the anomalous one via both the static and dynamical kernels, which is formalized by introducing the generalized quasiparticle propagator of the Gor'kov type. The dynamical kernel in the factorized form is associated with the quasiparticle-vibration coupling (QVC), with the vibrations unifying both the normal and pairing phonons. The QVC vertices are related to the variations of the Hamiltonian of the Bogoliubov quasiparticles, which can be obtained by the finite amplitude method.
Impact of complex many-body correlations on electron capture in thermally excited nuclei around 78Ni
Impact of complex many-body correlations on electron capture in thermally excited nuclei around 78Ni
We link complex many-body correlations, which play a decisive role in the structural properties of atomic nuclei, to the electron capture occurring during star evolution. The recently developed finite-temperature response theory, taking into account the coupling between single-nucleon and collective degrees of freedom, is applied to spin-isospin transitions, which dominate the electron capture rates. Calculations are performed for 78Ni and for the surrounding even-even nuclei associated with a high-sensitivity region of the nuclear chart in the context of core-collapse supernova simulations. The obtained electron capture rates are compared to those of a simpler thermal quasiparticle random phase approximation (TQRPA), which is standardly used in such computations. The comparison indicates that correlations beyond TQRPA lead to significantly higher electron capture rates under the typical thermodynamical conditions.
E. Litvinova and C. Robin, Phys. Rev. C 103, 024326 (2021)
Equation of Motion Method for strongly correlated Fermi systems and Extended RPA approaches
Equation of Motion Method for strongly correlated Fermi systems and Extended RPA approaches
The status of different extensions of the Random Phase Approximation (RPA) is reviewed. The general framework is given within the Equation of Motion Method and the equivalent Green's function approach for the so-called Self-Consistent RPA (SCRPA). The role of the Pauli principle is analyzed. A comparison among various approaches to include Pauli correlations, in particular, renormalized RPA (r-RPA), is performed. The thermodynamic properties of nuclear matter are studied with several cluster approximations for the self-energy of the single-particle Dyson equation. More particle RPA's are shortly discussed with a particular attention to the alpha-particle condensate. Results obtained concerning the Three-level Lipkin, Hubbard and Picket Fence Models, respectively, are outlined. Extended second RPA (ESRPA) is presented.
Temperature evolution of the nuclear shell structure and the dynamical nuclear effective mass
Temperature evolution of the nuclear shell structure and the dynamical nuclear effective mass
We study the fermionic Matsubara Green functions in medium-mass nuclei at finite temperature. The single-fermion Dyson equation with the dynamical kernel of the particle-vibration-coupling (PVC) origin is formulated and solved in the basis of Dirac spinors, which minimize the grand canonical potential with the meson-nucleon covariant energy density functional. The PVC correlations beyond mean field are taken into account in the leading approximation for the energy-dependent self-energy, and the full solution of the finite-temperature Dyson equation is obtained for the fermionic propagators. Within this approach, we investigate the fragmentation of the single-particle states and its evolution with temperature for the nuclear systems 56,68Ni and 56Fe relevant for the core-collapse supernova. The energy-dependent, or dynamical, nucleon effective mass is extracted from the PVC self-energy at various temperatures.
H. Wibowo, E. Litvinova, Y. Zhang and P. Finelli, Phys. Rev. C 102, 054321 (2020).
Many-body correlations in nuclear superfluidity
Many-body correlations in nuclear superfluidity
The two-fermion two-point correlation function in the pairing channel is discussed within the equation of motion framework. Starting from the bare two-fermion interaction, we derive the equation of motion for the two-fermion pair propagator in a strongly-correlated medium. The resulting equation is of the Dyson type with the kernel having static and one-frequency dependent components and, thus, can be regarded as a Dyson Bethe-Salpeter equation (Dyson-BSE). The many-body hierarchy generated by the dynamical interaction kernel is truncated on the level of two-body correlation functions, thus neglecting the explicit three-body and higher-rank correlations. The truncation is performed via a cluster expansion of the intermediate three-particle-one-hole correlation function irreducible in the particle-particle channel, that leads to the coupling between single fermions and emergent bosonic quasibound states (phonons). The latter couplings are, thus, derived in terms of the exact mapping of the in-medium two-fermion correlation functions onto the domain of phonons without introducing new parameters. The approach is applied to calculations of the pairing gaps in medium-mass nuclear systems, that include calcium, nickel and tin isotopic chains.
Fragmentation of Single-Particle Strength around the Doubly Magic Nucleus 132-Sn and the position of the 0f5/2 Proton-Hole State in 131-In
Fragmentation of Single-Particle Strength around the Doubly Magic Nucleus 132-Sn and the position of the 0f5/2 Proton-Hole State in 131-In
Spectroscopic factors of neutron-hole and proton-hole states in 131-Sn and 131-In, respectively, were measured using one-nucleon removal reactions from doubly magic 132-Sn at relativistic energies. For 131-In a 2910(50)-keV γ-ray was observed for the first time and tentatively assigned to a decay from a 5/2− state at 3275(50) keV to the known 1/2− level at 365 keV. The spectroscopic factors determined for this new excited state and three other single-hole states provide first evidence for a strong fragmentation of single-hole strength in 131-Sn and 131-In. The experimental results are compared to theoretical calculations based on the relativistic particle-vibration coupling model and to experimental information for single-hole states in the stable doubly magic nucleus 208-Pb.
Toward an accurate strongly-coupled many-body theory within the equation of motion framework
Toward an accurate strongly-coupled many-body theory within the equation of motion framework
Non-perturbative aspects of the quantum many-body problem are revisited, discussed and advanced in the equation of motion framework. We compare the approach to the two-fermion response function truncated on the two-body level by the cluster expansion of the dynamical interaction kernel to the approach known as time blocking approximation. Such a comparison leads to an extended many-body theory with non-perturbative treatment of high-order configurations. The present implementation of the advanced theory introduces a new class of solutions for the response functions, which include explicitly beyond-mean-field correlations between up to six fermions. The novel approach, which includes configurations with two quasiparticles coupled to two phonons (2q⊗2phonon), is discussed in detail for the particle-hole nuclear response and applied to medium-mass nuclei. The proposed developments are implemented numerically on the basis of the relativistic effective meson-nucleon Lagrangian and compared to the models confined by two-fermion and four-fermion configurations, which are considered as the state-of-the-art for the response theory in nuclear structure calculations. The results obtained for the dipole response of 42,48-Ca and 68-Ni nuclei in comparison to available experimental data show that the higher configurations are necessary for a successful description of both gross and fine details of the spectra in both high-energy and low-energy sectors.
Time-reversed particle-vibration loops and nuclear Gamow-Teller response
Time-reversed particle-vibration loops and nuclear Gamow-Teller response
The nuclear response theory for charge-exchange modes in the relativistic particle-vibration coupling approach is extended to include for the first time particle-vibration coupling effects in the ground state of the parent nucleus. In a parameter-free framework based on the effective meson-nucleon Lagrangian, we investigate the role of such complex ground-state correlations in the description of Gamow-Teller transitions in 90-Zr in both (p,n) and (n,p) channels. We find that this new correlation mechanism is fully responsible for the appearance of the strength in the (n,p) branch. Comparison of our results to the available experimental data shows a very good agreement up to excitation energies beyond the giant resonance region when taking into account an admixture of the isovector spin monopole transitions to the data. The parent-daughter binding-energy differences are also greatly improved by the inclusion of the new correlations.
Nuclear Response in a Finite-Temperature Relativistic Framework
Nuclear Response in a Finite-Temperature Relativistic Framework
This article is dedicated to the memory of Pier Francesco Bortignon and devoted to the advancements related to his pioneering ideas. We review the recently developed approach to the finite-temperature nuclear response. It is based on quantum hadrodynamics in the form of the covariant density functional theory, as the first approximation, and accounts for the medium polarization effects in two-fermion propagators. The latter effects are included in the leading approximation by applying an imaginary-time projection operator to the integral part of the Bethe-Salpeter equation and, thereby, selecting the most relevant many-body configurations. In addition to the dipole response, which dominates nuclear spectra, the approach is applied to the monopole and quadrupole excitations to investigate their evolution with the temperature increase.
Nuclear Dipole Response in the Finite-Temperature Relativistic Time Blocking Approximation
Nuclear Dipole Response in the Finite-Temperature Relativistic Time Blocking Approximation
We present a consistent microscopic theory and a numerically stable and executable calculation scheme for computing nuclear response at finite temperature, which takes into account the particle-vibration coupling (PVC) mechanism of spreading, in addition to the Landau damping. The presented calculations of the dipole response within a self-consistent relativistic framework reveal that, although the Landau damping plays the leading role in the temperature evolution of the strength distribution, however, (i) at moderate temperatures the PVC effects remain almost as strong as at T=0 and (ii) at high temperatures they are tremendously reinforced because of the formation of the new collective low-energy modes. In the dipole channel, the latter effect is responsible for the "disappearance" of the high-frequency giant dipole resonance (GDR) or, in other words, brings the GDR to the low-energy domain. Figure: proton and neutron transition densities for the strongest dipole peak below 10 MeV at various temperatures in 68-Ni (top) and 100-Sn (bottom).
Temperature dependence of the nuclear Gamow-Teller response
Temperature dependence of the nuclear Gamow-Teller response
A microscopic approach to the proton-neutron nuclear response is formulated in the finite-temperature relativistic nuclear field theory framework. The approach is based on the meson-nucleon Lagrangian of quantum hadrodynamics and advances the relativistic field theory to connect the high-energy scale of heavy mesons, the medium-energy range of the pion and the low-energy domain of nuclear medium polarization effects in a parameter-free way at finite temperature. The medium polarization due to the emerging strongly-correlated particle-hole excitations (phonons) is taken into account by means of the soft-blocking finite-temperature technique adopted now to the proton-neutron channel of the nuclear response. In this framework we investigate the temperature dependence of the Gamow-Teller resonance in the closed-shell nuclei 48Ca, 78Ni, and 132Sn and of the associated beta-decay rates.
Coupling charge-exchange vibrations to nucleons in a relativistic framework: effect on Gamow-Teller transitions and beta-decay half-lives
Coupling charge-exchange vibrations to nucleons in a relativistic framework: effect on Gamow-Teller transitions and beta-decay half-lives
Nuclear response theory for isospin-transfer modes in the relativistic particle-vibration coupling framework is extended to include coupling of single nucleons to isospin-flip (charge-exchange) phonons, in addition to the usual neutral vibrations. This new coupling introduces dynamical pion and rho-meson exchange, beyond the Hartree-Fock approximation, up to infinite order. We investigate the impact of this new mechanism on the Gamow-Teller response of a few doubly-magic neutron-rich nuclei, namely 48-Ca, 78-Ni, 132-Sn and 208-Pb. It is found that the coupling to isospin- flip vibrations can have a non negligible impact on the strength distribution and quenching of the Gamow-Teller resonance, globally improving the agreement with the experimental data. The corresponding beta-decay half-lives of 78Ni and 132Sn are also calculated, and found to be decreased by the inclusion of the new phonons. Overall the lifetimes are very close to the experimental data using unquenched value of the weak axial coupling constant gA.
Finite-temperature relativistic nuclear field theory: an application to the dipole response
Finite-temperature relativistic nuclear field theory: an application to the dipole response
Nuclear response theory beyond the one-loop approximation is formulated for the case of finite temperature. For this purpose, the time blocking approximation to the time-dependent part of the in-medium nucleon-nucleon interaction amplitude is adopted for the thermal (imaginary-time) Green's function formalism. We found that introducing a soft blocking, instead of a sharp blocking at zero temperature, brings the Bethe-Salpeter equation to a single frequency variable equation also at finite temperatures. The method is implemented self-consistently in the framework of Quantum Hadrodynamics and designed to connect the high-energy scale of heavy mesons and the low-energy domain of nuclear medium polarization effects in a parameter-free way. In this framework, we investigate the temperature dependence of dipole spectra in the even-even nuclei 48Ca, 120Sn and 132Sn with a special focus on the giant dipole resonance's width problem and on the low-energy dipole strength distribution.
Soft modes in the proton-neutron pairing channel as precursors of deuteron condensate in N=Z nuclei
Soft modes in the proton-neutron pairing channel as precursors of deuteron condensate in N=Z nuclei
Relativistic nuclear response theory is formulated for the proton-neutron pairing, or deuteron transfer, channel. The approach is based on the meson-nucleon Lagrangian of Quantum Hadrodynamics (QHD) and advances the relativistic field theory to connect consistently the high-energy scale of heavy mesons, the medium-energy range of the pion and the low-energy domain of emergent collective vibrations (phonons) in a parameter-free way. Mesons and phonons build up the in-medium nucleon-nucleon interaction in spin-isospin transfer channels, in particular, the phonon-exchange part takes care of the leading-order retardation effects. In this framework, we explore Jπ = 0+ and Jπ = 1+ channels of the nuclear response to the proton-neutron pair removal and addition in 56Ni and 100Sn with a special focus on the lowest (soft) modes as precursors of deuteron condensate and candidates for being the mediators of the proton-neutron pairing interaction.
Observation of the First Isovector Giant Monopole Resonance via the 28-Si(10-Be,10-B[1.74 MeV]) Reaction at 100 AMeV
Observation of the First Isovector Giant Monopole Resonance via the 28-Si(10-Be,10-B[1.74 MeV]) Reaction at 100 AMeV
The charge-exchange reaction (10-Be,10-B[1.74 MeV]) at 100 AMeV was presented as a new probe, which is capable of isolating the isovector ( T = 1) non-spin-transfer ( S = 0) nuclear response. The N=Z neutron deficient nucleus 28-Si was chosen for this study at the National Superconducting Cyclotron Laboratory (NSCL). A secondary 10-Be beam produced by fast fragmentation of 18-O nuclei at the NSCL Coupled Cyclotron Facility, the dispersion-matching technique with the S800 magnetic spectrometer, and the high-precision gamma-ray tracking with the Gamma Ray Energy Tracking Array (GRETINA) were used to obtain a clean S = 0 excitation-energy spectrum in 28-Al. Monopole and dipole contributions were extracted through a multipole decomposition analysis, and, thereby, the isovector giant dipole (IVGDR) and the isovector giant monopole (IVGMR) resonances were identified. The results show that this probe is a powerful tool for studying the elusive IVGMR, which is of interest for performing a stringent test of theoretical approaches at high excitation energies and for constraining the bulk properties of nuclei and nuclear matter. Fig. reprinted from [PRL118, 172501 (2017)] shows the extracted distributions compared with theoretical calculations based on the normal-modes (NM) formalism and on our strength functions computed within the proton-neutron relativistic time blocking approximation (pn-RTBA). One can see that the latter describes very reasonably the shapes of the experimental cross sections, which can not be achieved within the proton-neutron relativistic random phase approximation (pn-RRPA). This emphasizes the importance of long-range correlations for isospin-flip resonances.
Isovector excitations in 100-Nb and their decays by neutron emission studied via the 100-Mo(t,3He + n) reaction at 115 MeV/u
Isovector excitations in 100-Nb and their decays by neutron emission studied via the 100-Mo(t,3He + n) reaction at 115 MeV/u
Another recent application of the proton-neutron relativistic quasiparticle time blocking approximation (pn-RQTBA) is the spin-isospin excitation spectrum in 100-Nb, which was studied by the charge-exchange 100-Mo(t, 3-He) reaction at NSCL. The neutron decays from the excited 100-Nb were also observed. The statistical and direct decay branches were both identified in the spectra. The upper limit for the direct-decay branching ratio was determined to be 20 +/- 6%, which revealed the decay predominantly happened via the statistical process. The Figure presents the isovector spin monopole (IVSM) resonance extracted from this measurement, together with the theoretical pn-RQRPA and pn-RQTBA calculations in the form of histograms consistent with the experimental energy resolution. The IVSM resonance is the overtone of the Gamow-Teller resonance: their operators differ by the radial formfactors only. In practice, the IVSM resonance reflects the leading-order effect of the momentum transfer dependence of the spin-isospin response dominated by the GTR. It has been shown, in particular, that the IVSM resonance can absorb a few percent of the total Ikeda sum rule and, thereby, contribute to the quenching of the GTR. Thus, understanding the formation of the IVSM resonance is of a great importance because the identification of microscopic mechanisms of the GTR's quenching remains one of the most difficult unsolved problems in the nuclear structure physics. One can see from the Figure that both pn-RQRPA and pn-RQTBA give reasonable strength distributions, which means that for the IVSM excitations the long-range correlations are most likely less important than for the non-spin-flip isovector monopole resonance. The discrepancies between the data and calculations can be, therefore, attributed to possible deformation effects or to deficiencies of the static interaction, such as the overall simplicity of its one-boson-exchange character and the absence of the delta meson. This points to further work in those directions.
Nuclear response theory for spin-isospin excitations in a relativistic quasiparticle-phonon coupling framework
Nuclear response theory for spin-isospin excitations in a relativistic quasiparticle-phonon coupling framework
A new theoretical approach to spin-isospin excitations in open-shell nuclei is presented. The developed method is based on the relativistic meson-exchange nuclear Lagrangian of Quantum Hadrodynamics and extends the response theory for superfluid nuclear systems beyond relativistic quasiparticle random phase approximation in the proton-neutron channel (pn-RQRPA). The coupling between quasiparticle degrees of freedom and collective vibrations (phonons) introduces a time-dependent effective interaction, in addition to the exchange of pion and ρ-meson taken into account without retardation. The time-dependent contributions are treated in the resonant time-blocking approximation, in analogy to the previously developed relativistic quasiparticle time-blocking approximation (RQTBA) in the neutral (non-isospin-flip) channel. The new method is called proton-neutron RQTBA (pn-RQTBA) and is applied to the Gamow-Teller resonance in a chain of neutron-rich nickel isotopes 68-78Ni. A strong fragmentation of the resonance along with quenching of the strength, as compared to pn-RQRPA, is obtained. Based on the calculated strength distribution, beta-decay half-lives of the considered isotopes are computed and compared to pn-RQRPA half-lives and to experimental data. It is shown that a considerable improvement of the half-life description is obtained in pn-RQTBA because of the spreading effects, which bring the lifetimes to a very good quantitative agreement with data.
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